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A 523088
THE TESTING
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MATERIALS
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THE TESTING
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THE TESTING
OF
72221
MATERIALS OF CONSTRUCTION
A TEXT - BOOK FOR THE
ENGINEERING LABORATORY AND A COLLECTION OF
THE RESULTS OF EXPERIMENT
BY
WILLIAM CAWTHORNE UNWIN , F.R.S.
M.INST. C.E.
PROFESSOR OF ENGINEERING AT THE CENTRAL INSTITUTION OF THE CITY
AND GUILDS OF LONDON INSTITUTE : FORMERLY PROFESSOR OF
HYDRAULIC AND MECHANICAL ENGINEERING AT THE
ROYAL INDIAN ENGINEERING COLLEGE
LONDON
LONGMANS,
GREEN, AND
AND NEW YORK : 15 EAST 16th STREET
1888
All rights reserved
CO .
PREFACE .
The present work is a treatise on the Strength of the
Materials used in Construction , considered in connection
with the instruments and methods by which the pro
perties of materials are investigated experimentally .
The data on which the engineer relies in designing
structures cannot be fully understood without some
knowledge of the methods by which they are ascertained .
But for several reasons a knowledge of the methods of
testing has become of late of greater importance. With
the introduction of new materials the engineer has been
forced to make greater use of the testing machine, both
in estimating the constructional value of materials and
to escape the danger of employing material which is
unsuitable .. A considerable advance has been made in
the construction of all the apparatus used in testing ,
and the operations of testing are carried out with more
care and skill. Lastly, the establishment of Engineering
Laboratories in connection with Schools of Engineering
72221
vi
TESTING OF MATERIALS OF CONSTRUCTION
has made experimental investigation an essential part
of engineering education .
The following treatise consists of three parts. In
the first, the mechanical properties of materials are ex
plained that is, the phenomena of elasticity and plasti
city, and the relations between stress and deformation, so
far as they have been scientifically ascertained . In the
second , the apparatus used in the engineering laboratory
is described .
The author has had opportunities of ex
amining nearly every form of testing machine, and of
using very nearly all the subsidiary measuring and other
apparatus here described . Lastly, the third part contains
a collection of the most complete and trustworthy results
of testing, of all the ordinary materials of construction .
This third part, no doubt, traverses ground occupied
by several excellent treatises. Nevertheless, it will be
found to contain a large amount of information, either
new or at least not easily accessible to English readers .
The mass of data accumulated in the last forty years
is enormous , and in the selection of results of testing
for the present work some definite principles have been
steadily kept in view. Where laws were established first
careful and adequate experiment, it seems historically
just to reproduce the original investigation. When ,
as in some of Hodgkinson's experiments , very simple
PREFACE
vii
means of measurement were used , accurate enough for
the purpose in view, this adds value to these early
results. But beyond question more recent investiga
tions have, on the whole, been carried out with better
appliances, and with greater skill and knowledge . In
selecting amongst these, the point of greatest importance
seemed to be that the investigations should be complete.
That is, that all the facts useful to observe about a
material should have been ascertained. If the tenacity
of one sample of a material is determined, the shearing
strength of a second , the crushing strength of a third
—these results are less instructive than if one sample
of material had been tested in all three ways. In giving
tables of results they have all been reduced to common
units, so as to be most easily understood and compared .
It will be noted that a large number of the results
are borrowed from
German and American sources.
The establishment of Testing Laboratories, supported by
Government, in Berlin, Munich and Vienna, and more
recently at Watertown in the United States, is perhaps
a procedure not likely to be followed in this country.
But it can hardly be doubted that those laboratories
have in a very important degree assisted foreign
engineers and manufacturers. No mechanical investi
gations of the properties of materials at all comparable
viii
TESTING OF MATERIALS OF CONSTRUCTION
in completeness to those undertaken in the Berlin
and Munich laboratories have been carried out in this
country.
Whether or no the minuteness and delicacy
of measurement and elaboration of method have been
pushed beyond practical needs there may be difference
of opinion . But everyone who studies the memoirs
issued by the accomplished directors of the Continental
laboratories must admire the patience and insight and
skill which they exhibit. It is perhaps true that the
full and unreserved publication of methods and results ,
so necessary for scientific progress, is hardly possible
except in the case of public Institutions directed by
men of acknowledged eminence.
Results obtained by the author himself have been
introduced sparingly, and chiefly where they filled gaps
in the information available.
Kensington : February 1888.
CONTENTS .
CHAPTER
PAGE
INTRODUCTION
I.
1
MECHANICAL PROPERTIES OF BODIES ACTED ON
BY
STRESSES
II.
PLASTIC PROPERTIES OF MATERIALS
III.
STRESS-STRAIN DIAGRAMS
IV.
TESTING MACHINES
V.
VI .
VII.
VIII.
IX.
X.
17
SHACKLES FOR HOLDING TEST BARS
45
56
.
.
1
106
171
.
MEASURING INSTRUMENTS
192
AUTOGRAPHIC RECORDING APPARATUS
228
ELASTIC CONSTANTS FOR METALS
246
CAST IRON
259
IRON AND STEEL
276
XI. COPPER, COPPER ALLOYS, AND MISCELLANEOUS TESTS
OF METALS
XII.
339
EXPERIMENTS ON REPETITION OF STRESS. ENDURANCE
TESTS
356
XIII.
TIMBER
394
XIV .
STONE AND BRICK
410
LIMES AND CEMENTS
441
INDEX
483
XV .
a
Y
3
r.-:
LIST OF PLATES .
PLATE
PAGE
I.
ENGINEERING LABORATORY AT THE CENTRAL INSTITUTION
OF THE GUILDS OF LONDON INSTITUTE
II.
100 - TON
TESTING
MACHINE
OF
Frontispiece
MESSRS .
BUCKTON & Co. ,
to face 136
III.
OLSEN AND GRAFENSTADEN TESTING MACHINES
IV .
GENERAL VIEW OF THE WATERTOWN 450 - TON
142
TESTING MACHINE
‫ܕܕ‬
V.
PLAN AND ELEVATION OF
TESTING MACHINE
160
THE WATERTOWN
160
:...
Erratum .
Page 159, line 8 from bottom. For one per cent. ' read ' one -tenth
of one per cent.'
.
1
:
章
THE
TESTING
OF
MATERIALS OF CONSTRUCTION .
INTRODUCTION .
The arts of construction probably arose out of simple
need of shelter, and in house-building men were first
driven to apply natural materials to purposes involving
the consideration of their mechanical properties. As
communities were formed and social relations became
more complex , the builder's art developed and extended .
Roadways were necessary for traffic, temples for wor
ship, fortresses for defence.
Now, in all works of construction are involved
questions of the strength of materials. In the rudest
house-building, materials must have been selected
because they were strong, and proportioned with some
reference to the forces to which they would be sub
jected ; with every increase of size and complexity in
the structures crected reconsideration was necessary of
the materials available, and more attention would be
given to securing adequate strength . Other considera
tions would have weight. Granite might be chosen for
B
2
TESTING OF MATERIALS OF CONSTRUCTION
durability, marble for polish, bronze for lustre, gold for
costliness, metal to be beaten, wood to be carved. But
in no case could considerations of strength be entirely
ignored. The forms which give character to mediæval
architecture - arch, buttress, groin , and tracery , are due
to the desire to obtain great structural strength consis
tently with other requirements. And amongst those
other requirements one must always have been to
economise the amount of material used.
It is, however, under the pressure of quite modern
necessities that the problem of using materials to the
greatest advantage in securing strength has come to be
before all other considerations in the mind of the
designer. In modern structures and machines , what
ever other objects are in view, the designer has always
to consider what are the straining actions to which the
structure will be subjected , and what is the safest
material, and the best disposition of it, and the least
amount of it necessary to resist those straining actions.
The cause may be the increased value of labour, or
the greater use in construction of artificial or manu
factured materials, or the greater scale of modern works,
or the commercial conditions under which they are
undertaken. Whatever the cause, the modern engineer
or constructor has always to consider what is the least
amount of material required to give adequate strength.
The simplest mode of ascertaining the safety of a
structure, say of a railway bar, or a bridge, is to apply
to it a testing-load greater than the maximum load to
INTRODUCTION
3
which it is likely to be subjected. To a certain extent
this testing of completed structures is , and always will
be, carried out. Before a boiler is put under steam it is
tested by hydraulic pressure ; before ordinary traffic
passes over a railway bridge, a heavy testing-load is
placed on it.
Such tests sometimes reveal unknown or
unsuspected sources of weakness . But little informa
tion is derivable from tests of completed structures , from
the necessary limitation of the testing -load. No load
can be applied likely to injure or deform the structure,
unless it is quite seriously ill -proportioned or ill-con
structed. And an extreme testing-load may damage
a structure, such as a boiler or bridge, without any
possibility of the injury being detected at the time.
It would also be very inconvenient if structures were
erected at hazard with a chance of breaking down
under the testing -load.
Such tests of completed struc
tures have become to a great extent superfluous . They
are useful as affording a final guarantee of security, but
they do not supply very important or specific informa
tion as to the margin of safety which exists. In by far
the largest number of cases no testing -load can be
applied except the ordinary working load .
It is here that purely theoretical studies come to the
assistance of the engineer . For the materials he uses ,
the deformations due to the stresses are small , and
within working limits of stress they are very nearly
proportional to the stresses. Assuming the deforma
tions to be small and proportional to the stresses , it is
B 2
4.
TESTING OF MATERIALS OF CONSTRUCTION
possible to reduce the straining actions in the most
complex structures to comparatively simple straining
actions in their separate members. With that part of
applied mechanics which deals with the determination
of the simpler straining actions on the members of
complex structures we have not in this treatise to deal.
Supposing, however, this reduction made, then experi
ment on pieces of material subjected to such simple
straining actions will show how the members of complex
structures should be proportioned. Hence, for a hundred
years or more, engineers have been constantly experi
menting on small pieces of different materials subjected
to simple straining actions. Experiments of this kind
are called tests of the strength of the material, and the
machines for making these tests are called testing
machines.
There are two distinct objects in view in subjecting
materials to mechanical tests .
The one is scientific,
the other commercial. When the object is scientific, the
experimenter aims at the determination of the physical
constants of the material and at verifying the assump
tions on which theoretical calculations proceed . When
the object is commercial, the experimenter endeavours
to ascertain whether samples of a material comply with
certain more or less arbitrarily chosen standards of
quality. That the methods of testing for scientific and
for commercial purposes more or less coincide should
not be allowed to obscure an essential difference.
Absolute results are wanted in scientific testing, rela
INTRODUCTION
5
tive results in commercial testing.
What is the elastic
limit, the modulus of elasticity, the working limit of
stress in given conditions of a given material, are ques
tions in the one case .
Which of two samples of mate
rial is the better sample on the whole, is the kind of
question in the other case.
Scientific Testing.— The object of scientific testing
being to determine the physical constants for a material,
it will be useful to enumerate those which for the pur
poses of the engineer are most important .
The definite physical constants required in the ap
plication of theories of the resistance of materials are
as follow :
1. The density or heaviness. A great part of the
straining action in most structures is due to the weight
or inertia of the structure itself. Besides this , in many
materials the density is directly connected with other
properties of the material.
2. For some purposes and for certain materials
it is useful to determine the hardness or resistance to
abrasion
3. Certain co -efficients of clasticity or ratios of stress
to strain . For practical purposes it is usually accurate
enough to assume a material to be elastic , homogeneous,
and isotropic . In that case its deformation by any
straining action can be determined if two elastic co
efficients are known — the co -efficient of elasticity of
form , and the co - efficient of elasticity of volume. But,
for application, other elastic co -efficients dependent on
6
TESTING OF MATERIALS OF CONSTRUCTION
these are also convenient. These co -efficients are re
A structure must be designed
so that not only does it resist the straining action
quired for two reasons .
without breaking, but also without prejudicial deforma
tion, and the elastic co -efficients are required to deter
mine the deformations from the stresses . Next, in
many cases the stresses depend on the deformations and
the co -efficients of elasticity appear in the equations for
determining the stresses.
4. Limits of Elasticity. — Certain materials, like cast
iron, are not perfectly elastic in their initial condition
for any straining action. They are permanently de
formed , or take a permanent set with very small loads.
But many materials are almost perfectly elastic, and
most important materials of construction become so for
a certain range of stress. It is only within that range
of stress that the ordinary rules of strength of materials
are applicable. The limits of elasticity must be known
to determine the extent to which the rules can be
trusted .
If the limits of elasticity of a material were fixed by
the conditions of its manufacture, the modulus of elas
ticity and limit of elasticity, once directly ascertained by
experiment, would furnish all the data necessary to the
engineer in applying the theory of elasticity and fixing
the working limits of stress. That, however, is not the
case .
It has long been known that the elastic limit of
a bar is not a fixed limit. By loading and straining a
bar in one direction the elastic limit for that kind of
INTRODUCTION
7
stress is raised. More recently it has been shown that
if the bar is loaded and strained in different directions
the elastic limit may be lowered.
One of the most ordinary conditions of a structure
or machine is that it is subjected to reiterated working
stresses, all lying between a minimum and maximum
value, or between a maximum stress of one kind and a
maximum of the opposite kind . In such conditions ,
‫גן‬
new elastic limits are produced differing from the
original or primitive elastic limits. The determination
of what those limits are in given circumstances is the
object of remarkable and difficult researches, which are
beyond the range of ordinary testing.
No doubt it is accurate enough to treat ordinary
structures and machines as perfectly elastic and to
determine the distribution of stress on that assumption ,
for experience has fixed the limits of working stress
far within the primitive elastic limit.
But it is by
no means clear that the working stress is commonly so
fixed as to secure equal safety in different cases, and ,
if the proper working stress is to be determined on
rational principles, the study of the conditions in which
the elastic limits change becomes essential.
5. Breaking Stresses. - In the case of some materials
an increasing load produces simply an increasing defor
mation . Generally, however, a limit is reached at which
the bar suddenly fractures. Under defined conditions
of loading — for instance, with a gradually increasing
statical load applied in a short time—the breaking stress
i
S
TESTING OF MATERIALS OF CONSTRUCTION
is a perfectly definite constant for a material, and is
nearly independent of the form and dimensions of the
bar tested .
1
As ordinarily stated in tables of strength of materials,
the breaking stress is a somewhat fictitious quantity.
Most materials commonly tested are ductile. Suppose
the bar subjected to tension.
With such materials a
maximum load is reached before the bar breaks. At
that point the elongation becomes very rapid and the
section rapidly diminishes. The bar will no longer
support the maximum load, and it finally breaks with
å load 10 or 20 per cent. less than the maximum
load. What is ordinarily understood as the breaking
stress is the maximum load divided by the initial sec
tional area of the bar. That is, it is a load which is not
the breaking load, estimated on an area which no longer
existed when the bar broke .
There are, of course,
reasons of convenience for estimating the breaking
stress in this way, and no error need arise if the mode
of estimating the breaking stress is remembered.
But, further, the early experiments of the Railway
Commission, the experiments of Fairbairn for the Board
of Trade on a small plate girder, the splendid series of
researches by Wöhler, continued by Spangenberg and
Martens, and confirmed by similar experiments of Bau
schinger and Baker, all show that bars subject to contin
ually varying stress break with loads of from one- half to
two- thirds the statical breaking stress. The greater the
range through which the stress varies and the greater
INTRODUCTION
9
the number of repetitions, the lower is the breaking
stress .
These results are explainable if it is supposed
that, instead of fixed limits of elasticity , these limits
depend on the range and kind of variation of stress ,
and that, if the range of perfect elasticity possible in
given conditions is exceeded , deformations are produced
which, accumulating with successive repetitions of load,
finally lead to fracture. General experience accords
with this conclusion. Under a purely statical stress a
bar not too ductile would probably be safe with seven
eighths of the ordinary so -called breaking stress.
But
with a varying load no working stress as high as that
would be safe. If the range of variation is small , the
working stress may still be comparatively high. The
Conway Bridge, in which the rolling load is small
compared with the permanent weight of the bridge, is
subjected daily to stresses reaching 7 tons per square inch ,
or nearly one-third of the breaking stress . But ordinary
iron bridges with a larger proportion of rolling load ,
and therefore a greater variation of stress, are not sub
jected to more than 5 tons or at most a quarter of the
statical breaking stress. Even this limit proves to be too
high for bridges of very short span, in which the range of
variation of stress is greater. Ordinary shafting and
axles are rarely loaded beyond 4 tons to the inch, and
in many parts of machines subjected to alternating ten
sions and compressions the stress does not exceed 2 tons
per square inch , or one-twelfth of the breaking stress .
It has been common to assume that the margin
10
TESTING OF MATERIALS OF CONSTRUCTION
between the calculated working stress and statical
breaking stress, as determined by ordinary testing, is
merely an allowance for contingencies . But it is in no
way clear that in cases where this margin is in practice
greatest the probability of the working stress being
exceeded is greatest also. Further, the need of an
allowance of 400, 600, or 1,100 per cent. for mere con
tingencies neglected in calculating the stresses in the
structure is incredible. It is much more probable that
the elastic limit really fixes the safe limit of working
stress, and that this varies with the range of variation
of stress.
Hence, besides the ordinary so -called breaking
stresses determined in ordinary statical testing, it is
distinctly one object of scientific testing to determine
the breaking stresses under conditions of variation of
stress , and especially to ascertain the conditions of time
under which such variations of stress are effective in
altering the breaking stress ,
But besides these dynamical conditions which affect
the physical constants of a material, it is the object of
scientific testing to determine how far different con
ditions of manufacture, of mechanical treatment in the
forge, of chemical constitution, of temperature, and so
forth, affect the physical constants of the material, and
inferentially its value as a material of construction . It
is by researches of this kind that guidance is obtained
in seeking the improvement of any given manufacture.
6. The Yield Point. In iron and steel, and perhaps
INTRODUCTION
11
other rolled or hammered materials, at a stress exceed
ing more or less the elastic limit, there occurs a large
and almost sudden increase of deformation in the
ordinary method of testing , and the deformation is per
manent or plastic deformation. For greater stresses
the plastic deformation increases, and it amounts, before
fracture is reached , to many hundred times the whole
elastic deformation . The point at which this almost
sudden augmentation of plastic deformation occurs is
termed the yield point or breaking -down point. It is
obvious that a general plastic yielding of a structure
would ruin it for practical purposes , hence the yield
point seems to fix a limit of stress independent of that
determined from considerations of safety against frac
ture, which the working stress should not exceed . The
yield point is raised by loading, which exceeds the
primitive yield point, but it is not usually practicable to
raise the yield point of a material artificially before using
it in a structure, and consequently the primitive yield
point due to the mechanical operations of manufacture
fixes with respect to deformation the dangerous limit of
Professor Kennedy has especially insisted on
stress .
the yield point as fixing the greatest working limit of
stress .) But the case is not quite so simple as at first it
appears .
In almost all actual structures the maximum
stresses are confined to very limited portions of the
structure . It is not quite clear that a riveted joint is
either sensibly deformed or permanently injured, even
Professional Papers of the Corps of Royal Engineers, vol. x. 1884.
12
TESTING OF MATERIALS OF CONSTRUCTION
if the yield point at the dangerous section is exceeded .
In testing large riveted girders the deflections are
regular and proportional to the loads, almost to the
breaking weight, and show no indication of a yield
point.
By careful scientific testing most of the constants
enumerated above have been determined for the various
materials which are used by the engineer. But a ques
tion arises which should not be entirely passed over.
How far do such tests as have been made afford a
trustworthy foundation for the wide extension which is
given to their results by the aid of applied mechanics ?
It is , perhaps, desirable at least to point out some of
the differences between the conditions of even the most
1
careful testing and those which obtain in engineering
structures. In the first place, most experirnents have
been made on test specimens of very small size ; and it
is not always safe to infer that the material in the small
test-bar, and that in the large structure, are of identical
quality and in precisely similar conditions . In the case
of timber, for instance, Professor Lanza's experiments
show a wide discrepancy between small and large
specimens. In another respect, at least, there is still a
considerable difference between engineering structures
and ordinary test-bars. Engineering structures are
almost always compound structures made up of me
chanically connected parts. To what extent a com
pound structure of that kind can be taken to be
equivalent to a simple homogeneous structure is at
3
13
INTRODUCTION
present, at least, so far as direct experiment is con
cerned, very imperfectly known. Happily, the very
defect of elasticity in ordinary materials tends to dimi
nish the variation of stress in compound structures
which is due to imperfection of the mechanical connec
tions.
But it is probable, and, to a certain extent, it is
in accordance with practice, that the limiting stress
should be rather lower in a compound than in a
simple structure ; that stresses, for instance, are safe
in a simple railway bar or axle, which under similar
conditions would be unsafe in a riveted girder.
The
differences between ordinary tests and actual structures
as to time and frequency of repetition of load have
already been spoken of. Lastly, in many actual cases
in practice, the parts of a structure are subjected to
combined stresses , and but little progress has been
made experimentally in determining the effect of such
combined stresses .
Commercial Testing - The materials used by the
engineer are natural or artificial products, and generally
several sources of supply are available. It is important
to be able to distinguish the quality of the materials
coming from different localities or from different manu
facturers, or which differ considerably in quality or
A manufacturer may be skilful or careless ; may
use good raw materials or bad raw materials ; or acci
dental circumstances may interfere with the processes of
cost .
manufacture.
The conditions involved in the success
of a manufacture are numerous and complex.
No mere
14
TESTING OF MATERIALS OF CONSTRUCTION
supervision of the processes or examination of the re
sulting product is an adequate guarantee of quality.
Now, the engineer requires to know if he is getting
material good of its kind, and suitable for the purpose
intended . To determine this no method is so convenient
or safe as the selection of sample portions of the mate
rial, which are then subjected to appropriate tests, and,
since a rapid and definite judgment is required, more or
less arbitrary standards of quality must be accepted .
Qualitative or comparative testing of this kind may be
called Commercial Testing, to indicate its character
without any intention of depreciating its importance.
Since the physical constants of a material really
determine its value for constructive purposes, com
mercial tests may be made to approximate as closely as
is practicable to tests for scientific purposes. But this
is by no means always convenient. Shorter and readier
methods are often sufficient for comparative purposes.
What the user of a material requires to know is whether
a material supplied is as good as material previously
employed in similar cases ; or, of two materials equally
available, which is the better. Generally he is content
to adopt one or two easily applied tests , and to judge
by comparison of the results of these alone. All that
needs to be noted at present is that these commercial
standards of quality are often arbitrary to an extent
which has been too much overlooked .
In testing steel, for instance , it has been common to
look to the breaking stress and the ultimate elongation
INTRODUCTION
15
as marks of quality. Admitting that a steel of 30 tons
tenacity and 30 per cent. elongation is better than a
steel of 28 tons tenacity and 25 per cent. elongation ,
the results are relative merely, and give no absolute
measure of the difference in constructional value of the
two materials.
If one steel has 30 tons tenacity and
25 per cent . elongation, and the other 28 tons tenacity
and 30 per cent. elongation, it even remains doubtful
which is the better material . Neither the breaking
stress nor the elongation represent conditions of stress
or deformation which can be even approached in the
actual application of the material.
Again , it is sometimes convenient to make chemical
analyses of materials instead of mechanical tests . No
doubt the physical properties of a material are often
closely connected with, and can, to a certain approxi
mation , be inferred from its chemical composition .
Particular defects, such as adulteration , are better de
tected by chemical analysis than by mechanical tests,
and in some cases particular constituents have a defi
nite effect on quality . Sulphur and phosphorus are
prejudicial when present in iron . The physical pro
perties of steel depend somewhat closely on the amount
of carbon, silicon , and manganese it contains. Lime
and gypsum are sometimes mixed with cement , and
injure its quality. But, in fact, the engineer has to do
with the mechanical properties of materials ; and the
indications furnished by chemical analysis , though
valuable, are indirect , and not for the engineer's pur
16
TESTING OF MATERIALS OF CONSTRUCTION
pose completely reliable. Steels made from the same
raw materials, and having identical chemical consti
tuents, may, from difference of mechanical treatment
and other causes, have differences of quality of im
portance to the engineer .
The engineer is, therefore, in most cases obliged to
use mechanical tests in discriminating the quality of his
materials.
Then there arises the question, what are
the mechanical tests most readily applied and most
trustworthy in their indications ? Complete experiments
on the physical properties of the material are in general
too laborious and costly. Certain physical properties
must be selected as marks of good quality. For practical
purposes, limited tests of this kind have been established,
and contracts are made for the supply of material under
specified test conditions.
What tests of this kind are commonly applied will
be discussed later on.
At present it is only necessary
to point out that, in proportion as the test is limited to
a few properties of the material, and especially when it
differs widely from the conditions in which the inaterial
is used, it is an empirical test of quality and sometimes
misleading. Examples are not wanting of the general
adoption of commercial tests which have tended to pre
vent the production of the best material, and to retard
the progress of a manufacture.
PROPERTIES OF BODIES ACTED ON BY STRESSES
17
CHAPTER I.
MECHANICAL PROPERTIES OF BODIES ACTED
ON BY
STRESSES.
The systems of forces to which bodies are subjected ,
due to their weight or to the loads they support , or to
other causes, are termed stresses .
These stresses pro
duce in the body on which they act alterations of size
or of shape, and these alterations are termed strains.
One of the principal objects of testing materials is to
determine the relation between stresses and the strains
they produce . Very commonly stress is considered as
the mutual action of two bodies at their plane of con
tact, or the mutual action of two parts of a body at an
imaginary plane of division . A hanging chain carrying
a load is in a condition of stress due to the upward re
action at the point of support and the downward pull of
the load .
Each link is in a condition of stress due to
the upward and downward pull of the two neighbour
ing links ; and if a link be considered divided by a
horizontal plane, the stress at that plane is the upward
and downward action of the half link on either side.
1. Elastic and Plastic Materials.
The most important
C
18
TESTING OF MATERIALS OF CONSTRUCTION
distinction between bodies, from a mechanical point of
view is that some are elastic and others non - elastic or
imperfectly elastic. Elastic bodies recover their form
after the stress is removed ‫ ;ܪ‬non -elastic bodies or imper
fectly elastic bodies undergo a permanent change of
shape when a stress is applied.
The most important
materials of construction are nearly perfectly elastic for
a certain range of stress, and imperfectly elastic for
greater stresses.
But there are materials which can be
greatly changed in form without losing continuity or
breaking into fragments. To these we give the names
malleable, ductile, or plastic, according to the mode of
application of the stress. Gold is beaten into leaves,
copper is drawn into wire , clay is moulded by pressure.
The word which best expresses the property of
suffering an indefinitely large deformation is the word
plastic. A material is termed brittle if it breaks under
an increasing stress before any great permanent de
formation is caused . It is called tough if, under an
increasing stress, it becomes plastic and undergoes a
large permanent change of shape.
2. Summary of the Elastic Properties of Materials.
When a body is subjected to the action of external
forces, it undergoes a deformation which is either a
deformation which disappears if the load is removed
( elastic deformation ), or a deformation which remains
after the load is removed (plastic deformation ). Ac
cording to the best experiments , and especially those of
Bauschinger, all the materials used in construction,
PROPERTIES OF BODIES ACTED ON BY STRESSES
19
except perhaps hard tool steel, show a small amount of
permanent set after loading the first time, even if the
loads are comparatively small. But in many materials,
and up to a certain limit of stress called the elastic limit,
the permanent sets are very small, and may perhaps
rather be ascribed to initial want of straightness of the
bars tested or to small defects of homogeneousness than
to any inherent property of the material.
Within the limit of elasticity a very simple relation
holds between the stresses or deforming forces and the
strains or deformations. This law was published in 1676
by Robert Hooke, in the form of an anagram : ' The
true theory of elasticity or springiness, ce iii nosss tt uu .'
The key to this anagram was given, two years later, in
the phrase , ' Ut tensio sic vis ; the power of any spring
is in the same proportion with the tension thereof."
Using more modern terms, we say the stress is propor
tional to the strain .
Later it will be shown to what
extent actual materials conform to this law and behave
with sensibly perfect elasticity. At present it is enough
to assume that with most naterials, and for straining
actions within the elastic limit, the plastic or permanent
deformations are so small that they may be neglected ,
and that the temporary or elastic deformations conform
to Hooke's law .
3. Tension and Compression . When a prism is sub
jected to a stress parallel to its axis and uniform on
cross-sections perpendicular to the axis, it extends in
length and diminishes in section or shortens and in
C 2
20
TESTING OF MATERIALS OF CONSTRUCTION
creases in section .
Let P be the stress reckoned on
unit of area ,and a the extension or compression reckoned
per unit of length .
Then, by Hooke's law
1
(
.
)
1
E , a constant
a
This constant is termed the coefficient of direct elasticity,
or Young's modulus. It has the same value for tension
and compression .
4. Poisson's Ratio ... When a bar is extended or com
pressed by a simple longitudinal stress of the kind de
scribed above, it contracts or dilates laterally.
If = a is
FIG . 1 .
k - di
A
1
7
1
1
1
1
1
1
1
1
1
2
? (2 * A )
a
!
1
d /2 + )
7 (1-1 )
1
1
1
K
V
the longitudinal extension or compression , reckoned per
unit of length, then the contraction or dilation trans
versely is F a !9 , where 1/12, the ratio of lateral con
traction to longitudinal extension , is a constant termed
Poisson's Ratio.
For most solid bodies in has values
between 3 and 4, and for metals its most general value
is nearly 4 ; for india -rubber, m = 2 nearly, when the
deformation is small .
Hence a simple longitudinal stress, p , per unit of
PROPERTIES OF BODIES ACTED ON BY STRESSES
21
area produces a longitudinal strain, a = p / E , and a
transverse strain, – a /m = - p /m E.
It might be questioned whether 2 should be reckoned
unit of original or per unit of stretched length of
the bar. For ordinary solids a is so small that it makes
per
no sensible difference, and 2 is calculated per unit of
original length. But for india -rubber, equation ( 1 ) is
much more nearly satisfied if 2 is calculated per unit
of stretched length . If a is the elongation per unit of
2
is the elongation per unit of
original length,
1 + a
stretched length.
5. Change of Volume under simple Direct Stress.
Suppose the prism has initially the length l and cross
section a .
Subjected to a longitudinal tension, the
m )?
length becomes 1 ( 1 + a ) , and the section at (1
Consequently the initial volume al is changed to al
(1
1 ta
small .
- 2 ) very nearly,since the deformations are
The change of unit volume is a – 2a / m .
Thus , if m = 4 , as for metals, the change of volume
of one cubic unit is ta , the volume being increased
by longitudinal tension ; if m = 2 , as for india- rubber ,
there is no change of volume. Similarly, for com
pression , the change of unit volume is - ja for metals ,
the volume being diminished .
Work done in Extending or Compressing a Bar . - If
the stress is gradually increased from zero to a limit p ,
22
TESTING OF MATERIALS OF CONSTRUCTION
since equal increments of stress produce equal incre
ments of strain, the mean stress is p / 2, and the work
per unit volume done on the bar is
W = įra
(2).
6. Numerical Values of the Constants.
In order to
have some idea of the numerical importance of the
quantities which are under discussion it is desirable to
examine a few cases .
The following are values of the
modulus E in tons per sq. inch, and the extension à
and lateral contraction 2 / m per unit length for each
ton per sq. inch for some materials :
Lateral con
Extension
E
Material
per
traction per ton
ton per sq . inch per sq . inch per
per unit length
13,250
.000075
Wrought iron
Mild steel
12,200
14,400
13,250
6,250
000082
000069
· 000075
00016
00010
00028
00023
Cast iron
10,020
Glass
Bronze
Yellow deal
.
3,530
4,400
715
unit width
000019
000020
·000017
000019
•000040
000025
· 000071
000058
00139
Taking ordinary Bessemer steel, such as is used in
riveted work , the elastic limit will not be below 10 tons
per sq. inch. Up to that limit the extension will be
·0007 , or about 14 orth of its initial length. Hence the
lateral contraction will be about tooth of its initial
width. The increase of volume when stretched will be
about yg'ooth. The work in stretching the bar up to
23
PROPERTIES OF BODIES ACTED ON BY STRESSES
11
Angles.Consider a small
cube, of unit length of
side, with simple stresses
FIG . 2 .
P
A
normal to two pairs of
faces and parallel to
Under
B
P2
2.0
the third pair.
02
10 tons per sq.inch will be } ( 10 x 2240) 1400x12
of a foot-pound per cubic inch of the bar.
7. Superposition of Two simple Direct Stresses at Right
the action of pi there
C
will be the following
P2
strains :
parallel to OC,
E
Pi
ME
parallel to OB and OA ,
Under the action of p2, the strains are :
parallel to OB, P:
E
;
P2
in E
parallel to OA and OC ,
Adding the parallel strains,
parallel to OC,
P2
a
E
mE'
OA , 13 = -P2
mE
P2
mE
‫ول‬
OB , 2 = P2 - P1
mE '
E
24
TESTING OF MATERIALS OF CONSTRUCTION
Now let the stresses Pu, P2, be of equal intensity, P,
but opposite sign.
The strains become
€ (1-5); - (1+ ) n20 ... (3),
or putting
E
(1+ ) ,
the lengths of the sides of the cube will be
1 + 2 ; 1-2.; and 1
(4),
and the volume neglecting ’ is unchanged .
Fig. 3 shows the distorted cube. A square traced
on the side of the original
FIG. 3 .
cube will be distorted into a
rhombus, the angles of which
are greater and less than a
1-ad
right angle by the equal
1
1
amount 0 .
k
}
1 +/
Now
1
tan
‫)ܟ‬
‫ܟܬܬ‬9‫ܨ‬
1 - a
4
2
= tan
1 ta
1 + tan
2
Or, as 0 is small ,
and 0 = 22
aa
11
(5).
2
8. Isotropy.A material is quite conceivable which ,
tested by a direct tension for instance, should give one
PROPERTIES OF BODIES ACTED ON BY STRESSES
،21
value of E for a stress in one direction and a different
value of E for a stress in another direction . The
materials used in construction are produced by processes
of forging, rolling, &c . , in which the mechanical actions
have definite directions with reference to the piece pro
duced . The pressure of the rolls on a bar is perpen
dicular to its axis , and while the bar is squeezed down
vertically it has different degrees of freedom of expan
sion in all horizontal directions . It is quite conceiv
able that this mechanical action should make the elastic
properties in the direction in which the bar was com
pressed different from those in the direction in which
it expanded. The bar would then be said to be not
isotropic .
Now, fortunately, most of the mechanical operations
in producing iron and steel are effected at temperatures
at which the material is alınost perfectly plastic, and
they do not produce such great differences in the elastic
properties in different directions as similar operations
at lower temperatures would do. We may for most
purposes treat ordinary materials as isotropic, alırays
remembering that the assumption can only be approxi
mate .
The extent to which there are variations of
isotropy in ordinary materials has hardly been experi
mentally examined .
9. Normal and Tangential Components of Stress.
Shearing Stress. — Suppose a simple stress, P, applied
parallel to the axis of a bar, so that the distribution on
cross - sections perpendicular to the axis is uniform .
If
26
TESTING OF MATERIALS OF CONSTRUCTION
a is the area of such a cross- section the intensity of
stress is
P
(6) .
р
a
To find the stresses on an oblique section, ab, it is con
venient to resolve P into normal and tangential compo
nents .
FIG . 4 .
Let @ be the
P
p
angle between the nor
LP
mal to the section and
the axis of the bar, then
8
18
N
T
N = P cos 0 and T
P sin 0.
?
As the tan
gential stress T tends
a
to cause sliding at the
section, it is called the
P
shearing stress, while
the normal component is often termed the direct stress .
The area of the oblique section ab is a sec 0. Hence
the intensities of normal and tangential stress on a b are
Normal stress = px
P cos 0
a sec o
?
COS
20 .
( 7).
P sin 0
Tangential stress = p . = a
p sin 0 cos 0 .
(8) .
seco
For an oblique section at right angles to ab , substituting
TT
A for 0 , we get
2
Normal stress =P1
p . = p sin 20.
Tangential stress = pi = p sin 0 cos 0.
27
PROPERTIES OF BODIES ACTED ON BY STRESSES
So that the intensity of tangential stress is the same
on two oblique sections at right angles.
stress is greatest and
The shearing
1p for planes at 45 ° with the
axis .
Now let us consider a case in which the stresses can
be reduced to simple shearing stresses .
angle A B C D represent a parallel
opiped, the stresses on which can АA
Let the rect
FIG . 5 .
P
B
be reduced to tangential stresses
on two pairs of the faces. Then P
it can be shown that the stresses
СC
D
on the faces at right angles are
equal. For the lengths of the sides represent the areas
of the faces, so that the total stresses on the faces are
P2 * A B and P1 * A D. Equating the moments of the
two couples, Pz * A B x B C = P. X AD X A B, that
is , p2 = P1 .
Let Fig. 6 represent a cube of unit length of side,
subjected to equal shearing stresses
FIG . 6 .
‫وه‬
В
on two pairs of faces at right angles A
7
in directions parallel to the third
pair of faces. The effect of these s
S
1
stresses will be to distort the square
face of the cube into a rhombus ,
each angle being altered by an
amount 0. Assuming Hooke's law,
- Сө
S =
D
.s
•
C
(9 ) ,
where C is a modulus of elasticity of a somewhat dif
ferent kind from that already described . For Young's
28
TESTING OF MATERIALS OF CONSTRUCTION
modulus applies to a case where there is a change both
of volume and figure. In this case there is a distortion
of shape only. C is called the modulus of transverse
elasticity or coefficient of rigidity.
The tangential stresses here assumed as acting on
the faces of the cube are cquivalent to a tension and
compression along its dia
FIG . 7 .
-S S2
gonals . For obviously half
S
/SS
the stresses on each adjacent
pair of sides is equivalent to a
S 2 along a dia
stress
gonal, and the shearing stress
s!
on the four faces is therefore
Assz
ssa
S
-552
equivalent to a tension along
one diagonal and an equal thrust along the other.
But the section of the cube along the diagonals is v2.
Hence the intensity of the tension and thrust is p = $.
The case is, therefore, identical with that previously
-treated , in which a tension and thrust at right angles
were superposed .
In that case it was found that
0= 2 a
1
Therefore
(11 + m.).
a
0
21
272 + ]
E
m ,
( 10) .
But by the definition of the coefficient of rigidity ,
remembering that the shearing stresses and direct
stresses to which they are equivalent are equal,
p =: Co.
PROPERTIES OF BODIES ACTED ON BY STRESSES
Hence
1
2
C
( 11 ) .
+ 1
= 4,
=
C
10
Oil
For metals in which m
12E
ገገ
172
0
29
E.
10. Coefficient of Elasticity of Volume.- When a
body is acted on by a stress uniform all round, like a
fluid pressure , its volume is increased or diminished .
Let v be the change of volume reckoned per cubic unit
of the body under a stress, ſ', per sq . unit of area .
Then
K
7
( 12 )
V
is called the coefficient of elasticity of volume. All
systems of stress acting on a body may be resolved into
distorting or shearing stresses, which do not alter the
volume, and a fluid stress .
The relation between K
and the other constants is
easily found . For suppose a cube of unit length of side
acted on by a longitudinal stress,
3
P, on two opposite faces.
FIG . 8 .
It
1P
will in no way alter the condi
1P
-
tion of stress to introduce stresses,
+ p and - P , on each of the
-P
2Р.
remaining four faces. Considering
the stress shown in the figure, a
+ p on cach horizontal face and
a - pon opposite vertical faces
lp
lp
tp
together form a shearing or distorting stress ; simi
30
TESTING OF MATERIALS OF CONSTRUCTION
larly, another + p on each horizontal face, and a р
These produce no
on the two other vertical faces.
change of volume . There remains, therefore, a stress
+ p on every face, together constituting a fluid stress
of intensity , P.
But it has already been shown that a longitudinal
stress , 3 p , would produce a change of volume equal
to
,
.
stresses, a simple longitudinal stress, 3 p , produces the
same change of volume as a fluid stress, p. Hence
12
K=
3 (a – 2 m );
or since
2. = p / E
E 172
K=
3m - 66
But
E =
2C ( m + 1 )
222
K
2C (m + 1 )
( 13 ) .
3m
M
6
6K + 20
3K - 20
According to the view generally adopted in this country
C and K are the fundamental coefficients in the theory
of elasticity of isotropic bodies.
11. Examples of the Value of Constants. — The follow
ing short table gives values of the constants discussed
above in tons per square inch :
PROPERTIES OF BODIES ACTED ON BY STRESSES
31
COEFFICIENTS OF ELASTICITY .
Volume
Simple
rigidity
Young's
Reciprocal of
elasticity
modulus
Poisson's Ratio
K
C
E
112
Water
141
Flint glass
Brass
Steel
Wrought iron
Cast iron
4 :1
2,204 to 2,6361,492 to 1,524 3,645 to 3,829
6,363 to 6,890 2,185 to 2,560 6,020 to 7,112
.
Copper .
11,690
9,245
6,123
10,690
5,200
4,883
3,378
3.0
3.25
3.6
3.7
2.6
12,820 to 15,560
12,470
8,567
2,794 to 2,839 7,442 to 7,836
12. Torsion.- When a prismatic bar is fixed at one
end and a couple is applied at the other end , in a plane
at right angles to the axis of the bar, it suffers a de
formation termed torsion , which gives rise to simple
shearing stresses in the bar. The theory of torsion of
prismatic bars in general
is difficult.
FIG . 9 .
initie
It is sufficient
1
for testing purposes to con
sider a cylindrical bar, the
theory of which is simple.
1
1
In such a bar A A, B B ,
/
2
e!
A
each plane transverse sec
hiiy
tion remains plane after
twisting and its dimensions
1
1
#
are unaltered .
The dis
1
B
B
tance between two trans
verse
sections
is
un
changed , so that the length
of the bar is unaltered .
6-10
a
A
longitudinal strip on the surface of the bar initially
parallel to the axis becomes a helix in the twisted bar.
TESTING OF MATERIALS OF CONSTRUCTION
32
Any small square on the surface of the bar becomes a
rhombus, of gh. This deformation corresponds to that
produced by cqual shearing forces on the opposite sides
of the square e f g h, or to stresses of tension and com
pression of equal intensity with the shearing stresses
along the diagonals of e f g h, that is, at 45° with the
axis of the bar.
Hence the general condition of stress in the bar is
that there are shearing stresses on transverse sections
and on radial longitudinal
FIG . 10.
sections. Or there are ten
sions
f
eе
2
along helixes drawn on
-T
lý
k
---
h
and compressions
concentric cylindrical sec
==
g'
tions at an inclination of
45 ° with the axis .
Let o be the angle
through which the bar is twisted, per unit of length,
expressed in circular measure. That is, if a b is the arc
through which a point on the surface of the bar at the
radius pl turns, then--ab
0
7.1 /
[ If n is the torsion angle per unit length of bar in
7
degrees, 0 =
n .]
180
Consider the slice between two transverse sections
at a distance dl. One twists relatively to the other
Odl. A square, cfgh, on the
through an angle f of"
PROPERTIES OF BODIES ACTED ON BY STRESSES
33
surface of the slice becomes a rhombus, ef' I'l. Now
the arc ff" = r ; A dl. For any intermediate cylindrical
section of the slice at radius r, the corresponding de
formation is kk = r @ ill. The angle of deforination
of the rhombus on the surface of the bar is ff" lef = $ 1
= 1'1 0 ;; and the corresponding angle of deformation of
a rhombus on the cylinder of a radius r is 0 = 16.
Now consider the stress on a ring between radii /
and r + dr at the end of the slice.
ring is 2
r dr.
The area of the
If f is the stress per unit of area, the
whole stress on the ring is 27 fr dr, and the moment
of this stress about the axis of the bar is 2 7 f dr.
Hence the whole moment of stress on the end of the
bar, which must be equal to the external twisting
moment, must be
T = 2 * f- dr.
But in shearing, the relation of stress and strain gives,
at the surface of the bar,
fi = C 0. = Crio,
and at radius r',
f = C
= C16
Hence
T = 2 CO
3 dr
= 1 Corint
}
( 11).
Or putting in fi the shearing stress at the surface of
the bar ,
T= 1
finis
( 15 ) .
1)
4
34
TESTING OF MATERIALS OF CONSTRUCTION
When the section of the bar is not circular, the
determination of the relation of the moment of torsion ,
greatest stress , and angle of twist
greatest stress is in the cases most
those points of the boundary of the
nearest the centre. The following
is difficult. The
likely to occur at
section which are
are the equations
obtained by St. Venant :
Let A be the area of the section .
I the polar moment of inertia of the section
relatively to its centre of gravity.
I' the moment of inertia relatively to an axis
through the centre of gravity, and coinciding
with its greater diameter.
a, b, the greater and less semi- diameters if the
section is elliptical, the greater and less half
lengths of the sides if rectangular.
fi the greatest stress .
Then
Τ
0
Ι
k
CA1
( 15a ),
T
f=7
I
( 151 ) ,
where
k = 47° for elliptical sections,
40 approximately for rectangular sections ;
y = 0 · 5 for elliptical sections ,
0.75 for rectangular sections.
PROPERTIES OF BODIES ACTED ON BY STRESSES
35
It may be pointed out that experiments on torsion ,
in which the stresses are within the elastic limit, afford
the easiest means of determining the coefficient of trans
verse elasticity C.
13. Determination of C by Torsional Vibrations.
When the value of C is required for thin cylindrical
bars or wires the method of torsional vibrations may
be used .
It can be shown that torsional vibrations of
a wire fixed above and supporting a weight are nearly
isochronous, and that the time of a single oscillation
is given by the relation
t
I
TY
T
TT
where t is the time in seconds , I the moment of inertia
of the vibrating system about its axis of rotation , and
T the twisting couple when 16 = 1.
Hence, since
2.1
T = 2" c ? 11
C =
2πΙι
ť ,
( 16 ) .
11. Beniling Stress . - A bar is subjected to simple
plane bending when the following conditions are satis
fied : ( 1 ) the unstrained bar is straight, and has a
longitudinal plane of symmetry ; ( 2 ) the bending
forces are applied in that plane normally to the axis .
These conditions are easy to obtain, and the deforman
tion which occurs is one of the easiest to observe .
Hence materials are often tested by bending.
2
36
TESTING
OF MATERIALS OF CONSTRUCTION
The nature of the stresses to which the bending
4
forces give rise is not difficult to trace. Suppose a
prismatic bar (Fig. 11 ) ,
FIG . 11 .
end and
loaded with Wat the
fixed
Is
1
-
2
QK
F
other .
at
one
If the bar were
F
divided at ab, equilibrium
might be re- established
by introducing a vertical
force-- S, equal to W, and
6
1
pair of equal horizontal forces F ,-F, forming a tension
and thrust, and having a moment F h equal and opposite
to the moment W l of the couple formed by W and S.
This illustration serves to show that at a cross
section of a bent bar, normal to the axis , the molecular
forces must in general consist of a shearing stress cor
responding to S , and of direct stresses of tension and
compression having resultants corresponding to F F.
The existence of these direct tensions and compres
sions at the upper and lower edges of the bar is easily
shown, thus :
FIG . 12 .
C EMIUMIA
n
1
Meli
e -7
Suppose a rectangular bar of wood to have thin
pieces of steel fitted in grooves in its top and bottom
surfaces.
3
PROPERTIES OF BODIES ACTED ON BY STRESSES
37
Let these be fixed to the bar at one end , but
otherwise free to slide longitudinally. If the bar is
now bent it will be found that the bar has shortened a
distance c on one side and lengthened a distance e on
the other, as shown by the projection or retraction of
the thin steel plates . Further, the compression c will
be equal to the extension e if the bar is symmetrical
above and below its axis .
The following table gives measurements made in
this way by J. Jorin and M. Tresca on a deal bar,
8 inches deep, 5 inches wide, and 152 inches long,
between supports .
It was loaded in the middle .
Deflection in ins.
Load in lbs.
Total
per 220 lbs.
440
• 1056
880
2160
3840
• 4352
• 5360
• 6512
0528
0544
0640
· 0472
0:524
0576
1,320
1,760
2,204
2,644
Means
Bar reversed
Again reversed
Compression ,
per 220 lbs.
Extension ,
per 220 lbs.
C
e
· 01036
· 00992
00968
01000
00984
· 01020
·00992
00972
-00928
00970
00984
01000
•00944
*01012
00980
00976
01048
01020
These observations suggest a conception of the
action which occurs in bending, which proves to be
exact enough for nearly all purposes. Suppose that
plane parallel transverse sections of the unstrained
bar remain plane after bending, and then radiate to
the axis of curvature.
It follows, since the bar is
lengthened on one side and shortened on the other,
that at some intermediate surface, termed the neutral
38
TESTING OF MATERIALS OF CONSTRUCTION
surface, the material is neither lengthened nor shortened .
Further, for other parts of the material, the elongation
or shortening (parallel to the longitudinal axis ) will be
proportional to the distance from the neutral surface.
The stresses will therefore also be proportional to that
distance.
15. Generally, as has been shown, there is a shear
ing force at the transverse sections of the bar, and the
FIG . 13 .
р
P
K
. *
1
?
3
FIG . 14 .
1
Ý
-1
d
1
1
u
០
moment of the bending forces varies along the bar. In
one particular case the action is simpler (Fig . 13).
Suppose equal couples of moment Pa applied at the
ends of the bar, then between A and B the bending
moment is uniform and the curvature circular, Letp
be the radius of curvature measured to the neutral
surface al . Then a fibre of the length a b before cur
vature has the length cd after bending. But
ed
а )
27(Pty) = p+y
27 p
FA
PROPERTIES OF BODIES ACTED ON BY STRESSES
39
and the extension (or compression, if is negative) is
y/e per unit of length .
Hence, if f is the stress at a distance y from the
neutral surface ,
f
E?
= E
( 17 ) .
‫م‬q
On an element of area a the stress is fa , and the
total stress on the whole section of the bar is , therefore,
$ (fa) = £ (E % a).
But, since the pressures and tensions across the section
form a couple,
E (E ? a) = 0 ;
Р
or, since E / P is constant, & y a = 0.
This equation is only true if the distances y are
measured from a line passing through the centre of
gravity of the section. Hence the neutral surface of
the bar passes through its longitudinal axis of figure.
The moment of the stress fa about the neutral axis
of the section ( intersection of neutral surface with the
section) is fay= E ;'a
The total moment of the couple
РP
formed by the tensions and pressures at the section isE
Σ
Р
P
Now, the quantity Ea ya is known as the moment of
inertia, or second moment of the section, and is usually
denoted by I. Hence, putting M for the moment of
40
TESTING OF MATERIALS OF CONSTRUCTION
the forces on one side of the section , which is equal to
the moment of the molecular forces at the section,
EI
M
( 18) ,
which expresses the relation between the bending
moment and the curvature of the bar.
Let f, and fo be
the tension and pressure at distances y ,
and Yc from the
neutral surface.
Then
f
E
E
PР
РP
I
I
M
y.
11
fo
You
11
f,
( 19 ) .
fo
f
Yi
Yc
Generally it is necessary to consider the greatest
tension and pressure at any point of the cross-section .
Then Yt and
y must be taken as the distances of the
parts of the section furthest from its neutral axis .
It
is convenient to call the quantities 1/4 , 1 / y. the moduli
of the section for tension and compression . If Z , Z
are put for these moduli,
M = f, Z ,= f. Z.
( 20 ) ,
which gives the relation of the bending moment to the
stresses induced .
If the bending moment varies along the beam the
radius of curvature p also varies. Then Eq. 18 gives p
for the section at which the bending moment is M. If
I varies, then Eq. 18 gives different values of Mor f
at different sections .
16. Deflection of a Beam .---Let a be a point on the
PROPERTIES OF BODIES ACTED ON BY STRESSES
41
11
neutral axis , and b a neighbouring point ; let x and y
be co -ordinates of a, c the centre of curvature , and a c
P.
Then a cb = 10 is equal to the angle between
FIG. 15 .
1
1
del
1
1
1
Y
2
t
0
the tangents to the neutral surface at a and b, or the
increment of slope of the beam. Let ab = ds = pdf,
and, since ds = d x very nearly,
0
1
e
da
dx
Р
rdx
P
du
ΕΙ
( 21 ) ,
which can be integrated when M and I are expressed
in terms of x.
Further, if the deflection of O below a = y, dy/d x
= 0,
= fødx..
Y =
which again is integrable .
( 22 ) ,
}
?
42
TESTING OF MATERIALS OF CONSTRUCTION
17. Application to the Simplest Cases occurring in
Testing. — The value of I and Z for the simplest forms
of section is as follows :
Arca, A.
Moment of
Modulus of
Inertia, 1.
Section , 2 .
1
blu
h
6703
12
hoUR ?
6
S
1
51
4
so
‫در‬
1
12
Crime
S
6
IT
IT
TT
d?
d
4
B
d!
64
dl
32
= .0982 d3
B
BH - 61 ?
ab
hH
H
BH - oh
12
BH
- 013
6 H
I.
Hollow rectangle, or I,
with equal flanges
For irregular sections, such as rail sections, the area
and moment of inertia must be determined by well
known graphic methods. But the following approxi.
mation is suitable for ordinary rails.
Let A be the area of section, h the height of the
rail.
Then
I = 0.126 A hº,
Z = 0.2525 A h.
PROPERTIES OF BODIES ACTED ON BY STRESSES
43
The greatest bending moment for the simplest
modes of loading is as follows : ----
I. Beams encastré at one end, length l.
Load W at the free end 1 from support
WI .
M at support
Load w per unit of length uniformly distributed
M at support
I w 12.
=
II. Beams supported at each end, span
1.
Load W in centre
M
at centre = 1W1
.
4
Load w per unit of length uniformly distributed
M at centre
ś w 12.
The greatest longitudinal tension or compression for
a given bending moment and section is
6 M
Rectangular section f
bha
10.2 M
Circular section
11
d3
11
I section
6 HM
B H3 – 673
"
The greatest deflection à is as follows for beams of
uniform section :
I. Beam encastré at one end , length l.
Loaded at free end with W
Il
1 W13
at the free end .
3 EI
44
TESTING OF MATERIALS OF CONSTRUCTION
Loaded uniformly with w per limit of length
1 2011
at the free end.
8
EI
II. Beam ,supported at each end , span l.
Loaded at the centre with W
W /3
48 EI
at centre .
Uniformly loaded with w per unit of length.5 w14
at centre .
384EI
If there is a concentrated and distributed load , the
deflections due to cach may be added .
18 .-- Determination of Young's Modulus by Experi
ments on Bending.--If a uniform prismatic bar is en
castré at one end and loaded at the other with a weight
W, and the deflection ô is measured ,
1 W13
E
.
3
( 23 ) .
Ô I
Similarly, if a prismatic beam of uniform section is sup
ported at the ends and loaded at the centre with W ,
W7
E
( 21).
4801
It is assumed, of course, that the stresses do not
exceed the elastic limit, and that the observations are
repeated often enough and the measurements sufficiently
delicate to give trustworthy values of the deflection .
45
CHAPTER II .
PLASTIC PROPERTIES OF MATERIALS .
19. Plasticity in materials has long been recognised ,
and the terms malleable (capable of being hammered
into sheets ), ductile (capable of being drawn into wire ),
plastic ( capable of being moulded ), have been used with
more or less clearness to denote the property of under
going an indefinitely large deformation and retaining it
permanently. The characteristic of plasticity is not the
largeness of the deformation but its permanence when
the stress is removed.
Cork may be compressed to
one -eighth of its volume by a fluid stress , but it recovers
its original volume again if the stress is removed, so
much so that it has been proposed to use cork in gun
compressors to absorb the force of recoil and restore
it again . Cork is compressible in volume, not plastic.
Indiarubber can be extended to eight times its original
length with little change of volume, but it recovers its
figure when the tension is relaxed. It has a long range
of somewhat imperfect elasticity. But iron at welding
heat takes any figure given to it in the rolls or under
the hammer and retains it. It is almost perfectly plastic.
In a paper by M. Henri Tresca, who first studied
scientifically and carefully the plastic properties of
1
TESTING OF MATERIALS OF CONSTRUCTION
46
solids, there is a passage which precisely indicates the
relation of the phenomena of plasticity to those observed
1
in ordinary testing :
· For all bodies two distinct periods are recognised :
the period of perfect elasticity , which corresponds to
variations of length proportional to the forces applied ;
and the period of imperfect elasticity, during which , on
the contrary , the changes of dimension increase more
rapidly than the forces producing them . If the second
phase of deformation be alone considered, it is easily
understood that it tends towards an ultimate condition
in which a given force, sufficiently great, would continue
to produce deformation, so to say, without limit-- as
may be observed in the process of drawing lead wire.
This particular condition, in which the deformation is
indefinitely augmented under the operation of a suffi
ciently great force , constitutes in fact the geometrical
definition of a third period , which has been designated
by the author as the period of fluidity. The period of
fluidity is more extended for plastic substances ; it is
more restricted , and will even disappear altogether, for
some vitreous or brittle substances . But it is perfectly
developed and extremely extended in the case of clays
and of the most malleable metals .'
M. Tresca observed in early experiments with lead
1 Proc. Inst . of Mechanical Engineers, 1878, “ The Flow of Solids, ' by
M. H. Tresca . See also a paper in the same Proceedings in 1876. Also
Cours de Mécaniquc Appliquée, professé à l'École Centrale, by H. Tresca.
Also numerous Mémoires sur l'Ecoulement des Solides in the Comptes
Rendus.
PLASTIC PROPERTIES OF MATERIALS
47
and similar plastic metals that the large plastic defor
mation was unaccompanied by any sensible change of
density . Assuming a deformation without change of
volume, M. Tresca has chiefly studied the geometrical
conditions of the phenomena of plasticity. There is
another feature of plastic deformation , however, and
that is the dependence of the deformation on time.
Even within the elastic limit there is an internal mole
cular friction or viscosity resisting deformation of shape,
and greater as the rate of deformation is greater. But
the time influence is very much more marked in plastic
deformation . Under a stress producing plasticity the
deformation gradually increases, either indefinitely or at
a diminishing rate, as the time during which the stress
acts is indefinitely prolonged. "
The following simple cases of nearly pure plastic
deformation , selected chiefly from M. Tresca's Memoirs,
will serve to indicate the geometrical laws of the defor
mation .
20. Suppose a cylindrical block of plastic substance
{
supported on a die-block and perforated by a punch .
It will be found that the height of
FIG. 16 .
the punching or wad ( Fig. 16 ) is in
H
general much less than that of the
block .
Thus with a block 10 c.m.
high, through which a hole, 2 c.m.
diameter was punched, the wad was only 3 c.m. high.
1 See the article on Elasticity ' in the Encyclopædia Britannica, by
Sir W. Thomson , F R.S.
48
TESTING OF MATERIALS OF CONSTRUCTION
A precise determination showed that there was no
increase of density in the wad. Consequently during
punching seven-tenths of the metal must have flowed
FIG . 17 .
laterally into the block. A partially
punched nut ( Fig. 17 ) showed a wad
having a thickness visibly less than the
penetration of the punch. Some super
posed discs of lead punched similarly and then divided
showed the appearance sketched in Fig. 18. The wad ,
FIG . 18.
like the original block , con
sisted of a series of discs,
the lowest being nearly of
the thickness of the original
discs and the higher ones
thinner.
Of
the
metal
forced laterally, therefore ,
the higher layers furnished
the larger part. What hap
pens in punching thick blocks is therefore now
obvious . The metal under the punch becomes plastic
and flows, till the remaining metal is so thinned that its
resistance to shearing is less than the pressure on the
punch.
21. Formation of a Jet by Plastic Flow.-Suppose
a series of lead discs are placed in a strong cylinder
( Fig. 19 ) and subjected to pressure in an hydraulic
press. If the pressure exceed a certain limit, and if there
is an orifice in the bottom of the cylinder, the lead will
flow like a liquid , forming a jet exhibiting contraction .
49
PLASTIC PROPERTIES OF MATERIALS
Each disc originally superposed in the box contributes
FIG . 19.
to form part of the jet. Let the
thickness of the layers originally
6
in the box be H , and let this be
diminished after flow to h, while
d
c
#
h
the jet attains a length l ; let R
C
7
be the radius ofthe box , and r that
h
of the jet ; then from the con
stancy of density of the lead, we obtain the equation
R ?( H - 1 ) = T 1:21
T
R ?
1-2
( 1 ).
H-h
Concentric Contraction of Central Cylinder.- Imagine
in the block a cylinder of radius 1 (Fig . 20 ) forming
a prolongation of the jet, so
FIG . 20.
that the lead in the chamber
---R
1
consists of an annulus of radii R
--1
名 , 也
and r , and a cylinder of radius
7 .
16
it
1
《
-
C
1
1
When the thickness of the
metal in the chamber diminishes
1
by a c = d h ,the material forced
out
of the
annulus can es
cape neither towards the piston
nor towards the sides of the
chamber .
It must necessarily
flow into the space occupied by the central cylinder.
From symmetry that cylinder will remain a cylinder , ?
diminishing to y -- Il 1. Equating the volume forced
E
50
TESTING OF MATERIALS OF CONSTRUCTION
out of the annulus to the diminution of volume of the
central cylinder
( R ? – ,- 2 ) dh = 2 7 hr dr,
2rdr
R2-72
ah
nh
(2 ) .
Proportional Contraction of Cylinders forming the
Central Cylinder.-Let Fig. 20 represent in plan a sec
tion of the central cylinder. When that cylinder changes
radius from 9 to go - dr, from matter forced in from the
external annulus, any other cylindrical space of radius
p must also diminish in radius. It is natural to sup
pose that the areas diminish proportionally, so that--2 Trilr_27 pile
1
TT gol
Topk
( ”
(3 ).
P
Transformation of Central Cylinder ".--Let p be now
the radius of the cylinder which was initially of
radius 7 .
From ( 2 )
dh
2rdr
R2_2
Replacing d r from ( 3 ) ,
al
h
2,2
de
R ? — 227
РP
Integrating,
27
logh
R2 — 72
log P + *.
51
PLASTIC PROPERTIES OF MATERIALS
Let H , as in ( 1 ) , be the initial height of the layers
in the chamber .
For h = H , p = r .
Then , --
2 72
H =
log H
log r +
R2 —2.2
.
Eliminating c,
2
2,2
H
R2-72
log
log
R?
11
)
C
7?
РP
7*
2 point
(4).
3
Which gives the radius p of the portion of the central
cylinder initially of radius 1 after any amount of flow
into the jet .
If A B ( Fig. 21 ) is the original surface of the lead ,
CD the surface after
FIG . 21 .
the flow of the jet
cdgh, then the matter
x
A
initially occupying the
central cylinder abcd
B
ZZ
та a
1
C
le
D
f
1
}
will be found occupy
ing the space efg h, ef
being the diameter to
which the original cen
tral cylinder is now
reduced .
H
h !
1
1
с
re
1
1
1
?
1
Also kl is
the value of
1
P
when so
much of the jet was
g
h
T
1
formed that kl was at cd, and O k = 2 was then the
length of the jet.
E 2
52
TESTING OF MATERIALS OF CONSTRUCTION
Now, in the equation
R
porno
2
=6)
let
Р
be the radius of the central cylinder when the
length of the jet is l. But from ( 1 )
2.2
h = H
1,
R2
Рe
7
= (1-
R"
2 262
22
R2H
(5),
.
which is the cquation to the curve fl, p being the
abcissa when the ordinate measured above O X is l.
2,2
The curve varies with the value of
If that
R2 -.7.2
quantity is greater than 2 the curve may be regarded as
a parabola of a higher degree. If it is equal to 2,
R
when 2:2 = RP – , or r = V : the curve is a parabola
R
of the second degree . If 7 =
the curve reduces
V3
to a straight line.
M. Tresca has experimentally verified the law
; the
verification proved entirely satisfactory.
22. Pressure of Fluidity.- These experiments show
that a ductile body is deformed when the pressure
exceeds a certain amount according to geometric laws,
and permanently, so that there is no indication of
elasticity or tendency to return to the primitive shape.
3
PLASTIC PROPERTIES OF MATERIALS
5?
M. Tresca designates by the term “ pressure of fluidity '
the stress necessary to induce this state.
23. Application to the case of Prisms subjected to
Tension or Compression . - M . Tresca perceived perfectly
well that, in testing, a bar passed from the elastic state
through an imperfectly plastic state to an almost per
fectly plastic condition, but he has not investigated the
phenomena which occur in testing. There is, however,
a general relation deducible on the assumption of a
condition of perfect plasticity which will be useful
hereafter.
Suppose that in the deformation of a plastic bar the
volume does not change. Let l be the initial length
and d the initial diameter of a bar which, when elongated
plastically, has the length 1 + 2 and the diameter 1 -- .ô
1
From the constancy of volume we get
I 1121= + (17 – )2 (1 + )
(4 )at
Now, the contraction of area is,
I for – (1 – 3)"}= , ha
Hence ,
contraction of area
initial area
a
1
tao
So that for a perfectly plastic material the percentage
| This deduction was given in the Engineer, May , 1885 .
54
TESTING OF MATERIALS OF CONSTRUCTION
of contraction of area is not proportional to the per
centage of elongation calculated on the original length
of the bar, but to the percentage of elongation calculated
on the stretched length of the bar.
Now, during plastic elongation the intensity of the
stress remains constant.
Hence, the initial load on the
bar when the plastic condition is reached is , if p is the
pressure of fluidity
d2 .
4
Similarly, when the elongation is a,
P = 4 ( d – *8)? p.
Hence,
E = (4-7 ) = ita
the load diminishing as the bar stretches. It will be
seen that this phenomenon occurs in the last stage of a
tensile test .
If the stress is compressive,
dilatation of area
original area
(d + 8) –
d2
7
I- a
P
Pi
the load increasing as the prism shortens, as occurs in
crushing short prisms.
24. Work done in Plastic Deformation . - Consider
the case of a prism which shortens a length d a while
PLASTIC PROPERTIES OF MATERIALS
the load increases from P to P + d P.
55
The work done
in compression is P da . But
P da = P_17da-3
Hence the work in compression from an original length
I to a length 1 – 2 is
W = L Pil I
da
- a
Z
- Pil logo I - a
77
But P1
d ? P,
and, putting V for the volume of the
4
prism,
W = p V log. Tr7 a
.
56
TESTING OF MATERIALS OF CONSTRUCTION
CHAPTER III .
STRESS -STRAIN DIAGRAMS .
25. Suppose a cylindrical bar of uniform diameter
placed in a testing machine, and the load gradually
increased while measurements are made of the length
of a marked portion of the bar. For every value of
the stress there will be a corresponding value of the
strain . The strains may be plotted as abcissa and
the stresses as ordinates, and points will be obtained
FIG. 22 .
on a curve giving the rela
TENSIONS
[ 10
tion of stress and strain
B
for the whole test .
Cс
This
may be called the stress
D
strain curve for the bar.
COMPRESSIONS
LLLLLLLL
0
EXTENSIONS
For a perfectly elastic
bar the stresses are pro
5
portional to the strains.
E
Hence
T
the
Culve
is
а
10
AА
THRUSTS
straight line, such as A OB.
By setting off compressions to the left, extensions to
the right, thrusts downward and tensions upward, a
continuous line is obtained representing the relation of
57
STRESS - STRAIN DIAGRAMS
stress and strain for the whole range of perfect elasticity
of the bar.
For a perfectly plastic bar, the load would have to
attain some value , P = 0 C or -P = 0 E , these being
the so- called pressures of fluidity , ' before plastic de
In a bar in compression the
formation commenced .
section increases as it shortens.
Hence, since the pres
sure per unit of area in a plastic material is constant,
In a bar in tension the section
the load must increase.
contracts as the har elongates , and hence the load must
be diminished as the elongation increases, if it is to be
kept in equilibrium with the resistance of the bar.
FIG . 23 .
Hence curves giving
the relation of stress
1
1
and
plastic
during
strain
G
deformation
1
such as
are curves
CD or E F.
!
1
D
It has been shown
-I-
that the relation of
X
0
O'
stress and strain dur
1
3
ing plastic deforma
1
tion is
E
7.
Pi = P
l ta '
H
where Pi is the load
F
which causes a de
formation Ia in a length l.
This shows that the
curves C D, E F are parts of hyperbolas having 0 X
58
TESTING OF MATERIALS OF CONSTRUCTION
and G OH as asymptotes, where G O'H is at a dis
tance I from CO E.1
Before examining some stress-strain diagrams for
different materials it may be pointed out that quite
similar diagrams are obtained by plotting moments
of torsion and angles of twist, or bending moments
and deflections .
26. Stress- strain Curves for a Brittle Material.-LA
brittle material may be defined as a material which
breaks without any considerable plastic deformation.
Cast metals may be taken as examples of materials
approaching to this description.
The right-hand curve in Fig. 24 shows the stress
strain diagram from
Hodgkinson's experiments on
long cast-iron bars. No part of the curve, except a
short portion , perhaps, near the origin , is quite
straight. Materials like cast iron take a sensible
though small set even with comparatively small loads,
and the set increases regularly with the loads. Such
materials have, strictly speaking, no elastic limit when
first subjected to stress. Further, in materials like cast
iron or steel castings the bar breaks before any great
plasticity is exhibited . The curve runs to the break
ing-points in tension and pressure without any great or
significant change of curvature .
? An account of stress and strain diagrams, indicating the different
character of the elastic and plastic portions of the curve, was given by
the author in the Engineer for May 22, 1885, and also in a lecture at
the Society of Arts on Autographic Diagrams, February, 1886.
59
STRESS-STRAIN DIAGRAMS
FIG . 24 .
Ton
per sq. inch
Load
in
29
tons
Bruke
7
28
27
26
25
24
23
22
per
sq.in
Ateta Point
5
*
3
21
Tension
.
20
19
I
18
16
002
003
-001
001
1
15
Compressions
14
Extensions
13
12
3
11
9
5
8
7
6
7
5
3
2
9
1
10 .
0.002
0.0di
1
Compressions
2
01.001
0.002
0.003
Extensions.
3.
52
5
7
8
9
+
11
12
13
2018
SalduOJ
6
++
15
* +6
17
113
to
14
15
19
16
20
18
21
19
22
21
22
23
123
24
24
25
Keld Heint
26
Stress - strain Curves for Cast Iron and Mild Steel .
.
60
TESTING OF MATERIALS OF CONSTRUCTION
The following short table gives a comparison of
the extensions and compressions for different loads :
Lond
in tons Extension per
unit length
per
sq . in.
1
2
3
7
9
12
000166
.000347
*000544
· 000765
·001021
001338
Compression per Increase of Exten- Increase of Com
sion per ton per pression per ton
wit length
unit length
per unit length
000174
* 000351
000531
· 000714
000899
001090
·00128
·00167
00229
000166
000181
·000197
000221
000256
*000317
·000174
·000177
000180
000183
000185
000191
000190
000195
000207
27. Elastic Stress - strain Curve. - Mostrolled materials
are almost perfectly elastic, both for tension and com
pression , for a considerable range of stress. The left
hand curve in Fig . 24 gives the stress -strain curves ,
up to points just beyond the elastic limits in tension
and compression, for two bars of mild steel, tested by
the Committee of Civil Engineers . The steel was cast
steel suitable for piston rods . The bars were 12 inch
diameter, and the deformation was measured by verniers
in a length of 10 feet .
The numbers given in the following table are taken
from a plotting of the results to a large scale . The
steel broke at 41.85 tons per sq. in. in tension.
It will be noticed that the deformation per ton per
sq. in. is nearly constant and nearly the same for ten
sion and compression .
Hence the results plot nearly
into a continuous straight line. Beyond 26 tons per
1 Experiments on the Mechanical and other Properties of Steel. By a
Committee of Civil Engineers, 1870.
61
STRESS-STRAIN DIAGRAMS
sq. in . the elastic limit in tension and compression is
passed, and the deformations quite abruptly become
larger.
Stress
Extension per ton Compression per
in tons Extension per Compression per
per
sq. in.
unit length
unit length
7
10
15
20
25
30
*00054
* 00076
00112
·00150
00192
*00583
00050
*00072
-00108
· 00146
·00188
per sq . in. per
Means
unit length
· 000077
ton per sq . in. per
unit length
000075
· 000071
000072
000072
000073
· 000077
000075
000076
000073
· 000076
000075
28. Stress- strain Diagram for Indiarubber . — India
rubber supplies an example of a solid in which the
deformations are not small compared with the origi
nal length . It has besides great incompressibility
FIG . 25 .
STRESSES
TENSION
COMPRESSIONS
EXTENSIONS
PRESSURE
The strong line shows the immediate strain .
some minutes.
The dotted that after
of volume, so that under considerable alterations of
form its volume is nearly constant. Dr. Winkler has
6
2
:
TESTING OF MATERIALS OF CONSTRUCTION
given the following results of experiments on india
rubber in tension and compression :
p is the load in kilograms per sq. cm .
a is the elongation or compression of unit length .
a' is the elongation or compression when the load
has been some time on the bar.
signs refer to compression ; the + signs to
The
tension :-Tension
Compression
NN
P
λ
X지
B
λ
-0.5
1 :0
1.5
2.0
2.5
3.0
-036
• 076
109
• 139
163
.185
+ 0.5
10
1.5
2.0
3.0
4.0
70
6.0
- 036
082
•115
147
173
198
11
+ '046
• 121
.207
• 316
•548
.859
1.309
1.794
+ 052
• 137
• 264
396
• 698
1.135
1.572
2 : 110
Fig . 25 shows these results plotted . It will be seen
that the stress -strain curve is without any straight
portion, the elongations increasing faster and the com
pressions less fast than the stresses . The modulus of
elasticity E = p /a , calculated in the ordinary way, is
therefore extremely variable. The section contracts so
that the volume of the bar remains constant. Then
the real stress in the bar is p . = p ( 1 + a ). Then the
modulus of clasticity, calculated from the real stress
and the elongation per unit of initial length , isE
1 ta
Pi
Pр
2
2
= E +p;
STRESS -STRAIN DIAGRAMS
63
and the modulus, calculated from the real stress and the
elongation a, per unit of stretched length , is
Pi
p (1 + a )?
E, = 2
2
au
E, ( 1 + 2)
= E + PI
= E + p ( 2 + 2 ).
The following table gives values of E , E1, and E,.
It will be seen that for a considerable range of stress
E, is even more constant than En, and both are more
constant than E :
Load
P
Real stress
-3.0
- 2 :5
- 2 :0
-1.5
- 1 :0
- 0.5
0
+0.5
+1.0
+1.5
2.45
2 09
1.72
1:34
92
.48
+ 2.0
+ 3.0
+4.0
+ 5.0
+60
E
Ei
E + P
Pi
16.2
15.3
14.4
13.8
13.2
13.9
13.2
E.
El + Pi
12.8
15.6
14.9
12 : 4
12 :3
12.2
13.4
13.61Mean
13.1 13.7
13.9
14:11
0
•52
1:12
1.81
2.63
4.64
7:44
11:55
16.76
10.9
8.3
7.2
6.3
5.5
4.7
3 :8
3 :4
11 : 4
9.3
8.7
8.3
8.5
8.7
8.8
9.4
11.9
10 : 4
Mean
10.5
11 :4
10.9
13.11
16.1
20.3
26.2
1
29. Stress-strain Curve for Ductile Materials. — In
soft wrought iron and steel the stress -strain curve has
the forin shown in Fig. 26. Between the elastic limits
A and C the curve is a straight line. The parts A B
and C D correspond to a partly plastic condition of the
material in which the larger part of the deformation is
64
TESTING OF MATERIALS OF CONSTRUCTION
permanent. In tension a maximum stress is reached
at D , but the deformation can be continued with a
diminishing stress till the bar breaks at some point E.
During the part DE the curve falls very rapidly,
because generally a local
drawing out begins, and
FIG . 26 .
TENSION
D
the deformation is confined
E
1C
to a small portion of the
bar
In the compression
curve A B there is a more
COMPRESSIONS
O
EXTENSIONS
gradual change of curvature,
because nothing like local
deformation occurs .
A
Up to
the points A and C there
A
PRESSURE
B
is almost immediate equili
brium
and strain .
between the stress
But in the parts A B and C D the deforma
tion is gradual, and requires time for its completion.
The deformation hardens the material, and at last ceases .
In the part D E probably no definite relation of stress
and strain is reached , and the deformation increases
without limit.
Yield Point, or Brcaking-down Point in Tension .>
It is somewhat remarkable that, amongst the ordinary
materials used in construction, a tolerably perfect
straight elastic line is chiefly found in the case of mate
rials, like wrought iron or rolled steel, which have been
subjected to severe mechanical pressure in manufacture.
For such materials, up to some point A , the line 0 A is
65
STRESS-STRAIN DIAGRAMS
extremely straight, and the stresses and strains are
almost exactly proportional. Between A and B a
sensible, but slight, curvature appears in the diagram ,
FIG . 27 .
and a sensible, though small,
D
deviation from proportion
ality begins to appear in the TENSION
E
stresses and strains.
Bau
B
schinger calls the point A the
limit of proportionality , but
C
A
it would be better to call it
the elastic
limit.
A little
beyond the elastic limit, at
B, there is , for some rolled o
or hammered materials, a very singular and marked
jump, or inflection B C in the stress - strain diagram.
This point is very clearly marked in the diagrams
of the Committee of Civil Engineers appointed to
make experiments on steel, and is shown in Fig. 24 ,
which is a plotting of two of their experiments on
steel .
The Committee call this point the ‘ yielding
point . '
The behaviour of the material at this point
was very accurately described by Bauschinger in
1879,2 and he adopted for it the term " Streckgrenze. '
Bauschinger indicated the very great suddenness of the
increase of extension , lateral contraction , and tempera
ture. In 1881 Prof. Kennedy, in a Report on Riveted
Joints to the Institute of Mechanical Engineers , called
attention to this peculiarity in rolled steel , and gave to
1
Experiments on Steel, 1870.
Civilingenieur, Bd . xxv. s. 81 .
F
66
TESTING OF MATERIALS OF CONSTRUCTION
the point A the name ' breaking -down point.' On the
whole this term seems very suitable, if by breaking
down is understood a breaking down of the primitive
molecular arrangement.
The phenomenon of breaking down is not due to
any action of the testing machine, for it is shown in
diagrams from a machine in which the load is auto
matically adjusted to the resistance of the bar, and in
machines in which the loading is effected entirely by
hydraulic pressure.. Probably the breaking -down point
is a kind of physical record of the condition of constraint
in the bar at the moment of rolling or hammering. Not
that the stress at the breaking- down point is identical
with the stress in rolling, for the temperature conditions
are different in rolling and testing. But still, it is pro
bable that at the breaking -down point a mechanically
produced condition of aggregation is passed, and the
artificially created rigidity suddenly gives way.
Beyond the inflection at the breaking -down point
the partly plastic, partly elastic, extension proceeds
regularly , again . But the precise extension for any
load between B and C depends more or less on the
time during which the load acts. During any pause in
this part of the curve the extension increases without
increase of load , and when the load is increased again
the rigidity of the bar is found to be greater than before,
and the curve becomes steeper (Figs. 35 , 39 ) . Next
to the breaking -down point the most important point
to observe is the point D, where the maximum load is
67
STRESS-STRAIN DIAGRAMS
reached . For this point it would be convenient to have
a name, and , by analogy with elastic limit, the term
'plastic limit ' may be proposed . This implies, what
of
seems to be the case, that at the point C the pressure
fluidity is reached for the part of the bar at which frac
ture ultimately occurs . It is probably at the point C ,
or very near it, that the local contraction begins which
is so characteristic of the last stage of testing of ductile
materials .
21
TONS
OF
FIG . 28 .
TOTAL
PULL
30. Form of the Stress- strain Curre at the Yield Point.
The form of the stress - strain curve near the yield
15
81
.
B
7
h
12
la /
2.C
2.5
80an
to
120
FC
Extensions in inches.
point is very variable, being greatly affected by small
stress differences and by differences in the time rate of
extension . Further, in most autographic arrangements
F 2
OS
TESTING OF MATERIALS OF CONSTRUCTION
the record of stress is affected , when the specimen is
yielding rapidly, by the inertia of the load. In Professor
Kennedy's autographic apparatus the effect of the inertia
of the load is eliminated, and Fig . 28 gives some auto
graphic diagrams taken in this apparatus. It is difficult
to believe, however, that the irregular curves near the
yield point are not due to time differences, or perhaps
to small stress differences arising out of the inertia of
the elastic system formed by the test bar and testing
machine. The diagrams are, however, the most satis
factory autographic diagrams yet obtained .
1
31. Behaviour of a Ductile Material when broken by
Tension ; Local Drawing Out, or. Local Contraction . — A
bar or plate of ductile material such as soft steel is
placed in the testing machine and subjected to a gradu
ally increasing stress till it is broken. At first, as the
extensions are small, it is easy to keep the lever of the
testing machine floating with almost any rate of loading.
At the yielding point,however ,the stretching suddenly
becomes rapid , and with most testing machines it is not
possible to keep the lever floating. The lever can only
be kept floating if the pumps which work the hydraulic
press are capable of moving the press ram as rapidly as
the rate of increase of stretch. With a single-lever testing
machine the author finds it possible in most cases, but
not always, to just keep the lever floating during the
1 In Professor Kennedy's diagrams tlle ordinates are curved :-a is a
diagram for a Swedish iron bar ; b, Shelton bar iron ; c, Swedish iron ;
d, Landore rivet steel ; c and f, Landore steel plate ; I, cast steel ; li,
mild -steel bar .
STRESS -STRAIN DIAGRAMS
09
stretching at the yielding point, but to do this it is often
necessary to run the weight back a little to diminish the
When the rapid stretch at the yielding point is
ended, and the bar has again become capable of sup
porting an additional stress , it is quite easy, in general ,
stress.
to adjust the rate of loading so that the press just takes
up the stretch, and the lever remains floating almost
without movement. And this continues till the maximum
load is reached . Beyond that point the drawing out of
the specimen at a restricted portion of its length begins,
and the reduction of area is so rapid that the stress
must be diminished. It is here again difficult to keep
always the lever floating. Finally, the bar breaks sud
denly with a load considerably less than the maximum
load it was sustaining just before the local drawing out
commenced .
Suppose the bar ruled with straight lines at right
angles to the direction of the stress. As the bar
stretches the distance between these lines increases , but ,
so far as can be judged, they remain straight and
parallel during the increase of stress till the maximum
load is reached . During the local drawing out the
lines become curved in the part which is drawing out.
The line exactly at the centre of the part which is draw
ing out, however,remains straight. Professor Kennedy
has inferred from this curvature of the lines that the
stress becomes very ununiform on the section of fracture,
being greatest at the centre of the bar. Some slight
1 Proc. Inst. Mech . Eng. 1881, p . 218 .
70
TESTING OF MATERIALS OF CONSTRUCTION
variation of stress probably is produced , but the author
doubts if the variation is at all large. In fact, the ex
tension measured along the curved edges of the bar is
not
very different from the extension at the centre, and
if the material is plastic great variation of deformation
is possible with small variation of stress.
Fig . 29 is from photographs of a strip of mild -steel
plate taken during the process of testing.
A was taken
just when the maximum load was on the bar. No be
ginning of the drawing out is visible, and the lines
drawn on the bar are still straight, as far as can be ob
served . Fig. B was taken just after the drawing out
became visible, and when the stress on the bar had been
a little diminished. At the centre of the part drawn
out the line is still accurately straight, but the lines on
each side are curved .
Fig. C was taken at the very
moment before fracture . The drawing out is here more
considerable. Fig. D is the bar after fracture.
32. Distribution of Drawing Out along the Bar . - If
a bar is divided into inch lengths before testing, and
these are measured again after the bar is broken , the
plastic extension in each inch length will be determined .
It will be found that the amount of extension is more
or less irregular along the bar. In the inch length in
which local contraction and fracture occur the exten
sion is very great. On either side it diminishes, at first
rapidly, afterwards more slowly, and is least near the
enlarged ends at which the specimen is held . But there
are irregularities, showing that there are differences of
71
STRESS -STRAIN DIAGRAMS
D
BANNE
c
MILE
HUO
B
2
9
.FIG
Mild
.
Steel
of
out
Drawing
T
A
由
72
TESTING OF MATERIALS OF CONSTRUCTION
plasticity along the bar, and in rare cases two local
contractions form at different parts of the length . It
is possible that some of the irregularities are due to the
fact that the elongation is usually measured on one side
of the bar only. It is desirable that the measurements
should be taken on opposite sides of the test bar and
averaged .
The following table gives some measured values for
different materials :
ELONGATIONS IN ONE INCH LENGTH OF BAR AT DIFFERENT DISTANCES
FROM THE FRACTURE.
( The elongation in the division in whion fracture occurred is indicated in
italic type ).
Inches along the Bar
Material
1
2
3
4
5
6
7
8
9
01
10
11
12
I
Lead
Brass
0:18:15 30 -17 14 22 -16 -17 1:01
0.23.20 .20 1:30 .21 22 24 21 ! 21 21
.
+
Wrought iron :
Angle iron
6.05
Square bar
0.09.06 06 06 06
11 08:10 23
1 0.09
0:17 195 23 51-26
0.24 22 -22 -22 -21
Flat bar
0.11.16 .14 .10
Channel iron
Rivet iron
1
10
005 07
.14 .11
-23 -25
-27 1:50
08
135 08
10.10.09
23 23 18
50 .26 · 18 :17 1.17
10 10 10
10
Steel :
ma
Steel plate
0170-30 22 19 19 15 15:16
Steel axle
Steel tire
0:16 17 -21 21 '18 .17 1:21 *65
46 :17 13 -10 ?
0.02.06 :08 21 OY 22 -05 02
.03 .06.08 12 ?
It follows that the ultimate extension , reckoned as a
percentage of the length of the bar, varies as the length
is greater. Thus, taking the square wrought-iron bar,
1 H. R, Towne,
& Steel Committee.
The other measurements aro the author's.
73
STRESS -STRAIN DIAGRAMS
and taking lengths symmetrically situated with respect
to the fracture, the ultimate extension per cent. is
In two inches, including fracture .
50 per cent.
In four inches
38
>>
.
32
7 )
eight
29
‫וי‬
27
> )
ten
>>
twelve ,
six
+
> )
ñ
,
73
26
> >
‫ܕ ܕ‬
‫ול‬
>
But not only does the ultimate extension depend on
the length measured, it depends also, in bars of a given
length, on the position of the fracture. It is desirable
for comparative purposes to calculate the extension for
all bars in such a way as to give the nearest approxi
mation to the extension of a bar which broke at the
centre of the measured length . Thus the ultimate ex
tension of the rivet-iron bar in a length of ten inches is
best obtained thusa
0.51
1.335
Extension in fourth inch (fracture) .
Extension in divisions 1, 2, 3, 5, 6 , 7
Double extension in division 8
Extension in division I
+
Extension in ten inches symmetrical with fracture
Elongation per cent., 25:35 .
0:46
0.23
2.535
This has not been the usual method of calculating
the ultimate extension, but it obviously gives results
more comparable than the usual method , and it has
been recommended for adoption by the German testing
laboratories .
Furtlicr results on the variation of ex
tension with distance between gauge points will be given
in the chapter on the form of test pieces.
cine
4
• 0
.30
060
7
•0
с
9
.80
4
3
2
1
Dist
of ribution
.out wing
Dra
0
FIG
.30
2
Eictension in Each Inch
10
3
Inches
Distances
in
Fracture
from
d
4
5
Afcle
S..fteel
Iyon
.Rivet
9.
,.e keel
Plate
S
9
6
Iron
Channel
2.
Iron
Angle
C.
7.
Brass
.
I
.alead
7
74
TESTING OF MATERIALS OF CONSTRUCTION
A good idea of the distribution of drawing out along
the bar is obtained by plotting the extensions per inch
.
Fig
.
75
STRESS -STRAIN DIAGRAMS
as ordinates at the centre of each inch length, and con
necting the points by a curve. Fig . 30 shows some of
the results so plotted .
It may easily be seen that the length of the part in
which local contraction occurs must depend in some
way on the sectional dimensions. The local contraction
will be longer for a larger bar. Hence it might be ex
pected that two bars of the same material and the same
length, but differing in section, would draw out differ
ently, and give different values of the ultimate elonga
tion. The following results obtained by M. Barba show
that this is so :
DIFFERENCES OF ELONGATION IN BARS WITH DIFFERENT PROPORTIONS
OF LENGTH TO DIAMETER ,
(Pieces cut from bar of soft steel rolled to 14 inch diameter and annealed . Also on a
harder steel. )
Limit of
Length
Diameter,
between
Length
elasticity,
Breaking
Elongation
gauge points
Diameter
tons per
sq . in .
stress , tons
inches
per ceut .
15.85
15.72
16:00
21.90
21:25
20.94
23:47
23.40
23.85
37.CO
37.67
38.05
in inches
-787
394
.197
3.94
3.94
3.94
3.94
3.94
3.94
5
•787
•394
• 197
10
20
5
10
20
per sq . in.
37.5
30 : 2
25.0
25.9
21.0
17.0
Similar Test Bars ( Barba's Law ).— M . Barba inferred
that to get identical values of the drawing out from dif
ferent pieces of the same material they must be either of
identical dimensions or of similar form .
This law can
TESTING OF MATERIALS OF CONSTRUCTION
76
hardly be considered to have been absolutely cstablished ,
but the following results show that it is at least a good
approximation :
IDENTITY OF PERCENTAGE OF ELONGATION IN SIMILAR BARS (BARBA) .
A billet of extra soft steel was hammered to an octagon of 31 x 34 inches, rolled to
a bar 14 inch diameter and annealed. Three test pieces gave the following results :
Diameter ,
inches
787
394
197
Lengths be
Length
tween gange
points, inches
Diameter
7.87
10
10
10
3.94
1.97
Means
Limit of
Breaking
elasticity, tons stress, tons
per
Elongation
per cent .
per sq . in .
sq . in .
15.72
15.08
15.72
23.85
23:35
23.90
31.4
15.71
23.70
31.0
31 : 0
30.5
EXPERIMENTS ON Two HARDER QUALITIES OF STEEL, ROLLED TO BARS
1. INCH DIAMETER AND ANNEALED .
Diameter,
Lengths be
Length
tween gauge
inchies
.272
Means
Contrac
tioni per
cent.
Elonga
09.3
09.0
09.17
68.6
69.2
69.7
08.8
69.5
32.8
tion per
cent .
7.87
15.22
15.22
15:34
15:16
15.10
15.22
15.28
8.86
15.22
26-70
26.45
26:40
25.95
25.40
25.11
15.22
26 20
09.2
33.3
20.76
23:21
22-65
24:10
25.76
24:16
24:10
41:11
41.20
40.50
40.17
40.30
39.34
40:10
36.5
38.0
37.4
38.4
31.8
35.8
34.4
20.0
18 8
18.2
18 : 1
18.0
18 : 1
19.5
23:53
40.37
36.1
18.6
1.97
2.95
3.94
4.92
5.91
6.89
1 to
7.24
Means
.272
-407
• 543
.697
.815
.950
1.090
1.22
Breaking
stress, tons
tous per sq.in. per sq . in .
points
•407
• 543
.679
.815
950
1 : 090
1.22
Limit of
elasticity ,
Dian .
1.97
2.95
3.94
4.92
5.91
6.89
7.87
8.86
1 to
7.24
26.77
26.65
33.2
33.0
33-5
33.6
33.2
33.0
34.0
77
STRESS -STRAIN DIAGRAMS
EXPERIMENTS ON PLATES,
Dimensions of
Lengti
between
Widtli
Thickness: &illige
points
Width Thickness
-787
1 : 575
2.362
.197
394
591
Lengti
Narcil
4 to 1
1.97
3.94
5.91
Ti
07
test bar
Limit of
Breaking
elasticity,
stress ,
tons per
$ . in .
Elonga
tons per
. in .
10.07
10.86
13:14
23.00
24.25
24.70
31
39
39
tion per
cent.
33. Suppression of the Drurcing Out.- The drawing
out in ordinary test bars is measured on a portion of
uniform section, and the measurements are not extended
quite up to the enlarged ends by which the specimen
is held . The enlarged ends diminish the drawing out
of the parts nearest them , and if the part between the
enlarged ends is very short the drawing out, contrac
tion , and strength are all affected . For the present,
cases will be considered in which the change of section
is gradual not abrupt.
A plate perforated with a row of holes, or formed
like B or C ( Fig. 31 ) , is virtually a very short test bar.
In reporting on riveted joints for the Institute of
Mechanical Engineers, the author noticed that in some
cases a perforated plate was stronger than a plain test
bar of the same material. Shortly after, this was shown
more distinctly in some experiments of the Board of
Trade on riveted joints , and in experiments by Professor
Kennedy for the Institute of Mechanical Engineers.
In these last experiments , perforated steel plates inch
1 Proc. Inst. of Mech . Engineers, 1881 , p . 319 .
? Experiments on Stecl.
P. 18 .
Memorandum of the Board of Trade, 1881 ,
78
TESTING OF MATERIALS OF CONSTRUCTION
thick were 10 7 per cent . and 3-inch plates 11.9 per
cent . stronger than plain test bars of the same material.1
PERFORATED PLATES.
BOARD Or TRADE REPORT, 1881.
Mild-steel plates .
Ultimate or breaking stress per sq. in .
of initial net section , in tons
" plate
" plate
1" plate
27.69
25.33
29.39
30.86
31:37
27.84
22.94
29.31
28.81
30.23
28:17
21:26
29.12
29.15
28.43
Unperforated
30:17
Punched
28.32
Punched and annealed
31 : 6
31.23
31:46
Punched and bored to size
Drilled
6
h" plate
It will be seen that the punched plates lose from
per cent. of strength in 1 -inch plates to 25 per cent. in
1 - inch plates. But in all other cases there is a gain of
strength in the perforated plates. This amounts to about
4 per cent. in the 4 -inch plates, 10 per cent.in the l -inch
plates, 51 per cent. in the 2 -inch plates, and 21 per cent.
in the 1 - inch plates .
That this is due to the diminution
of contraction the following table shows. In punched
plates the contraction is diminished, but the metal is
also injured by the process of punching .
Contraction of arca per cent .
Unperforated
Punched
Punched and annealed
Punched and bored
Drilled
" slate
" plate
" plate
1" plate
53 : 3
24 : 1
41 : 3
24.0
36.6
50.0
19.1
37.4
28.9
32.7
39+
13.0
30.7
19.4 .
32.1
38 8
5.4
24.7
15.9
33 : 2
' Proc . Inst. of Mech . Engineers, 1881 , p. 215.
.
STRESS - STRAIN DIAGRAMS
79
Some experiments by Mr. Strohmeyer ' illustrate
very clearly the dependence of the breaking stress , es
timated in the usual
FIG . 31 .
?
way by dividing the
‫الد‬
}
6
и
breaking load by the
initial section, on the
B
amount of drawing
6
d
out before fracture.
1
The test bars of
m
m
the forms shown in
Fig. 31 were all cut from the same plate, and the holes
were in all cases 24 mm . ( 0.96 inch ) diameter. The
width b varied in different test bars.
Form
Dimensions
Thickness
Width
Ratio
6
Elongations per cent.
of hole
t
d
‫וון וון‬..
mm .
A
35
12
B
46.8
31.8
18 :0
12
12
12.5
12
54.0
44.0
12
12
12
12
12
o
34.0
28.4
23 : 3
18.6
13.0
7.6
12
12
12
12
in
50 mm .
in 200
mil .
25 .
Breaking stress,
kilos . per sq . mm .
44.0
1.94
1:32
0.75
0.52
50
40
21
26
18
14
12
2.25
1.83
54
28
50
1:42
1:18
46
0.97
0.77
0:54
0.32
37 :
33 ;
26
22
22
20
16
46.6
47.0
45.8
45.0
48.8
45.2
25
21
14
10
45.1
27 .
41.
477
48.0 Mean
47.17
478
480 )
Mean
45 7
45.5
It will be seen that form B is 9 per cent. and form C
4
per cent.stronger than the simple test bar A. This
is the effect which the author attributes to diminution
1 Proc . Inst. of Civil Engineers, 1884.
SO
TESTING OF MATERIALS OF CONSTRUCTION
of the contraction of area by the nciglibourhood to the
breaking section of less strained material. Now , as the
breadths at corresponding points of B and C are exactly
equal, it looks, at first sight, as if B and C ought to
behave exactly alike, whereas, apparently, in the ex
periments B is stronger than C. It will be seen , how
ever, that the material near the point of fracture is not
in identical conditions in the cases B and C.
Suppose
two bars of the form D are placed back to back and
broken . The material at the place of fracture is now
identically in the same state as in form C , and contrac
tion takes place not only round the semicircular holes,
but along the edges n m . Weld together the pieces
along this line, and the contraction along m m can no
The piece is then identical with form B ,
contraction
than C, and ought to be stronger
it has less
The experiments show that it is so.
longer occur.
Mr. Richards made a very interesting series of ex
periments at the Barrow Company's Steel Works on
test bars similar to Mr. Strohmeyer's bars A and B.
The material was mild steel made by the Siemens pro
The plate was } inch thick . Two pieces had
parallel sides like ordinary test bars. The other speci
cess .
mens were indented on each side by a semicircular.
drilled hole, leaving a section between of varying width .
The results are given in the following table .
Here the plates of form B , cquivalent to perforated
plates, are on the average 12.6 per cent. stronger than
the parallel-sided bars of form A , and the strength is
81
STRESS-STRAIN DIAGRAMS
per cent .
Contraction of
width
per cent .
27.5
Contrac
Width
Form
Thickness
tion of
t
area
inches
A
B
1
.495
.490
52 : 5
53.5
• 045
.650
-995
.995
1:47
1.46
2.28
2.27
.495
• 500
-502
.495
•502
-50
•495
.495
45
46
47
1
42
31
36
42
43
27.0
19
19
11
12
8
10
9
8
Contrac
tion of
Breaking
thickness
tons per
per cent .
sq . in .
33.3
35 : 9
32.01
32:47
32
33
37
34
26
30
36
37
36.64
36.52
36.82
37.05
36:18
35.88
35.72
35.72
stress in
very uniform considering the different widths of the
specimens. The contraction of area in form A is 53
per cent. , while in form B it is only 41 per cent. , so
that there is a diminished contraction to account for
the increase of strength . Further, while the con
traction of thickness is nearly the same in form A and
form B , the contraction of width, which is what would
be affected by the form of the specimen , is 27.2 per
cent, in form A , and only 11.9 per cent. in form B.
The shortest possible bar is formed by turning a
groove with a very slightly rounded bottom . The
following experiment on two bolts of Whitworth com
pressed steel gives the strength of a bar of extremely
tough material thus shaped. The heads and nuts of the
bolts were turned to fit spherical seatings, so that the
stress was quite fairly applied . A groove , a little rounded
at bottom , precisely likę a Whitworth screw thread , was
turned in the body of one bolt as at A (Fig. 32 ) , and
the other was turned in the form shown at B.
G
82
TESTING OF MATERIALS OF CONSTRUCTION
Brenking load ,
Breaking stress, in
in tons
tons per sq. in .
Diameter
Form A
1 : 500
B
1 :487
4
.
53.25
101.77
62.35
35.87
Belongated 60 per cent. , and the contraction of
arca was 54: 6 per cent .
For A the elongation and
FIG . 32 .
contraction were practically
UOTI
nil.
21h
34. Abrupt change of Sec
24 .
tion - Nicked Specimens. - At
13
A
B
any abrupt change of section
the stress on cross sections
cannot be uniform. The less
strained
extension of other metal near it.
metal hinders the
If the material were
perfectly elastic the stress at any re-entrant angle would
be infinite, but the plasticity of all ordinary materials
diminishes very greatly the inequality of stress. Never
theless the inequality exists, and it counteracts the gain
of strength due to suppression of drawing out.
Two pieces of the same cast iron were tested , one
in the form of an ordinary test bar, the other with a
square collar in the middle of its length. The re
entrant angles at the collar were virtually nicks.
breaking weights were
Plain bar
Collar bar
.
13 :875 tons per sq. in .
11.980
Decrease
The
99
‫לו‬
1.895
71
showing a loss of 13 : 6 per cent. of strength, due to
83
STRESS -STRAIN DIAGRAMS
the inequality of distribution of stress caused by the
collar.
Mr. Baker made some interesting experiments on
steel plates with artificially produced cracks. A fine
saw -cut was
made
at
one
or both edges of the
specimen, and then, raising the specimen nearly to
welding heat, the saw- cut was closed up so far as to be
rendered invisible. Fig. 33 shows a set of specimens
of the same steel . Specimen a was an ordinary test
FIG . 33 .
PUTN
32.50
31:40
24.70
36.30
28.00
bar ; d was a bar with semicircular notches, so that it
was virtually a short bar ‫ ;ܪ‬I was a bar with a saw
cut or crack on both sides ; ( a bar with a saw-cut
or crack on one side ; e a bar perforated with a crack
on each side of the hole .
The breaking weights in tons per sq. in . are
given under the figures. It will be seen that the
short bar d is stronger than the plain test bar « by
3.8 tons, or 12 per cent. ; but the nicked bar 1 is
weaker by 1.1 ton, or 31 per cent. Considered as a
short bar, b should have carried as much as d, the
| Minutes of Proc. of Inst, of Civil Eng. , vol. Ixxxiv. p. 165.
G 2
84
TESTING OF MATERIALS OF CONSTRUCTION
inequality of distribution of stress has therefore re
duced its strength by 157 per cent. Similarly e is
weaker than d by 8 tons, or 22 per cent.
It is clear,
therefore, that, in the case of nicked bars, the increase
of strength which would result from the virtual short
ness of the bar is more than counteracted by the
inequality of stress on the section of fracture. Mr.
Baker found with specimens of indiarubber a loss
of strength in nicked specimeng of 60 or 70 per cent. ,
and that is probably due to the fact that india
rubber, although it deforms enormously, is really less
plastic than steel, and consequently the variation of
stress is greater .
Relation of ultimate Elongation to Contraction of
Area. It is now common , in testing iron and steel by
tension , to record the ultimate elongation in a length of
8 or 10 inches , and the contraction of area at fracture,
as data useful for deciding on the value of a material .
Both the ultimate elongation and the contraction are
supposed to indicate the ductility of the material, and
a good deal of confusion arises from the discrepancy
between these two quantities.
It has already been shown ( S 23 ) that for a per
fectly plastic material
contraction of area
initial area
1 + 2
phare de
that is , the percentage of contraction is equal to the
percentage of elongation, calculated on the stretched
1
85
STRESS -STRAIN DIAGRAMS
length of the bar.
Hence, a definite relation between
the elongation and contraction will only be found for
the short length of the bar, which becomes almost per
fectly plastic, and draws out during the last stage of
the test.
That a definite relation does exist between
the elongation and contraction in the immediate neigh
bourhood of the fracture is easily shown . From the
experiments on steel by a Committee of Civil En
gineers, Tables A , B, C, D , it is possible to get the
elongation in a length of 1 inch or 2 inches of the bar
in the neighbourhood of the fracture, and to compare
it with the contraction of area .
Length , in
Material
No. of bar
Contraction
Initial area
Elongation
Stretched length
Ω
1 + λ
inches
λ
1
943
1,194
1,285
1,028
1,174
1,305
Bessèmier steel
923
1,038
1,184
1,295
1,275
1,255
1,265
873
Crucible steel
1,078
1,147
1,068
Means
2
2
1
1
2
1
1
1
2
2
2
1
2
1
1
1
2
32
.22
5ā
•44
: 58
•50
: 37
.47
• 50
31
35
34
36
.30
:35
.44
· 41
34
.42
09
.44
32
• 27
27
.30
09
.29
25
.40
•03
28
37
-54
03
.40
•42
Here the agreement is as close as could be expected ,
the percentage of elongation ( estimated on the stretched
length ) being three - fourths of the percentage of con
S6
TESTING OF MATERIALS OF CONSTRUCTION
Had it been possible to measure the
traction of area .
elongation in, say, a 4 -inch length, the approach to
agreement would , no doubt, have been closer.
The following numbers are from some measurements
by the author :
2
Iron bar
.
.
Angle iron
.
Iron plate
Steel plate
Delta metal
•
.
‫ܙ ܕ‬
+
2
2
2
2
2
2
2
2
24
.28
.42
-15
-12
39
09
•27
< ~
31
Lengile
Material
• 20
.20
.27
: 15
11
.29
• 07
.32
If there is this near agreement in the contraction
and elongation in the short, plastically - yielding part of
the bar near the fracture, then there can be no agree
ment in the contraction and elongation in greater
lengths of bar. The contraction does measure in a
definite way the plasticity of the material under the
breaking stress . The ultimate elongation in an 8- or
10 -inch length measures partly the plasticity of a short
length under the breaking stress, partly the plasticity
of the rest of the bar before drawing out commenced .
The two measures of the ductility are only in agreement
when the elongation is taken for a very short length of
bar near the fracture.
35. Influence of Time on the Stress- strain Curve.--It
has been seen that plastic yielding is gradual , either
increasing indefinitely or at a diminishing rate under a
87
STRESS-STRAIN DIAGRAMS
given stress. Hence it might be expected that the
plastic part of the stress -strain curve would be flatter
the slower
the rate
FIG . 34 .
20
of loading. Professor
Ewing
gives
st
Fa
ow
the
sl
shown in Fig. 34 for
two similar pieces of
soft - iron
wire, one
loaded to rupture in
four
Stress
T
, nons
per
.isq
curves
stress - strain
minutes,
10
the
other at a rate about
5,000 times slower.
In the same way ,
in taking autographic
stress- strain diagrams
0
10
20
30
Extension per cent
there is a notch in
the diagram at any pause in the increase of loading .
Fig . 35 shows a diagram for a manganese steel bar ,
tested with a pause of five minutes at each successive
ton .
Fig. 36 shows the stress -strain curves for four pieces
of wrought iron cut from the same bar. For bar 319
the extensions were measured on a length of 41 inches ;
for the other bars on a length of 9 inches . In the case
of bars 319 and 154 the extension increased at a nearly
uniform rate during the plastic stage . In the case of bar
313 there were four -minute pauses at each successive
ton , and the diagram is notched . In the case of bar
SS
TESTING OF MATERIALS OF CONSTRUCTION
FIG . 35 .
Load
Tons
20
-
15
10
5
.
2 inches.
2
Extension
in 8 inches.
FIG. 36.
Tons
w
313
39
914
'1184
i
16
10
% Iruches
1
314 the load was taken off and a pause of six minutes
allowed at each successive ton.
!!
It may be noticed that
STRESS-STRAIN DIAGRAMS
89
the breaking-down point is more marked with the
longer bars . The following table gives a summary of
the tests :
Tons per sq . in.
No. of bar
319
154
313
314
.Elongativo per cent .
Yield point
Maximum load
12.97
14:37
13.68
14.23
22:19
22:10
22.34
22:47
34 : 7
25.8
29.5
28.2
36. Influence of Time on the ultimate Elongation .Some remarkable experiments of Colonel Maitland at
Woolwich ? show that, contrary to a common prejudice,
the ultimate elongation is increased by very rapid load
ing. Colonel Maitland experimented on a steel which, in
unhardened specimens of 2 inches in length between
shoulders, broke in the testing machine at 26 tons per
sq .in . and with 27 per cent. of elongation. A specimen
was then screwed into blocks arranged so as to fall ver
tically in a slide. After a certain height of fall the top
block was arrested by stops and the specimen broken by
tle momentum of the lower block . Broken in this sudden
way the ultimate elongation was 17 per cent. Specimens
were then screwed into plugs fitting a strong tube and
broken by exploding gunpowder and guncotton between
the plugs . The plugs were driven out in opposite
directions, breaking the specimen connecting them .
Under these circumstances the ultimate elongation was
" The Treatment of Gun Steel. ' Proc. Inst. of Civil Engineers, vol.
lxxxix . p . 120.
90
TESTING OF MATERIALS OF CONSTRUCTION
The explanation of these
results appears to be that with very rapid increase of
from 47 to 62 per cent .
stress there is not time for the formation of a short
local contraction, but the general extension continues up
to the breaking point.
Hardening Effect of long-continued Stress. — Experi
ments on the influence of time on the extension and
breaking stress of wires have been made by Mr. J. T.
Bottomley in Sir W. Thomson's laboratory . Eight
specimens of soft-iron wire were tested by gradually
increasing stress, applied in ten minutes of time in each
case. They broke with 431 to 46 lbs. (mean, 45 • 2 lbs . ) ,
with elongations varying from 17 to 22 per cent.
Another specimen , left with 43 lbs . hanging on it for
24 hours and then broken by gradual increase of stress
during 25 minutes, broke with 494 lbs . , with 15 per
cent. elongation . Another, left for 31 days with 43 lbs .
hanging on it and then broken by increasing stress , bore
51 ] lbs . and elongated 14: 4 per cent. A bar, loaded
first with 40 lbs . and broken by gradual addition of load
during two months , broke with 57 lbs. The slower
loading had therefore increased the strength by nearly
27 per cent .
The increase of breaking stress and
diminution of elongation is commonly attributed to a
hardening effect of long-continued stress. But the
result seems complicated by the influence of time on
the local drawing out in the neighbourhood of the
fracture. Generally the more slowly the load is applied
1 Article ' Elasticity,' in the Encyclopædia Britannica.
91
STRESS-STRAIN DIAGRAMS
the shorter is the local contraction and the less the
contraction of area.
37. Correction of the Stress -strain Diagram to show the
actual Stress in the Bar. - In ordinary stress -strain dia
grams the loads are plotted as ordinates, and the elonga
FIG . 37 .
TONSI
45
71
m
1
1
1
I
1
1
40F
f
1
1
1I
1
351
[
3
1
30
25
de
B
201
h
1
1
35
|
1
1
1
Steel Plate! N. 7.5
101
1
1
Area 904
in .
1
sq;
55
1
X
1
IN
1
I
Ic '
-
--
-9.3 "
2 "
-
-8 "--
аa
1
o
tions of the bar between two gauge points initially
marked on the bar as abcissæ. By a mere alteration
of vertical scale the ordinates represent equally the
stress per sq . in . of the initial section of the bar.
Thus, in Fig. 37 () a represents the elongation la
in l inches length of bar which has extended a per inch
when the load is that represented by ab. If the bar is
92
TESTING OF MATERIALS OF CONSTRUCTION
wo sq. ins. section , al will measure on a scale w times
that for the loads the stress per sq . in . of initial section
of the bar. Up to the yield point the section of the
bar changes very little , but beyond the yield point the
deformation is so large that the section sensibly changes .
Then ab does not represent the stress per sq . in . of the
actual section of the bar at the moment.
To find this
it is approximate enough to consider that the change of
density is small compared with the deformation. Ilence,
so long as the deformation is general over the marked
length of bar --that is, up to the maximum load pointi,
the section of the bar can be found from the measured
length .
Letl wo be the length between gauge points and sec
tion ofthebar initially, and 1 ( 1 + 2 ) anil w , the length and
section when the load is P.
Then , w / = w ,1 ( 1 + 2 ) ,
(0)
001
1 ta
If p is P / « , the stress reckoned on the initial section,
then the real stress on the actual section is
P
= P ( 1 + 2 ).
21
( 1) ,
In the diagram tako O C = 1 to the same scale as
that on which O a = la . Draw bd horizontal. Through
I draw Cie, cutting ab in c. Then ac represents P1,
the actual stress on the reduced section, to the same
scale as that on which ab represents p , the stress calcu
lated on the initial section. If several points are thus
STRESS-STRAIN DIAGRAMS
93
found we get a curve feg, lying above the ordinary
stress - strain curve and extending to the point of maxi
mum load .
This is sometimes called the curve of true
cohesive strength.
It is simply a curve giving the
relation of the actual stress and strain .
Beyond the point of maximum stress the construc
tion fails, for the extension becomes chiefly local and
the l in the formula above is no longer the length
between the gauge points. But another point in the
curve may still be found. If the contracted section is
measured after the bar is broken , then the breaking
load h k divided by that section gives the real stress
k m at the moment of fracture. It is obvious, however,
that the part gm of the curve is distorted , for while the
abcissæ up to the point i represent extensions of a fixed
length 1, the abcissæ from i to l represent extensions
of an undetermined portion of l. The real elongation
per unit of length at the moment of fracture in the part
which is drawing out is given by the equation
( 0)
(V1
1
21
( U1
and if Ok' is taken equal to lan, and k' m' set off equal
to km , the general form g m ' of the final portion of the
real stress - strain curve is determined .
It is quite
possible to measure the contracted section at inter
mediate loads between i and h during testing and to
calculate intermediate points along gm '. So far as can
be judged from one or two instances , the portion gm ' of
94
TESTING OF MATERIALS OF CONSTRUCTION
the curve shows a regular increase of tenacity with
increasing strain without the abrupt inflection of the
distorted curve gm .
38. Stress- strain Diagrams for nearly Plastic
Materials.- When very ductile materials are loaded
with pressures which approach or reach the pressure
of fluidity the strains follow approximately the plastic
law, and the stress-and - strain curve becomes nearly a
hyperbola.
In tension experiments a difficulty arises from the
extension becoming local instead of general. It is im
possible after local contraction sets in to determine
what length of bar is being elongated, and hence the
strain per unit length cannot be determined. In com
pression experiments this difficulty does not arise. But,
on the other hand, it is difficult to keep long bars
straight during compression, and hence experiments
must be made on short cylinders , for which accurate
measurements are more difficult. Besides this, in short
cylinders a barrel-shaped distortion occurs, due partly,
no doubt, to friction at the ends against the plates
which apply the pressure . Nevertheless , these results
are interesting as showing an approach to a perfectly
plastic condition . Fig. 38 shows the stress-strain
curves for short cylinders of lead , copper , and wrought
iron . The lead curve is from an experiment by Prof.
Kick . The cylinder was initially 50.05 mm . diameter,
1 Proc. Inst. of Civil Engineers, vol . I. p . 188.
The lead curve is
plotted with loads on specimen as ordinates, not stress per sq. in.
‫ (؟‬:(
STRESS -STRAIN DIAGRAMS
FIG . 38 .
Pressure in Tons
per sq. inch
Compressions
0 :3
0-2
0 :1
0:4
}
Lead
70
Co
20
pp
1
er
I
-0
mer
0-
-0--O
1
1
--
30
-
- -- 2-
-0
40
50
I
1
I
1
80
90
200
n
Iro /
t
gh
70
ola
ou
60
erb
Wr
Hyp
0-5
0.6
96
TESTING OF MATERIALS OF CONSTRUCTION
and 64 : 4 mm . in height. The following table gives the
loads and compressions
CRUSHING OF A LEAD CYLINDER (KICK ).
ion,
Load, in tons IIcight, in inches Compress
in inches
2:9
3.25
3.35
3.45
3.95
5.65
2.576
2.312
1.904
1716
1.036
1.376
1 : 128
Diameter at
centre, in inches
• 264
•072
.860
930
1.200
1.448
Stress, in tons
per sq . in , of
2.00
2.16
2.40
2:52
2.60
2.84
3:16
central area
•79
• 72
.67
• 65
.62
72
It appears that the pressure of fluidity was reached
at about 0.75 tons per sq . in. , and the stress remained
approximately constant notwithstanding the large de
formation .
Fig. 38 shows a similar curve for a wrought-iron
cylinder. The experiment was made by Fairbairn, and
the results are discussed in Cotterill's “ Applied
Mechanics,' p . 418 .
Plastic Compression of Copper Cylinders.—Small
copper cylinders made of the softest and purest copper
are used in crusher - gauges for determining the powder
pressure in the bore of the gun . Tlie copper cylinders
are made in two sizes , 24 sq. in. and 1, sq. in. in
section, and the initial length is 0-5 inch .
Tables
have been published " giving the compression of these
cylinders when compressed by hydraulic pressure, the
compressions being measured by a Whitworth meaşur
ing machine.
| Industries, March 25, 1887.
II
.23
.24
.25
:33
•2
3
3
•1
:30
•29
.28
.27
•26
.25
.34
1
:6
1
: 7
.18
:19
.20
• 1
2
•22
1
: 5
:12
1
: 3
:14
1
: 1
.40
:39
•38
:37
3
· 6
35
L-
1
· 0
a
Compression
,
inches
in
inches
,in
length
Compressed
>
tons
i, n
area
22
1:
22
:1
:0
22
4,103
22.2
.22
333
.30
.29
.28
-27
10,666
11,000
23
.22
21
.20
'19
2
•9
30
3
:1
7,666
8,000
8,333
8,666
9,000
9,333
9,666
10,000
10,333
28
•25
*24
26
6,600
4,666
5,000
5,333
5,666
6,000
6,333
4,333
7,000
4,000
Pressure
.,in
lbs
31
P
4
• 0
.39
.38
:37
:36
.35
3
:4
3
• 3
:32
λ
,iinches
length
n
Compressed
.27
.26
.23
.24
•5
2
.
1
·0
1
:7
.18
1: 9
.20
.21
1
: 5
1
: 4
1
Compress
ion
,
in
inches
1
:0
1
· 1
12
1
• 3
Pres
per
.sq sure
. f pressed
com
oin
17.9
18.7
19.3
19.8
20.3
20.7
21.1
21
:4
21.6
21.9
22.1
22.2
3,968
2,494
2,091
2,225
2,359
iPressure
., n
lbs
2,628
2,763
2,897
3,031
3,162
3,296
3,431
3,565
3,700
3,834
P
Cylinder
0.5
linitially
in
ong
and
a24
.isq
nrea
COMPRESSION
SOFT
C
CYLINDERS
.-OFOPPER
171
:1
18
0
19
19
:3
20.5
21
:2
21.8
:3
22
22
:8
23
:2
23
5
:8
23
23.9
240
:0
24
24.0
24
:0
23.7
23.5
23.2
22
:
8
22
:1
:
:
o.inf pressed
com
Pre
per
.sq ssure
tons
i
,n
area
Cylinder
0: .5
linitially
in
and
1.
nong
.aisq
rea
STRESS - STRAIN DIAGRAMS
97
98
TESTING OF MATERIALS OF CONSTRUCTION
The preceding table gives the compressions a, com
pressed length 1 – 2, and observed pressure producing
the compression . Neglecting the barrel-shaped distor
tion the stress reckoned on the deformed prism is
Pi
pl - a
2
col ?
and the values of this have been calculated and placed
in the tables . When the material is completely plastic ,
p, is the pressure of fluidity.
It will be seen that for compressions exceeding
two -fifths of the original length the pressure on the
actual deformed section is nearly constant. Further,
the numbers for the cylinder of i'u sq. in. area are
almost exactly double those for the cylinder 24 sq. in .
area . According to both tables the pressure of fluidity
for soft copper must be about 22 tons per sq. in.1
39. Raising the Elastic Limit by Stress. It has
g
lon been known that for iron , steel, and other metals
a load exceeding the elastic limit raises that limit.
Thus , Bauschinger gives the following results of ex
periments on five gun-metal bars , of a section about
2.8 x 0.5 inches . The elongations were measured in
8 inches by the mirror apparatus :
No. of
bar
1
2
3
limit, in tons
per sq . in..
in tons per
4.62
3.82
3.84
3.50
3.77
6:56
6.10
6.56
5.85
6.02
sq . in .
Raised elastic
Tenacity , in
set, in inches limit, in tons
per sq . in .
tons per sq.
in .
Permanent
00061
00061
*00067
00054
* 00057
6.15
5.74
5 • 77
5.80
5.66
14.2
14.9
13 : 3
12.9
13.2
♡
4
Original elastic Stress applied,
1 See also Treatise on the Manufacture of Guns (official), p. 92.
.
99
STRESS-STRAIN DIAGRAMS
In these experiments the second loading was effected
only a few minutes after the first loading .
Bauschinger noticed that if a bar after loading
beyond the elastic limit was left for twenty -four hours
Load
FIG . 39 .
in Tons
23
d
21
P
19
f
ia
2
0
I IN .
2 IN ,
Extensions
or more at rest it recovered partially the set previously
taken, and if then the elastic limit was again determined
H 2
100
TESTING OF MATERIALS OF CONSTRUCTION
it was in some cases raised not only up to but beyond
the load previously applied .
Fig . 39 shows a stress -strain diagram of a piece
of steel plate, taken autographically by apparatus
which will be described.
The yielding point, or break
ing-down point, is strongly marked at a load of about
18 tons .
At 19 tons, 21 tons, and 23 tons the load
was almost completely removed, the pencil tracing
downwards and retracing upwards almost exactly
straight lines parallel to the primitive elastic line.
Thus, at 19 tons the pencil described while the load was
removed and replaced the straight line ab. The distance
ob represents the permanent set produced by the load
of 19 tons, and the stress - strain diagram for the material
Similarly for
altered by loading is the line bac.
The
removed.
was
load
the other points at which the
peculiarity specially to be noted, and which indeed is
only shown in such autographic diagrams as this, is the
steepness and almost straightness of the curve at a f.
The material is not only nearly perfect in its elasticity
in the reimposition of the load up to the point a , corre
sponding to a load of 19 tons, but is nearly perfect in
elasticity to the point f, corresponding to a higher load .
More accurately, f is a new yielding point in the material
altered by loading.
Viscosity of Solids. Elastic After -Working. If a
wire carrying a heavy vibrator is set in vibration tor
sionally within its limits of elastic stress, the vibrations
subside more rapidly than can be accounted for by
STRESS -STRAIN DIAGRAMS
101
external causes or by heating effects. There must,
therefore, be an internal molecular friction or viscosity .
In a wire kept vibrating constantly more molecular
friction is found than in one allowed to rest between
each experiment'— that is , the arc of vibration dimin
ishes more rapidly.
This is due to an elastic after
working,' by which the strained metal recovers its
original condition gradually during a period of rest. If
the limit of elasticity has been exceeded, there is a still
more marked change of the material after straining and
during subsequent rest, due to elastic or plastic after
working.
40. Bauschinger's Experiments on the Influence of Rest
after Drawing Out on the Elastic Limit.-- Bauschinger first
indicated that, by drawing out a metal by stress beyond
its elastic limit, the elastic limit is raised , not merely
during the continued action of the load, but during a
period of some days after the load is removed . The
elastic limit may in certain cases rise above the stress
corresponding to the load imposed .
In a later paper 4 he gives a series of experiments on
different metals loaded successively up to a point at
which yielding just began . In one series, the successive
1 Sir W. Thomson , Proc. Roy. Soc., vol . xiv. 1865, p . 289. Article,
Elasticity ,' in Encyclopædia Britannica , $ 34 .
? Mr. Tomlinson states that this fatigue of elasticity does not occur if
the stresses are kept well within the elastic limit .—Trans. Roy . Soc., vol .
clxxvii. part 2, 1886.
3 Dingler's Journal, Bd. 224, s. 5.
4 Ueber die Veränderung der Elasticitätsgrenze,' Civilingenieur , 1881 ,
s. 290 .
.
3.5
2C
20
10
ezlo
·002
Tons per Sq: inch.
Ingot
Iron
006
·
" 2
00
B
"
004
.Yi
eltd
po
. in
.
FlasticElastic
-o,Note
limit
.
004
lig
ez
FIG
.40
·010
"
0
· 08
.
Extensions
pe
.008
Bly
二 二
二
셨7
"
010
4
3
2
022
'-
46
47
99
0
• 14
interval
.
"
1.014
‫גן‬
3
2
51
hours
after
2
·016
-1B.irst
F
loading
A.
Reloaded
without
018
102
TESTING OF MATERIALS OF CONSTRUCTION
ez pe by
二
二
STRESS -STRAIN DIAGRAMS
103
loadings followed each other immediately ; in the other,
a pause of one or more days was allowed after each
loading before again loading.
Generally the results
were of the character indicated in the plotting of two
series of the results in Fig. 40. Four stress-strain
curves for cach series are shown , plotted to a very large
scale for the extensions, and each line extends up to
the point (marked by a dot) at which yielding just
sensibly commenced . The elastic limit ( or exact limit
of proportionality ) is shown by a circle marked e.
In the series A the bar was reloaded without any
sensible interval of time. The yield point rises at each
loading but the elastic limit falls, in the second loading
almost to zero .
In series B an interval of about
fifty hours was allowed between each loading. In this
case the yield point rises as before, but the elastic limit
rises also at cach successive loading. Comparing the
two series, it appears that the elastic or plastic recovery
during the fifty -hour pause ( unloaded ) raised the elastic
limit from the positions shown in A to those shown in
B. Bauschinger's results seem to be expressed in the
following conclusions :
If a material is strained to or beyond the yield
point, unloaded , and again immediately loaded :
( a) The breaking extension is diminished, and the
breaking load somewhat increased.
( 6 ) The clastic limit is lowered sometimes to zero,
and the modulus of elasticity is a little
diminished .
104
TESTING OF MATERIALS OF CONSTRUCTION
(c ) The yield point is raised to the stress corre
sponding to the previous loail.
If after the first loading a period of quiescence is
allowed before the second loading :
( a ) The elastic limit rises sometimes above its
initial value .
(1) The yield point rises gradually above the
stress corresponding to the previous load.
41. Use of the Stress - strain Diagram in estimating the
Work done on the Bar . - Let Fig . 41 be a stress-strain
diagram , the ordinates
FIG . 41 ,
C
being as usual loads, in
tons, on the section a of
D
B
the bar, and the abcissä
extensions of a length 1
1
between
.
{
0
2
1
1
1
1
1
1
F
G
gauge
Draw verticals
B , C , D. Then ,
done on the bar
yield point is
points .
through
the work
up to the
the area
OBE, work done up to the
plastic limit is O BC F , and work done in break
ing the bar is OBCDG. The areas are easily mea
sured by a planimeter. If m inches = 1 ton , and n
inches = 1 inch of extension, then
Work in inch tons =
area of diagram in sq. ins.
772 77
STRESS -STRAIN DIAGRAMS
105
By dividing by the volume al of the bar we get
the work per
cubic inch of material.
From what has
already been said the elongation at rupture varies for
the same material with the length between gauge points,
and to a certain extent with the section of the bar.
It
is only with similar test bars that the work in breaking
the bar, estimated per cubic inch of material, will
furnish comparable numbers. But further, the part
CD of the diagram is in most diagrams, if not in all ,
somewhat badly determined , and at any rate is ex
tremely affected by time differences in the rate of exten
sion . The work represented by FCDG is almost
entirely work expended in local drawing out of the bar.
If this is discarded , the area O BCF represents the
work up
to the plastic limit, at which , so far as carry
ing a load is concerned, the bar is virtually destroyed.
If this is divided by the volume of the bar, values are
obtained nearly independent of the dimensions of the
bar, and therefore affording a good measure of its joint
strength and ductility.
106
TESTING OF MATERIALS OF CONSTRUCTION
CHAPTER IV.
TESTING
MACHINES .
A TESTING MACHINE is simple or complex according as
it is intended for a few or a greater number of purposes .
If the machine is to be used for determining the quality
of one kind of material subjected to one kind of strain
ing action it may be of very simple construction . In
that case it will be desirable that all the test pieces
should be of one size and form , and this simplifies the
construction of the machine. In an ordinary cement
testing machine simplicity is obtained by the limitation
of the purposes for which it is available. If, however,
a testing machine is to be used for varied investigations
on many materials, under different kinds of straining
action , for specimens of different shapes and sizes , then
the machine must be more complicated, and accessory
apparatus must be provided . In the adaptation of a
machine to diverse purposes there must be some sacri
fice of convenience, some compromise between conflict
ing requirements. Hence, there is no testing machine
absolutely preferable to all others. Almost every form
of testing machine has special merit for some particular
kind of work .
A
TESTING MACHINES
107
It must be remembered that,with every increase of
complexity in the machine, and with every addition to
the accessory apparatus, greater difficulty in using the
machine, more care in adjustment, and more loss of
time in adapting it to particular experiments is involved.
Hence, the extent to which it is desirable to combine
different functions in a single machine is a matter for
careful consideration in any given case. Some testing
machines are like special tools in a workshop, doing one
kind of work only, and with these the rapidity of work
is greatest, and the liability to errors of oversight or ill
adjustment is least.
42. The simplest mode of testing is to apply a dead
load directly to the test bar. Many of the earlier
experimental investigations were made in this way, and
the method is still used in testing the weaker materials.
It is, however, laborious and inconvenient to have to
handle a load equal to the stress required. By using a
lever between the load and specimen the weight to be
handled is diminished in the ratio of the lever arms.
Many of the earlier testing machines were little more
than a lever for applying the stress. But here a prac
If the specimen is held
between a fixed abutment and the lever , the position of
the lever alters as the specimen deforms , and so much
tical inconvenience arises .
the more the greater the ratio of the lever arms.
Some
arrangement must be made for neutralising the effect
of the deformation .
The abutment must be moved to
keep the lever horizontal. In some machines a screw
108
TESTING OF MATERIALS OF CONSTRUCTION
and nut afforded the only means of adjustment. In
these cases it was necessary to remove or reduce the load
while the adjustment of the abutment was made. Some
times the load was lifted by a crab and tackle while the
nut was screwed up.
To escape some of the difficulties of a lever arrange
ment a hydraulic press has been used to produce the
stress in the specimen. The specimen being held at one
end by a fixed abutment, the other is strained by attach
ment to the ram of the press, the movement of which
takes p the deformation .
In such machines the stress
u
in the specimen must be inferred from the fluid pressure
on the plunger, indicated by a pressure -gauge. Then ,
an allowance must be made for the friction of the cup
leather or packing of the ram .
As this allowance is
large, and varies with the condition of the ram and the
packing, machines of this type are not susceptible of
great accuracy .
According to experiments of Mr. John Hick, the
friction of a press cup-leather on a ram dinches diameter,
with a pressure of p lbs . per sq . in ., is—
F
= cdp
But the whole pressure on the
ram is 1 + d2p. Hence, the fraction of the load on the
where c is a constant.
ram expended in friction and not transmitted to the
specimen is 4 c /Td ; that is, it decreases as the diameter
of the ram is greater. Hence, the proportional error
likely to be introduced by miscalculation of the cup
TESTING MACHINES
109
leather friction is less as the size of the ram increases.
Machines of this type are, therefore, most suitable for
testing test pieces of large section. However, the law
of cup - leather or packing friction is not really known,
and its amount is certainly extremely variable. "
It next appeared possible to combine the advantages
of the hydraulic press machine and the lever machine in
this way. The test bar was placed between a hydraulic
press and a lever, or system of levers , acting as a steel
yard . Roughly speaking, it may be said that in such
a machine the stress is applied by the hydraulic press
and measured by the steelyard . All good modern
machines are essentially arranged in this way, though
in some screws and gearing are substituted for the
hydraulic press, and in others a manometric arrangement
is substituted for the steelyard .
43. Machines for Testing in various ways Iron, Stecl,
and other. Strong Materials.-Machines for general testing
purposes almost always now consist of :
( 1 ) A lever, or system of levers , with weights,
forming a complete weighing apparatus. This is con
nected with one end of the specimen, and its purpose is
to indicate from moment to moment the exact stress
applied to the specimen . In a few cases, in place of
the lever and weights a manometric apparatus is em
1 The friction in testing machine rams is certainly greater than Mr.
Hick's formula gives . Probably the friction is greater at very slow speeds
than it was in his experiments.
* This arrangement appears to have been first used by Bramah, in a
machine constructed for Woolwich Dockyard, earlier than 1837 .
TESTING OF MATERIALS OF CONSTRUCTION
110
ployed, the stress being balanced by fluid pressure,
which is measured by a mercury column or a pressure
gauge.
( 2 ) A system of shackles for holding the specimen to
be tested , so guided that the straining action is exactly
of the kind required. Shackles must be provided suit
able for the different sizes and forms of specimens to be
tested , and different shackles for each different kind of
straining action to be applied .
( 3 ) To neutralise the effect of the deformation of the
specimen on the position of the weighing apparatus, a
movable abutment must be provided to hold one end
of the specimen . This is most commonly the ram of a
hydraulic press, which can be actuated by a pump, a
screw - compressor , or an accumulator. In other cases,
worm -gearing acting on a nut and screw , or even a
sliding-wedge driven by mechanism , has been used.
The object of all these arrangements is to take up
regularly and smoothly the deformation of the speci
men, so that the point of attachment of the weighing
apparatus is practically immovable.
44. With regard to their general arrangement,
testing machines may be divided into- ( a ) Horizontal
testing machines, in which the stress is exerted hori
zontally ; and ( 6 ) Vertical machines , in which the stress
is exerted vertically. The difference is one of con
venience chiefly. Where very long specimens have to
be tested the machine must be horizontal.
All chain
cable testing machines, for instance, are horizontal .
TESTING MACHINES
111
But there is a difference of action not entirely unim
portant in horizontal and vertical machines .
In hori .
zontal machines the weight of the shackles and other
parts connected with the specimen acts transversely to
the load applied by the machine. If not neutralised by
guides the weight would produce straining actions not
measured by the weighing apparatus. No guides can
quite perfectly prevent this transverse action , though
they may render it comparatively harmless. And the
guides themselves introduce some frictional resistance
which gets measured as part of the stress . In vertical
machines , on the other hand , the weight of the shackles
acts in the direction of the load, and can be balanced ,
without guides, so as not to affect the measurement of
the stress .
45. In designing a testing machine the qualities to
be aimed at are as follows :
( 1 ) The machine must have adequate sensitiveness
that is, the power of indicating decisively and accurately
small differences of stress.
To obtain sensitiveness in
a lever machine, the fulcrum on which the lever rests
and the supports of the shackles and weight are hard
steel knife -edges acting on hard steel planes. The sen
sitiveness depends on the smallness of radius of the
knife -edges and their accurate straightness. If initially,
or under the action of the load, the knife -edge bends ,
it virtually becomes broader, and the sensitiveness is
diminished . Now, the amount of sensitiveness required
in a good machine is not a quantity which can be
112
TESTING OF MATERIALS OF CONSTRUCTION
definitely assigned, nor is it easy to measure in an
actual machine, except in the case of an unloaded
machine.
But there is no doubt that the sensitiveness
attained in good machines is in excess of practical
requirements . This point will be discussed later ; but
it may be pointed out that two specimens cut from the
same plate quite commonly differ in strength by more
than 1 per cent. Supposing the strength of the test
bar to be 20 tons, 1 per cent. of this would be 4 cwt . ,
and a reasonably good machine indicates differences of
stress of far less amount than this. In most machines,
probably, the sensitiveness varies with the load and
increases as the load is greater. That is, the ad
ditional stress required to distinctly move the weighing
apparatus becomes a less fraction of the load as the
load increases . In a good 100-ton machine, carrying
its full load, the lever will be distinctly moved by an
addition to the stress of too ton . That is, the sen
sitiveness is such that Tobou of the load is indicated .
This is equal to the sensitiveness of a good chemist's
balance. The sensitiveness of machines with mano
metric apparatus may be made still greater.
( 2 ) The machine must be accurate in the indications
given — that is, the stress indicated by the machine must
differ very little from the real stress. A sensitive
machine may be inaccurate if the ratio of the leverage is
imperfectly known, and it must be inaccurate if, from
any flexure of the parts , the leverage changes with the
load. Hence, it is of much more importance than has
TESTING
113
MACHINES
generally been supposed that a testing machine should
be so arranged that it can itself be tested . The weights
used to load the lever can, of course, easily be stan
dardised. But in many machines the leverage, or ratio
of the weight applied to the stress on the specimen, has
only been determined by measurement of the distances
between the knife-edges, and very generally the original
determination of the leverage by the maker is accepted
as sufficient, however long the machine may have been
in use .
t is clear that, however carefully the leverage
was determined in the first instance, the wear or dis
placement of the knife- edges may seriously alter it in
course of time.
If the fulcrum distance is 2 inches , a
displacement of joinch would introduce an error of
1 per cent. into all measurements made by the machine
on the assumption that the leverage had remained
constant.
The determination of the leverage of the machine
by measurement of the knife-edge distance only is not
satisfactory, and in machines used for scientific pur
poses direct means of testing the leverage by weighing
should be provided .
(3 ) Facility of adjustment for different kinds of
straining action, and for specimens of different dimen
sions. The importance of this quality in a machine
depends very much on the kind of work it is intended
to do .
But it should be remembered that the shackles
used for different kinds of stress are somewhat heavy
and cumbrous , and the operation of changing the
I
114
TESTING OF MATERIALS OF CONSTRUCTION
arrangements for various kinds of work is somewhat
laborious.
( 4 ) Capability of casy and rapid manipulation
during a test. In commercial testing it is of great
importance that the testing should be accomplished
rapidly. The means of gripping the specimen must be
convenient, and often the manipulation of the weighing
and hydraulic apparatus can best be effected by engine
power.
( 5 ) Autographic apparatus for registering the
results is very convenient, and is a safeguard against
errors in recording the results.
Some machines are
adapted, and others are not adapted, for the addition of
autographic apparatus.
( 6 ) It is very objectionable if, during a test, the
specimen is subjected to shocks and vibrations.
Shocks or vibrations may arise either in the weigh
ing apparatus ( in adding loads , for instance ) ; or in
the hydraulic press ( by the action of a pump) ; or,
lastly, from the energy acquired by parts of the machine
which move when the specimen more or less suddenly
takes an increment of deformation .
Suppose a cubic inch of water suddenly forced into
the hydraulic press by the pump. If the lever and
weights had no inertia, no harm would result. But, in
fact, the movement of the press ram induces a movement
of the whole system , and the stress in the specimen is
for the moment increased by the inertia of the whole
system connected with it.
If the specimen suddenly
115
TESTING MACHINES
extends 1067 inch, the weights on the lever move
through a not inconsiderable distance. They acquire
energy in falling, which again is expended in momen
tarily increasing the stress on the specimen.
The question whether a machine with small leverage
or large leverage is likely to produce greater stresses in
the specimen in consequence of its inertia has been a
good deal discussed . If a specimen is loaded with a
dead weight M, the inertia of the loa: reckoned at the
specimen is M. But if the same specimen is put in a
machine with a leverage n , with a load M/n producing
the same stress , the inertia of the load reckoned at
the specimen is ( M / n ) n ?, or Mn. Hence it has been
argued that the stresses due to shock increase directly as
the leverage of the machine. All that the calculation
shows is that, with a given velocity of movement at
the specimen, the stored energy of the load liable to be
expended in straining the specimen increases with the
leverage. But the inference ignores the practical con
ditions in which testing machines are used . In propor
tion as the leverage of a machine is greater, its movements
are more narrowly linited by the stops at the free end
of the lever. The greater the leverage the more easily
is any tendency to acquire velocity in the machine
Hence, practically, it is
probable that the greater the ratio of the leverage, the
less is the liability to unknown and prejudicial stresses
detected and
controlled.
due to inertia of the machine.
In the Buckton machine
the maximum leverage is 50 to 1 ; in the Werder
I 2
116
TESTING OF MATERIALS OF CONSTRUCTION
machine it is 500 to 1 ; while in some compound -lever
machines it is 20,000 to 1 , or more. If the mere amount
of leverage produced so serious an effect as that inferred
above it would long ago have been detected in the use
of the machines. In fact, however, in skilful hands,
each machine is used in a manner suited to its construc
tion and so as to reduce any action of this kind to a
negligable amount.
46. Arrangement of the Lever or Steelyard and Weights.
- In the oldest form of lever machine a bent lever
FIG . 42
17
IV
(Fig. 42 ) was used, the three principal knife -edges being
in one straight line. The object of this arrangement
was to secure a constant leverage notwithstanding some
change of position of the lever. The leverage is the
ratio of the perpendiculars from the fulcrum f on the
directions of the load w and stress s, and if the knife
edges are not in one straight line the ratio of those dis
tances sensibly changes with the alteration of inclination
of the lever. In more modern machines the lever is
left straight, and is formed of sufficiently rigid side
plates ( Fig. 43 ) , between which are the knife-edges , fixed
in rigid cross supports.
117
TESTING MACHINES
In the older machines and in some modern machines
the loading is effected by placing separate weights in a
scale-pan. Unless the leverage is large this is laborious,
and, unless the lever is supported when weights are
TIC , 43 .
I
added, shocks are produced on the specimen . Two
modes of overcoming this difficulty have been found.
In one the separate weights are successively added by
mechanical arrangements ; in the other a single travel
ling, or jockey, weight is rolled out along the lever. In
the former, the leverage is constant ; in the latter, the
leverage varies as the jockey weight is rolled out.
Fig. 44 shows diagrammatically these arrangements .
At A is the ordinary lever and scale ; B and C are two
arrangements in which jockey weights are used . In C
the weight is so contrived that its centre of gravity lies
in the line through the knife-edges. In order that the
variation of position of the lever may not affect the
stress on the specimen the centre of gravity of the lever
must be on the line through the knife -edges, and the
jockey weight must either have its centre of gravity on
that line or must be hung from a knife- edge which
travels on that line.
At D is shown the mechanical
TESTING OF MATERIALS OF CONSTRUCTION
118
arrangement for adding weights to the lever. The
weights are carried by a frame which can be raised or
* ---* -- 6
FIG . 41.
»
E
1
A
O
U
wJ
B
сC
0
o
D
日
lowered by a screw . As the frame is lowered the weights
are deposited in succession on projections upon the rod
connected with the lever.
In Fig. 45 this mode of carrying the weights is
shown in more detail. The central rod a is suspended
from the lever. The side rods 6,6 are connected with a
screw raising or lowering arrangement; w , w are the
carefully -adjusted weights. When not in use the weights
rest on lugs on the side rods b, b. By lowering b, b the
weights are successively dropped without shock on the
corresponding lugs on a .
119
TESTING MACIIINES
There is one other arrangement of the lever which
should be mentioned.
In the testing machines of
FIG . 15 .
Thurston, Michaelis, and Polmeyer, a
al
bent pendulum lever is used ( E , Fig. 44 ) ,
carrying a single heavy load . As the
pull on the specimen is increased, the
pendulum - bob moves outwards and
upwards . If a and I are the perpendicu
lars from the principal fulcrum on the
directions of the load and stress, the
01
WS
‫שה‬
9:
10
varying leverage is the ratio v/a.
47. Principal Types of Testiny Ma
chines. It is proposed in the following
paragraph to indicate the principal types
of testing machine which have been used
as a key to the more detailed description
of some of these machines which will
be given later.
It must be understood ,
1!
ti
7
however, that the figures are merely
diagrams .
It will be seen that the most obvious arrangement
is to place the weighing apparatus at one end of a speci
men and the straining apparatus at the other. In fact,
a large number of machines are thus constructed. Later,
it appeared that certain advantages were obtainable by
placing both weighing and straining apparatus at the
same end of the specimen.
Simplest of all arrangements, probably, is that
adopted first in a complete shape in the testing machine
120
TESTING OF MATERIALS OF CONSTRUCTION
at St. Chamond , and later adopted by Wicksteed ,
Martens, and Michaelis. In this machine (Fig . 46 )
the specimen s is held between a shackle attached to
a horizontal weighing lever above and the ram of a
FIG . 46.
Wicksteed
Martens
S
Michaelis
P.
P
hydraulic press below. The weighing of the stress is
effected by rolling out a jockey weight along the lever,
or, in the Martens machine, by the arrangement shown
in Fig. 45 .
Somewhat similar is the arrangement of the test
ing machine of Messrs . Fairbanks & Co. , of New York
( Fig. 47 ) . In this case a worm -wheel and screw are
substituted for the press .
The Fairbanks machine is
virtually an ordinary platform weighing machine adapted
121
TESTING MACHINES
to the purpose of testing. It should be pointed out
that, instead of the simple-lever systein shown in this
diagram , the actual Fair
FIG. 47 .
banks machine has a com
pound -lever system , involv
S
ing the use of nine levers
and twenty - seven knife
edges, the object being to
gain so enormous a lever
age ( in some cases 24,000
UU
to 1 ) that the stress is
balanced by very small
weights. Fig . 48 shows
diagrammatically the
Thomasset machine, the
c
Fairbunks
FIG . 48 .
0
0 ;
d
E
S
HE
Thomasset
general arrangement of which is the same, but in which
a manometric arrangement d is substituted for the
122
TESTING OF MATERIALS OF CONSTRUCTION
The end of the lever
weights used in other machines .
minihan
presses on what is virtually a frictionless diaphragm
supported by fluid pressure. A pressure-gauge or mer
cury column, indicating the amount of fluid pressure
FIG . 49.
W. W
S
Grafenstaden
2
" X
bit
и :
-
on the diaphragm , gives data for determining the stress
when the area of the diaphragm and leverage is known .
Fig. 49 shows the machine of the Grafenstaden
Company at Mulhouse, which has a peculiarity adopted
in the testing machines of Riehle Brothers, extensively
used in America. In order to get a very short knife
edge distance on the main lever the fulcrum is not
placed in the lever itself but in a subsidiary lever
below , connected to the main lever by links. The
123
TESTING MACHINES
distance x is the virtual fulcrum distance, or the short
arm of the lever. It is obvious that this may be made
as small as desired on this arrangement without intro
ducing any mechanical difficulties of construction .
Fig. 50 shows the arrangement of the testing
machine of Messrs . Greenwood & Batley, of Leeds,
FIG . 50 .
Greenwood
S
10
2
ho
which has perhaps been more generally adopted than
any other in this country.
It is adapted to give a
horizontal pull , and has a compound -lever system . This
involves the use of a bent lever between the weighing
lever and specimen.
Fig. 51 is a sketch of the Maillard machine, in which
manometric arrangements are substituted for a lever
FIG . 51 .
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un
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Emery
system. To a certain extent this is also the arrange
ment of the great 500-ton testing machine at Water
?
town Arsenal.
Lastly, Fig. 52 shows the Werder machine, which
124
TESTING OF MATERIALS OF CONSTRUCTION
has been adopted very extensively in Germany. This
differs from all the preceding machines in this, that
both the weighing and straining apparatus are at one
FIG . 52 .
7
S
P
WA
Werder
end of the specimen. Hence , the expensive parts of the
machine being all at one end , arrangements can be
made to take in specimens of almost any length, by
prolonging the bed of the machine, without much extra
expense .
All the German Werder machines take in
specimens in both tension and compression 30 feet in
length, a result not obtained in any other type of
testing machine except that at Watertown, and there
only with greater difficulty, as the press must be
movable. In the Werder machine the hydraulic press
acts on the short arm of a single bent lever l. This
lever is carried by the specimen , so that the other end
of the specimen requires only a fixed abutment. By
the action of the press the lever is kept horizontal,
notwithstanding the deformation of the test bar. The
Werder machine may be described as a machine in
which the principal lever is supported on a moving
fulcrum . The great advantage of having only a fixed
abutment to provide for the back end of the specimen
is obvious. Another advantage in this machine is, that
TESTING MACHINES
125
the short arm of the lever can be reduced as much
as one pleases without shortening the knife -edges. It
will be shown presently that actual Werder machines
for testing specimens up to 30 feet in length, and up to
a load of 100 tons, have a short lever arm of 4 m.m. ,
or
inch in length only. Thus a leverage of 500 : 1
is easily obtained, and the loads to be handled are small .
On the other hand , these very considerable and practi
cal advantages are not obtained without some sacrifice.
The sensitiveness of the main lever is so great that it
must be adjusted by a spirit-level. Further, the ratio
of the leverage must be determined by direct experiment
with a control lever and weights.
48. The Woolwich Dockyard 100 -ton Machine.
This machine, which embodies nearly every feature of
importance in modern testing machines, is described and
figured in the first edition of Barlow's ' Strength of
Materials,' and must therefore have been constructed at
a very early date. It was intended chiefly for testing
cables, but was used for ordinary testing also. Barlow
describes its principle thus :-- The Admiralty have
had constructed in Woolwich Dockyard for testing iron
cables a machine in which the strain is brought on by
hydrostatic pressure, but its amount estimated by a sys
tem of levers , balanced on knife- edges, which act quite
independently of the strain there is on the machine,
and exhibit sensibly a change of pressure of į ton,
1 Treatise on the Strength of Timber and Iron . By P. Barlow, F.R.S.
London , 1837 , p . 237 .
126
TESTING OF MATERIALS OF CONSTRUCTION
even when the total strain amounts to 100 tons.
The
machine, which was constructed by Bramah, had a hori
zontal cast- iron frame of 1041 feet in length. On
one end of this was a hydraulic press, the position
of which could be adjusted by gearing . At the other
end was a system of levers , taking the pull and weighing
it.
The first lever was a bell- crank lever, as in most
horizontal testing machines, and there were two other
levers. The total leverage was 2,240 to 1 , so that
1 lb. in the scale -platform balanced 1 ton of stress.
The hydraulic press was worked by pumps, arranged
with great ingenuity to suit the varying pressure re
quired . Friction -grip shackles are shown for ordinary
test bars, to which reference will be made later.
The
distinctive features of this machine reappear in all
modern testing machines .
49. Fairbairn's Machine.:--The testing machine con
in many
structed by Fairbairn and used in
of Eaton
Hodgkinson's experiments, consisted of a heavy wrought
iron lever, with arms in the ratio of 8 to 1 and of the
bent form ( Fig. 42 ) . The lever rested on a short knife
edge at the top of a box -shaped casting, and at its free
end carried a scale-platform . There was no hydraulic
press, and the deformation of the specimen was taken up
by a nut on a screwed rod. The lever was used in
1
several ways both for tension and crushing
1 This lever machine, which has a certain historical interest from the
importance of some of the researches made with it, is figured in its original
form in Fairbairn’s paper on the ‘ Strength of Wrought -iron Plates and
Riveted Joints,' Phil. Trans. 1850 ; Useful Information for Engineers,
TESTING MACHINES
127
Creusot 30 -ton Machine. — This is a single - lever
machine, arranged very similarly to the Fairbairn ma
chine in its original form . But worm - gear is added to
neutralise the effect of the deformation of the speci.
men, and a ram is placed under the lever to lift the load
off the specimen when necessary.
The leverage is
17 to 1 .
Machine of Major Wade. — In tests of cast iron for
guns in America in 1855 a machine was used designed
by Major Wade, and a similar machine was used for
many years at Woolwich. It is chiefly noticeable for
being one of the first compound -lever machines . One
lever had a ratio of 20 to 1 , and the second lever, to
which the specimen was attached , a ratio of 10 to 1 .
Consequently, the loads on the specimen were two hun
dred times the applied weights. It was only adapted for
very short specimens . ?
Machine at St. Chamond, for tensions up to 50 tons.3
This rather remarkable single-lever machine has some
peculiarities adopted in more modern machines. The
lever is constructed of two I -beams of wrought iron ,
about 14 feet long and 12 inches deep.
A rigid knife
The same machine, somewhat altered in arrange
Fairbairn , p . 252 .
ment, and in the form in which the author often used it between 1855
and 1865, is figured in a paper on ' The Strength of Iron at Different
Temperatures, ' Brit. Assoc. Report, for 1856. See also Downing, Practical
Construction , pp. 3, 68, and Plate I.
1 Lebasteur, Les Méteaux, 1878, Plate I.
* Report on Metal for Cannon ,' by the American Ordnance Depart
ment, pp. 305, 315 .
3 M.M. Denizeau and Lechien , Mémorial de l'Artillerie et de la
Marine, 1883.
128
TESTING OF MATERIALS OF CONSTRUCTION
edged bar îixed between these side beams rests on the
top of a strong iron standard . At 0: 6 inch only from
the fulcrum knife-edge is the knife-edge supporting the
shackle. The lever is prolonged backwards, and carries
a counterweight for putting it in balance initially. A
travelling jockey weight runs along the lever, which is
virtually a steelyard, and so balances the strain in the
specimen. A peculiar arrangement is adopted to take
up the deformation and keep the lever horizontal. This
is a wedge, sliding in guides, and driven by a screw and
gearing. As this arrangement produces no shock, it
is probably very meritorious, at least for light machines.
SINGLE-LEVER MACHINES .
50. The Werder 100-ton Testing Machine.-- In 1852
a testing machine was designed for the Railway Com
mission of Bavaria by Ludwig Werder, and con
structed by Messrs . Klett & Co. , of Nuremberg.
Similar machines have been built for the Government
testing laboratories at Berlin and Munich , for the
Polytechnic Schools at Zurich and Vienna, and for
several manufactories and railways. Probably it is not
too much to say that by far the largest part of the
original mechanical investigations carried out in the
last fifteen years has been accomplished by the aid of
In the hands especially of Dr.
Bauschinger, of Munich, tests of materials have been
Werder machines .
made with this machine with a precision and accuracy
never before attained .
129
TESTING MACIIINES
The Werder machine is a horizontal testing machine
with hydraulic press worked by pumps and single- lever
weighing apparatus. By an ingenious arrangement the
press and lever are kept on the same side of the specimen .
All the complicated and expensive parts of the machine
being thus brought to one side of the specimen , com
paratively simple and inexpensive arrangements can be
made for extending the machine to take in specimens
of very great length . Usually the Werder machine is
made to test specimens both in tension and compression
up to 30 feet in length .
The general principle of the arrangement of this
machine has already been indicated . Fig. 53 shows a
sectional elevation of the more important working parts,
and detailed drawings will be found in the treatises
R is the hydraulic press ram , which acts
cited below. )
against a knife- edge on what is really a bent lever Li.
The crosshead C1, which holds one of the shackles Si ,
is connected by the long bolts t, t with a crosshead car
rying the other knife- edges which support the lever. If
the specimen stretches , C, moves to the right, and the
lever falls ; if the press ram is then moved to the right
the lever is again lifted . The back crosshead C ,,which
holds the other shackle S2, slides on a cast-iron railway
behind the machine. It is spaced at any distance from the
fixed frame of the machine by the loose distance pieces d, d.
? Mittheilungen a. d . mechanisch -technischen Laboratorium in Mün
chen , Heft 1 & 3. Maschine zum Prüfen der Festigkeit der Materialien
und Instrumente zum Messen der Gestaltsveränderung der Probekörper.
München , 1882. Also Lebasteur, Les Métaux.
K
130
TESTING OF MATERIALS OF CONSTRUCTION
At s is a tension test-bar,
and m is Bauschinger's mirror
-
arrangement
for
measur
TINKPW
da
ing extensions. In testing,
weights are placed on the
a
LI
scale platform of the lever
1 , and then by the pumps
the ram R is moved out till
the lever is in balance.
To obtain a high ratio of
leverage, so that the weights
to be handled may be small,
P
4T
R
the short arm of the lever Li
is reduced to the extraordi
ne
Wi
53
.FIG
narily small distance of 4 mm .
or i inch .
The lever is of
such a length that the lever
C)
age is 500 : 1 .
the short -arm length of the
lever cannot be directly mea
sured with accuracy enough
to determine the leverage of
Si
m
Of course
the machine. Hence a second
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lever (control lever) L, is
C
ad
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provided , acting on the cross
head C1.
This
lever
has
a ratio of 10 : 1 , and its
can be accurately
arms
ed
ur
as
.
me
131
TESTING MACHINES
By putting weights acting on L, in balance with
weights acting on L, the leverage of the principal lever
L , is determined . With so small a fulcrum distance as
3 inch the width of the knife- edges is a quantity com
parable with the short arm-length of the lever. It is
necessary, therefore, that the lever L , should have an
FIG . 54 ,
а.
С
t
..
1
1
1
-
еl
Li
7
R
--
R
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Us
WT
extremely small range of motion. This is secured by
placing a spirit-level on the lever. g is hand -gear for
returning the press ram after a test.
The arrangement of the hydraulic press and lever
will be better understood from the diagrammatic sketch ,
Fig. 54. Here R, is the press cylinder cast in one with
K 2
132
TESTING OF MATERIALS OF CONSTRUCTION
the frame of the machine,and R, is the press ram . The
press ram, cased in gun-metal, is 12 inches diameter.
The hand-pumps for working the press have rams of 1 : 2
and 0 : 4 inch diameter.
The ram R, carries a horn a,
with cross-shaft, from which the great lever L is sus
pended by links, and also the crosshead C connected
with the front shackle. The back part of the lever Li
is a large U -shaped casting, partly surrounding the
press, so that the centre of gravity is near the knife
edges . It carries a scale platform and adjusting weight.
The pair of crossheads C pass through the lever, and
are connected each by two longitudinal tie-rods t to the
shackle crosshead .
The press ram carries in front a
hard steel prism 14 ] inches long, against which one
knife -edge on the lever acts. The crossheads C each
carry a prism 75 inches long, against which the other
knife-edges act ( shown dotted ) . The distance between
inch in
the upper and lower knife -edges, reduced to
the actual machine, is the short-arm length h of the bent
lever, the long arm being l.
Fig. 53 shows the arrangement of the machine for
testing bars in tension. For crushing cubes and short
specimens the space between C, and the back of the
press is utilised, proper seatings being introduced.
Longer specimens can be crushed between C, and C2,
the tie-bars t, t being then extended to the cross-head
C2 . Convenient arrangements for transverse testing
and for torsion are also easily fixed .
51. Single-lever Testing Machine of Messrs. Buckton
133
TESTING MACIIINES
and Co., of Leeds. This machine was described at the
Leeds meeting of the Institution of Mechanical En
gineers. The machines then constructed were 50-ton
machines for testing ordinary short commercial test
bars . It appeared to the author in 1883 that a larger
machine, capable of taking in moderately long speci
mens, could be constructed on the same general plan .
In correspondence with Mr. IIartley Wicksteed , plans
were made for a 100-ton machine, which would take
specimens 6 feet long. Two very satisfactory machines
were built of this size, under the author's direction, for
the engineering laboratories at Cooper's Hill and at
the Central Institute of the Guilds of London .
Other
machines of the same power have since been made.
Considered as an instrument of general scientific re
search , the Buckton machine, even on the larger scale ,
is inferior to the Werder machine.
But it is more
handy for ordinary testing, and probably it is more easily
kept in trustworthy adjustment.
Fig. 55 shows the general arrangement of the 50-ton
H is a rigid cast-iron standard
Buckton machine.
bolted to the foundations, and having at top a horn pro
jecting back to carry the principal knife -edge or fulcrum
The great lever L , L, with its jockey
weight W, forms the weighing apparatus, and the
of the lever.
hydraulic ram F, F takes up the deformation of the
specimen . A tension specimen is shown at S, between
the friction -grip shackles A , B. The knife -edges of the
1 Proc. Inst. of Mech . Eng. , 1882 .
134
TESTING OF MATERIALS OF CONSTRUCTION
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TESTING MACIIINES
135
lever L, L are 3 inches apart, one resting on the
standard H , the other supporting the shackle A. To
support the knife -edges and prevent flexure, they are
gripped by rigid castings bolted between the side plates
of the lever. The hydraulic press F has a stroke of
6 inches to take up elongation and slip of the test-bar
in the grips. The press is worked by means of a ' quiet
compressor.' This is a press with a ram driven by a
pair of screws, which again are driven by gearing and
belting. This secondary press, which is a substitute
for the pumps ordinarily employed, forces water into
the main press F quietly and without shock, and works
very satisfactorily indeed. More power, however, is
required than with pumps. The press is so used that
the lever is kept in balance '--that is, floating freely
between the stops which limit its motion . The jockey
weight weighs exactly one ton , and can be moved along
the lever by a screw driven at will, either by belting or
by the hand -wheel in front of the standard . Before a test
the jockey -weight is run back till the lever is in balance
with the test- bar free.
A vernier, attached to the
jockey-weight, is set to zero on a scale running along
the lever. Then the specimen is fixed, and the jockey
weight moved out along the lever, while the press is used
to keep the lever horizontal. Each 3 inches of movement
of the jockey- weight adds a ton to the load on the speci
men , and the vernier easily reads on the scale to Too ton .
52. 100 -ton Testing Machine of Messrs. Buckton and
Co.—The photographic frontispiece shows a general
136
TESTING OF MATERIALS OF CONSTRUCTION
view of the engineering laboratory at the Central In
stitute, with the 100-ton testing machine. Plate II. is
a general elevation of the same machine. F, F is the
main standard of such a height that moderately long
specimens can be tested .
To the foot of this standard
is bolted the principal hydraulic press R, the ram of
which acts downwards on a crosshcad ci, connected by
adjusting side screws to an upper crosshead Cz, to which
the lower specimen shackie S, is attached. There is
worm -gearing to the side screws to adjust the length
between the shackles Si , S2. The press-ram is kept
home by the balance-weight B , attached to it by spring
shackles. To work the press there is a second press or
compressor C, the ram of which is driven by the twin
screws , and gearing Ja . The crossed belts by and
fast -and-loose pulleys behind the standard drive the
compressor ram in or out, and so force water into or
allow it to flow back from the main press R. 1 , is a
hand -lever to the fork actuating the belts 12, which
drive the compressor .
The great main lever L , of wrought-iron side -plates,
rests on the top of the standard F, F by means of a
knife-edge, and a second knife-edge behind this supports
the upper
shackle S. These knife-edges are 20 inches
long, and are formed of hardened steel ground into a
rectangular groove in steel bars 4 inches in diameter.
These bars are further supported by castings bolted to
the side-plates. The distance between the knife-edges
is 4 inches.
The free end of the lever plays in a space
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TESTING MACIIINES
137
in the supporting pillar P. J is the jockey -weight,
weighing one ton , and straddling the lever so that its
centre of gravity is as nearly as possible on the plane
through the knife-edges . This runs on four rollers on
rails fixed each side of the lever, and is moved by the
long screw S, s. The jockey -weight can be put in
motion either by the crossed belts by connected with
the reversing handle 11, or by the hand- wheel h and
countershaft k, if very slow motion or fine adjustment
is required . Along the lever is the graduated scale a, a,
and a vernier v on the jockey -weight indicates the posi
tion of the jockey-weight. Initially the lever is put in
balance, and the vernier set to read zero on the scale.
Then each 4 inches the jockey -weight moves adds a ton
of stress on the specimen . The scale is 200 inches
long, so that with the jockey-weight at the end of the
lever a stress of 50 tons is ineasured .
For greater
stresses the jockey-weight is run back to zero, and the
25-cwt. load W is attached to the lever by a screw
coupling. As this hangs at a leverage of 40, it balances
a stress of 50 tons .
The jockey- weight is then run out
again. The vernier easily reads to zoo ton . Although
the arrangement of a double weight may seem cumbrous,
it is not so in practice, and the author prefers it to the
plan of making the jockey -weight 2 tons. In three
fourths of ordinary testing, or more, the stresses do not
exceed 50 tons , and the coupling up of the extra load
is very easily managed .
The tension shackles S1 , S, are shown in place,and will
138
TESTING OF MATERIALS OF CONSTRUCTION
be described in a later chapter.
The lower crosshead is
guided by a slide on the frame F, F. For compression
tests a table guided by the same slide is hung from
the upper knife-edge by four long suspension rods , and
specimens are crushed between this table and the lower
side of the crosshead Cz.
It will be seen that, standing by the standard, the
experimenter has complete control of the machine. The
specimen is in sight on the left ; the floating of the lever
can be seen to the right, and the two handles to the
belt-gear ri, r', and the hand - wheel h are within reach
without moving
The author has now had considerable experience in
the use of this machine, and has found it extremely
convenient and accurate . The specimen is very con
veniently placed for measurement during a test, and
specimens of a considerable range of size and form can
be tested.
The sensitiveness of the lever on its knife
edge is such that although, with the jockey -weight, it
weighs about five tons , it is very perceptibly moved by
half a pound placed on the shackle.
53. 50- ton Single-lever Machine of the Société Alsa
cienne of Grafenstaden, Mulhouse . — A larger compound
lever machine made by this firm was described in
6
Engineering,' June 25, 1880. The neatly arranged
machine shown in Plate III., Fig. 2, is a single- lever
machine of the type shown in Fig. 49. The specimen
is held between the shackles A1, A2. The upper shackle
is connected to the straining mechanism , which in this
TESTING
MACHINES
139
case is a screw having on it a long nut, driven by
gearing G. The screw is prevented from rotating by a
slide .
The lower shackle is attached to the main lever
F at a knife-edge.
This lever is connected by links to
the subsidiary beam F1, which carries the fulcrum
knife - edge. The links have knife -edges at the points
at which they rest on F and Fi. A jockey -weight
1‫ܕ‬
runs on the graduated lever F. The lever F, carries a
counterweight to put the main lever in balance. The
Grafenstaden machines are said to be in use at Essen ,
Creusot, and Terrenoire.
COMPOUND-LEVER MACHINES.
54. 100 - ton Testing Machine of Messrs. Adamson
and Co., Of IIyde, near Manchester.— The machine
shown in Fig. 56 is a compound-lever horizontal
machine .
Mr. Adamson attaches great importance to
getting a fairly large distance between the principal
knife-edges, and at the same time to having a very great
leverage. Hence a compound-lever system is necessary.
This machine is specially designed for use in large
iron and steel works, where specimens are required to
be tested for commercial purposes, rather than for very
accurate scientific work , although with care and pre
cision on the part of the operator very good results may
be obtained.
The machine, with all its appliances , is entirely self
contained ; it is mounted on a heavy cast-iron founda
1 Engineering, June 17 , 1887 .
TESTING OF MATERIALS OF CONSTRUCTION
MINUTE
140
Wi
FIG
.56
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1
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in
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ITA
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ii
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VILL
TESTING MACHINES
141
tion, which requires no bolting down. It is capable of
testing all kinds of materials in tension, compression,
and bending ; by a special arrangement it inay also be
used for torsion. The testing stress is obtained by an
hydraulic cylinder and ram 69 inches in diameter. The
cylinder is of forged steel, and is intended to carry a
working pressure of about three tons per square inch.
The pressure is obtained by a small double cylinder
pump, driven by cranks, and is provided with a fly.
wheel,pulleys, and handle for hand or power driving.
The plungers are made on the compound principle, one
small one working inside an annular plunger.
When
it is required to pump rapidly at low pressures both of
them are coupled together, forming one large plunger ;
but for high pressures the inner one only is used : then
the speed has to be sacrificed for pressure. This
arrangement permits two men to pump up to the full
power of the machine, viz . 100 tons. The pressure on
the ram is transmitted to a substantial cast- steel cross
head by means of two steel ties, 3 inches in diameter,
running along either side of the machine. These ties
are screwed at the ends to allow of the crosshead being
adjusted for various lengths of specimens .
The gripping -jaws for holding the specimens are
turned on the outside and then fitted into a circular
hole. This arrangement insures the perfect gripping of
bars or plates having tapered cross -sections. In or
dinary rigid jaws the thick side is gripped first, and
consequently a tearing action is produced instead of a
142
TESTING OF MATERIALS OF CONSTRUCTION
fair and uniform pull.
The other end of the bar is
similarly held by a second crosshead which is attached
to a set of three levers, and a steelyard provided with a
travelling weight, the position of which indicates the
load on the specimen under test. The leverage obtained
is 15,000 to 1 , so that a very small travelling weight
can be used, viz . 4 lbs. ; when greater loads are required ,
other weights of 3 lbs. each are hung on the end of the
steelyard.
All the levers and steelyard are arranged in a case
to protect them from dust and injury. The handle for
adjusting the traversing weight is placed outside of the
case, so that it never need be opened except for clean
ing ; the steelyard is visible through a glass door.
By means of very simple attachments this machine
may be adapted for testing specimens in compression or
bending. The hydraulic ram is provided with a chain
and weight to bring it back to its original position after
the fracture of the specimen . All the knife -edges on
the levers are of hardened steel, and specially arranged
to prevent warping in hardening. This machine is
very conveniently arranged for getting at the specimens
when under test ; it is also very compact .
55. Olsen Compound -lever 100 -ton Testing Machine
( Plate III. , Fig. 1).—This is of the type largely adopted
in America , the mechanism being in principle the same
as that of a platform weighing machine. Four columns
on the platform E carry the steel plate B, to which one
end of the specimen is attached . Four straining screws
.
Plate III
G
COLI
B
Olsen 100 Ton
F1.2
Machine.
с
Grafenstaden
O
59 Ton Machine .
F :
Fig.2.
АAz
Az
F
f
C
E'
tul
F
F2
F
F
Ę
F
EN
1
FLOOR
FLOW
H
T
H
V
2
mo
CiH.sk
3
U
AMERICAN AND ALSATIAN TESTING MACHINES.
1
1
!
5
6
7
8 FEET
TESTING MACHINES
143
carry the plate C , to which the other end of the speci
men is attached . The columns supporting B rest on
the lever system F, F. The straining screws carry the
large driving -nuts H, which are put into action by the
gearing below the levers. The nuts abut against the
frame through roller bearings, to diminish friction .
The platform E rests on three main levers, acting as
a single lever. Beyond the platform the three levers
act through a stirrup on the second lever F,, and this
again is connected with the third lever or graduated
steelyard F3. A small poise or jockey-weight gives the
measurement of stresses from 0 to 5,000 lbs. ;‫ ܪ‬a larger
poise, stresses from 5,000 to 100,000 lbs. ;‫ ܪ‬and an addi
tional weight on the end of the lever adds 100,000 lbs.
The screws and driving -nuts take the place of the
hydraulic press used in other machines. A crossed belt
on the pulley T , and open belt on the pulley U, drive
the gearing. ' A friction clutch engages either pulley
with the driving -shaft.
by friction - gear V.
There is also a slow motion
SIMPLE HYDRAULIC PRESS MACHINE .
56, 600-ton Testing Machine of the Union Bridge
Company, at Athens,Pa .--- This machine was constructed
with the object primarily of testing the full -size eye
bars which are so largely used in American bridge
construction .
Two horizontal riveted girders B , B (Fig . 57)
60 feet in length, supported by cross-girders on five
TESTING OF MATERIALS OF CONSTRUCTION
144
R
R
masonry
piers ,
form the frame of
the machine .
At
one
the
end
of
A
frame is a large
hydraulic
press
.
C
cylinder R , with a
IS
freely moving pis
ton . This has four
ELEVATION
B
FEET
10
a crosshead carry
ing shackles S, for
one end of the test
bar.
Ingrid
There
is a
S
5
movable tail- piece
C, which can be
attached
at
any
B
0
B
FIG
.57
PLAN
to
which is attached
0
B
piston - rods ,
point in the length
of the frame , which
a
similar
crosshead
and
carries
HE
shackle S, for the
other end of the
test -bar. The cross
heads are carried
on accurate wheels
TULUMTII
AN
7,1, running on a
track fixed to the
145
TESTING MACHINES
lower flange of the frame girders. The tail -piece having
been fixed to the girders at a suitable distance from
the hydraulic press, the specimen is introduced . Then
pressure is applied to the piston of the press, and in
creased till the specimen breaks . The pressure on the
piston is measured by a Shaw mercury column and by
a spring pressure-gauge. The load on the specimen
is taken to be equal to the pressure on the press
cylinder. It will be seen that in this very large and
important machine the principle of construction is
simple, the lever weighing apparatus being dispensed
with .
The hydraulic press cylinder R is of cast steel,
4 feet 32 inches bore and 6 feet O2 inch long. It has
an
area of 2,039 inches, and an effective stroke of
4 feet 11 inches.
The maximum water-pressure for
which provision has been made is 600 lbs.per square
inch. The cylinder is secured to the girders by bolts,
and its back end is left open, so that the piston can be
.
seen .
The main girders B, B are of wrought iron , 60 feet
long, 3 feet 6 inches high, built of plates and angle
bars, rolled in one length .
Holes, 61 inches diameter
and 18 inches apart, are bored through the web for the
bolts of the tail- block . Along this part of the web it is
21 inches thick .
The tail -block C is a steel casting, which may be
attached to the main girders by two pins each side,
fitting the 6 -inch holes. Geared steel nuts g give a
L
146
TESTING OF MATERIALS OF CONSTRUCTION
further adjustment of the distance of the shackle from
the tail-block .
To provide for recoil between the shackle and tail
block there is a rod attached to the shackle passing
through a friction- clamp on the tail-block . The eye
bars are attached to the shackles by a 71-inch pin in
an elongated hole 7. x 9 in the shackle. This permits
the specimen to recoil independently of the shackle.
When smaller pins must be used collars reduce the size
of the pin-hole.
The shackle attached to the hydraulic press piston
is similar. The piston has a gland and hemp packing,
and the piston -rods also pass through stuffing -boxes.
The piston-gland is tightened till the leakage, with
maximum pressure, is reduced to a thin film of water
discharging uniformly round the piston. After a spe
cimen is broken a discharge-cock is opened to a tank
4 feet 6 inches below the cylinder. The small vacuum
thus formed, equivalent to 11 lbs . per square inch on
the piston, is found sufficient to move it home. Hence
it has been assumed that 3,000 lbs . represents the
maximum allowance to be made for the friction of the
hydraulic press. For practical purposes this allowance
is disregarded .
The pressure is obtained by a pump with three
single -acting plungers, 24 inches in diameter and
10 inches stroke, working at slow speed. An engine
with two cylinders, 8 inches diameter and 8 inches
stroke , works the pumps .
147
TESTING MACHINES
With a maximum load the stresses on the parts of
the machine are as follows :
Main girders .
Steel castings
7,100 lbs. per sq. in. compression .
15,000
19
13,000 ,
Bolts
15,000 97
12,000 ‫ܝ‬,‫ܕ‬
‫ܕܕ‬
tension .
02
Connecting rods
shear .
9
All these stresses are for the net effective sections ,
and the margin of safety appears to have proved suffi
cient under the shock of sudden release of load.
Bars
varying from 5 to 18 square inches section have been
broken in the machine . It is intended to construct
.
compression apparatus for this machine.
The machine was designed by Mr. Charles Kellogg.
The idea involved in its design is thus stated by Mr.
Macdonald :
It is not contended that this is an instru
ment of precision , or that in sensitiveness or accuracy
it is the equal of the testing machine at Watertown
Arsenal. Mr. Kellogg would be the last person to in
vite comparison in that respect with the superb inven
tion of Mr. A. Emery. What he has accomplished has
been the construction of a machine at moderate cost
which will test to destruction full- sized sections as they
are required for structural purposes, with rapidity and
reasonable accuracy .
The particulars and description of this machine
have been taken from a paper read before the American
Society of Civil Engineers by Mr. Charles Macdonald ,
M.Am .Soc.C.E.1
| The Railroad and Engineering Journal, vol. lxi. p. 71.
L2
148
TESTING OF MATERIALS OF CONSTRUCTION
MANOMETER MACHINES .
57. The Thomasset Machine ( Fig . 48 ) .- M . H.
Thomasset , of Paris,constructed, apparently about 1872 ,
a machine differing in its mode of action from previous
machines in two ways. ( 1 ) To force water into the
hydraulic press a quiet compressor' (' compresseur
sterhydraulique ' ) , like that used in oil presses, is em
ployed instead of pumps. It has the advantage of
convenience, and of preventing the pulsatory action pro
duced by pumps. However, it requires more power to
drive it. ( 2 ) In the weighing apparatus the pressure of
a liquid column acting on a large diaphragm , which forms
a virtually frictionless piston, is employed to balance
the stress on the specimen.
This has the advantage of
convenience, cumbrous weights being dispensed with.
It has the further very important advantages that the
inertia of the weighing apparatus becomes very small,
and that the load adjusts itself perfectly automatically
to the stress .
The slightest variations of stress are
indicated by the rise of the liquid column, which
balances the stress independently of any manipulation
by the operator. Apart from the question of the suc
cess of M. Thomasset in overcoming the difficulties of a
new problem , his machine has very great merit from a
theoretical point of view. Other makers have proceeded
on the same lines, and probably the Thomasset machine
1 Lebasteur, Les Métaux, p. 52.
TESTING MACHINES
149
is in some degree the parent of the great machine at
Watertown .
One shackle of the machine being attached to the
ram of a press, the other is attached to the short arm of
a knee lever. The longer arm presses on the centre of
a diaphragm covering a circular cistern of mercury, or
of water communicating with the cistern of a mercury
The diaphragm is a vulcanised rubber
sheet fixed round its edge by a ring, and receiving the
manometer.
load from the lever on a loose circular metal plate only
slightly less in diameter than the cistern.
Let 2 be the area of the circular diaphragm in sq.
centimeters ; P the stress on the specimen in kilograms;
n the leverage of the bent lever. The total pressure on
the diaphragm is P/n kilograms, and the pressure in
the cistern is P / 12 n kilograms per sq. c.m.
But if
h is the height in c.m. of the mercury column in the
manometer, measured from the level of the cistern ( or,
strictly, from the point where the mercury stands with
no stress on the specimen ), -h
76
P
12 กา
If 12 = 5,000 sq. c.m. (about 2 : 6 feet) in diameter ;
n = 5 ‫ ;ܪ‬then a column of mercury li meters ( 5 feet)
high will balance 50,000 kilograms ( 50 tons) of stress.
As the section of the mercury column is only zooo of
the area of the diaphragm , the whole movement of the
diaphragm for a load of 50 tons is only half a millimeter
(0:02 inch ) .
150
TESTING OF MATERIALS OF CONSTRUCTION
58. The Maillard Testing Machine ( Fig. 51 ) .—A
very interesting machine, based on the same principles
as the Thomasset machine, was designed by Colonel
Maillard for use in the French arsenals, and one of
these machines is now in daily use at Woolwich .
Broadly speaking, it is a Thomasset machine in which
the lever is got rid of, and the pull taken directly on
the diaphragm .
This involves an enlargement of the
size of the diaphragm , and some other changes. The
machine as hitherto constructed is only suitable for
short specimens, and is only arranged for tension .
In this machine the specimen is held horizontally
between shackles, one attached to the ram of an hydraulic
press, the other to a crosshead which pulls on a dia
phragm in a cistern containing fluid .
This
short
cylindrical cistern has the same axis as the hydraulic
press, and necessarily the diaphragm which receives the
pressure is on the side furthest from the test-bar, so
that the crosshead is forked to surround the cistern .
The diaphragm is of caoutchouc, protected by a metal
plate. The cistern communicates by a pipe with a
Galy-Cazalet manometer, or a mercury manometer.
The cistern is carried on trunnions upon a carriage
sliding horizontally. By means of a screw and hand
wheel the position of this carriage can be adjusted to
suit different lengths of specimen .
The stress in the test-bar, transmitted through the
shackle and crosshead to the plate or piston at the
1 Lebasteur , p. 53.
TESTING MACHINES
151
back of the cistern , is exactly balanced by the fluid
The diaphragm moves at most only a small
fraction of a millimeter, so that the friction and bending
pressure.
resistance of the diaphragm is quite negligable. Con
sequently, if the graduation of the manometer is correct ,
the stress is determined with great accuracy. If P is
the stress on the bar, h the rise of the mercury column
in the manometer above the zero at which it stands
when no stress is applied, & the density of the mercury ,
S the area of the diaphragm , sį and s, the large and
small areas of the manometric piston,
P = 18 SE
S2
To eliminate errors due to uncertainty as to the areas of
the diaphragms, to capillarity, and so on , the manometer
is graduated by experiment. The cistern is removed
from the machine, laid horizontally, and loaded with
standard weights.
In a good manometer the tube must be at least
3 centimeters in diameter ( 14 inches ) ; with a smaller
column, drops of mercury remain attached to the tube
when the column falls.
The manometric piston in
the manometer used is so arranged that the centi
meter rise of column corresponds to the kilogram per
square centimeter on the smaller piston , and conse
quently on the diaphragm of the main cistern of the
testing machine. Hence if n is the rise of column in cen
timeters , and S the area of diaphragm in centimeters ,
P = ns.
152
TESTING OF MATERIALS OF CONSTRUCTION
In the machine at the Ruelle Foundry the diameter of
the large diaphragm is 9 feet.
59. Wire-testing Machine of Messrs. W. H. Bailey and
Co., of Salford . — Fig 58 shows a very nicely arranged
small tension machine, on the same principle as Col.
Maillard's . One end of the specimen is held in friction
grips in a shackle attached to a screw and hand-wheel,
which takes up the elongation.
The other shackle is
attached to crossheads and links, which surround the
diaphragm chamber, and apply the load on the back of
the diaphragm . The pressure in the diaphragm chamber
is transmitted to a pressure-gauge and to a mercury
column , either of which can be used . There is a valve
on the pipe allowing flow towards the pressure-gauge
or mercury column, but preventing back flow . This
holds the gauge at the maximum pressure, and prevents
injury when the specimen breaks and the load is sud
denly removed. A small hand -wheel opens this valve
and lets off the pressure slowly. The machine will
give a tension of 4,500 lbs.
EMERY MACHINES .
60. The 450 -ton Emery Testing Machine at Water
town Arsenal, U.S.A. - In 1872 a committee of Ameri
can engineers was formed to urge on the Government
of the United States the importance of a thorough and
complete series of tests of American iron and steel.
Subsequently, by direction of the Government, a Board
was constituted for the purpose of carrying out tests
1
153
TESTING MACHINES
FIG . 58 .
4400
4300
4201
1: 1
14100
40001
3902
3801 )
3700
360!
3500
3400
3300
3206
1 .
3100.
300C
2900
2801
2700
2600
ZSOiui
2400
230D
22001
:: ...
21001
2000
19001
18001
17001
..
MO
16001
:
1500
1400
nic
ZBAI
LE SPATE , T antibiotiatinio
1300
ulte
1200
700
:
1000
1900
18001
1700
600
1500
300
4001
12001
M
N*
N
154
TESTING OF MATERIALS OF CONSTRUCTION
of iron , steel , and other metals, and an appropriation
was made of 75,000 dollars for the construction of the
necessary apparatus. In 1875 a contract was made
with Mr. A. H. Emery for the construction of a testing
machine capable of exerting a stress of 800,000 lbs. ,
and of taking in specimens for testing 30 feet in
length. In 1879 the machine was completed satisfac
torily, and it is probably the largest and most accurate
testing machine in the world .
Before acceptance by the Board , a link of hard
iron , 5 inches in diameter, was placed in the machine,
and slowly strained in tension till it broke at 722,000 lbs.
Without any readjustment, a horse-hair was then fixed
in the machine, and broken at an indicated stress of 1 lb.
No other testing machine would have permitted the
observation of so great a range of stress.
To give an idea of the sensitiveness of the weighing
apparatus of the Watertown machine, it may be com
pared with a delicate chemist's balance . A good assay
balance will carry 1 gram, and turn with To of a milli
gram , or Todou of the load. A fine balance exhibited
at Philadelphia , with 1 lb. in each scale, would turn
with gudron of its load.1 Ordinary fine balances
weighing to 1 lb. will turn with 1 grain , or todo of
the load .
Now before the Emery machine was com
pleted it was arranged as a balance. In seven weigh
ings of a load of 100 lbs . the greatest difference in the
observed weights was 1757too of the load. In nine
1 Mechanics, November 3, 1883.
155
TESTING MACHINES
weighings of 200 lbs. the difference between the
greatest and least observed weight was only 2350000
of the load.
Since the construction of the Watertown testing
machine, smaller machines of the same kind have been
made by the Yale and Towne Manufacturing Company
of Stamford, U.S.A. The ingenuity displayed in the
mechanical arrangement of these machines, the perfec
tion of their workmanship, and the delicacy and pre
cision of their indication of the smallest differences of
stress are so remarkable, that it is difficult to speak of
them without seeming to exaggerate. In a 75 - ton
machine, which the author examined in Paris , every
half-pound of load was precisely and instantly indi
cated , whatever the stress the machine was exerting.
At the same time, in no other machine is the stress
exerted in such a purely static manner.
It is almost
impossible for any shock or inertia stress to be exerted
on the specimen. As a machine of precision the Emery
machine is far in advance of any other. It may seem
that the delicacy of the machine must be such as to
unfit it for ordinary rough commercial testing. On this
point the author cannot speak from personal experience,
but, so far as he can judge, this is not the case .
Igno
rance and want of skill are certain to lead to false results,
even when the roughest machine is used. Granted a
reasonable amount of skill in the operator, the Emery
machine may be used for ordinary rough testing as
easily and safely as machines of less precision.
156
from
TESTING OF MATERIALS OF CONSTRUCTION
The Emery machines differ essentially in principle
any others. They are really compound lever
machines, with an hydraulic press acting on one end of
the specimen, and a lever weighing apparatus on the
other end. But their greatest peculiarity is that a
kind of hydraulic lever is introduced between the speci
men and the weighing apparatus.
The pull of the
specimen is taken on an ' hydraulic support,' the action
of which is like that of the diaphragm in the Maillard
machine. The fluid pressure in the hydraulic support,
which is exactly proportional to the stress on the test
bar, is transmitted through a very small pipe to act on
a frictionless diaphragm of comparatively small size, and
it is the pressure on this diaphragm only which has
to be balanced by the lever weighing apparatus. The
weighing apparatus can therefore be made of small size,
and of the utmost refinement and accuracy .
In the 75 - ton machine the ratio of areas of the dia
phragms is 20 : 1 , so that the lever weighing apparatus
has to balance 3.75 tons only with the full load.
There
are three levers with ratios of 1 : 20,1 : 20 , and 1 : 40,
so that the resultant leverage is 320,000 to 1 .
The action of the Emery machine may, perhaps, be
made clear by the diagrammatic sketch of a vertical
machine ( Fig. 59 ). A tension specimen is shown
between the shackles S1, S2. The upper shackle is held
by the ram of the hydraulic press, which can be adjusted
on the guide- screws G, G. These screws are fixed on
the frame F , F of the machine .
The lower shackle is
157
TESTING MACHINES
attached to a yoke or frame Y, Y , which transmits the
load to the hydraulic support. At s is a thin circular
brass sac , filled with alcohol and glycerine, supported
over all its area, except a ring / inch wide at its cir
cumference, by the strong and rigid crossheads P1, P2.
When the machine
FIG . 59 .
1
is acting as shown
in tension the yoke
R
transmits the load
to the crosshead P2,
JOIGOO
TADA
1977
JINE
and thence through
sac
s to
P1 ,
BORZONGAT
the
THUNAHITAN THUNDURUL
which rests against
the stops a, a on the
frame.
For
com
G
G
pression the yoke
presses downwards
S.
on P1, through s to
P2, and P, then rests
F
Y
a
on the stops b, b.
The whole play of
the crossheads
be
tween the stops a and
b is only gobo inch.
P,
6
n
Y
F
The movement of the yoke and compression of the
hydraulic support is determined by the amount of
motion permitted in the lever weighing apparatus.
With the 75 -ton machine, when the indicating lever
moves 4 inches ( 2 inches above or below mean position)
158
TESTING OF MATERIALS OF CONSTRUCTION
the greatest compression of the sac s is only goody inch .
The movement of the smaller diaphragm and of the
fulcrum of the first lever is qovo inch ; the free end of
the first lever moves zou inch , and that of the second
lever lo inch . Mr. Henning assures me that it is easy
to keep the indicating lever within 1 inch of its mean
position, and the movements of the system are then
only 1 of the amounts just stated . It is on the small
ness of the movement that the exactitude of the action
of the hydraulic support depends.
It is a peculiarity of the lever weighing system that
knife-edges are replaced by an arrangement more sen
sitive and exact, and less liable to injury by wear.
In
FIG . 60.
CU
B
place of the knife- edge Mr. Emery uses a thin flat blade
of steel rigidly fixed in the lever and its support.
If
the lever moves, this bends . But the resistance becomes
insensibly small if the motion of the lever is small and
the blade of steel thin. Fig. 60 shows two arrange
ments of these substitutes for knife-edges. In a the
steel blades are in tension ; in b they are in compression .
The steel is 0 · 004 to .05 inch thick , and the blades are
1 A somewhat similar device seems to have been proposed by Weber
at Gottingen in 1841, and by M. Taurines in 1867 .
TESTING MACHINES
159
so wide that the stress in the steel does not exceed 18 to
30 tons per sq . inch . The blades are fixed by forcing
them into grooves by hydraulic pressure, about three
times as great as the working load .
A somewhat similar arrangement is adopted to get
rid of all sliding friction in the moving parts of the
testing machine ( Fig . 59). The yoke and crossheads
do not slide in the frame, but are free. They are guided
without friction, and for a minute amount of motion
without sensible resistance, by four flat flexible plates
attached to each piece and to the frame.
‫רו‬
the change of arrangement
In the vertical ‫ן‬machine
from tension to compression or transverse stress is
extremely simple. Gripping wedges of a new pattern
for test-bars not machined are used , which are designed
to ensure a perfectly fair pull, and to ensure the speci
men not breaking inside the clips . In some cases the
lever weighing apparatus is dispensed with, a very large
and accurate pressure - gauge being used instead .
This
pressure-gauge has a pressure diaphragm and lever
system made on the same plan as the lever weighing
apparatus The accuracy of the pressure- gauge to one tenth
per cent., is guaranteed. The machine can be easily
calibrated by placing a standard weight on the lower
shackle and weighing it by the weighing apparatus.
Plate IV. gives a general view and Plate V. a plan
and elevations of the Watertown Emery machine. The
bed of the machine consists of a long track , built in
sections set on masonry .
At the right hand is the
one
TESTING OF MATERIALS OF CONSTRUCTION
160
hydraulic press 1569 (Fig . 1 ) , with its shackle or holder
1475. At the left is the hydraulic support , the cross
heads of which are seen at 1455 , 1456 , with the other
shackle 1475.
The frame at the left end is connected
with the press by the guide-screws 1450. The hydraulic
press
is carried on a four -wheel truck, and can be set at
any distance from the hydraulic support, to suit different
lengths of test-bar. The guide- screws are 48 feet long
and 81 inches diameter , and are driven by the geared
nuts 1569 and the gearing at the extreme right of the
figure. When the gearing is not acting the press is
locked to the screws. The press has a 20-inch ram , with
a piston -rod 10 inches diameter. The press is worked
by accumulators, and acts in both directions, according
as tension or compression is required.
In each of the test-bar holders there are two 14 - inch
hydraulic presses, which grip the specimen with a force
of 500 tons .
The space for the ends of the specimen is 10 inches
deep in the middle and 5 inches at the sides, and it is
30 inches wide .
The hydraulic support rests on a longitudinal slide,
its motion being controlled by powerful buffer -springs,
which absorb the recoil when the specimen breaks.
In
ordinary conditions the buffer-springs merely hold the
hydraulic support in its middle position. When a
specimen breaks, the press and hydraulic support recoil
in opposite directions, the forces developed being op
posed by the guide -screws. But as the recoiling forces
1
Plate IV
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WATERTOWN 450 Ton TESTING MACHINE.
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Scule
WATERTOWN 450 Ton TESTING MACHINE.
1
OO
MUIST
1011111
!
8
161
TESTING MACHINES
are not exactly balanced , the buffer -springs come into
play and gradually bring the machine to rest. In ten
sion, the pull is transmitted from the test- bar holder ,
through a great central link , to the back crosshead
1455 , and so through the brass sack and front crosshead
to the frame. In compression , the thrust comes first on
the crosshead 1456 .
The fluid pressure in the hydraulic support is trans
mitted through a small pipe to the pressure-gauges
1708, and also to the secondary diaphragm and the
lever weighing apparatus in the case 1705 .
In the general view ( Plate V. ) the hydraulic support
is on the right, and the press and lever weighing
apparatus on the left.
SPECIAL TESTING MACHINES.
61. Torsional Testing Machines.- In some testing
machines a special shackle is used for torsional stresses .
But an ordinary large testing machine is too clumsy for
a comparatively delicate test of this kind, and some of
the shackles used in this way are defective in arrange
ment. For torsional tests a special small machine is
desirable, but hitherto no sufficient attention seems
to have been given to the best arrangement of such a
machine. A very neat little machine of this kind, by
M. Thomasset, is figured in Lebasteur.1
One end of the specimen is turned by worm - gear,
while the other acts through a lever on a diaphragm and
| Les Métaux, Lebasteur, Plate V.
M
162
TESTING OF MATERIALS OF CONSTRUCTION
manometer . This seems to contain the essentials of a
perfect torsion machine, but the shackle arrangements
for holding torsion specimens do not seem as yet to have
been fully thought out . Prof. Kennedy gives details of
a small torsional machine.1
Thurston's autographic torsional machine will be
described in a later chapter.?
62. Machines for Transverse or Cross-breaking Tests.
-Shackles for cross - breaking are provided with most
large testing machines, and will be described in the
next chapter.
For transverse tests of cast iron small
special testing machines are useful. Bars of cast iron
31 feet x 2 inches x 1 inch, laid on supports 3 feet
apart, with the deeper side vertical, break with from 25
to 40 cwts. placed at the centre , so that the loads to be
dealt with in tests of this kind are not very great .
FIG . 61.
OWTTTTT
0,411
UNMINUMINIRA !
18/10
CASTRONICARII
SQUARE
TIUNI
Fig . 61 shows a small machine, made by Messrs.
Tangye Brothers, for tests of this kind . The bar rests
on knife-edges on the base -plate, and is loaded at the
1 ' Engineering Laboratories.' Proc. Inst. Civil Engineers,vol. lxxxviii.
2 First described in Proc. An . Soc. of Civil Engineers, 1874, p . 350.
163
TESTING MACHINES
centre by a lever and jockey weight. Somewhat similar
machines are made by Messrs. W. II. Bailey & Co. , and
probably by other engineers.
M. Kuhlmann hos introduced a machine of rather
more elaborate construction for breaking cylindrical
test -bars inch in diameter and 8 inches in length .
It is suggested that small test-bars of this kind can be
more easily and accurately cast, can be cast vertically,
and are, if desired , easily turned in the lathe, so as to
be quite accurate in form . The pattern for casting
them is a polished metal bar. There is an arrangement
in the machine for indicating deflections.
Another convenient arrangement, known as the
· Balance Monge,' is in use in some gun factories. It
consists
of a
bracket
FIG . 62
( Fig. 62 ) , fixed to a wall,
having two opposed
knife- edges. By a bridle
V
and block a scale -plat
form is attached to the
N
bar.
.
N
63. The Bending and
Temper Test.-- A very
convenient practical test of the ductility of a material is to
bend a strip about 17 inch wide over a corner of small
radius, and observe the angle at which it cracks on the
extended side .
Sometimes the test is made on strips in
the condition in which the material is received.
In the
case of steel, strips are heated to cherry red and plunged
M
2
164
TESTING OF MATERIALS OF CONSTRUCTION
in water of a temperature of 80° before bending.
This
shows whether the steel tempers or hardens by sudden
cooling. Sometimes the strips are simply sheared strips .
At other times the edges of the strips are planed or the
strips annealed, and they then bend to greater angles
before cracking
The roughest plan of bending is to put the strip of
plate over a V -block , and bend it by blows of a heavy
swage ; the bending is continued by light endway blows
of a steam hammer. A press for bending angle iron
may be used in a somewhat similar way , the
pressure
being applied first transversely, then endways. In
experiments by Prof. Kennedy , bars 11 inch square
t
were supported on knife- edges 6 inches apart. A load
was applied steadily on a central bearing -piece of
1 inch radius . When the angle reached 90° the bear
ing -piece was reduced to ] inch radius. In experiments
for the Board of Trade, strips were placed on supports
10 inches apart and bent by hydraulic pressure to an
angle of 90° by a ram with a rounded end of 2 inches
radius . The bending was then continued till the strip
cracked or the angle reached 180° by quiet pressure ap
plied at the ends, in the testing machine. Mr. Stroh
meyera clamped pieces between a steam hammer and its
anvil, hammering the projecting end till the strip was
bent through an angle of 45 °. It was then reversed and
1 The Use of Steel Castings, ' Parker.
Journal of the Iron and
Steel Institute.
2 The Working of Steel, ' Strohmeyer.
neers, vol . lxxxiv.
Proc. Inst. of Civil Engi
165
TESTING MACHINES
bent in the opposite direction , and the bendings con
tinued till fracture occurred . The number of bendings
is taken as a measure of the ductility of the material.
To ensure accurate bending to a given angle , an anvil
mould , with a radius of curvature of 14 inch , was used
below the test piece.
A lever apparatus for quietly bending strips of plate
is described in the work cited below . Fig . 63 shows
a small apparatus of this kind introduced by Mr. A.
FIG . 63
NUT.
H. Kuhlmann . It has a screw worked by a handwheel
or by a ratchet lever.
The piece to be tested is bent in
the middle, and the angle measured subsequently. It
will bend strips 2 inches wide and
inch thick .
64. Testing Pipes.--- As water mains of cast iron are
ordered in very large quantities, special arrangements
for testing them before delivery are generally adopted .
The general quality of the mctal used is determined
by testing sample bars cast once or twice a day from the
same metal as the pipes. These are most commonly
bars 2 ins . * 1 inch x 40 ins . , which are broken trans
1 Die Eigenschaften von Eisen und Stahl.
Wiesbaden, 1880.
166
TESTING OF MATERIALS (F CONSTRUCTION
versely on supports 36 inches apart.
In some cases,
however, a tension test is made ; and this is no doubt
the more rational proceeding.
Next to this, the regularity of form of the pipes is
tested. The thickness is tested by callipering , long cal
lipers of special construction being used. A variation
of 3 inch in thickness is the most generally allowed. A
pipe with 1 inch variation in thickness should be re
jected unless the working pressure is light. In rolling
the pipes they usually come to rest with a thin side
uppermost, and this is some guide in determining the
thickness. Ordinary callipers are 18 inches in length ;
special callipers have been made up to 6 feet in length ,
but these , from their springiness, require a good deal of
care and skill in use. Deviation in weight is also noted .
Usually pipes with a deviation of 2 to 5 per cent. are
rejected . Socket and spigot gauges for the inside of
the socket and outside of the spigot are also used.
A
disc with a long handle passed through the pipe is
used to show deviations from cylindrical form . The
disc is usually 1 inch less in diameter than the nominal
bore of the pipe. This dise should pass fairly through
the pipe while held square .
The most important test, however, is the hydraulic
pressure test. The testing machine consists of two
standards on a frame, carrying discs which are pressed
against the ends of the pipe. One disc is fixed,the other
A grummet , consisting of an iron ring
served with tarred rope or yarn , is inserted between the
movable.
167
TESTING MACHINES
discs and pipe to make a joint. The movable head is
forced up by a screw, which exerts considerable pres
sure .
Water is then run in till the pipe is full from a
cistern, the air escaping by an air - vent.
The air- vent
and supply -pipe are then closed, and a pressure pro
duced by a small force-pump. A weighted valve and a
pressure- gauge show when the pressure required for
testing is attained . For pipes of 30 inches or more in
diameter 4 to 5 lengths can be tested per hour.
The
pressure prescribed is usually double the working pres
sure .
While under pressure the pipes are struck hard
with a hammer of 5 to 7 lbs . Leakage through the
pipe is indicated by the fall of pressure shown by the
gauge. If proved before coating with tar or asphalte
defects are more easily seen .
64 a. Calibration of a Testing Machine.-- Experi
mental verification of the accuracy and sensitiveness
of a testing machine is absolutely necessary , both in the
first instance and at intervals afterwards.
It will be
sufficient to describe the process of verification adopted
for the 100-ton Buckton testing machine. The stress
in this machine is weighed by a jockey weight, and the
first point to verify is that this jockey weight is exactly
1
ton .
The jockey weight was adjusted at the
Standards Office, and certified by the inspector. It is
not difficult to verify this weight from time to time by
lifting it, with one of the convenient steelyard weigh
ing machines interposed between the crane- hook and
weight.
168
TESTING OF MATERIALS OF CONSTRUCTION
Adjustment to Zero of Scale.— Theadjustment is easily
effected , and is necessary after any change of the shackles
used . The jockey weight is run back till the lever rests
in absolute equilibrium midway between the stops. The
vernier attached to the jockey weight is then set to zero
on the scale.
Verification of the Jockey Weight by the use of the
Lever . — A very simple test of the accuracy of the
jockey weight is made in this way. A uniformly
graduated scale runs along the lever. Division 5 co
incides with the principal knife -edge on which the lever
rests, and at division 45 a subsidiary knife -edge has
been fixed . Bring the lever to balance , and set the
vernier to zero . Then run back the jockey weight to
1 on the scale. A weight of 56 lbs . , hung at divi
sion 45 , or forty divisions from the fulcrum , ought to be
in balance with the jockey weight moved one division
back . If it is not, the jockey weight is not a ton. This
simple test , which can be made in ten minutes, is suffi
cient at any time to check the accuracy of the jockey
weight to about 12 lbs.
Verification of the Agreement of the Scale Divisions
with the Short-arm Length of the Lever.— The fulcrum
distance in this machine is 4 inches, and the unit of the
The agreement of the
scale must be 4 inches also .
scale unit with the short-arm length is best determined
by weighing. For this purpose a standard 1 -ton weight,
made of a suitable form , is hung from the shackle of
the machine.
The lever is balanced, and the vernier
TESTING MACHINES
169
set to zero. The ton weight is then hung in the shackle,
and balanced by the jockey weight. The vernier ought
then to read 1 ton on the scale.
If it does not, the
fulcrum distance must be altered, as it is inconvenient
to alter the scale . Perhaps it is still more accurate to
balance 56 lbs . at a leverage of 40 by the ton weight in
the shackle without moving the jockey weight.
Test of Sensitiveness.- In this machine the lever and
jockey weight, with the parts attached to them , weigh
altogether about 5 tons, and this is therefore the
minimum weight on the knife-edge. With this weight
resting on the knife-edge there is a perceptible move
ment of the lever when j lb.is placed on the shackle ,
and a return if the weight is removed. If the friction
of the knife -edge is assumed to be proportional to the
load , the error in 100 tons of stress would only be
107 lbs.
Probably a greater sensitiveness than this could be
obtained if necessary. The knife- edge of this machine
is of the exceptionally great length of 22 inches. Any
initial or induced flexure virtually broadens the knife
edge and reduces the sensitiveness . Hence a very long
knife-edge, though more durable, is likely to be less
sensitive than a shorter one.
Test of Neutrality of the Lever .— The centre of gravity
of the lever and jockey weight should be on the line
passing through the knife-edges. If it is not so, the
leverage alters, either decreasing or increasing as the
inclination of the lever alters ..
The author bas tested
170
TESTING OF MATERIALS OF CONSTRUCTION
this directly by ascertaining the pull, with the lever in
different positions , by a weighing machine suspended
in the shackles . The following tests were made by first
placing weights on the shackle and taking them off ;
afterwards, by repeating the operation with weights on
a small scale suspended from the long arm of the lever.
Throughout the whole of these tests the lever was
absolutely untouched, so that no vibration or swing
was given to neutralise any friction in the machine.
The weights placed on the shackle were, of course, at
4 inches from the fulcrum ; the weights on the other
side are reduced to equivalent weights, also at 4 inches
from the fulcrum . The figures are the mean of the rise
and fall in two series of tests taken at different times ;
the rise and fall in the two series of tests differed very
little :
Weight on
shackle,
Movement of
in lbs.
in inches.
1
2
3
5
.09
•26
-48
1.10
end of lever ,
1:53
Movement of
Movement
per lb.
Weight on
long arı
end of lever ,
Movement
in inches
per lb
09
.13
1 :4
•12
•52
1.21
1.98
2.49
08
2.9
.16
.22
.22
5.7
8.6
11 :5
.18
.21
.23
.21
171
CHAPTER V.
SHACKLES FOR HIOLDING TEST BARS .
I.
TENSION SHACKLES .
65. The load required to fracture a bar varies with
the mode of holding it in the testing shackles. The
proper form of test bars to ensure comparable results in
different tests will be discussed later.
But the follow
ing general remarks may serve as an introduction to
the examination of the methods of holding test bars in
the machine.
Let w be the section of a bar A ( Fig. 64) , which
breaks at ab with a tension T normal to ab. Then, if
the direction of T passes through the centre of figure of
FIG . 64 .
AP
al
c
‫ہونے‬
bi id
A
B
1)
E
ab, the stress is uniformly distributed, and T / w is the
real tenacity of the bar. But , if these conditions are
not satisfied, the stress is not uniformly distributed ,and
172
TESTING OF MATERIALS OF CONSTRUCTION
T /c is the apparent tenacity, which may be less than
the real tenacity to almost any extent.
( 1 ) The stress on the cross section will cease to be
uniform if the resultant of the load P ( Fig. 64, B ) , does
not pass through the centre of figure . The stress is
then a varying stress, varying uniformly so long as the
elastic limit is not passed , and according to some other
law if it is passed. The specimen tears from the edge
where the stress is greatest.
At
the load is also
eccentric, and this indicates how non -uniformity of
stress may be produced by unhomogeneousness of the
material itself. A patch of material of different extensi
bility from the rest produces a similar effect to a hole .
( 2 ) The stress on cross sections may be rendered
non -uniform by the local action of contiguous material.
Thus, bars of the form D are known to break with a
low apparent tenacity. The unstrained material a pre
vents the elongation of the adjoining material b, and
virtually renders the material unhomogeneous . In the
form E a similar action occurs ; but here the less strained
material on either side of the section of fracture hinders
contraction so much as to raise the apparent tenacity
(see
33 ) .
66. Pin Grips.--- The oldest way of holding plate
specimens is to drill a hole at each end and narrow the
bar in the middle by slotting or milling.
The test bars
are then of the form A ( Fig. 64 ) . A steel pin in the
jaws of the testing machine shackles passes through
each pinhole in the specimen . This method of holding
SIIACKLES FOR HOLDING TEST BARS
173
plate specimens is convenient and satisfactory, especially
when the test bar is of large size.
The pinholes must be accurately on the axis of the
narrowed part of the bar to ensure uniformity of stress.
But, besides this, it is important that the pins should be
so large as not only to be safe against shearing, but so
that the crushing pressure on the surface of the pin
holes is not great enough to largely deform them . If
this is not attended to the bar will almost certainly
break from the pinhole across the enlarged ends, even
when these are considerably larger than the narrow part
of the test bar.
Let a be the area of section of the bar at ab , and d
the diameter of the pin.
Then, the shearing section of
the pin will be sufficient if
TT
2
dº f = kf.
‫وبال‬
,
where f, and f, are the tearing and shearing resistances
of the plate and pin, and k a factor of safety not less
than 3.
If f: = f.,
d = 1.38 Va .
Thus, for breaking specimens of 4 sq. ins. area, a pin
is required of 23 inches diameter.
Now let t = thickness of test bar, and f.the pressure
at which it crushes. Then, in order that the pinhole
may be safe against deformation,
fi a must be less than f.dt.
174
TESTING OF MATERIALS OF CONSTRUCTION
Suppose the pinhole is safe if the crushing pressure is
not greater than ife, then
2α
d
‫ܕ‬
t
or d must be twice the width at the narrow part of the
bar. This gives a very large diameter to the pin , much
more than has generally been allowed . The calculation
is of course based on assumption, but it indicates why
plate specimens with pinholes often give trouble by
breaking through the ends .
With cast-iron test pieces the ends may be thickened,
and then a smaller diameter of pin suffices.
With
wrought iron , cheeks may be riveted on .
Sometimes a number of smaller pins are used instead
of one large pin. The objection to this is the great
difficulty of drilling a number of loles so accurately
that all the pins bear equally. Some specimens tested
in this way break through the pinholes at sections very
much larger than the middle of the bar, clearly showing
a want of uniformity of bearing of the pins .
67. Friction Grips.- In the ' Journal of the Society
of Arts, vol. li . 1837 , there is a description of what
are termed ‘ nippers' for iron bars by Mr. J. Kingston,
of Woolwich Dockyard. These nippers appear to be
precisely the friction grips used at the present time for
holding test bars . The shackles consisted of two iron
blocks with a rectangular hole, having the two opposite
sides inclined. Two gripping pieces, or wedges, fitted
SIIACKLES FOR HOLDING TEST BARS
175
in the mortice gripped the specimen . As the tension
on the bar increased, the pressure of the gripping pieces
increased proportionately, in consequence of their sliding
down the inclined surfaces of the shackle .
The inside
of the gripping pieces was formed like a coarse screw
thread to give greater bite. The paper contains in
teresting details of experiments on copper, Muntz metal ,
and iron bars made with these nippers."
About 1860 the author used at Sir W. Fairbairn's
suggestion some wedge grips of a similar kind .
These
were for cylindrical bars, and were made in three parts ,
like the cone keys at one time used for fixing pulleys on
shafts. The wedges had a taper of 1 in 8 , and fitted
in a conical hole in the shackle.
Of late, pairs of flat
wedge grips have been very generally used in testing
plate specimens.
Fig . 65 shows a shackle for wedge grips designed
by Mr. Wicksteed, and not unlike the shackles used
in many machines. The hardened -steel wedges with
serrated faces are seen at w , with the test bar s betireen
them.
These wedges have a slope at the back of 1 in
6. They are held in slots in two conical pieces b which
fit a conical hole in the shackle.
These seatings allow
the wedges to swivel , so as to hold test bars with faces
not quite parallel . For round and square bars V -shaped
grooves are formed in the face of the wedges .
1 Mr. Trueman Wood pointed out this very early record of testing
appliances to the author. The grips are figured also in the 1837 edition of
Barlow's Strength of Materials.
176
TESTING OF MATERIALS OF CONSTRUCTION
FIG . 65 .
U
3
‫م‬
8
S
S
n
Wi
nh
111
1111
linn
nihin
/
ma
Fig. 66 shows the arrangement of the wedge-grip
shackles in the Werder Machine. This shackle differs
from those most used in this country- ( 1) in the short
177
SHACKLES FOR HIOLDING TEST BARS
ness of the wedges ; (2) in the slot in the shackle being
open at the ends , so that any width of plate can be held .
On the other hand, there is no provision for fairly
T'IG . 66 .
☺
.
고
holding test pieces the faces of which are not parallel.
Perhaps this is less important when the wedges are
short. For with short wedges the serrations bite deeply
into the bar, and so to a certain extent adjust themselves
to a small defect of parallelism in the faces.
Riehle's Wedges. - In order to ensure the coincidence
of the tension with the axis of the specimen, Messrs.
Riehle Brothers, of Philadelphia , adopt a plan different
from that used in this country.
The shackle has a
rectangular recess, so that the wedges which grip the
specimen cannot swivel. There would , therefore, with
ordinary flat-faced wedges be a likelihood that the
wedges would grip the specimen more on one side than
N
178
TESTING OF MATERIALS OF CONSTRUCTION
the other ; in fact, if the specimen were thicker on one
side they would inevitably do so . To avoid this the
wedges are made with a round face.
CET
Informe
FIG . 67 .
BВ
1.7
.:10
1110111
intu
k7'1111
B
B
.
im
E
1110111
E
ce
F
B
The shackle is shown at A (Fig. 67 ) , and the round
faced wedges at C, C, with the specimen between them ;
FIG . 68 .
e is a pin used to adjust the specimen
between the wedges. Fig. 68 shows on
a larger scale the form of one of Riehle's
wedges .
Shackles of the Emery Testing Machine.
These are as original and ingenious as
the other details of the machine, and
more nearly comply with the conditions
required for perfectly holding a test bar
than any other shackle. Fig. 69 shows the shackle. 9
is the end of the press ram , or yoke, to which the shackle
is to be attached. f is a nut forming part of the shackle .
In the shackle two oblique cylindrical holes are bored ,
forming the seats for the sliding wedge pieces b. In
these wedge pieces are fitted the various gripping
179
SHACKLES FOR HOLDING TEST BARS
pieces c, to suit flat plates of different thicknesses or
round or square bars. The wedges b slide so that their
faces are perfectly paral
FIG . 69 .
lel. The gripping pieces
are cylindrical, so that
h
they can adjust them
selves to plates of un
equal thickness .
The
a
wedges b are not, as in
other machines, loose,
but form a permanent
part of the shackle ; a
1
toothed rack is formed
e
on the side of them , en
gaging a pinion driven
by the shaft h, so that
a
they can be moved for
mat
TRUJI
ward to grip the test
piece. A ratchet and
a
IA
from
click prevents the slack
ing back . The wedges
h
z
are traversed by a bar d
carried by the rod C,
a
which is pressed by a
spring, against which
e
the rotation of the shaft i
b
moves them . Under f is
an elastic packing to pre
Ih
vent injury by shock .
N 2
180
TESTING OF MATERIALS OF CONSTRUCTION
The gripping pieces c are each in two parts, the back
part being roughened with teeth , the front part plain .
This allows a certain stretch of the specimen in the
length of the gripping pieces , and at the same time
holds them by a double bite. This prevents fracture
of the test piece inside the shackle.
68. Colonel Maillard's Grips.- In the Maillard
machine very convenient grips are used in the form of
BE
n
With
FIG . 70 .
S
ๆ
经
nп
ll
hi
two half-rings n, 12, screwed on the outside .
bar is formed with shoulders at the ends .
The test
A pair of
grips enclose the shoulder, and these are then screwed
into the shackles of the machine. Fig. 70 shows these
grips, which are extremely simple and convenient to use.
69. Shackles with Spherical Bearing-surfaces. For
very accurate experiments, especially for experiments
on the modulus of elasticity, the coincidence of the ten
sion with the axis of the bar is of great importance.
It is best secured by carrying the bar on bearing
surfaces which are spherical.
This has been done in
several testing machines for round bars , but has not
been accomplished for plates.
The easiest way of supporting round bars is to form
SIIACKLES FOR HOLDING TEST BARS
181
a screw-thread on the ends, and then fix on the bar a
steel nut with hardened spherical face.
Fig. 71 shows
two arrangements the author has used, and found both
convenient and simple . The
screwing of the end of the
FIG . 71 .
;
test bar, which should be
1
done in the lathe, is tolerably
inexpensive. The steel nuts
may have the forms shown,
and they rest on steel rings
which drop into the conical
recess ofthe ordinary shackles.
1
Cast-iron specimens are con
veniently tested in this way,
the screwed end being made
FUL
rather extra large .
Spherical Seatings for Burs
with
Shouldered
Ends --Pro
bably the most satisfactory
form of test bar for very accurate tension experiments
is that adopted as the standard form in Germany. The
round bar is turned in the lathe , leaving square shoulders
at each end . As a seating for these shoulders two half
rings may be used , as shown in Fig. 72. The author
has used both forms.
In one the displacement of the
half-nuts during the test is impossible. But even with
the other form , which is simpler, displacement does not
occur .. The half-rings should be of hardened steel.
Fig. 73 shows the shackles used in the machine of
182
TESTING OF MATERIALS OF CONSTRUCTION
the Grafenstaden Engine Co. , of Mulhouse. Two hinged
boxes grasp the test bar, which is formed with shoulders.
FIG . 72 .
FIG . 73 .
0
中
1
TE
eg
Between the shoulders of
the bar and the boxes
half-rings with spherical
seats are inserted ,so that
the bar may swivel into
the line of pull .
op眾
70. Bauschinger's Ten
sion Shackle for Specimens of Wood . — Fig. 74 shows a
cast-iron shackle for specimens of timber used in
Bauschinger's researches. The dovetailed end of the
shackle fits into the ordinary tension shackle of the
SHACKLES FOR HOLDING TEST BARS
183
testing machine. The shackle is in two halves, and the
specimen is centred by the set screws. In order to get
FIG . 74 .
nori
W
ODOCOON
S
wa
S
a uniform distribution of stress in the neighbourhood
of the shoulders, two thin wedges, or keys, are driven
in at the back of the specimen .
71. Kortum's Patent Rope Attachment . — Ropes are
amongst the most difficult of materials to hold satisfac
torily in the testing machine. Fig. 75 shows a form of
attachment which appears to have been used satisfac
torily both for hemp and wire ropes. The figure shows
an ordinary attachment, and not one made specially for
testing. But shackles of precisely this kind ,made some
what more strongly, have been used in the testing
laboratory at Berlin for testing ropes. By any process
of splicing or knotting the rope is injured, or at least
bending stresses are introduced which weaken the rope
in the neighbourhood of the shackle.
184
TESTING OF MATERIALS OF CONSTRUCTION
Kortum's shackle consists of a conical shell or
thimble, provided with a hook or loop, and having
internal gripping wedges k
which compress the rope be
tween them .
The wedges
FIG . 75 .
are so formed as to compress
the
-0
rope concentrically, and,
having a greater taper than
the thimble, the pressure is
a
8
greatest at the free end of
the rope and least near the
mouth of the thimble. Hence
the bite on the rope increases
regularly from the mouth
backwards. The wedges have
teeth on the inside, which indent the rope without
sensibly injuring it near the mouth of the shackle.
They are easily fixed, and adjust themselves automatic
ally as the tension comes on the rope.
II.
SHACKLES FOR OTHER TESTS,
72. Fig. 76 shows a crushing shackle , designed by
the author for short specimens. There s is the speci
men , a cube of stone, for instance, which rests between
the two parts of the shackle.
The pull on the shackles
exerts a crushing force of equal amount on the stone.
The shackles are guided by the side bolts, so that the
opposite faces remain parallel.
To distribute fairly
the load on the stone block , which may be, to a small
SHACKLES FOR VIOLDING TEST BARS
185
extent, out of truth, a cup- and-ball distance piece, with
well lubricated surfaces, is placed between the upper
face of the stone and the shackle .
FIG . 76 .
l
FZ
WOWO
+53 : 5
1
73. Kennedy's Torsion Shackle. — Fig. 77 shows a
form of friction grip used by Prof. Kennedy for holding
specimens subjected to torsion ; & is the specimen, held
between two V -shaped fixed jaws and a third movable
jaw. This last is centred eccentrically to the curvature
of its surface, so that the slight rotation of the specimen ,
186
TESTING OF MATERIALS OF CONSTRUCTION
tending to turn the jaw, produces a considerable fric
tional grip .
1
74. Transverse or Cross-breaking Shackles . - Fig. 78
shows shackles for transverse tests supplied with the
machine of Messrs . Buckton.
Fig. 77 .
A
vertical machine lends itself less
S
1
HD
conveniently to transverse test
ing than a horizontal machine,
but, on the other hand, no slides
interfere with the accuracy of
the test. The shackles shown are
steel castings. The specimen s s ( in the figure a rail
bar ) is shown supported between two standards a a,
fixed on the lower shackle, and the centre shackle b.
The standards a a can be adjusted through a limited
range for different lengths of
FIG . 79 .
span. There are rough knife
edges at the points of sup
port.
The shackle shown is
intended for loads up to 50
tons .
Cog
the Werder machine.
75. Shearing Shackles.
Fig. 79 shows a simple form
of shearing shackle used in
The shackle is formed so as to
be held in the ordinary tension shackles. The rivet or
I
bolt to be sheared is in double shear.
1
' Iron and Steel, ' by P. V. Appleby. Proc. Inst. Mech. Eng.
vol . lxxiv .
1
187
S
SHACKLES FOR HOLDING TEST BARS
no
09
1
S
FIG
.78
j
a
e
11
C
C
Babe
AL
$
B ယ်
76. Shackle for Indenting Bars to determine the Hard
ness.It is for certain purposes necessary to determine
the relative hardness of different specimens .
For this
188
TESTING OF MATERIALS OF CONSTRUCTION
purpose the plan generally used is to indent the speci
men by a given load, and measure the depth of indenta
FIG. 80 .
tion.
Major Wade used a hardened
steel pyramidal point, or knife- edge,
as shown at A (Fig. 80) , held in a
guide -block which could be placed
А
in the testing machine. A
pressure
of 5 tons was used to force the point
or edge into the specimen , and the
relative hardness was taken to be
proportional to the volume of inden
One
2013
tation . Colonel Rosset has improved
this arrangement by adopting the
B
form of point shown at B.
)
The
point consists of two knife -edges
inclined at 163 °, the angle of the knife-edges being 90°.
Mr. Turner has used a quite different method. He
fixes a diamond in a wooden lath, so that it rests nor
mally on the specimen. The weight in grams which
must be placed on the lath to cause the diamond to
scratch the specimen is taken to be proportional to the
hardness .
77. Forms of Test Bars for Tension . - In Fig. 81 , a
shows the old form , used by Hodgkinson for cast iron,
with pin shackles
;
b shows a form suitable for cast
iron, used by Professor Kennedy. For cast iron the
author prefers the form k, with screwed ends and nuts
with spherical seatings.
For ductile materials, such as wrought iron and soft
189
SHACKLES FOR HOLDING TEST BARS
TIG . 81 .
1
kt
1
16 "
k
1
19
1
120
15
ra
d
-
C
4
8
a
0QI-
+
200 1
сC
-100 --
1
" da
8
1
4
10 "
K
Less
Or
3
lan
1
I
4"
k
a
1
"36
- 16 to 18
I
e
3"
- 10 to 12
V
f
(
1
- 240
1
24
0
ra
.d
25.
23
1
9
25:20
50
20
*
10
200
1
dia
25
2
50 2025
diad
20
→
35
6
、
1
1
1
* 30 * -50
40
* -50- * 30*
7
" _255
8 321 2 " 32 : 8
.564
0
10"to 12 "
"3ķ--
4"
MOR
4,7
32
13 :
.. ܼ‫ܒ݂ ܐܸܛ‬
kk
HI
m
‫هاما‬
77 /
NDO
2-k
$ Full Size
55
steel, the forms c, d , e, f, g, h, k, l are used, and the
ordinary size of these is marked in metric or English
190
TESTING OF MATERIALS OF CONSTRUCTION
dimensions. c, d , e are ordinary forms for plates , the
two last being for wedge grips . The recessed form d is
better than e, but in ductile materials the form
e,
which
is cheaper, may be adopted without much fear of the
specimen breaking in the shackles ; f is a form for round
bars, held in wedge grips with V-shaped recesses in the
faces; g and h are standard formsin the German Imperial
testing laboratories ; k is a very convenient form , the
ends being chased to a screw -thread in the lathe --- nuts
FIG . 82 .
are put on when the specimen is
2 %
tested ; l is the general form for which
1
the shackles of the newer American
machines are adapted, and is often made
of greater length ; m is the form adopted
by Bauschinger for wood .
Fig. 82 shows the most usual form of briquette for
The briquette is made in a
mould . Stone and similar materials may be tested for
tension in wedge grips, and test specimens are then
generally simple prisms .
tension tests of cement.
78. Shearing and Torsion Test Specimens. - Fig. 83
shows a specimen prepared for shearing of the form
FIG. 84 .
.625
-2
2 →
$
134
FIG . 83 .
a
K 1' *
1 * 1 *
B
used by Professor Kennedy. Two narrow grooves are
cut, so that the shearing planes are defined . Fig. 84
191
SIIACKLES FOR HOLDING TEST BARS
shows Thurston's form of torsion test piece, the ends
being square to fit the shackles and the centre part
cylindrical.
Test Specimens for Crushing.-- Fig. 85 shows the
ordinary forms of test specimens for compression. For
metals such as iron, steel, cast iron, or brass , small
FIG . 85.
ta
a
K - 142 -
--
84€
6
6
C
4 China
cylinders a are used . For cement, stone, &c. , cubes, as
at b. For wood, Bauschinger has found it to be de
sirable to protect the ends with a metal plate, a sheet of
paper being interposed. The form he adopts is that
shown at c.
192
TESTING OF MATERIALS OF CONSTRUCTION
CHAPTER VI .
MEASURING INSTRUMENTS .
ORDINARY graduated measuring instruments are re
quired in the engineering laboratory to determine the
dimensions of test bars .
In some cases the deforma
tions (elongations, deflections, &c. ) can be measured
accurately enough by the same instruments. For the
more accurate measurement of strains, however, special
measuring instruments are required.
79. The Graduated Straight-edge.-- Steel straight
edges of different lengths, graduated on the edge, are
used for several purposes . For the rougher tests dimen
sions may be callipered, and the callipers placed on the
graduated straight-edge. Extensions of ductile ma
terials can be measured in a similar way . Two slight
}
centre punch -marks are made on the bar , and the dis
tance between these is taken by a beam compass , which
is then placed on the graduated straight-edge. The
differences of successive measurements are the elonga
tions. The most convenient graduated straight-edges
are made by the Brown & Sharpe Manufacturing
Company, of Providence, U.S.A. These have gradua
MEASURING INSTRUMENTS
tions into
1
10
193
inch and Too inch, and into millimeters
and fifths of millimeters .
80. The Straight Vernier Calliper. - The beam com
pass of the draughtsman is very commonly graduated
along the beam, and a vernier is fixed on the sliding
head. The fault of the beam compass, however, is the
springiness of the points, and want of perfect truth of
the sliding surfaces of the beam. A straight vernier
calliper is, in fact,a beam compass with very rigid points
and a metal beam . Fig. 86 shows the construction of
FIG . 86 .
B
‫المسلسملسلسل مسلسل مسلسل سلسا‬
€
‫سلسبيليسلبيليسيل‬
120 1910
Icc :
in
Le
a vernier calliper as made by Messrs. Brown & Sharpe.
A steel straight-edge of very accurate form is bent
down at b to form one leg. On this slides very accu
rately the sliding head B , carrying the second leg a.
For more accurately adjusting the position of the sliding
head B there is a third slide C, which can be clamped
to the bar, and from which the position of B can be ad
justed by a fine-pitched screw.
away
The face of B is cut
to show the scale, and the bevelled face of the slot
is graduated as a vernier.
The most convenient graduation for English mea
sures is for the scale to be divided into tenths, and each
0
194
TESTING OF MATERIALS OF CONSTRUCTION
tenth into quarters . A quarter-tenth reads twenty -five
thousandths. If now on the vernier a length of twenty
five quarter -tenths is divided into twenty -five, the vernier
will read off thousandths of an inch.
The outside diameter, or width, of bars is obtained
by placing them between the jaws a l, and sliding the
moving head till contact with gentle pressure is obtained .
The calliper should be held lightly in both hands, and
by slight movements it is easy to determine if the jaws
are square with the bar to be measured. No excessive
pressure must be used or the instrument will be injured .
Inside diameters of rivet -holes and similar measure
ments may be obtained by using the rounded outsides
of the jaws a b. There is then a fixed quantity to be
added to the reading on the scale. Some callipers, how
ever, have two verniers, so placed that one reads out
sides and the other insides .
The steel vernier callipers of Messrs . Brown &
Sharpe are extremely useful and trustworthy, and will
even bear moderate rough usage without much injury .
The shortness of the jaws is, however, sometimes incon
venient.
Instruments of the same kind, somewhat more finely
graduated, and with longer jaws and heavier slides, are
made by Messrs . Holtzapfel and Messrs. Elliott
Brothers .
81. The Screw Micrometer . This instrument ( Fig.
87 ) is a kind of calliper, and is useful for determining
the dimensions of the smaller test bars .
At one end of
195
MEASURING INSTRUMENTS
a bent frame is a fixed abutment, at the other a cylin
drical bar C, moved by a fine-pitched screw. By
turning the sleeve D , the bar C advances to or retires
from the abutment. An object to be measured is placed
FIG . 87 .
C
10
a
D
in the jaws, and C is advanced till there is contact with
Some tact is required, and it should
be remembered that a force applied to the sleeve pro
duces a much greater pressure between the jaws. There
gentle pressure .
is a graduation along the straight cylinder at a into
tenths of an inch and quarter -tenths, and the edge of
the sleeve D is itself graduated into twenty -five divi
sions, each of which corresponds to a movement of the
jaw of job , inch. As the divisions are open , it is quite
possible to read the scale by estimation to one - fifth
of doo inch .
But although this reading is easy,
it is not equally easy to ensure the delicacy of
touch required for so great accuracy . In the Brown
& Sharpe micrometer calliper the adjustment to zero,
if the instrument wears, is effected by withdrawing the
sleeve D , and applying a small wrench to a nut inside.
0 2
196
TESTING OF MATERIALS OF CONSTRUCTION
The instrument should be tried occasionally to see
whether, when screwed home till the faces of the jaws
touch, the scale really reads zero. If not, adjustment is
required. The accuracy of this instrument depends
entirely on the accuracy with which the fine-pitched
screw is cut. When obtained from a really trustworthy
maker the screw can generally be relied on to read
accurately to the nearest Tūro inch . Beyond this
degree of accuracy, however , no screw can be trusted
which has not been independently tested .
Usually
these instruments take between the jaws either 1 inch
or 2 inches at most.
82. Professor J. E. Sweet's Screw Micrometer.-- This
instrument ( Fig. 88 ) is made by the Syracuse Twist
FIG. 88 .
1
Drill Company. It has a ratchet - threaded measuring
screw , the working face of the screw- thread being
MEASURING INSTRUMENTS
197
normal to the axis of the screw, and the back face
inclined. The tops of the thread, both in screw and nut,
are removed , so that after wear a perfect bearing is still
obtained by closing the split-nut. A slight looseness
of the nut will not affect the measurement , on account
of the square bearing of the thread . The screw and nut
are of equal length ( 3 inches), to ensure equality of
wear .
The screw is moved by a sleeve provided with a
milled head and held between washers , one of steel and
the other of felt, to produce an adjustable friction , so
that equal pressure may always be obtained between the
measuring points . The index -bar projecting over the
divided circle is adjustable. The pitch of the most
carefully made screw is more or less variable, and no
two screws are absolutely of the same pitch. This
error is corrected by inclining the index -bar forward
for a screw of too fine pitch, backward for one too
coarse .
Each instrument is adjusted by the makers to
a standard 1 -inch distance- piece. The index-bar is
mounted on a split- sleeve, threaded upon the extended
end of the measuring nut with a thread of correspond
ing pitch. This allows the index-bar to be thrown
backward or forward to a convenient position for read
ing, or even turned a half -revolution , if desired , to
measure work on the lathe, and read the dimension in
that position .
The above, which may be termed the
head -gearing, is used only for determining the fractional
parts of an inch . Whole inches are measured by the
aid of standard distance-pieces , furnished with the
198
TESTING OF MATERIALS OF CONSTRUCTION
The tail-spindle is unclamped, drawn
back , and a distance -piece inserted, and the spindle again
clamped. No special pains need be taken to do this
instrument.
accurately, as the final adjustment is effected by setting
the index -bar and its sleeve . The milled head is double ,
being graduated for 1ooo inch, and for binary fractions
as small as 4 of 3'z, orzuty inch. The milled head
by which the screw is turned is mounted freely on the
spindle, and held between a washer of felt and one of
steel dowelled upon the end of the spindle, and tightened
by an adjusting screw. The friction thus produced
secures uniform pressure between the measuring points ,
and climinates the personal equation.
A variation of
Todoo inch can be recognised . The capacity of the in
strument is 0 to 4 inches.
83. Whitworth's Millionth Measuring Machine and
Workshop Measuring Machine.—These are fixed instru
ments, of heavier and much more accurate make than
the ordinary screw micrometer. The screw has 20
threads to the inch , the screw wheel 200 teeth, and the
micrometer wheel is divided into 250, so that each
division represents Tuvě007 inch . The end of the fast
headstock and the end of the movable headstock are
true parallel planes. The ends of the piece to be mea
sured must also be true parallel planes . In measuring
to an accuracy beyond odoo a feeling -piece is used.
This is a piece of steel about
faces.
inch thick, with parallel
It is introduced between the bar to be measured
and the fast headstock .
When proper adjustment has
199
MEASURING INSTRUMENTS
been reached, the movement of one division of the
micrometer wheel will set fast the feeling-piece . Without
the feeling -piece it is said that a movement of quvo
inch can be distinctly felt and gauged.
Fig. 89 shows a machine of this type of American
construction ( Richard's machine ), with a standard
test piece in the jaws.
The machine consists of a solid
CHIPIUTTI
Lannan
JUKUAHID
FIG . 89 .
fill !
HITRAMUNTAR.13?! T :Si Mitol:1147 (
TIPURTINTI
tim
2 :11:13 : 7777 111111*
1 * 1111!!
bed , something like a lathe-bed, with two headstocks,
one fixed , the other moved by the accurate fine-pitched
screw . The screw has a graduated head , and sometimes
with a vernier also. The machines are guaranteed to
be correct to noooo inch . They will read to zgovo inch,
but, without special means of ascertaining the pressure
at the point of contact, such accuracy of reading is
stated to be fallacious.
INSTRUMENTS FOR MEASURING STRAINS.
84. In almost all experiments on the elastic
proper
ties of materials it is necessary to measure the strains
or deformations which correspond to different stresses.
Thus, in tensile tests the elongations are measured, in
torsional tests the twist, in bending tests the deflection.
200
TESTING OF MATERIALS OF CONSTRUCTION
In ordinary commercial tests of the quality of ductile
materials, such as wrought iron and steel, only the
ultimate permanent deformation is measured , and since,
in such cases, this deformation is considerable, compara
tively rough measurements are sufficient. Thus, if a
soft-steel bar is broken by tension, the permanent
stretching of an 8 - inch length may amount to 2 inches.
An error of even by inch in measuring this would be
only 1 per cent. of the elongation , and that is accuracy
enough for practical purposes. Of course, for somewhat
more rigid material, such as wrought- iron plates , the
extension is less , and it is desirable to make the
measurement more closely . But even in that case no
very refined measurement is practicable, because of the
difficulty of fitting together the broken pieces.
To
ascertain the strains in ductile materials during the
progress of a test, after the elastic limit is passed , some
what rough measurements are also sufficient.
But it
is altogether different in observing the strains within
the elastic limit.
A mild - steel bar, 10 inches long, is
stretched less than to inch when the elastic limit is
reached. For an accuracy of 1 per cent. the error of
measurement must, therefore, not exceed odoo inch ;
and measurement to this degree of accuracy is more
difficult than is commonly supposed .
If the true
elastic limit is to be determined , measurements to at
least Toodoo inch are necessary . The smallness of this
quantity may be realised by the aid of an illus iti
due to Sir J. Whitworth : Tod'oro inch is only a ou of the
201
MEASURING INSTRUMENTS
thickness of a sheet of thin foreign letter - paper.
In
the case of standard measures of length, with bars of
the most suitable form, the measurement, even to this
degree of accuracy, is comparatively easy. But mea
surements of deformation have to be made on test bars
of a form less suited for measurement and under con
ditions of some difficulty . Hence special methods are
necessary, and instruments specially arranged for the
purpose.
In the case of test bars, a difficulty of measurement
arises out of the occurrence of a change of curvature of
the bar during the test. The bar may initially have a
small curvature , and be straightened by the load ; or, if
the load does not act accurately along the axis of the bar,
FIG . 90.
it may become curved during
the test. Suppose a bar curved
like the bar in Fig. 90 in the
plane of the paper. If the bar
( 12
straightens by loading, the dis
tance between a and I will in
1
сC
crease, not only by the amount
of the elongation , but by the
02
difference of the chord and arc
63
length a b. Suppose two clips
fixed on the bar normal to its axis, and measurements
taken between two points (12, bz.
By straightening of
the bar the clips will become parallel , and the distance
a, b, will be lengthened by the alteration of inclination
of the clips still more seriously . It is important to
202
TESTING OF MATERIALS OF CONSTRUCTION
notice that if the points (a, b, had been taken on the
other side of the bar, an opposite error would have
arisen , the distance being shortened by the straighten
ing of the bar. Consequently, we may infer at once that
the mean of measurements on opposite sides of the bar
will be much more free of error due to curvature than
any single measurement.
Suppose a , b are two points on the axis of a bar
initially bent in the plane of the paper. Let arc length
ab = 2 c, chord ab = 2 a, versed sine = h.
Then
c = v (a? + } ??) , nearly.
If now measurements are taken on a straight scale
between a and b, and the bar straightens by tension, it
will have an apparent elongation 2 ( c - a ) , due merely
to change of curvature, and this will enter as an error
into the measurement of the extensions . For instance,
suppose the chord length a b is 10 inches , and the
versed sine of the curve o inch .
The bar would then
have a curvature probably as great as could occur in a
reasonably good test bar. Then the arc length would
be 10.000026 inches , and an error might arise, from the
straightening of the bar during a test, of 0.000026 inch.
This, however, is a quantity too small to be of import
ance in any ordinary measurements of extension .
Con
sequently, if measurements were really made between
points on the axis of the bar, it does not appear that
serious error would arise from any probable amount of
initial curvature of the bar.
MEASURING INSTRUMENTS
203
In fact, however, in all measuring instruments the
measurement is made at a distance from the axis of the
bar. Under the best circumstances the bar would be
measured at two points an, bi on its surface, which , in
the straightening of the bar, would move apart to a
distance equal to the arc length al, the lines oa, ol
becoming parallel. In most mcasuring instruments the
case is much worse‫ ;ܪ‬the measurements are made between
two points, such as (2, bz, rigidly connected with the
bar, and the error introduced into the measurements is
the difference of the length a, b, and the arc length ab.
Since, as has been shown , the difference of the arc and
chord length ab is very small , it will be a sufficient
approximation to say that the error of measurement
will be the difference of the straight lengths a, b, and
ab .
Let aa a,
d2= l, and oa = 1 .
Let
a, ba
al
Then
a2 + 12 – 2 1 x
r
no
a2 + 12
If, as before , al = 2 a = 10 inches, h = 30 inch , and
X = 2 inches, then a, b2 = 9.968 inches . Then, if by
the straightening of the bar the lines on, ob become
parallel, an error is introduced in the measurements of
0.032 inch ; a very appreciable quantity, even in rough
measurements of elongation. The error is more than
1,000 times as great as it would be if the measurements
were really taken directly at the axis of the bar. If
the measurements are taken on the surface of the
bar at an,bi , the error will be less .
Thus, if a dy = x
204
TESTING OF MATERIALS OF CONSTRUCTION
= 0 • 375 inch, we get a li
9.994 inches , and the error
due to straightening would not exceed 0:006 inch ; a
quantity much less, but still large enough to be of con
sequence in elastic measurements .
If measurements
are taken at points symmetrically placed on either side
of the bar, the error due to curvature is nearly elimi
nated,the lengthening of the distance on one side being
compensated by shortening on the other.
85. The Wedge Gauge. The wedge gauge is a tri
angular plate, with sides sloping at 1 in 10 , graduated
FIG . 91 .
2
‫لبلبلییلیید‬
аa
wurdemilos ‫ܨܝ‬
‫ܢܝܢܠܝ‬
along the longer side. If this is pushed between two
pins, or shoulders , the distance between them can be
read off on the scale , magnified by the ratio of the
sloping sides ten times . Professor
TIG . 92 .
Eaton Hodgkinson used wedge
gauges, and the author also used
wedge gauges, for measuring ex
011
(1
tensions, about 1856.
6
20
Two loose
pieces , a, b ( Fig . 92 ) , were clamped
on the test bar, and the wedge
gauge pushed between them. They
were made to bite into the test bar
slightly at two points on the test bar, at a distance l.
As the test bar extended, the wedge gauge slipped
205
MEASURING INSTRUMENTS
further in , and the differences of readings gave the elon
gations to do inch .
86.
Micrometer Screw E.ctensometer. - A screw is
equivalent to a wedge gauge in a more convenient form ,
It is virtually a wedge gauge wrapped
FIG . 93 .
pitch of screw ,
round a cylinder . If p
uhua
nuel
d = diameter of graduated head of the
on which readings are taken ,
ô = the distance to be measured parallel
screw
MITIN
to the axis of the screw , A the dis
tance on the circumference of the head which corre
sponds to an axial movement o, then
nico
T d
>
P
A = 7 do / p.
Let the screw have 25 threads to the inch ( p = 0· 0+ ) ,
and the head be about 21 inches in diameter, and
divided into 100 parts of about zo inch each . Then
each division corresponds to zoo inch, and can be
read by estimation to quarter -divisions, or Tuboo inch .
The accuracy of the instrument depends on the uni
formity of pitch of the screw, which is often less accu
rate than it is intended to be. A difficulty also arises
in consequence of the elasticity of the instrument.
Differences of pressure at the point of contact cause
differences of reading.
Professor Thurston ? appears to have first used an
1 Materials of Engineering. Thurston. Vol. ii. p. 369.
206
TESTING OF MATERIALS OF CONSTRUCTION
instrument with two micrometer screws placed symme
trically on each side of the axis of the test bar. These
screws were carried in a clamp fixed on the test bar,
and were brought into contact with steel pins fixed on
a second clamp. By using twin micrometer screws the
error due to curvature of the bar is nearly eliminated ;
for if the straightening of the bar, by tilting the clips,
lengthens the distance on one side, it shortens it equally
on the other. To get rid of the error of different pres
sures at the point of contact, Professor Thurston con
nected the two clips with the poles of a battery, so that
contact of the micrometer screw and abutment completed
circuit and gave a signal. It is not quite clear, however,,
that circuit is always established with just the same
pressure, and the clips were of very imperfect form ,
leaving uncertain the length which was extending.
87. Electric Contact Screw Micrometer, by Messrs .
Henning & Marshall.
The
micrometer
shown
in
Fig. 94 is probably the most accurately and carefully
designed screw micrometer which has hitherto been
used . It is described in a paper read before the American
Society of Mechanical Engineers in 1885 , and the instru
ment was made by the Brown & Sharpe Manufacturing
Company.
It consists of two clips, or carrying frames, A and B ,
which grip the specimen s symmetrically between two
steel points and two knife -edges on each clip. As the
distance between the clips increases with the extension
of the specimen , the increment is measured by two
1
207
MEASURING INSTRUMENTS
symmetrically placed micrometer screws m m , carried
by one clip, and brought into contact with a pair of
plugs g g on the other clip . The pointed screws which
grip the test bar are at lh, and the spring-pressed
knife -edges at c c. The bars d d are used in fixing
FIG . 94 .
n
CMT
IHR
n
TI
TI
C
c
FIV1
Z
S
G
е
S
d
d
f
LLL
TUM
TUUU
AUTO
Dünit
UU
说。
11 ,
Itin
”
m
mu
Z
1
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um
B
C
INLOVILI
70
LA
74
S
IN
the clips initially at the right distance apart. They are
then moved out of the way while the instrument is in
use .
Vertical scales ee are provided, as well as the
graduation on the heads of the micrometer screws m m .
Each of the frames is connected with an electric bell ,
a circuit being established when the point f of either
micrometer screw touches the contact-plug g. To
208
TESTING OF MATERIALS OF CONSTRUCTION
ensure proper adjustment in a plane normal to that of
the micrometer screws, the centring screws hh are
brought to bear on the surface of the test bar, after the
rods dd have been thrown into gear, and the points of
the micrometer screws placed over the centre of the
contact-plugs. Then the centring screws are forced
slightly into the test piece, so as to hold securely. After
this, the side bars dd are gently removed, and the
electric wires attached. The plane of contact of the
micrometer screws and contact -plugs is in the middle
of the measured length.
It is claimed for this apparatus that :
( 1 ) Its construction is symmetrical.
( 2 ) It is applicable to various shapes of test bar.
3 ) It can be adjusted with certainty, so that the
screws are symmetrical with the test bar.
( 4 ) The micrometer screw -heads are of large size,
giving readings of small extensions.
88. Screw Extensometer" with Levels.'_Fig. 95 shows
diagrammatically an arrangement the author has adopted ,
and which obviates most of the difficulty of employing
Two clamps grip the specimen
between pointed set screws, a a and 00, at points on a
plane passing through the axis of the bar. The lower
clip carries the micrometer screw e, on the hardened
point of which the upper clip rests . If, then , the clips
can be kept exactly normal to the axis of the test bar,
a micrometer screw .
the micrometer screw measures the distance between
1 Proc. Pluysical Society, vol. viii . p . 178 .
209
MEASURING INSTRUMENTS
two points on the axis of the test bar - namely, the points
on the intersection of a a and bb with the axis.
Or, to
put it another way, the micrometer screw being at the
middle of the width of the clips, it measures the mean
extension of the two sides of
FIG . 95 .
the bar.
Now to set the clips
accurately normal to the axis
of the bar they are provided
with delicate levels .
EN
С
Before
taking a reading these are ad
102
101
justed. The lower clip is first
‫بسلسليللرأ‬
set, level by the adjusting screw C
d. Next, the upper clip is set
level by the niicrometer screw
e ; lastly, the reading is taken
on the graduated head of the
micrometer scrow.
Fig. 96 is
a general view of the instru
ment applied to a flat test bar.
C1 C2 are clips ; Il levels ; m the
B
micrometer screw ; r a bar of
adjustable length to suit dif
ferent test bars .
a
The instru
C
ment is very easy to use ; the
pressure on the micrometer screw is constant, being the
weight of the upper clip ; and lastly, the measurements
are virtually measurements made on the axis of the bar,
so that errors due to curvature are nearly eliminated .
The instrument constructed reads to 10doo inch .
P
210
TESTING OF MATERIALS OF CONSTRUCTION
89. The
Cathetometer.- The cathetometer
is
an
instrument for determining the difference of level of two
points by a telescope sight. It may therefore be applied
to determining the elonga
FIG . 96 .
tion of a bar under stress by
reading the length between
tiro fine diamond scratches
7
before and after the stress is
UNIT
C2
WS
WITH
with cross wires , carrying a
uuw
m
applied.
It consists of a telescope
WEEN
watatlilatel
sensitive level, and sliding
on a very accurately formed
vertical slide.
The slide is
carried on a support , round
which it can rotate. Suppose
7
the axis of rotation adjusted
r
accurately vertical, and the
slide adjusted accurately
l
parallel to the axis of rota
Ca
tion . Lastly, let the axis of
the telescope be adjusted to
the horizontal by the aid of
its level - tube .
Then if the
telescope be set in succession on two points , and readings
taken on a scale attached to the telescope-slide by a
vernier attached to the telescope, the difference of the
readings will be the difference of level of the points.
The cathetometer is for certain purposes extremely
211
MEASURING INSTRUMENTS
valuable. The readings are taken froin any convenient
distance, without its being necessary to touch or even
approach the bar to be measured . The mcasurements
are taken directly on an accurate scale, and are absolute
measures ,not needing any reduction , and not depending
on any other measurements.
On the other hand , in
determining elongations or deflections the cathetometer
is laborious in use.
The need of taking two vernier
readings for each measurement of the bar wastes a good
deal of time.
The author has used a cathetometer by Breithaupt ,
of Cassel. This has a cylindrical central support, which
can be set by a circular level indicating to 10 seconds.
The prism on which the telescope slides is of cast iron ,
with an inlaid silver scale 1 metre in length , divided
into millimeters .
This prism is balanced by a weight
on the other side of the axis of rotation. To adjust
this prism accurately vertical a special separate adjusting
level of great sensitiveness is provided. The telescope,
fixed in Y's on a brass slide- block , is reversible, and
carries a striding -level, also reversible. By a clamp
and tangent screw the telescope cross wire can be
brought into accurate coincidence with the object. The
block carrying the telescope has a vernier reading
on the silver scale on the prism to zu mm. ( or do
inch) .
By means of a micrometer eyepiece a cathetometer
may be used to read to nudou inch . In connection
with one of the testing machines at Berlin there is a
P 2
212
TESTING OF MATERIALS OF CONSTRUCTION
cathetometer with two telescopes, having micrometer
eyepieces, so that both marks on the bar can be read on
the cathetometer at the same time.
90. Touch Micrometer. -Every mechanic is accus
tomed to take dimensions in callipers with very great
accuracy. Hence it appeared that a process equivalent
to callipering would be delicate enough even for mea
suring small elastic extensions . The author constructed
an instrument of this kind in 1883 which proved simple
and convenient.
Suppose two clips fixed on a test bar in some way
which strictly defines the length of bar which in extend
ing carries the clips. Let there be on the clips case
FIG . 97 .
С
of
-
(
TY
B
A
PREBENARIANTRADIENIAZTATU
பாயினர்
hardened plugs in pairs opposite each other. If the
distance between these plugs is callipered during a test
the amount of extension can be determined .
Fig. 97 shows a kind of micrometer calliper . It
consists of a frame having a sliding-piece A , which
slides without shake, and can be fixed by a set screw.
213
MEASURING INSTRUMENTS
The piece D is merely an adjusting piece, ordinarily
clamped , which can be replaced by a longer piece if
necessary, to suit different lengths of test bar.
Both
the sliding-pieces A and D have hard -steel plugs at
their ends .
In use the instrument is held in the hand
between the clips on the test bar, and the steel plugs
brought into contact with those on the clips with gentle
pressure. The slide is then clamped, and the reading
taken .
The sliding- piece has two scales, A and B.
The
scale A is read by sight against a vernier on the frame
to hundredths of an inch ; the other scale is read
through the microscope micrometer. Fig. 98 shows the
field of view in the microscope : ab is a fixed cobweb,
FIG . 98 .
corresponding with the zero on the
scale A.
In the field is rather more
than a tenth of an inch on the scale
B , the tenths being divided into fifths
of tenths (or fiftieths) of an inch .
From the reading on the scale A the t
i
precise tenth in the tield of view
known. Suppose that e reads on the fixed scale 2.2.
Between e and the zero g are two fiftieths and a fraction
of a third . The point f therefore reads 2.24, and it
only remains to measure the distance fg.
This is done
by bringing the crossed cobiebs to f by means of the
graduated head C of the micrometer , when the number
of tenths of thousandths of an inch which measure fg
is read off on the graduated head. The process is
214
TESTING OF MATERIALS OF CONSTRUCTION
tedious to describe, but it is extremely simple in
practice. Further, as the same tenth of an inch usually
remains in view for the whole period of a test in which
the elastic extension is measured, it is in general only
necessary to note the reading on the graduated head C
after the first reading.
The instrument is simple ; the readings are taken
on a finely graduated scale, and the errors of the micro
meter screw are virtually reduced, because an enlarged
image of the scale is measured. The author has found
it
easy to read to noooo inch , with an error of not more
than 5 jooth , and even more delicate reading is possible.
It is also more rapid to use than without experience
would be expected . Two or more readings on different
sides of the bar can be taken if desired .
Cowper's Extensometer.— Mr. Cowper has described
an extensometer used in testing long bars for the Kieff
Bridge in 1850. It consisted of a light iron tube about
4 feet long, with a small brass fork at each end which
fitted against pins attached to the test bar. One fork
slid on an accurate slide and carried a vernier.
This
fork was pushed home against the pin by a spiral
spring. For comparatively rough measurements the
author has used a vernier extensometer of the same
kind on short 8 -inch or 10 -inch bars. It gives readings
to looo inch .
91. Lever Extensometers.Many instruments have
been used in which the extensions of a bar are me
1 Proc. Inst. of Mechanical Engineers, 1878, p. 256.
215
MEASURING INSTRUMENTS
chanically magnified by a lever.
The defect of such
instruments is that the extension is measured between
clips often attached to the bar in an unsatisfactory way,
and that, to obtain sufficient magnification, the short
arm of the lever is so short that the range of indication
is very small .
Col. Paine's Lever Extensometer . - In Mr. A. V.
Abbott's work on testing machines there is described
a neat and simple form of lever
extensometer shown in Fig. 99.
This was used by Col. Paine
FIG . 99 .
H
G
in tests made at the East River
N
Bridge.
The apparatus con
sists of two bars, A and B ,
arranged to slide parallel to
50
each other.
At one end of
AА
each bar there is a knife-edge
Fin a brass slide, and initially
these knife-edges are adjusted
The instrument is clamped to
the test bar K by springs
G G, which press the knife
edges into small indentations
in the bar.
100
to a known distance apart.
1
NE
G
A lever C is fixed on the bar B.
Its
short arm bears on a projection 0 on the bar A , while
its long arm moves a vernier D , which slides in the
projecting guide E.
Abbott, Testing Machines (Van Nostrand's Science Series), r. 86.
216
TESTING OF MATERIALS OF CONSTRUCTION
Kennedy's Lever Extensometer .—Prof. Kennedy has
designed and very largely used the simple lever extenso
meter shown in Fig. 100. This consists of a light frame
FIG. 100.
¿
'U
i
W
G
.
C
S
f carrying a simple lever i. The two steel points , one
on the frame f, the other on the lever i, are 10 inches
apart. These are placed in centre punch marks on the
1 Proc. Inst. of Civil Engineers, vol. lxxiv.; also lxxxviii. p. 24.
MEASURING INSTRUMENTS
217
specimen s, the apparatus being held in position by elastic
bands cc, a weight w helping to preserve the balance.
The lever i turns on two set screw points, and the other
end moves over a plane covered with section paper,
attached rigidly by an arm to the frame on the test bar.
As the piece extends the steel points move apart, turn
ing the lever round its axis . The leverage is 100 to 1 ,
and readings can be taken to Toboy inch. The ratio
of magnification was determined by measurement with
vernier callipers .
Dupuy's Extensometer for Actual Structures. —The
object of this apparatus is to ascertain by direct
measurement the alterations of length of different mem
bers of iron structures by loads. Assuming that a bar
of iron is elongated or shortened to dogth part of its
length by stress in tension or compression of 1.27 ton
per sq. in . , it is possible to calculate from the observed
alterations of length the stresses in the bars produced
by the loads . To the bar to be tested a fulcrum pin is
attached , on which works a lever arm , with a leverage
of 20 to 1 , terminating in a pointer moving over a
graduated arc carried by the fulcrum piece . To the
short end of the lever is jointed a bar 1 metre (3 · 28 feet)
in length, a pin at the other end of this bar being also
attached to the bar to be tested . With the proportions
adopted , each millimeter of movement of the pointer
on the scale corresponds to a stress of a kilogram
| Ann . dés Ponts et Chaussées, 5th series, vol. xiv. p. 381.
218
TESTING OF MATERIALS OF CONSTRUCTION
per sq . mm . in the bar to be tested ( 0.635 ton per
sq . in.)
92. Differential Cathetometer.— This instrument was
exhibited by Dr. Heinrich Streinitz, of Gratz, at
South Kensington in 1876," and appears to have been
used by him some years earlier in researches on the
elasticity of wires . Dr.
FIG . 101 .
a
m
c
10.
Streinitz appears to have
originated a method of
d
measurement which is ex
*S
6
SA
tremely delicate. Fig. 101
s shows the principle of the
apparatus : a a is a stout
chius
c
glass rod carried by a
d
v
in
heavy foot ; on this are
clamped the two frames
bb ; cc are rods sliding
in the frames
, and dd are jointed prolongations,
serving to adjust the instrument ; m m are light touch
levers, which by weights or springs are kept in contact
b
a
with the bar s to be measured .
These levers rotate in the plane of the sketch on
pins at the ends of the bars dd, and each lever carries
a mirror m perpendicular to the plane in which it
rotates .
Every movement of either end of the bar s
will cause a rotation of the corresponding mirror. Now,
suppose a telescope and scale so placed that the gradua
1 Catalogue of the Special Loan Collection
South Kensington Museum , 1877 , p. 60.
of Scientific Agraratris at
MEASURING INSTRUMENTS
219
tions of the scale are seen after reflection at the mirror
in the telescope. Then, as either mirror rotates , the
graduations will move in the field of the telescope.
Now let O be the movement of one end of the bar to
be measured, and A the corresponding change of scale
reading. Let L be the distance of telescope and scale
from the mirror, and , the radius of the lever m to the
point of contact with the bar s.
Δ
Then
2 L
1
Now, as r can be made as small as one centimeter, and
L as much as 5 meters, the movement can be magnified
1,000 times. If a good telescope is used, tenths of milli
meters can be read on the scale , and consequently the
movement of the end of the bar can be determined to
Todoy millimeter.
The difference of the movement of
the two ends of the bar gives the change of length of
the bar.
It is obvious that the method of measurement
is one of extreme delicacy.
The apparatus in no way
interferes with the free movement of the bar.
There is
some labour in taking the two readings and computing
the difference, and perhaps some difficulty in deter
mining with sufficient accuracy the small radius of the
lever r. Dr. Streinitz determined 1 by using a sphero
meter .
The rod a a is of glass on account of its small
coefficient of expansion. Moreover, the glass tube may
be filled with water, and the temperature ascertained by
thermometers . A correction for any change of tem
perature can then be applied .
220
TESTING OF MATERIALS OF CONSTRUCTION
In 1879 Prof. Kennedy exhibited at the Institution
of Civil Engineers a two-mirror arrangement similar in
principle to that of Dr. Streinitz . But he has given
up its use in favour of the lever extensometer already
1
described .
93. Bauschinger's Roller and Mirror Extınsometer.2
To Prof. Bauschinger belongs the credit of first sys
tematically taking double measurements on opposite
sides of a test bar. A pair of clips, formed like parallel
vices , are clamped on the bar at a and ( Fig. 102 ) .
FIG. 102.
Iz
ei
7
--
--
1
d1
C7.
‫ ܢ‬e2 ,
l2 Gb
a
C2
6
ga
These grip the bar between knife -edges. The clip b
carries a pair of hard ebonite rollers dı, d ,, on accu
rately centred spindles . The spindles are prolonged
upwards and carry the mirrors G192, which rotate in the
plane of the figure as the spindles rotate. The rotation
of the mirrors is measured by reading - telescopes C1, C2,
1 ' Engineering Laboratories,' Kennedy. Proc. Inst. of Civil Engineers ,
vol. lxxxviii. p. 22 .
% Maschine zum Priifen der Festigkeit der Materialien , construirt von
Ludwig Werder, und Instrumente zum Messen der Gestaltsveränderung der
Probekörper, construirt von Joh . Bauschinger . München , 1882. Also
Mittheilungen a. d. Mech. Techn . Laboratorium in München, Hefte
1. und 3.
221
MEASURING INSTRUMENTS
and scales f at a distance of 10 or 15 feet.
The scale
divisions, seen by reflection in the mirrors, cross the
wire in the field of view of the telescope.
The mirrors
have vertical and horizontal adjustments for bringing
initially the scale into the field of view of the telescope.
To turn the rollers dı, de proportionally to the extension
of the test bar, the clip a carries a pair of spring pieces
The face of these
spring pieces is slightly roughened by a file or by
C1, C2, which touch the rollers dı, d. .
attaching a strip of the finest emery -paper , and they
turn the rollers by frictional contact . It will now be
obvious that any extension ở of the distance between
the vices a and b will cause a rotation of the mirror I
through an angle Olr, where , is the radius of the
The apparatus is equivalent to a lever ap
paratus having for small arm the radius of the roller I,
and for long arm the double distance of the scale
from the mirror. Suppose , for instance, as in one of
Bauschinger's instruments , the radius of the roller is
roller.
0.3214 cm ., and the scale distance 160.7 cm .
Then
the magnification of the extension is ( 160 : 7 x 2 )
-0.3214 = 1,000 .
The scale is divided into fifths of
centimetres . Each division has, therefore, in measuring
extensions the value of oo millimeter, or about
jodoo inch. As it is possible to estimate tenths of
divisions, the readings can be taken to sooo millimeter .
Since in Bauschinger's apparatus there are two
mirrors, two readings are taken , giving the extensions
on the two sides of the bar.
The mean of these is
222
TESTING OF MATERIALS OF CONSTRUCTION
taken to be the true extension, free from error due to
initial or induced curvature of the test bar.
Bauschinger used instruments similar in principle
for measuring compression of stone, the lateral con
traction of metals, & c. For rougher measurements the
mirror and telescope are abandoned , and a light index
finger moving over a scale is substituted.
An apparatus similar in principle to Bauschinger's
was used by Col. Flad in the tests of material for the
St. Louis Bridge. This apparatus had , however, only
one roller and mirror, which for delicate measurements
is essentially defective. According to the St. Louis
Bridge experiments, the modulus of elasticity of the steel
deduced from the measurements varies from 11,000,000
to 50,000,000 lbs . per sq . in.
But it is almost cer
tain that the modulus has only a range of about
27,000,000 to 33,000,000. Prof. Bauschinger pointed
out this to the author as an indication of the error of
taking measurements on one side only of the bar.
94. The Author's Roller and Mirror Micrometer. __ The
author has attempted to get rid of the trouble of taking
two readings by a device similar in principle to that
used in the screw extensometer. Two clips, a and 1
( Fig. 103 ) , are attached to the test bar s by pointed set
screws on a plane passing through its axis. The lower
clip is supported by the adjusting screw d , and the two
clips are spaced apart by a distance- piece e with knife
edge ends.
A roller " , carrying a mirror m , is fixed
1 Proc. Physical Society, vol. viii . p . 178.
223
MEASURING INSTRUMENTS
in the upper clip at the same distance in front of the
distance- piece e as the set screws are behind it, so that
if the bar extends the roller approaches the lower clip
by the same amount that the set screw
FIG . 103 .
a retires from it. In moving it rotates
against the finger -piece f, and turns
the mirror. By a reading- telescope and
m
ola
scale the amount of rotation of the
mirror is observed . The roller being
at the middle of the clip between the
set screws gets a movement propor
S
tional to the mean extension of the
two sides of the bar.
95. Strohmeyer's Roller Extenso
meter. – Mr. Strohmeyer has designed
an apparatus acting similarly to Bau
schinger's, though the principle is car
ried out in a different way. A wire
of small diameter is used for the roller ,
Рe
B
and a light index -finger attached to the
a
wire, moving over a graduated arc, gives
hone
the extensions magnified sufficiently .
Fig. 104 shows one form of the apparatus . Two
clips are fixed on the bar by pointed set screws. Each
of these carries two flat plates of steel , about 1 ] inch
wide, one on each side of the test bar. The pairs of
plates on each side of the test bar are pressed together
1 .
" A Strain Indicator for use at Sea. Trans. Inst. of Naval Architects,
1886.
224
TESTING OF MATERIALS OF CONSTRUCTION
by springs, and between them is placed the wire roller ,
carrying a light index - finger. As the bar extends, the
plates slide relatively and rotate the rollers .
Mr.
FIG . 104 .
luna
watu
IH
TIT
WHITE
Strohmeyer states that he has obtained good results
with a wire of 0.015 inch circumference. Then, the
graduated arc having divisions equal to 1bo of the cir
cumference, each division corresponds to Todoo inch
extension .
Comparing Strohmeyer's apparatus with Bauschin
ger's, it is obvious that the most essential difference is
225
MEASURING INSTRUMENTS
the extreme smallness of the rolling pin which Mr.
Strohmeyer uses. That this is convenient may be
easily granted. It is more difficult to believe that such
very small wires can be trusted to be circular in section .
Further, the absolute measurement of the elongations
depends on the exact measurement of the diameter of
this very small wire ‫ ;ܪ‬and this must in fact be impossible
to anything like the same proportionate degree of
accuracy as in the case of the larger rollers of Bau
schinger.
It would seem, therefore, that Mr. Strohmeyer's
apparatus is rather better adapted to cases where relative
extensions only are required . To such cases Mr.
Strohmeyer has applied it with remarkable skill. By
its means he has determined the relative extensions of
members of bridges, and of different parts of the skin of
a ship and the shell of a boiler, under their ordinary
loads.
96. Instrument for Measuring the Compression of Short
Blocks.For measuring the compression of short blocks,
such as cubes of stone, extremely ninute measurement
is necessary . The author las employed the arrange
ment shown in Fig. 105, which combines lever and
optical magnification, and at the same time gives by a
single reading the mean compression of the two sides of
the block .
A rectangular frame C2 C2, with adjustments for
blocks of varying size, is clamped on the base of the
stone cube by four pointed set screws .
It carries an
Q
226
TESTING OF MATERIALS OF CONSTRUCTION
upright pillar P ,
C2
with a hardened -
adjustable
steel
top, on which rests
Y
an upper frame c ,
which is clamped
on the cube by
273
BILSTONE
the knife- edge of
P
TI
C1
S2
10
Si
two
set
screws
near the
middle
and near the top .
frames
The
are
prolonged by the
12
T2
FIG
.105
levers
l1, 12, SO
that
the ends
and
į move two
a
and a half times
1
D
as much
as
the
points of theframes
fixed in the cube .
The ends of the
M
levers carry silver
plates with a fine
‫ותחן‬
‫מ‬
diamond scratch,
ti
:7
9TITEL
1:
1111111
CINTAIN
CRIMITE
UB
m
TH
1
and these plates
are adjusted to be
near together in
itially by the ad
justing screws at p and a.
The lever l, has a constant
227
MEASURING INSTRUMENTS
position relatively to the plane through the points in the
set screws in the frame ca.
The lever 11, turning on its
knife -edge on the pillar p, rises at i two and a half times
as much as the stone compresses between the set screws
on C1 and those on Cg. Further, as the instrument is
entirely carried by the stone cube, it is not affected by
any movement or elasticity of the machine.
During
the test the distance between the diamond scratches on
a and i is measured by the microscope M and micro
meter m . Readings to you and yotou inch can be
taken with moderately powerful object glasses. The
chief difficulty is to get the diamond scratches fine
enough. The fixed cross wire of the micrometer is first
set on one diamond scratch, the movable wire on the
other. Then the reading of the micrometer head gives
the distance.
Q 2
228
TESTING OF MATERIALS OF CONSTRUCTION
CHAPTER VII.
AUTOGRAPHIC RECORDING APPARATUS .
97. All ordinary testing is largely concerned with the
determination of the relation of stress and strain at
different loads. In Chapter III. it has been shown that
the relation of stress and strain throughout a test can
be graphically exhibited by a stress-strain diagram . If
a testing machine could be made itself to describe a
stress-strain diagram , it would be a very interesting
record of the behaviour of the test bar. Such a diagram
would show the yield point, if there was one, the
maximum load and breaking load , and the elonga
tion at each period of the test. From sufficiently
detailed measurements during the test such a diagram
can be plotted, and many such plotted diagrams are
given in the Report of the U.S. Testing Board.
But
such plotting is laborious, and it is very convenient to
have it done mechanically. Further, an autographic
diagram is free from personal bias and accidental errors
of record .
1 Much of the information in this chapter was given in a lecture on
' The Employment of Autographic Records in Testing, ' at the Society of
Arts, February 1886.
AUTOGRAPHIC RECORDING APPARATUS
229
It has been stated that an autographic diagram taken
in the absence of an inspector of materials might be
accepted as equally satisfactory as the inspector's report.
But that is claiming too much for the autographic dia
gram, which could be tampered with as easily as any
other record of a test.
The datum line can be dis
placed to increase the loads, and a finger on the pencil
will increase the extension record . Still
Still,, a perfectly
continuous record , showing all that has happened during
a test, is no doubt extremely useful.
98. Thurston's Autographic Testing Machine. — This
machine is intended to test the quality of materials by
means of inferences from the torsional strength and
rigidity. Tests of that kind are convenient because
the specimens do not require to be large, and the twist
ing moments necessary can be produced by comparatively
small forces at a moderate leverage. The deformation
before fracture is also large and easily measurable.
Inferences from torsional experiments, however, are
hardly so trustworthy as those from direct stresses ,
except in the case where a material is intended to be
| This machine has been very often figured and described. Professor
Thurston's papers will be found chiefly in the Trans. Am . Soc. of Civil
Engineers, and the following may be referred to : The Mechanical Pro
perties of Materials of Construction ,' 1874, vol. ii. p. 349 ; vol. iii. p. 1 .
This paper contains the first account of the autographic torsion machine.
' Note on Resistance of Materials,' 1875 , p . 334 ; ‘ Strength of Materials
deduced from Strain Diagrams,' vol. v . p. 9 ; “ Resistance of Materials as
affected by Flow ,' vol. v . p . 199 ; ‘ New Method of Detecting Overstrain ,'
1878, vol . vii. p. 53. It may be pointed out that the regression of the
stress-strain curve at the yield point (see § 30) appears to have been first
shown in some of the diagrams in these papers of Thurston).
230
TESTING OF MATERIALS OF CONSTRUCTION
used to resist twisting.
Hence it is with some reserva
tion that assent can be given to Professor Thurston's
claim , that the machine is capable of revealing charac
teristic properties upon which to base sound practical
judgment as to the relative usefulness of materials for
the various purposes for which they may be required,
and under the different conditions of their production or
manufacture.
The test bar for this machine is a small
cylindrical bar ] inch to
inch in diameter,with square
ends. It is placed in a pair of jaws, one connected
with a heavily weighted pendulum , the other with a
worm and wheel. By driving the screw -gearing one
end of the specimen is rotated, and the twisting moment
is balanced by the weighted pendulum , acting at the
other end and is measured by the sine of the angle
through which the pendulum is moved .
A drum covered with a sheet of specially ruled
section paper is fixed to the worm-wheel shackle, and a
pencil attached to the pendulum turns with it. Hence,
the pencil traces on the drum a circumferential line pro
portional to the difference of motion at the two ends, or
to the twist of the speciinen . The pencil has another
movement parallel to the axis of the test bar ; as it
rotates with the pendulum, it is forced by a guide curve
to move a distance axially proportional to the twisting
moment ( sine of angle of inclination of pendulum ).
Hence, the pencil draws a stress-strain curve , the
abscissæ of which are the strains or angles of twist,
and the ordinates the twisting moments. Professor
AUTOGRAPHIC RECORDING APPARATUS
231
Thurston's machine is simple and ingenious, and its
use enabled him to detect directly that when a load is
applied, removed, and reapplied, the yield point is
found to be raised . But the machine has defects.
It is
wrong in principle to take the register of the strains
from the clips which hold the specimen. The crushing
of the ends gets registered as part of the deformation .
The arrangements do not secure perfectly that there is
no longitudinal or bending stress .
The friction of the
pendulum journal and the momentum of the pendulum
may both influence the results..
Professor Ewing's Experiments.- In 1880 Professor
Ewing made some experiments in Japan on the stress
strain curve for small wires . The wire was loaded by
filling a bucket with water .
A pencil attached to the
wire marked a line on a sheet of paper, which at the
same time moved transversely a distance proportional
to the load. The paper was moved by a string attached
to a float. The diagrams are very similar to the earlier
diagrams of Thurston.
99. The Polmcyer Autographic Apparatus. --- In 1882
the author saw at Dortmund a 50 -ton tension testing
machine, designed by Professor Polmeyer expressly
for autographic testing. It is a pendulum machine, with
a very long pendulum , having a ton weight at the end.
As one end of the specimen is pulled by a hydraulic
press , the other pulls on the pendulum, and the stress is
related to the angular rise of the pendulum . It is easy
Proc. Royal Society , 1880.
.
232
TESTING OF MATERIALS OF CONSTRUCTION
to see that a paper connected by one wire to the
pendulum , and a pencil connected by another wire to
the specimen, can be so arranged as to draw a true
autographic diagram .
Fairbanks'Autographic Apparatus. — In Mr. Abbott's
little treatise on Testing Machines there is described in
considerable detail a large testing machine, constructed
by Messrs.Fairbanks in America ,with an autographic
apparatus attached . The machine is a 100- ton machine,
and adapted for tension, compression, bending, and
other tests .
It is a compound -lever machine, in which
the final lever is a steelyard with travelling weight or
counterpoise.
Now to effect the adjustment of the counterpoise
on the steelyard to the stress on the specimen, a very
ingenious electrical arrangement is used . As the steel
yard rises or falls against its stops it completes an
electric circuit,which starts an electro-magnetic engine,
which moves the poise. Thus, if the lever rises , showing
that the stress exceeds the load applied by thesteelyard,
the electro -magnetic engine moves outwards the counter
poise till , balance being restored, the circuit is broken .
Geared to the arrangements for moving the counterpoise
is a drum or cylinder on which the record is made, and
the rotation of this drum is therefore exactly proportional
to the movement of the counterpoise on the steelyard .
Consequently, a pencil held fixed over the drum would
trace a circumferential line the length of which is pro
portional to the load on the specimen .
AUTOGRAPIIIC RECORDING APPARATUS
233
The pencil, however, has a second motion parallel
to the axis of the cylinder , derived from a thin flexible
steel tape attached to two clips on the specimen . This
is led off over pulleys, so as to move the pencil axially
along the cylinder. The defect of the arrangement is
that the elongation is not magnified, and the tape is so
long that it is hardly possible it can give the pencil a
quite true movement free from any error due to slack
in the tape. It is stated, however, that the error does
exceed ido inch .
100. Mr. Wickstecd's Autographic Apparatus . - This
is an apparatus fitted to the Buckton testing machine,
shown in Fig. 55 , p . 134. The motion of the pencil
which indicates the load is derived from the fluid
pres
sure in the hydraulic press , and not from the weighing
apparatus. A pipe from the hydraulic press F is led
to a small cylinder like an indicator cylinder, with a
This piston is controlled
by a strong spring, 15 inches long when unloaded ,
5 inches long when loaded with 22 cwt. , the full pres
sure on the piston when the pull of the machine is
50 tons. During a test, as the pull and consequently
the fluid pressure, increases, the spring is compressed ,
piston of 1 sq. in. in area.
and the pencil P moves horizontally along the recording
drum D. On the test bar s are two clips J J, and a
wire attached to weights resting on the lower clip is
carried over a pulley on the upper clip , and over the
links G, finally serving to rotate the recording drum D
by an amount proportional to the elongation. Hence,
234
TESTING OF MATERIALS OF CONSTRUCTION
the pencil having an axial motion proportional to the
load, and the drum a motion of rotation proportional to
the extension, a stress- strain diagram is described.
To eliminate the influence of the friction of the
small indicator piston , it is kept in rotation by the
pulleys shown at the end of the recording apparatus.
The friction at a high speed is small, and practically
the friction of the cup-leather of the small piston
appears to be neutralised by this rotation.
The object
of the link - work , G, is to eliminate the influence of
the motion of the test bar as a whole , due to the sway
of the lever or slipping in the clips. The arrangement
is perfectly correct in principle.
There is some practical convenience in taking the
load indication from the hydraulic press instead of the
weighing apparatus. But although the author believes
that practically correct diagrams of small size are
obtained by Mr. Wicksteed's apparatus, yet he has not
altered his opinion that it is faulty in principle to infer
the load from the pressure in the press cylinder, and
likely in unskilful hands to lead to errors.
The pressure in the hydraulic press is chiefly due to
the tension of the specimen, but a not unimportant part
of it is due to the unbalanced part of the counter -weight,
to the friction and inertia of the crosshead and slides ,
and to the cup -leather friction of the main ram . The
diagram can only have a uniform scale so far as these
additional pressures are proportional to the load on the
specimen. Further, the cup -leather friction acts upwards
AUTOGRAPIIIC RECORDING APPARATUS
235
or downwards according to the direction in which the
ram is moving, and therefore has a doubled effect on
the position of the pencil . Mr. Wicksteed determines
the scale of the diagrams by occasionally checking them
by the use of the lever. He has also found that for the
small diagrams taken, the scale is practically uniform , if
the ram is kept moving in one direction . Mr. Goodman
has added an electrical arrangement, by which a second
pencil marks the diagram as the jockey weight passes
each ton .
101. The Author's Autographic Apparatus. — In 1882,
when selecting a testing machine for Cooper's Hill Col
lege, the author perceived that Mr. Wicksteed's type of
testing machine, with a single jockey weight, moved by
a screw, lent itself very conveniently to the application
of autographic apparatus, and of autographic apparatus
of a very simple kind , which would not interfere with
the ordinary operations of testing. About that time the
author saw the Polmeyer machine, and was convinced
that, if only a small diagram was required , say, 5 or 6
inches square, the movement of the pencil corresponding
to the elongation could be perfectly well transmitted by
a thin wire. An apparatus on a somewhat large scale was
completed at Cooper's Hill in 1883, and subsequently,
at the Central Institute , in 1885 , the smaller apparatus
on the same principle which is shown in Fig. 106. The
chief merit of the apparatus is its extreme simplicity ,
while at the same time it is accurate in principle.
In the Buckton type of testing machine ( Plate II. )
236
TESTING OF MATERIALS OF CONSTRUCTION
FIG . 106.
a
B
A.
मA
Autographic
PР
Apparatus
C
w
C
S
the stress is weighed by a steelyard, on which there is
a travelling jockey weight weighing one ton . This is
driven by a large screw ; consequently , the rotations of
AUTOGRAPHIC RECORDING APPARATUS
237
the screw are exactly proportional to the movement
of the weight, and to the stress on the specimen . It
is from this screw that a vertical paper cylinder d is
driven. A small catgut belt drives a worm, acting on
a worm -wheel of 200 teeth on the paper cylinder .
As
the resistance of the paper cylinder is very small, the
motion given by the belt is quite accurate, and it has
this convenience , that by means of a stepped pulley a
several scales are available for the diagram . Neces sarily, the specimens vary in size and strength, and it
is extremely convenient to enlarge the load scale of
the diagram for small specimens, and diminish it for
large ones . The pencil p slides on guides parallel to
the axis of the paper, and it is connected to the speci
men by a very fine wire w, kept strained by a counter
weight e. The wire is so fine that a counter-weight of
2 or 3 ounces is quite sufficient to keep the wire taut,
and overcome the friction of the slides .
On the specimen s are two clips c c, the construc
tion of which is so arranged that they are perfectly rigid
in position on the bar, and which define exactly the
length in which the elongation is taken, and do not
become slack as the bar contracts .
It is extremely con
venient to magnify, more or less, the elongation, so as
to get a larger diagram .
The author has tried several
plans. That most generally convenient is very simple .
The thin wire is attached to the top clip, taken over a
pulley on the bottom clip, again over a pulley on the
top clip, and then horizontally to the guide pulley f on
238
TESTING OF MATERIALS OF CONSTRUCTION
the autographic apparatus.
In this way the extension
is exactly doubled.
At first it was feared that movements of the speci
men would affect the record of extension , and the author
adopted a plan of taking two wires from the specimen,
one neutralising any error in the motion of the other.
He has since found that, by properly placing the appa
ratus , and leading off the wire from the specimen parallel
to the knife- edge of the testing machine, no measurable
error is introduced due to motions of the specimen.
Parallel to the knife-edge the specimen has no
motion . It has a small vertical motion, due to variation
of position of lever, slipping in clips, &c. But the
greatest possible motion of this kind would not intro duce an error in the diagram of Töv inch .
102. Electric Semi- Automatic Recording Apparatus. —
All the ordinary forms of autographic apparatus fail to
register in any useful way the small strains within the
elastic limit.
The strains are indicated on the dia
grams, but on a scale too small to be measured . A
lever arrangement has been tried to magnify the exten
sions, but with a great magnification the difficulty and
error introduced render the arrangement worthless. It
occurred to the author that a totally different method
of registration would in some cases be very convenient.
A large recording drum is connected with the screw
of the jockey weight so as to turn circumferentially
a distance accurately proportional to the load on the
specimen. A pencil moves on a slide parallel to the
AUTOGRAPIIIC RECORDING APPARATUS
239
axis of the cylinder. To give motion to the pencil
there is an arrangement of electro -magnets and ratchet
With a commutator in hand the observer can
wheels.
send a signal which makes the pencil move a step
forwards or backwards at any moment .
Now suppose a test proceeding, and that by the
telescope mirror and scale the extensions are being
FIG. 107 .
Tonspor Se Inch
268
9
68
69
685
.67
167
66
68
.66
1.66
-66
4.65
68
-67
67 67
-67
185-765
65
166
166
.64
.64
Let
64
for
65
.65
6
-63
-63
63
.64
64
163
.62
62
163
-62
-63
J63
462
5
161
61
61
.62
F62
61
-CO
60
161
.60
59
61
.59
:59
59
.60
.60
3
.58
58 7:58
151 for
.57
게
1.58
158
.50-6
156
-56
55.57
-59
59
157
: 57
565
58
.57
56.5
J5
Ò
observed . If a signal is sent at each increase of ex
tension of, say , todo inch, a stepped figure will be
obtained , from which the extension at any moment and
240
TESTING OF MATERIALS OF CONSTRUCTION
the corresponding load can easily be read off. And the
record in this way is effected with great ease and
rapidity.
Fig. 107 shows one of the diagrams obtained , and
contains a record of more than 150 extensions, taken in
less than half an hour. Half the readings are taken
with an increasing load, the other half while the load
was being removed. The figure is about one-fourth
the actual size of the diagram , and the steps correspond
to zu'oy inch of extension .
The diagram is one of the
first taken in this way by students at the Central
Institute. It is not a particularly perfect diagram , but
it illustrates the kind of record obtained by this method .
103. Professor Kennedy's Autographic Apparatus.
An apparatus devised by Professor Kennedy and Mr.
A. G.Ashcroft is of a different kind .
The following
description is taken from Professor Kennedy's paper ::—
The apparatus cannot be said to be suitable for general
use, but for a laboratory, where it is in skilled hands,
and not subject to rough usage, Professor Kennedy
believes it to give more trustworthy diagrams than any
of the other forms yet devised.
It has also the advan
tage that it is wholly independent of either the poise or
the ram, or even any part of the framing of the testing
machine, and that its own parts are so light that the
diagram may be assumed to be free from any errors
due to inertia.
The test- piece a ( Fig. 108 ) is placed in
1 Proc. Inst. of Civil Engineers, vol. lxxxviii. p . 30.
drawing of the apparatus is given.
A detailed
241
AUTOGRAPIIIC RECORDING APPARATUS
the machine in series with a stronger bar b, called a
spring piece, and the two, which are connected directly
by a simple coupling, are pulled simultaneously, the
one through the other. The spring piece is of such
a material that its limit of elasticity occurs only at a
load greater than that which will break the test piece .
It must also be of material ascertained by previous ex
periment to be perfectly elastic, so that its extension is
strictly proportional to the pull on it, and therefore
to the pull on the test bar. By a simple arrangement
a very light pointer e is made to swing about an axis
FIG. 108 .
d
b
a
through an angle proportional to the extension of the
spring piece, and proportional, therefore, to the pull on
the test bar.
The end of this pointer touches a sheet
of smoked glass d , to which is given a travel — in its
own plane-- proportional to the extension of the test
piece, and in this way the diagram is drawn. After
the experiment the glass is varnished to fix the black ,
the necessary particulars are written on it with a
scribing point, and the whole is used as a negative ,
and multiplied by photography.'
Some of the diagrams taken with this apparatus are
shown in Fig. 28 , p. 67. It is a small and not serious
R
242
TESTING OF MATERIALS OF CONSTRUCTION
objection that the load ordinates are curved. The great
merit of the instrument is the very perfect registration
of the stress, free from errors due to any accidental
action of the machine.
Some particulars of a machine acting in a similar
way, and taking a very small diagram , which could
afterwards be magnified, were given by Herr Martens
in the correspondence which is appended to Professor
Kennedy's paper.
Elastic - strain Diagrams.-. The only apparatus for
drawing purely autographic diagrams of the strains
within the elastic limit is also devised by Professor
Kennedy. It acts on the same principle as the last
FIG . 109,
MY
TI
1
III
D
B
5000
1000
10,000
POUNDS
PER
O'INCH
apparatus, but the swinging pointer is placed on the
test piece and used to record its extensions. The frame
is carried by the test piece, and is moved by the poise -
weight of the testing machine.
Fig. 109 shows three elastic strain diagrams taken
by this apparatus for a piece of cast iron 0.75 inch in
243
AUTOGRAPHIC RECORDING APPARATUS
diameter and 10 inches long. The distance A B is the
set after the first loading.
There is a small further set,
B C, at the third loading. Exaggeration of extension,
150 to 1 .
104. Autographic Extensometers, recording Time and
Extension . — Many attempts have been made to study ex
perimentally the action of a travelling load on a structure
such as a bridge. In such cases the train which forins
the travelling load moves with uniform speed across
the structure, each member of which passes through a
cycle of changes of stress related to the position of
the moving load . If a diagram can be drawn with the
strains ( extensions or compressions ) as ordinates and
the time as abscisse, it is possible to infer the stresses
corresponding to each position of the moving load .
The first instrument of this kind was designed by Dr.
W. Frankel, and constructed by Oscar Leuner in
Dresden . )
Fig. 110 is a diagram of the instrument.
Two
clips C1 , C, are attached to the member of the structure
the strain of which is to be recorded .
Between these is
the tubular link attached to the clip C, at b, and acting
at the other end a on the unequal- armed lever ly . The
lever l is toothed at the edge and drives the lever la,
and this, in turn, gears with a small pinion on the
spindle of the drum D. The levers form a spur-wheel
train magnifying the extension 200 times, and the drum
D moves under the pencil P a distance proportional to
1 Civilingenieur, 1881 ; vol. xxvii. $ 250.
R 2
244
TESTING OF MATERIALS OF CONSTRUCTION
the strain .
The clock F at the same time moves the
pencil axially at a uniform speed, driving the pinion m
and rack n . Consequently, a diagram is obtained with
FIG . 110 .
n
771
F
D
2
Ca
SLU
1775
med:
С,
V
А
8 celuh
12
2
BICO
BRICOLAGE
abscissæ proportional to the time and ordinates pro
portional to the strain.
The most ingenious mechanical contrivance in Dr.
Frankel's instrument is that by which loss of time, or
backlash in the spur-wheel multiplying gear, is pre
vented. Each toothed driver consists of two parts,
connected by a spring only, which presses one part
AUTOGRAPHIC RECORDING APPARATUS
245
forwards and the other backwards against the two
faces of contiguous teeth of the driven wheel. There is
always contact, therefore, between driving and driven
teeth for motion in both directions, and any motion in
either direction is communicated instantly and without
loss of time.
Autographic Deflectometer of Askenasy. — This is a
small apparatus for drawing the deflection curve of a
beam during the passage of a load over it. A paper
recording- drum , moved by clockwork, is clamped on
the beam or bridge. An independently supported style
traces a curve on the drum . The style is on a vertical
rod, at any point of which it can be fixed, and this can
be clamped to a wooden beam supported independently
of the deflecting beam .
and deflection ordinates.
The curve has time abscissæ
246
TESTING OF MATERIALS OF CONSTRUCTION
CHAPTER VIII .
ELASTIC CONSTANTS FOR METALS .
105. THE accurate determination of the coefficients of
elasticity and limits of elasticity depends on the measure
ment of extremely small deformations. Some of the
practical difficulties of measurement have been discussed
in Chapter VI . These difficulties are not the only ones
in the path of the experimenter. For many materials
the elastic constants change with the amount of stress
applied and with every repetition of stress, and , to add
to the confusion, there is not complete agreement as to
the definition of the constants or the methods of deter
mining them.
The nature of the coefficients of elasticity has been
explained in Chapter I. Let it be proposed from
observations on a bar of cast iron to determine its co
efficient of direct elasticity. When a bar is subjected
to simple longitudinal stress, the coefficient of direct
elasticity E is the ratio of the stress p per unit of section
to the extension or compression l per unit of length .
That is, E = p /l. But the total extension of an inch of
bar I consists of two parts-- an clastic extension e,and a
plastic extension or set s.
If the bar is again strained ,
ELASTIC CONSTANTS FOR METALS
247
the set s will be smaller and the modulus of elasticity
p/l will be different. What is, then , the real coefficient
of elasticity ?
If a coefficient of elasticity E' = ple is calculated ,
values will be obtained which vary less with repetition
of loading than the values of E. In most cases, also, E'
will be more constant than E for different ranges of
stress .
Hence it is a temptation to an observer to get
rid of the sets, and to give values of the coefficient
of elasticity which are values of E ', not values of E.
Virtually this is often done ; and either the sets are
determined and deducted from the extension used in
calculating the coefficient of elasticity ,' or, what amounts
to the same thing, the bar is loaded once or twice nearly
up to its elastic limit before proceeding to measure the
extension used in calculating the coefficient of elas
ticity.
The following table contains Hodgkinson's results
for the tension and compression of long bars of cast
iron . These results on long bars are chosen because ,
although the methods of measurement were somewhat
crude and rough, they are free from any possible
objection arising out of complexity in the measuring
apparatus. It will be seen that both E and E' diminish
as the stress increases , but that E' varies much less than
E. The coefficients are in tons per sq. in. The next
table contains some results on bars of gun -barrel steel,
1 See Lanza's statement as to what is done at Watertown .
Mechanics, p. 419.
Applied
Total
3.685 •0788
4.607
5.530 •1203
5,694
5,480
5,257
4,968
5,262
4,898
4,677
4,262
·0066
• 030
·0106 1
01611
• 287
• 618
02411
4.703 1
• 136
5.644 1
• 448
6.603 1
• 859
·0793
2.765
5,879
5,525
0
· 037 0
• 576
2.821 •0613
inches
in
6.451 •1416
·0994
Total
0
· 183
120
c
sion
0
• 558
•0141
·0109
1
• 275
·1094
0
· 909
• 723
0
· 065 0
:0085
compres
Total
elastic
PRESSURE
• 365
·0023 0
·0005
120
s
inches
i, n
set
·0598 0
• 040
1.843 •0388
•0188
6,053
3.762 0
• 859
TStress
|,inotal
com
,
pression
7
120
5,775
р
0
· 018 •0373
'
E
1.881 •0391
E
tons
Coefficient per
.isq
n
6,269 9• 212
120
e
elasticity
coefficient
direct
of
Ordinary
6,067
s120
inches
extension
Total
elastic
-0006 0
• 180
1207
in
inches
extension
,in
,
set
Total
•0186
•9404
р
ton
pers
n
i.sq
,in
Stress
TESSION
.1Q
A
NREA
I
S
AND
5,947
5,549
6,066
6,071
5,467
6,080
5,516
5,560
6,116
6,059
5,701
5,611
6,039
'E
TESTING OF MATERIALS OF CONSTRUCTION
Coefficient
5,879
E
elasticity
coefficient
of
direct
Ordinary
LENGTH
FEET
10
RRESULTS
TO
EDUCED
,.CAST
BARS
NINE
M
ON
EAN
-IRON
EXPERIMENTS
HODGKINSON'S
248
249
ELASTIC CONSTANTS FOR METALS
made by the Committee on Steel, and which are chosen
for similar reasons . For wrought iron and steel the
set in the earlier part of the test is comparatively in
significant. Yet E' is more constant than E, even in
the earlier part of the test, and is nearly constant even
for stresses considerably beyond the elastic limit. For
wrought iron and steel E diminishes almost to zero as
the breaking weight is approached .
EXPERIMENTS OF STEEL COMMITTEE .
( Bars, 11 inch in diameter. Extensions and compressions in 10 feet.)
Stress , in
tons per
sq . in .
Total
extension ,
in feet
Elastic
Set, in
extension ,
feet
in feet
Ordinary
coefficient of
direct
Coefficient
elasticity
р
120 7
E
E'
0070
12,830
12,800
12,770
12,830
12,800
12,960
·0077
12,920
13,260
0087
12,750
12,740
12,600
11,900
13,030
13,140
13,090
13,400
13,300
13,480
13,570
13,770
13,690
13,620
13,480
120 e
120 s
TENSION
6.80
7.94
9.07
10.21
11:34
12:48
13.61
17.01
·0053
0062
0071
0079
0089
0098
·0108
0143
0001
0002
0002
.0003
0004
·0016
•0095
0104
0127
PRESSURE
6.92
10:38
13.84
15:28
16:15
17:31
18:46
·0047
·0078
•0105
• 0117
0125
·0138
0172
0001
0003
*0006
0007
0011
0035
.0047
· 0077
0102
0111
0118
0127
•0137
13,180
13,060
12,920
12,540
10,740
No doubt in most cases values of E are given as the
coefficient of elasticity, and it will be understood that
it is so in what follows.
But then materials like cast
iron and all the brasses and bronzes have no definite
coefficient of elasticity.
250
TESTING OF MATERIALS OF CONSTRUCTION
106. If in loading a bar the yield point is passed ,
the material is altered , and generally this is shown in
an alteration of the coefficient. With a rest of a day
or more after loading the bar partially recovers, so
that the alteration of the coefficient is less . The follow
ing table gives some results from Bauschinger’s paper
on the Change of the Elastic Limit ' : - 1
COEFFICIENT OF DIRECT ELASTICITY IN SUCCESSIVE LOADINGS OF THE
SAME BAR, IN TONS PER SQUARE INCH .
First
Second
Third
Fourth
loading
loading
loading
loading
Material
Bars unloaded and relnaded immediately .
Weld iron .
12,470
12,640
13,080
13,080
13,960
14,460
Ingot iron
>>
Copper
7,436
Bronze
5,372
12,360
14,060
3
14,170
13,370
7,702
7,214
5,683
5,575
12,300
11,930
13,610
12,600 2
7,042
Bars unloaded and reloaded after a pause varying from 3 to 80 hours.
Weld iron
.
‫ול‬
1
.
Ingot iron
92
.
92
Bessemer steel
Copper
:)
Bronze
.
12,970
12,920
13,040
13,080
12,680
12,860
13,270
12,800
12,790
14,240
14,530
14,500
13,330
7,1503
7,188 3
5,503
12,780
14,270
14,400
14,180
13,200
7,278
7,494
5,499
12,590
12,720
12,610
12,600
12,720
12,760
14,240
14,390
14,150
12,950
7,144
7,176
5,575
12,810
12,9002
13,210 2
14,470
12,580
13,880 2
14,1002
13,460
7,036
6,910
In these experiments the measurements of exten
sions were probably as perfect as any such measure
ments which have been made.
The differences of the
2 Vibrated after each loading.
? Civilingenieur, 1881 .
3 Yield point not reached in first loading.
251
ELASTIC CONSTANTS FOR METALS
coefficients for the same bar may seem not very large,
but they are large compared with the variation of the
coefficient in different qualities of the same material, and ,
indeed, in some cases exceed 10 per cent.
With iron the coefficient generally diminishes with
repetition of loading if there is no pause. It diminishes
less if there is a pause. With bronze the coefficient
increases with repetition if there is no pause, and is
practically constant if there is a pause between the
loadings. With copper the coefficient diminishes in either
case .
107. The following are some of the best values of
the modulus of elasticity which have been obtained .
Kupffer's values were obtained by bending and trans
verse vibrations, and represent values of the coefficient
for small stresses :
COEFFICIENT OF DIRECT ELASTICITY ( KUPFFER ).
Iron plate, in direction of rolling
>>
across
72
>>
Rolled English band iron
>
bar iron
Forged Swedish
+
Soft cast steel .
.
Steel adapted for files
.
Density
Coefficient E,
in tons per sq.in.
7.676
7.678
7.643
7.641
7.832
7.842
7.819
11,200
12,160
12,710
12,850
13,560
13,540
13,440
The following table gives a summary of the values
of the coefficient, determined by Knut Styffe, for iron
and steel. According to these experiments the co
efficient increases slightly by annealing . Styffe also
1 Iron and Steel. Styffe. Translated by Sandberg, p. 147.
1
252
TESTING OF MATERIALS OF CONSTRUCTION
made experiments on the change of the coefficient with
change of temperature . He found that it decreased
about 0.03 per cent. for each degree rise of temperature
( Centigrade) . After a permanent stretching of the bar
it diminished by 4 to 9 per cent.
COEFFICIENT OF DIRECT ELASTICITY OF IRON AND STEEL FROM
TENSION EXPERIMENTS .
Coefficient E, in tons per sq. in.
Probable
percentage
1
of carbon
Hammered Bessemer steel
97
72
iron
19
>>
) ,
Rolled cast steel
Krupp
.
Rolled puddled steel
>
Lowmoor iron
Dudley
>>
.
+
Motala
Surahammar iron
Charcoal iron (Åryd)
( Hallstahammar)
97
9
>
19
1.35
1.26
1:05
0:1
0:15
1.22
0.61
0.66
0:56
0.2
0:09
0.09
0.05
0.2
0:14
0.2
0:1
0 :1
0.07
0.07
After heating to
Initially
slight redness
13,450
13,660
14,430
15,290
13,940
14,000
14,220
13,640
14,060
15,440
14,340
13,540
13,360
14,280
12,680
12,260
13,510
13,740
13,200
13,880
13,610
11,960
12,410
13,720
1
13,050
12,940
13,760
13,760
108. The following table ? gives values for steel,
obtained by Bauschinger, and the tables are interesting
as giving the coefficient for bending, tension, and
pressure. The coefficient of rigidity was also deter
mined by experiments on torsion . From the values of
1 Reduced from tables in Civilingenieur , 1879.
253
ELASTIC CONSTANTS FOR METALS
E and G we can deduce values of Poisson's ratio m.
( See S $ 4 and 10. )
BESSEMER STEEL FROM TERNITZ ,
COEFFICIENT OF ELASTICITY.
Coefficient of direct elasticity,
Percent
age of
carbon
Coefficient of
rigidity, C
E
Meer -1
From
tension
From
pressure
bending
tests
tests
tests
13,780
14,300
13,690
16,540
14,640
16,140
14,290
15,940
14,480
14,440
14,100
14,640
Froin
13,720
14,480
14,980
13,660
13,880
13,820
20
Mean
From torsion
tests
13,020 | 14,730
13,090 14,220
12,900 14,480
13,080
13,840
14,350 15,040
13,460 14,480
14,730 14,160
32
0.19
0:46
0:54
0:57
0.66
0.78
0.80
0.87
0.96
E
•
.30
33
:30
: 36
5,575
5,420
5,450
5,320
5,520
5,405
5,670
13,590 13,900
5,400
13,080 13,970
5,560
• 34
•25
.29
•26
0.305
Mean
I
(?)
14,740
13,960
14,800
14,500
0.29
5,625
SIEMENS -MARTIN STEEL FROM NEUBERG -MARIAZELL.
Coefficient of direct elasticity, E
Coefficient
Degree
of rigidity ,
of
hardness
7
6
5
From tension
From bending
tests
tests
13,450
13,090
13,370
13,390
13,620
13,520
13,340
13,480
13,430
13,390
Mean
C
13,460
13,210
13,400
13,400
13,340
5,470
5,260
5,295
5,401
5,150
Mean
E
7
1
=
20
-25
25
.27
.24
.30
0.262
The following values are from experiments at
Watertown Arsenal, and are, it is believed , values
obtained after deducting the permanent set. They are
values of E ' therefore.
1 Bessemer steel from Teschen .
254
TESTING OF MATERIALS OF CONSTRUCTION
Coefficient of elasticity
Wrought iron
For 10 rolled bars, single refined
For 9
For 10
For 9
>
double refined .
For 10 Phoenix "eye-bars
Highest
Lowest
Mean
13,790
13,100
15,200
13,105
12,040
12,310
12,540
12,530
12,335
11,410
9,996
13,230
12,950
12,680
11,150
13,345
12,070
For 6 steel
13,510
>>
Thurston has obtained from bending experiments
the following values for the bronzes .
The values given
are values of E for small stresses, the coefficient diminish
ing with increase of stress just as in cast iron.
A few
other values are added :
E
Cast copper
6,240 to 4,555
Cast zinc
Cast tin
Brasses
Bronzes
Lead
Thurston .
.
3,118
3,006
5,130 to 6,580
.
0
5,935 to 6,840
>
> >
> >
.
)
Wertheim .
1,116
0
Gold
5,130
10,710
Platinum wire
Rolled brass
Copper , hard -drawn
.
annealed
Steel castings
5,800
5,580
5,133
Bauschinger.
Wertheim .
Phosphor bronze .
.
6,704 to 6,536
5,555 to 6,060
Unwin .
.
4,762 to 5,376
5,950
09
.
.
22
.
)
.
8,400 to 14,000
Aluminium bronze
Delta metal .
Gun- metal
.
>>
109. The Elastic Limit.— The difficulty of determin
ing definitely the elastic limit is even greater than that
of determining the coefficient of elasticity.
The earlier
writers took the elastic limit to be the stress at which a
noticeable permanent set was first observed. But then
the stress which is fixed on as the elastic limit depends
ELASTIC CONSTANTS FOR METALS
255
on the delicacy of the measuring instruments used .
In proportion as delicacy of measurement increased , it
began to be apparent that for most materials ( for all,
perhaps , except very hard steel or glass ) some set occurs
with the smallest stresses. To avoid this difficulty, and
get a definite measure of relative elasticity of different
materials, Wertheim proposed the arbitrary rule of fix
ing the elastic limit at that stress at which the total
permanent set amounted to podoth of the length of
the bar.
Apart from the purely arbitrary nature of
this rule, it makes the determination of the elastic limit
extremely difficult, and it leaves out of consideration the
fact that part of the apparent set is not really permanent ,
but disappears slowly during a rest. Bauschinger has
shown that for all ordinary materials Wertheim's elastic
limit is considerably above the point at which propor
tionality of stress and strain sensibly ceases.
In the
stress and strain curve of iron and steel the curve bends
somewhat sharply for stresses near those at which marked
Thalén proposed to take for the
elastic limit the point of maximum curvature. This
permanent set occurs.
makes the elastic limit depend on the scales to which
the stresses and extensions are plotted , and gives a point
even further from the limit of proportionality than
Wertheim’s . Knut Styffe, attempted to fix a definite
elastic limit, depending on the rate of increase of set as
dependent on the time rate of loading . This, again,
gives a point far above the limit of proportionality of
stress and strain .
· Poggendorff's Annalen, Ergänzungsband II.
256
TESTING OF MATERIALS OF CONSTRUCTION
In commercial testing of iron and steel some rough
estimate of the elastic limit is usually made. Thus , it
has been proposed to take the elastic limit at the stress
at which peeling of the skin is first visible ( Styffe, p.
36 ) , or at the stress at which the testing machine lever
drops (Kennedy ) , or at the stress at which a rough
measurement of the elongation by compasses is first
possible ( Lanza ). All these measures are extremely
rough ,and what they really determine is the yield point,
not the elastic limit.
In almost all tables what is given
as the elastic limit is the yield point, and this may differ
from the limit of proportionality to any extent. More
over, for materials other than wrought iron and steel
there is no definite yield point.
Where there is a yield
point it is best determined from an autographic diagram .
110. The only definition which agrees with the
theoretical conception of an elastic limit, and which is
practically available in testing, is that which makes the
elastic limit to be the stress at which proportionality
between the stresses and strains first visibly ceases when
measurements of considerable delicacy are being made.
Bauschinger has re-adopted this definition, and it is to
his observations chiefly that we must look for any know
ledge of the elastic limit thus defined.
The following measurements of the extension of a
piece of iron from old Hammersmith Bridge will show
how the limit of proportionality can be determined . In
this case the limit in successive loadings, none of which
reached much beyond the elastic limit, slowly rises.
257
ELASTIC CONSTANTS FOR METALS
Link from old Hammersmith Bridge, received froin
B. Baker, Esq .
This was planed all over to get surfaces for accurate
measurement , and its section was about 12 sq . in . Ex
tensions for each ton , taken with mirror apparatus : -Distance of gauge points, 7.94 inches.
Extensions per ton in 1o00ooths of an inch
Load in tons
per sq . in,
First loading
58
56
58
58
57
58
58 E. L.
61
60
7
58
57
59 E. L.
60
60
8
9
10
11
12
Set, load re
moved
62
>>
}
+ 13
1 to 7
1 to 8
79
79
1 to 9
Mean
58
56
58
58
58
58
58
58
58 E. L.
60
59
58 E. L.
60
63
75
1st loading, 1 to 7 tons
2nd
3rd
4th
Fourth loading
54
56
58
58
58
1
57
58
55
5
6
Second loading Third loading
-2
+2
+ 32
Total extension
Mean extension
per ton
0.003437
0.003449
0.003996
0.004619
0.000573
0.000575
0.000571
0.000577
0.000574
Coefficient of elasticity, 7.94/ .000574 = 13,830 .
111. So long as the limit of proportionality is not
exceeded , the value of the coefficient of elasticity in
ordinary metals is tolerably constant in successive load
ings . The following are extensions in successive load
ings of two pieces of Hammersmith Bridge links :
S
258
TESTING OF MATERIALS OF CONSTRUCTION
Extensions for six tons
1
First piece
Second piece
00344
00345
·00342
00338
00346
00343
·00347
00339
1st loading
2nd
3rd
-
> >
>
4th
5th
6th
7th
> )
99
Second piece,
after threc days
00341
00342
00340
·00343
00342
00344
00343
If, however, the yield point is passed, the limit of
elasticity very sensibly alters, as is shown in the following
results deduced from Bauschinger's tables. A plotting
of some of these is given in Fig. 40, p . 102 .
ELASTIC LIMIT, IN TONS PER SQ. IN. , IN BARS LOADED UP TO THE
YIELD POINT .
Original
state. Second loading Third loading Fourth loading
First loading
Material
Bars loaded , unloaded, and reloaded immediately
Weld iron
Ingot iron
+
8.98
15.78
6:41
16.91
2:58
3.59
4:06
1
2.45 2
3:43
Copper
Bronze .
6.66
4:01
6:57
3.92
6.90
4.12
6.77
5.11
4.13
Bars loaded , unloaded, and reloaded after a pause of 24 to 80 hours
Weld iron
7
:)
‫ܕ ܕ‬
Ingot iron
Bessemersteel
8.98
10.34
10.22
10:30
15.09
11.60
Copper .
1.14 2
2.61 2
Bronze .
2.50
12.94
12.29
14:22
(6.57) ?
5.13
19.32
3.27
3.59
4:07
15.84
17.45
15.78
18.80
7.92
( 3.91 ) 1
3.61
4.62
3.82
17.45
20.35
18.94
(6.81) 1
6.83
6.69
5.14
6.87
Bars loaded, unloaded, subjected to vibration , and reloaded after a pause
Weld iron
29
Ingot iron
.
12.38
8.98
15.15
16.48
11.93
11.93
5.18
19:56
14.89
12.13
5.26
17:10
11:14
8.28
5.39
17.60
)
? No pause between loadings.
2 Yield point not reached.
259
CHAPTER IX .
CAST IRON .
112. Down to a recent period the ferrous materials
used in construction could be divided into three groups,
marked equally by difference of manufacture, of chemical
composition, and of mechanical properties. Cast iron ,
the product of the blast furnace ; wrought iron , the
product of the puddling forge, and steel , produced from
wrought iron by cementation , had characteristics so
marked that it mattered little which of their differences
was taken as a basis of classification .
As their content
of carbon seemed essentially connected with their pro
perties, that was generally selected as a means of
discrimination .
As to cast iron no difficulty arises ; both its method
of production , its properties, and its engineering uses
leave it in a class apart. It is otherwise with wrought
iron and steel.
Since the development of the Bessemer
essentially new
material has been introduced, which is commonly and
commercially termed steel, but which differs from the
and Siemens -Martin processes an
S 2
260
TESTING OF MATERIALS OF CONSTRUCTION
older material of that name.
The plates and bars of
so -called steel, which are superseding in construction
the old wrought iron, contain carbon, but in a quantity
varying without break, in different cases, from a percent
age as small as that in wrought iron to a percentage as
high as that in cementation steel . Such plates vary in
tenacity from that of wrought iron to a tenacity at least
double that of wrought iron. Lastly, by far the larger
part of this new material has not the characteristic pro
perty of the older steels of hardening when suddenly
cooled.
There is, however, a difference between wrought
iron and the new material which is replacing it im
portant enough to justify a difference of classification .
Wrought iron, and cementation steel as made from
wrought iron , have been in the condition in the puddler's
forge of granular or spongy masses bathed with liquid
slag. This slag is never entirely got rid of, and remains
in the forged material, not in great quantity indeed,
but so distributed as to give rise to a visible structure.
Bessemer, Siemens -Martin , and crucible steel , on the
other hand , have all been fused and more perfectly
cleared of mechanically mixed impurity. They have,
when rolled, a homogeneousness and absence of grain
which is definite and important.
If the difference
between puddled and cast material is recognised it will
be found that there are two parallel series of products ,
:
first clearly arranged by M. Greiner, of Seraing :
261
CAST IRON
PERCENTAGE OF CARBON,
0.0 to 0 ·15 1 0 ·15 to 0:45 | 0:45 to 0.55 | 0.55 to 1.5
SERIES OF THE IRONS,
Ordinary
Granular
iron
iron
Puddled
steel
Cemented
steel
SERIES OF THE STEELS .
Extra soft
steel
1
Soft
steel
1
Half-soft
steel
Hard
steel
This classification ignores the property of tempering
as a mark of distinction between iron and steel, which
is in some respects inconvenient. Hence in Germany
it is becoming common to class one series as weld metal,
the other as ingot metal. Weld iron and ingot iron
are those materials which will not temper ; weld steel
and ingot steel those which harden when suddenly
cooled .
113. Constituents of Cast Iron .-- Cast iron consists
of iron mixed or combined with carbon , silicon , man
ganese, sulphur, and phosphorus. Popularly, and
with partial truth, the carbon is regarded as chiefly
determining its characteristics. The carbon exists in
cast iron either combined with the iron or mixed with
it in the form of graphite. The greyer irons contain
most graphitic carbon, and are weaker, more fusible, and
softer than whiter iron. The white iron contains most
combined carbon ; but the other constituents have an
influence on the mechanical properties . The composition
of cast iron varies within the following limits ,if extremo
qualities, unsuited for foundry use, are excluded :
262
TESTING OF MATERIALS OF CONSTRUCTION
Per cent.
Combined carbon
0.15 to 1.25
1.85
3.25
Graphite
Silicon
Per cent.
2.0
to 4.5
0.15
7)
5.0
0.5
1 :3
9 ;
95.0
>
Sulphur
Phosphorus
Manganese
.
.
1
.
C
Iron
.
0.0
00
0.0
. 90.0
1 :5
Silicon tends to hinder the coinbination of carbon
with the iron, and to render it greyer . Manganese
appears to have a reverse effect.
Lately, attention has been paid to the influence of
silicon , and in some cases silicon is now added to cast
iron to improve its working properties. Ferro -silicon,
a cast iron with 10 per cent. of silicon , is used to mix
with other cast iron to render it greyer, stronger, and
more suitable for foundry purposes. The softest iron
used in the foundry has about 0:15 per cent. of com
bined carbon . With 1 per cent. the transverse strength
is greatest ; with more the crushing strength increases,
but the tenacity and transverse strength diminish . The
amount of graphitic carbon has less influence. The
silicon , when it does not exceed 31 per cent. , appears
to be advantageous in securing a soft, grey , strong iron .
Manganese in small quantity appears to be advantageous,
but when it exceeds 1 per cent. the iron becomes white,
and weak except for crushing. Sulphur should not
1 See papers by Mr. Thomas Turner : ' On the Influence of Silicon on
the Properties of Cast Iron, ' Journal of Chemical Society, August, 1885 ;
December, 1885 ; and March, 1886 . ‘ On the Influence of Remelting, '
ibid. , July , 1886 . " The Constituents of Cast Iron, ' Journal of the Iron
and Steel Institute. See also a paper by Ferd. Gauthier, of Paris, " On
Silicon in Foundry Iron ,' Journal o Iron and Steel Institute, 1886.
263
CAST IRON
exceed 0.15 per cent. Phosphorus in small quantity
renders the iron fluid , but with much phosphorus the
metal is brittle.
Remelting cast iron improves its
strength, but if the remelting is repeated too long the
tensile and transverse strength suffer, though the
crushing strength and hardness increase. This change
of properties is connected with a change of the iron
from grey to white by increase of combined carbon
and decrease of silicon . The following analyses, by
M. Gauthier, show the kind of change which occurs in
remelting :
Graphite
本
Combined carbon
Silicon .
.
.
Fourth
Sixth
Original pig
melting
melting
2.73
0.66
2:42
2.54
0.80
1.88
2.08
1.28
1:16
In Mr. Turner's very valuable paper ( Trans. Iron
and Steel Institute,' 1885 ) an attempt is made, from an
examination of all existing data, to determine the best
composition of cast iron to obtain certain definite quali
ties. From this the following table of percentages is
compiled :
Greatest softness
.
.
Combined
Graphitic
carbon
carbon
0.15
3:1
0.50
2.8
hardness .
general strength
stiffness .
>>
tensile strength
crushing strength
1
|
22
over 1.0
under 2.6
Silicon
2.5
under 0.8
1:42
1 :0
1.8
about 0.8
TESTING OF MATERIALS OF CONSTRUCTION
264
The density varies with the composition in the
following way :
Wcight of a
Material
Dark grey foundry iron
Grey
.
‫و‬
cubic foot, in lbs.
6.80
425
450
458
474
7.20
9
Mottled
White iron
Density
7.35
7.60
The specific heat is 0.140 for grey iron, and 0.127
for white iron .
Cast iron melts at about 2,732. Fahr.
114. Mechanical Properties of Cast Iron.— Theelastic
properties of cast iron have already been discussed. In
tension and compression tests there is strictly no range
of stress for which the stresses and strains are propor
tional , and there is no fixed coefficient of elasticity or
elastic limit.
It has, however , already been shown that
the extensions and compressions are nearly the same
for equal stresses ( $ 26 ) .
Mr. Hodgkinson found that the relation of stress and
strain in cast iron was given very nearly by the follow
ing equations. Let p be the stress in tons per sq. in . ,
e the extension, and c the compression per unit of length .
Then
p = 6,220 €c – 1,298,000 e 2
5,773 C - 233,500 ca.
The author has found the following inverse relations
still more exact :
c = 1.503 p3 x 10-6 + 1.685 p * 10-4
c = 9 • 66 på x 10-8 + 1.782 p
10-4.
265
CAST IRON
These are from experiments on very long bars. For
8 - inch bars
e = 0.39 p8 x 10-6 + 1.62 p * 10-4.
The following table gives a few measurements of
extension in short cast-iron bars .
The cast iron was
the ordinary mixture of a good foundry :
EXTENSIONS OF CAST- IRON BARS .
(Extensions in 8 inches, measured by touch inicrometer. Bars screwed at ends
and fixed in nuts with spherical seatings.)
Diam . 1.0005
Load in tons
Area
• 7862
1.005
• 7862
999
• 7832
1.000
• 7854
999
• 7832
.993
• 7743
Extensions in 8 inches, in inches
2.5
4.5
5.5
6.5
7.5
8.5
9.5
0043
.0073
0093
• 0114
0139
* 0168
· 0215
0036
0069
0087
0107
0132
· 0034
0062
· 0080
0105
0134
· 0037
·0069
0089
0112
0142
·0039
· 0074
0096
• 0116
0147
0034
• 0061
0083
0104
0131
Extensions per ton in 8 inches, in inches
2 :5
4.5
5.5
6.5
7.5
8.5
9.5
·00172
00162
-00169
00175
·00185
·00196
00226
00144
00153
·00158
· 00165
00176
00136
00138
00145
· 00162
·00178
00148
·00153
·00162
00172
·00189
14.37
13.87
13.04
00156
00175
·00178
00196
00136
· 00136
00151
· 00100
· 00175
14.21
13.90
· 00165
Breaking
weight, in
12.94
tons per sq. in.
115. Ultimate Tensile Strength of Cast Iron.— Tensile
tests give much the best indication of the quality of cast
iron for structural purposes. The crushing strength is
greatest in qualities of iron quite unsuitable for foundry
use , and the transverse strength depends in part on the
crushing strength .
266
TESTING OF MATERIALS OF CONSTRUCTION
In making and in comparing tensile tests the follow
ing points must be kept in mind . A few not entirely
satisfactory experiments show that in small castings the
strength varies a good deal with the size, the smaller
castings being stronger. Hodgkinson found test bars
of 1 , 2 , and 3 sq. ins. section to have tenacities propor
tional to 100, 80 , and 77.
The form of the test bar
has less influence. Hodgkinson found that bars of
cruciform section were about 1 per cent. stronger than
bars with circular or rectangular sections of the same
Tensile tests are most commonly made on rough
bars with the skin on, and there is a popular impression
area .
that it weakens a bar to take off the skin.
This is
almost certainly erroneous, and, as accurate measure
ments cannot be made on a rough bar, the test bars
ought to be turned . Tensile tests should be made with
shackles having spherical seats , as cast iron is greatly
weakened by non -axiality of the stress .
In very careful
tests the test bars should be cast in one with the work
for which the cast iron is used , and not separately .
They can be broken off, and turned to the required
form .
The short table on the following page gives a sum
mary of the most trustworthy results of tensile tests.
Mr. Turner attributes the higher tenacity observed
in some recent experiments to distinct improvement of
the metal, in consequence of more careful selection and
greater knowledge of the properties of the iron . He
states that a contract has been carried out in which a
Wade
3
6
Rosebank23
Foundry
4
6
53
-
Unwin
3 ner
Tur
Wade
4
Woolwich
bairn
Fairkinson
and
Hodg
81
Fair
and kinson
Hodg
Desormes
and
Minard
tests
2
4
153
0.5
20:55
18.2
475
4.9
15.7
7:19
Mean
Lowest
Highest
tons
,in
Tenacity
M
4 ean
of
best
specimens
.ten
13.7
15:31
9:12
13.71
:4
10
6.83
9.766.00
7:37
9.08
5.09
.sq
n
iper
10.5
Selected
good
iron
.as
0.75
1:0
t43o
t4
1o
0.23
13
0.5
to
i. ns
sq
of
Section
bars
in
2nd
2nd
2nd
2nd
2nd
and
3rd
Turned
Rough
Condition
Probable
No.
of
test
fusion
of
bars
Chem
.S,o1885.
JRough
fourn
“.' oc
for
Metal
on
“ eport
R1856.
for
Metal
on
R1856.
“ eport
RRough
.Iron
App
eport
“'on
1849.
ARough
.R
.'V
ssoc
ep
I
'Brit
1837.
1815.
RLove
:"ésistance
de
AI1887
,'' ndustries
pril
experimental
series
test
varying
proportion
,wSpecial
ith
.bars
silicon
of
obtained
result
H.* ighest
S.? elected
as
bad
iron
Cannon
Cannon
?
1858
of
Report
1856.
Fonte
la
-
bairn
No.
Experimenterof
TENACITY
OF
.
IRON
CAST
CAST IRON
267
268
TESTING OF MATERIALS OF CONSTRUCTION
e,and
minimum tenacity of 12 tons was stipulated for, and
only Cleveland iron was used.
Some qualities of iron are greatly improved by re
melting or by being kept long in fusion. The follow
ing results were obtained by Major Wade :
Pig
Fusion .
1st
Tenacity in tons per sq. in.
2nd
3rd
4th
5th
9:32 11:06
. 5 to 6} 9.32
11.06 11.96 12:45
116. Crushing Strength of Cast Iron . — Hodgkinson
used for compressive tests small cylinders and square
and triangular prisms, having heights equal to from one
to three times the transverse dimensions .
sheet of lead on the faces of the prisms.
placed a
.ItHeis not
clear
that this may not have diminished the strength . The
most common form of fracture is shearing at an oblique
plane making an angle of about 56º with the axis .
The crushing resistance is much increased if the
height is so decreased that the plane of least resistance
to shear cuts the faces at which the pressure is applied..
The following results were obtained by Hodgkinson on
cylinders į inch in diameter :
Height of cylinder, in ins.
Crushing strength, in
3
1
를
Do
69.3 63.5 60.0
tons per sq . in .
$
55.0
11
2
33
3 53.3 49•6 344
๕๖๐ ลง
533 53 :3 49.6 34 :4
4
The strength is pretty uniform if the height is between
one and three diameters .
117. Transverse Strength of Cast Iron . — Tests by
cross -breaking are so easily made that this kind of test
has been very generally adopted as the commercial test
Woolwich
Fairbairn
Turner
Wade
Form
of
test
piece
2
3
Cylinders 0.6
Cylinders
0.75
2
1to
31to
dimen
sions
,
inch
in es
Cylinders
Cylinders 23
to
1/2
Hodgkinson and
prisms
Authority
Transverse
11
273
81
tests
Width
of
No.
Height
Crushing
strength
in
40.6
S.percentage
1 eries
of
test
bars
,wspecial
ith
varying
silicon
tion
1, 858ort
Rep
1
H.after
2 ighest
result
repeated
remeltings
2 .9
95
34.11
44.6
74.5
92.5
19.8
38.5
7:
24
53.8
62.5
48.0
36.5
64.9
Lowest
Highest Mean
tons
.
per in
.sq
.
IRON
CAST
OF
RESISTANCE
CRUSHING
885
1SChem
ourn
J.'o• foc
1oApp
,'Iron
.C
nom
· f849
1RABrit
837
..'vVssoc
I
ep
1
I
Construc
MThurston
of
. aterials
CAST IRON
269
-
1
‫رظانم‬
1
270
TESTING OF MATERIALS OF CONSTRUCTION
for cast iron .
Square bars of 1 " x 1" cross section , or
more commonly of 2" x 1" cross section, are cast, and
these are placed on supports and loaded at the centre.
The distance between supports is most commonly 3 feet.
The ordinary formula for cross- breaking, which ,
however, is an empirical expression when thus used, is
M = f Z,
where M is the bending moment, Z the modulus of the
section, and f the coefficient of bending strength . For
a bar of rectangular section, loaded at the centre, this
becomes
W = ff bd
2
2
1
where W is the centre breaking weight in tons of a
bar of breadth b, depth d, and length l in inches ; f is
the coefficient of bending strength, which varies with the
quality of the iron and with the form of the section .
Even when the section is rectangular the propor
tions of the section affect the coefficient, and for bars of
the same proportions the coefficient is lower as the sec
tion is larger. The values of the coefficient,as given
in the table on next page, have been calculated from
comparable series of experiments .
It will be seen that, generally, a wide bar gives a
higher, and a deep bar a lower, coefficient. Comparing
Clark's results 1 , 4, and 7 , and again Millar's 1 and 2 ,
the coefficient decreases as the section is larger. The cir
cular section has a higher coefficient than the rectangular.
271
CAST IRON
COEFFICIENT OF BENDING STRENGTH, F, FOR RECTANGULAR BARS .
Centre
Dimensions of bars, breaking f, in
in inches
weight, tons per
Authority
in tons
6
Clark, E
.
1
3
1
1
3
Millar
Segundo
5
6
7
1
2
3
1
and
2
Robinson 2
3
1
3
1
1
2
1
2
3
2
3
2
1
1
0.9
2.93
2.93
0.9
4
1)
a
3
2 ins. diam .
$ .in .
W
54
216
27
162
108
54
162
36
36
361
20
20
20
0.252
0.429
1.376
0.475
1.800
2.410
1 : 436
1.67
0.358
0.785
4.82
1:50
3:35
20:41
15:45
18:58
14:43
16.20
16.27
12.92
22.6
19.6
21 : 3
18.75
19.05
24.28
D. K. Clark,
Rules , ' &c. , p .
562
Proc . I. C. E. '
lviii . p. 222
Proc. 1. C. E. '
lxxxvi. p . 248
The actual tenacity of the iron of Mr. Millar's bars,
determined from 66 tests , was 9.45 tons per sq . in .
That of Messrs . Robinson and Segundo's bars was
11.06 tons per sq. in . It is obvious, therefore, that the
coefficient of bending strength for such bars differs widely
from the tenacity, as has indeed long been known .
In Mr. Millar's experiments the ultimate deflection
was in ( 1 ) 0•4 inch ; in (2 ) 0-58 inch ; in ( 3 ) 0:84 inch .
Results which agree with the formula
$ = 8 W 1 / ) clº.
The values of the coefficent in some other experi
ments may now be given.
According to Mr. Millar, tapping a bar with a
hammer during test reduces considerably its strength.
Mr. Millar found no difference of strength in planed
1 Single experiment .
2 These bars were planed or turned .
272
TESTING OF MATERIALS OF CONSTRUCTION
bars and rough bars with the skin on. Messrs . Segundo
and Robinson found the rough bars to be somewhat
stronger than the planed bars. Mr. Millar found that
bars run with hot metal were a very little weaker and
deflected a little more than bars run with dull metal .
COEFFICIENT OF BENDING STRENGTH FOR CAST-IRON BARS .
Dimensions of
bars, in inches No. of
Authority
Coefficient, J,
in tons per sq. in.
tests
6
Fairbairn and Hodgkinson
Woolwich .
Millar
.
Stephenson, 1847
Turner, 1886
.
I
d
1x1
2 * 2
1 x 2
1x1
x
*
x
x
54
20
36
36
Highest Lowest Mean
270 21 : 0
564
30.0
12.9
69
1,344
50
25.6
28:31
16 : 3
18.9
22.6
19.6
16.5
For the ordinary test bar, 3 feet span ,2 inches deep,
and 1 inch wide, the central breaking weight varies for
different qualities of iron from 61 to 42 cwts. Common
iron ought to carry 20 cwts. , good iron 30 cwts. , and
Mr. Turner states that iron carrying 40 cwts. can be
produced with tolerable regularity if necessary . The
most common tests imposed in specifications vary from
25 to 32 cwts . It is usual to take the average breaking
weight of the bars of each cast, as from flaws, cold shots ,
&c. , individual bars vary a good deal. The breaking
weight in cwts. of the ordinary test bar is 40/27ths of
the coefficient of bending strength.
118. Resistance of Cast Iron to Shearing . – The resist
ance of cast iron to shearing is imperfectly known.
Mr. Stoney found a resistance of 8 to 9 tons per sq. in .
1 Maximum of special series of test bars.
273
CAST IRON
The following results are from a paper by Messrs . Platt
and Hayward , the experiments having been made at
University College. The cast iron had a tenacity of
about 11 :4 tons per sq. in .
The specimens were about
3 inch in diameter :
4
No. of tests
Material
Cast iron, No. 1, turned
No. 2,
No. 2, skin on
Shearing strength , in
tons per sq . in .
13
12
5:29
7
3.92
5:08
It is extremely difficult in shearing experiments to
ensure a uniform distribution of stress on the section,
and it is possible these values are too low.
119. Resistance of Cast Iron to Torsion . — The ordi
nary expression for resistance to torsion is T = fZ ;
where T is the twisting moment, Z the polar modulus
of the section, and f the shearing stress in the most
strained layer . For a circular section of diameter d this
becomes
T = 0 196 f d .
When T is the twisting moment which breaks the bar ,
this expression becomes an empirical one, and f then
has values greater than the real shearing stress, just as
in the case of bending. It is better to call the values
of f which correspond to the breaking twisting moment
coefficients of torsional strength.
Experiments by Messrs . Platt and Hayward on the
1 Proc. Inst. Civil Engineers, vol. xc. p. 406 .
T
T
274
TESTING OF MATERIALS OF CONSTRUCTION
same cast iron as that used in their experiments on
shear
gave the following results. The bars were about
5 inch in diameter . Some Woolwich results on 276
specimens of cast iron 1.8 inch in diameter are also
given , and some American results :
Coefficient of
torsional
Material
strength
f
Cast iron, No. 1 , turned
skin on
0
4
No. 2, turned
skin on
97
highest
>
lowest
9
mean
highest
>
lowest
事
Coefficient of
rigidity
Authority
С
Tons per sq. in . i Tons per sq. in.
15.9
3,197
18 : 1
3,402
17.1
2,947
15.3
3,147
22.0
8.25
13.5
23 :5
12.5
Platt and
Hayward
Woolwich
American
MALLEABLE CAST IRON.
120. Malleable cast iron is obtained by heating
castings to red heat in contact with hematite iron ore,
for a period varying from some hours to two or three
days. The amount of carbon in the cast iron diminishes,
and it becomes to a certain extent malleable and capable
of being bent or hammered .
The following tests were made by Professor P. C.
Ricketts, at the Rensselaer Polytechnic Institute ( Van
Nostrand's Magazine, 1885 ) .
The cast iron had a
tenacity ranging from 6 : 5 to 13.1 tons per sq. in. , the
mean tenacity being 10-1 tons per sq . in.
The elastic
limit given appears to be the yield point. The exten
sion was measured in series i. in a length of 5 inches ;
/
275
CAST IRON
in the other experiments in a length of 71 inches , except
in experiments 6 to 10, series iv., where it was measured
in a length of 10 inches .
TENSILE STRENGTH OF MALLEABLE CAST IRON.
Mean
Form of bars
Approxi- elastic
mate limit, in
size
Tenacity , in tons per
tion per traction
cent . per cent .
tons per
sq. in . Highest Lowest
>
.
1-8
11-14
å si
1-9
1-13
1-8
‫ناح‬
Rectangular, 1-7
Circular
0.45
1:01
1:33
1x
diam . 1.02
.65
>>
19.7
16 : 1
16.5
19.8
18.2
14.6
77
‫ماناه‬
Square
Elonga- Con
sq . in .
16 : 1
12.8
Mean
17.8
14 : 5
15 : 3
17 : 4
15.2
13:41
5.6
2.0
2.4
3.5
1.7
0.8
6.9
47
6.6
10.0
4 :3
3.5
Short prisms and cylinders carried loads of from 48 to
71.5 tons per sq. in . before crushing. In bars broken
by bending the coefficient of bending strength varied
from 20 to 40 tons per sq. in . Martens ? found the
ultimate tensile strength of malleable cast iron to be
16 4 tons per sq. in . ; contraction, 8.2 per cent. ; exten
sion in 8 inches, 2-5 per cent. ; limit of elasticity, about
4.4 tons per sq. in .
1 Skin turned off.
? Mitt. a.d. K. Techn. Versuchsanstalt zu Berlin , 1886 , p . 131 .
T2
276
TESTING OF MATERIALS OF CONSTRUCTION
CHAPTER X.
IRON
AND
STEEL ,
121. Constituents of Weld Iron .--Broadly speaking,
wrought iron is softer , more ductile, more trustworthy,
and more valuable the purer it is. All commercial iron,
however, contains some carbon, which renders it harder
and stronger, and some other constituents or impurities.
Amongst these sulphur, while little affecting its quality
when cold , makes it red-short and difficult to roll .
Phosphorus has an effect similar to that of carbon, but
phosphoric iron is cold-short and treacherous . Other
constituents are present in quantities so small that their
effect is not well marked.
Constituents of Ingot Iron and Ingot Steel. - It is to
the homogeneousness due to the mode of manufacture
that these materials probably owe their great ductility
as compared with wrought iron. Consequently they
will bear, and as commercially manufactured do in fact
contain , a greater proportion of those hardening con
stituents, which add to the strength at the price of some
loss of ductility. The purest of them , the low basic
steels, of a tenacity of 24 tons per sq. in. , are the most
ductile. In proportion, generally, as alloying materials
IRON AND STEEL
277
increase, the strength increases and the ductility di
minishes. Carbon, manganese, phosphorus , and silicon
are all hardening constituents , but, either in conse
quence of inducing differences of fusibility or differences
of density, they are not equally safe constituents of
steel . Phosphorus, sulphur, and silicon are dangerous
constituents , while manganese and carbon are the most
useful and least prejudicial. Carbon may exist in steel
in proportions varying from 0:15 to 1.5 per cent. , the
hardness, strength and capability of tempering increas
ing as the proportion of carbon is greater. Manganese
appears to be necessary in the manufacture of steel . In
the fluid metal it reduces the iron oxide, and forms with
silica a fluid slag.
The manganese which remains acts
like carbon in hardening the steel, but less energetically .
Perhaps , also, it diminishes the ductility less . Usually
steel contains 0.25 to 0.5 per cent. of manganese.
Chromium and tungsten have also been used in pro
ducing hard and yet ductile steels.
In obtaining steel castings silicon is added in such
quantities that the cast metal contains 0.2 to 0.3 per
cent. of silicon. To neutralise the prejudicial action of
silicon on the stability of the iron -carbon compound,
there should be also manganese to an amount exceeding
the silicon by one -half.
It is beyond the purpose of the present work to give
in detail analyses of wrought iron and steel, but the
1 Chernoff,
Proc. Inst. of Mech. Eng ., 1880, p . 174.
TESTING OF MATERIALS OF CONSTRUCTION
278
following short summary is a guide to the ordinary
composition of these materials :
Per cent.
Carbon
Wrought Iron 0.02-0.25
Man
ganese
Silicon
0-0 : 3
0-02
Phos
Sulphur
Iron
phorus
0-0.015 0-0.15 99-99.5
Steel :
Tyres
Rails 1
Mild Plates ?
Med . - hard do .
24 - .63
• 35-60
115
33
•21-52.16-3301 - .09.04-05
.80-1.0
• 504
1.008
-04-10 1.07-14-03-07
028
.055
065
022
037
•075
98 74
98.44
99.35
98.40
122. Interpretation of Observations in a Tensile Test
of Ductile Material. - For wrought iron and steel the.
tensile test is the most trustworthy. It is desirable to
examine fully what can be deduced from observations
taken in a careful tensile test, without considering at
present what indications of quality are attended to in
ordinary commercial testing. The table on next page
gives the observations taken in testing a piece of Low
moor plate . The direct observations are the loads
and corresponding elongations.
The inal elongation
is measured after the bar is broken, and at the same
time the area of the fractured section .
The maximum stress is 23.2 tons per sq. in. ,
reckoned on the original area. Beyond this stress local
contraction begins, and the load has to be reduced .
All through the test the section is diminishing, and
on the principle stated in 0 23 the reduced section may
| Mr. R. Routledge of the North Eastern Railway Laboratory .
2 Mr.John Rogerson Proc. Inst. of Mech . Eng. , 1881 , p . 564 .
279
IRON AND STEEL
PLATE OF LOWMOOR IRON, No. 142.
( Broken with stress in the direction of rolling. Section , 1 sq. in . Elongations
measured in 8 inches . )
(1)
( 3)
(2 )
Stress, in tonsper Elongation , in ins.
Area of section
sq . in .
P
17
18
19
20
21
22
23
23.2
22.7
·025
14
•20
•28
38
-56
duced section
0) ,
1
.997
983
976
966
17.05
18.31
19:47
20.69
22.00
23.54
955
935
1:34
.899
.857
[1.65 ]
[ -777]
.90
(4)
Stress per sq. in . of re
25:59
27.08
29.20
be calculated . If w is the section when the length is l,
and w, the section when the length is 1 + a , then
wl = w. ( 1 + ) , and
7
W
= W
1 + 2'
and the corresponding real stress at the section is
Pi = p/w.
Columns ( 3 ) and ( 4 ) give values thus calculated . It
will be seen that the real stress increases faster than the
nominal stress.
The final measured extension 1:65 consists of an
extension 1.34 due to the load of 23.2 tons, and dis
tributed over the 8-inch length, and a further exten
sion, while the load was diminished, in the local contrac
tion. By reversing the equation above, the rate of
extension at the section of fracture may be calculated .
It is easily seen to be (w - w ) 1/07. This gives for the
rate of elongation at the section of fracture 2.29 inches
in 8 inches, or 28 per cent. , which may be called the
!
280
TESTING
OF MATERIALS OF CONSTRUCTION
1
elongation at the contraction.
How far these deduc
tions are useful in practically determining the quality
of the material remains to be determined .
Obviously,
however, they represent the actual facts of the test more
closely than the usual mode of calculation. For com
parison a test of Lowmoor plate crossways of the grain
is appended :
P
16.0
17
18
19
19.7
λ
?
16.03
17.13
18.26
19.47
20:48
998
993
015
•06
•115
•20
986
-976
[ .962]
[ :32]
The area of fracture corresponds to an elongation of
0.316 inch in 8 inches, which agrees closely with the
measured elongation.
This shows there was no local
contraction .
The following table gives similar calculations for a
steel plate :
MILD STEEL PLATE .
Area, 1 sq. in.
(Elongations measured in 10 inches.)
Reduced
section
Stregs per sq . in . of re
19.17
20.65
21.84
23.08
24.29
25.68
1.20
2.15
• 991
968
•962
954
.947
935
920
893
.823
[2:55]
[ .576]
Stress, in tons per
Elongation in
sq. in .
10 ins., in ins.
P
λ
19
20
21
22
23
24
·09
•33
-40
•49
-56
•70
.87
.
25
26
26.43
25.5
duced section
P1
27.17
29.12
32.11
44.27
1 M. Considére proposes to call the elongation up to the maximum
load the proportional elongation , and the elongation calculated from the
contracted section the elongation due to striction .
IRON AND STEEL
281
The fractured area corresponds to an elongation of
7.3 inches in 10 inches, or 73 per cent. The yield
point of this steel was 16: 6 tons per sq . in.
123. Stress at which Local Contraction begins.- M .
Considére ? has indicated that local contraction must
FIG , 111 .
Lowmoor Iron Plates
inch
square
per
Tons
30
42
N4
N1504
зSNа
ObraM
Х
XITON
XBORON
e
0.5
1
2
Extensions in 8 inches
begin when the load on the bar is a maximum . The
total load on the actual section is piwi , which is in
creasing so long as maximum load is not reached.
Hence, the stress pz a given section will carry increases
1 L'emploi du fer et de l'acier, p. 22.
282
TESTING OF MATERIALS OF CONSTRUCTION
faster than the section diminishes. Consequently if any
section contracts more than the rest it thereby becomes
capable of carrying a greater load . But when the
maximum load is passed this condition, analogous to
FIG . 112 .
Lardore Sunens Slecl
os
30
N.
40
,
手?
6
5
25
N
!,
6
0
4
O
N
Load
Tons
.in
20
Mihe 451 Ni462
15
6
2
Exlusions in 10 inches
stable equilibrium , no longer exists .
Then Piwi is
diminishing, and pı does not increase so fast as w
diminishes. If any section contracts more than the
rest, it becomes less capable than they are of carrying
283
IRON AND STEEL
the load , and the deforming action gets concentrated at
that part .
124. General form of Autographic Diagrams of
Different Qualities of Weld and Ingot Iron and Steel.
Fig. 111 shows a series of autographic diagrams
from pieces of Lowmoor plate, 8 inches in length be
FIG . 113 .
Gun Steel
40
N:5
64
58
W85
25
N
0996
N
5
57
3o
SEÓSN
Tono
per e
squar
inch
35
15
10
5
Jih
scale
of Extensions
Extensions in 2"
tween the clips , at which the extension was taken.
Half these are plates broken in the direction of rolling
(marked L ) , and half across the grain (marked X ).
The yield point is less abruptly marked than in the
284
TESTING OF MATERIALS OF CONSTRUCTION
case of steel. The smaller plasticity of the material
across the grain is evident. Many of the plates break
at the maximum load .
FIG . 114 .
Steel Rauls
50
inch
square
per
Tons
N
O
36
40
N
3o
3
NOST
59
20
" 5*
5
Extensions in za
1.5
Fig. 112 shows diagrams from plates of Landore
Siemens steel.
The extensions are given for a 10-inch
IRON AND STEEL
285
length. The yield point is very definite, and the
plastic elongation beyond the yield point is very large.
All draw out locally, so that the final load is less than
the maximum load .
Fig. 113 shows diagrams for some specimens of a
harder steel use:1 for guns, the elongations being taken
in 2 inches. The yield point is distinct.
Fig. 114 shows diagrams for some pieces of steel
rails. The steel here is harder, and the yield point
almost disappears.
The drawing out, which seems
characteristic of very homogeneous rolled materials, is
well marked.1
125. Influence of amount of Carbon in Steel on its
Strength . — The results given in table on page 286 are
from Styffe . The steel was made at Surahammar, and
the carbon determined at the School of Mines in Fahlun .
Styffe states also that for Bessemer and Uchatius
steel the strength is increased and the extension
diminished by an increase in the percentage of carbon ,
until it reaches 1.2 per cent., when the strength is
61 tons per sq. in . If the amount of carbon is increased
1 The drops of the stress -strain diagram line beyond the maximum
load are easily understood if the extremely small amount of the elastic
extension on which the stress depends is remembered . These specimens
extended a great deal plastically just when the maximum load is reached ,
as is shown by the flatness of the curve at maximum load. It was im
possible then to keep the lever floating. The moment the lever came
on its stops the pump was stopped, and the weight run back till the lever
lifted again. A minute plastic extension goes on during running back ,
so that the lever does not lift till the lowest point of the drop is reached .
In running out the weight again an elastic line is described till plastic
2 Iron and Steel , p . 46.
extension again suddenly begins.
286
TESTING OF MATERIALS OF CONSTRUCTION
Material
Mark
Percentage of
Breaking strength ,
carbon
in tons per sq . in .
0.8
0.8
0.7
0.7
0.7
0.7
49.9
40.5
37.6
37.3
37.4
35.0
32.8
36.7
38.8
317
35.0
21 : 5
NP . 1
B. 1
Puddled steel
> )
"
NP . 2
>>
> >
2
)
7
)
)
‫ܕ ܕ‬
>>
>>
‫לל‬
Iron
.
.
NH .
NH .
G.
P.
P.
B.
B.
G.
B.
1
2
2
1
2
2
3
2
Iron
0.6
0.6
0.55
0.5
0.5
0.2
to 1.5 per cent. the strength and extension are both
diminished . The most complete experiments on the
influence of carbon on the strength of steel were made
by Bauschinger on twelve charges of steel made at the
Ternitz Steel Works. For tension, plates 24 inches long,
2.8 inches wide, and 0.48 inch thick , were used. For
compression, prisms 3.6 inches long, and 1.2 x 1.2
inch in section were used . The shearing test bars were
6 inches long, 2 : 8 inches wide, and 0.4 inch thick . The
results are given in the next table.
Various purely empirical formula have been pro
posed to express the relation of the tenacity of steel to
the amount of carbon and manganese it contains. Thus
M. Marché has given the following equations for the
tensile strength T of steel, in tons per sq. in ., in terms
of the percentage of carbon C :
J. Cockerill
.
T = 19:05 + 44.4 C.
Terre Noire
20:32 + 47.60 .
Creusot , Series A (ordinary steels)
(superior steels)
13:33 + 50.8 C.
‫נו‬
1
19
| Mittheilungen, IV . 1874.
15.90 + 50.8 0 .
coefficient
Mean
of
Strength
at
21.02
21.90
21.62
22:15
20.98
21:02
23.77
23.80
25:45
27:24
30.90
13,780
14,300
14,040
13,720
14,100
13,720
14,480
14,980
13,660
1· 3,900
13,820
•19
•46
•51
:54
5
: 5
.80
.87
9
• 6
•78
.66
5
• 7
18.73
ten
in
ticity
tsion
, ons
per
.i
sq n.
elas
of
limit
14,300
tons
per
sq
.in
tension
in
elasticity
within
elastic
limit
,
•14
carbon
of
Percentage
52
:7
46.7
45.9
1:41
40.0
35.6
35.9
35.3
35.6
33.8
30.4
28.1
.per
n
isq
tstrength
, ons
tensile
Breaking
6.6
8.1
9.0
4
:11
13.7
18.4
17.6
17.8
14.3
18.1
1:20
21.8
. t
cen
per
inches
16
10.0
16.5
:0
14
1:19
19.7
30.7
27.9
32.8
25.1
30.5
41.7
49.2
.cent
of
are
pera
14,600
14,100
14,480
31.75
25.00
28.20
23.95
23.95
15,940
14,480
21.85
14,280
22:22
21.85
16,130
15,040
20.64
14,540
21.85
19.20
16,580
14,660
65
17
i. n
sq
in s
ton
per
in
elasticity
of
Limit
17,080
i.sqn
sion
tons
i, n
per
elas
of
Coefficient
Elongation
in
Contraction
ticity
compres
25.4
25.0
25.5
22.8
23.6
21.7
37.0
31.7
30.6
26.3
27.2
:1
23
!
.per
tons
in
sq
shearing
re
,nistance ion
iscompress
Ultimate
IRON AND STEEL
287
288
TESTING OF MATERIALS OF CONSTRUCTION
Bauschinger's results on Ternitz steel agree well
with the formula
T = 27.62 ( 1 + C? ) .
M. Deshayes, of Terre Noire, gives the following
equations for the tenacity T and elongation in 4 inches,
per cent. , in terms of the percentage of carbon , manga
nese, and phosphorus :
T = 19 : 5 +11: 4 C + 30 C + 11 : 4 Mn + 9 :5Ph.
Elongation = 42 – 36 C - 5.5 Mn - 6 Si.
Col. Maitland gives for steel used for guns at
Woolwich, after oil hardening
T = 140 C + 20 Mn - 10 .
126. Increase of Strength from Reworking.- By
repeated piling and rolling wrought iron improves in
quality ; but, if experiments by Mr. Clay, of the Mersey
Steel Works, are to be trusted as giving a general law ,
there is a point beyond which reworking injures the
iron. He took some puddled bar and rolled it repeatedly,
trying the elongation each time.
The following are
the results :
Tenacity, in tons per sq. in.
19.6
23.5
26.6
Original State
Second Working
Third
.
‫ול‬
Ninth
27.5
26.0
Twelfth
19.0
Sixth
13
(maximum )
Influence of the Amount of Reduction in Rolling on the
Strength of Iron Bars.-- In the Report of the United
States Testing Board, for 1881 , data are given showing
289
IRON AND STEEL
that the amount of work put on a bar considerably
affects its tenacity and elastic limit . Tests of iron for
chain cables showed differences of strength for different
diameters, and this led to a special series of experiments,
in which bars of the same iron were rolled so that the
section of the finished bar had greatly different ratios
to the area of the pile from which it was rolled . These
bars were very uniformly heated, as it was found that
underheating in rolling tended to give an increased
tenacity and higher elastic limit, and overheating a
reduced tenacity and lower elastic limit.
INFLUENCE ON TIE TENACITY AND ELASTIC LIMIT OF THE AMOUNT
OF REDUCTION IN THE ROLLS .
IROX BARS.
Area of bar
Tensile strength, tons
per sq. in .
Size of bar
41214
4
23
21
2
11
1
Interesah
Illmer
mm
15
1}
1
1
15.7
13 8
12 : 0
10 : 4
8.8
7.4
6 :1
5.5
44
77
6.7
5.8
4.9
Rough bar
21.1
21.6
21 : 4
22 : 2
22.5
22.5
22.7
4:1
23.6
3.4
4.0
3.1
23.5
22.3
4.9
22.6
22.6
23 :3
3.6
2.5
2.2
3.7
1.6
Core, or bar
turned
down Rough bar
20.6
20.8
21.0
21 :0
21 : 3
2007
21 : 1
22 : 0
21.6
22 0
21 :8
21.9
23 : 1
21.8
22.2
24.1
22.5
22.8
22.5
22.4
22.9
23 : 5
24 : 1
25.4
26.6
23 : 1
23 : 3
11
3
tons per sq . in .
of area of
pile
3
3,
32
Elastic limit ( approximate ),
in per cent .
13.25
13.9
16.0
15.9
16 : 1
15.8
15.6
17.4
17.6
15.8
17.4
15 : 1
15 : 1
15 : 4
17 : 1
17.2
Turned bar
10:45
10.5
11 : 1
11.0
11.8
11.7
13.3
14.3
14.2
16.5
17.4
15.2
16 : 3
18.1
16 : 8
17.2
14.8
16 : 0
15 : 4
174
17.9
U
290
TESTING OF MATERIALS OF CONSTRUCTION
It is no doubt due to an analogous difference in the
amount of work done on the material in hammering and
rolling that large forgings are found to be weaker than
small bars, and the interior of large forgings weaker
than the exterior. Thus, for instance, a propeller shaft
of the U.S. despatch-boat Dolphin broke on the trial
trip , and test bars cut from the shaft gave the following
results :
Tenacity,
in. tons per sq. in.
Elastic limit,
tons per sa:
From centre of shaft
From surface of shaft
15.2
14 : 3
24 : 1
35.7
Elongation
per cent .
2
18
Some very interesting tests of wrought iron, cut in
different directions from forgings of large size, are given
by Mr. Mallet, in a paper on the “ Coefficients of Elas
ticity and Rupture in Massive Forgings. '
71
Mr. Mallet
was engaged in the construction of some 36-inch built
up mortars, and at the same time the Mersey Company
were engaged in constructing the first large forged
wrought-iron gun . The weakest wrought iron was
some cut radially from the end of a heavy cylindrical
forging, which had been exposed during forging to
heating during about six weeks. Its elastic limit in
tension was only 31 tons, and it broke at 61 tons per
sq. in. Mr. Mallet concluded that the iron of very
heavy shafts, forged guns, or cranks may be expected
1 Proc. Inst. of Civil Engineers, vol. xviii. , Session 1858–9. This paper
is interesting from containing probably the earliest carefully plotted stress
strain diagrams for tension and pressure.
IRON
291
ANI ) STEEL
to have an elastic limit of 7 tons per sq. in . , and to
break at a tension of 15 tons per sq . in . The following
are a few of Mr. Mallet's results :
Torsion, in tons per sq . in .
Material
It alastic linnit
Hammered slab (12 " x 4 ' ')
Rolled slab (12 '' x 4'')
Forged slab (48" x 48" x 12 " ).
Mersey guin :
Original faggot bars
Longitudinal cuts
Circumferential cuts
Transverse cut
15 : 3
10 : 9
At fracture
24 : 1
23 : 0
8.75
18 : 0
12 : 0
9.8 10.9
6.6 5.5
3.28
21 : 9
19: 7 17.9
16.4-16.7
6.50
5:47
22:32
Borings from gun, leforged and
rolled into a bar
127. Effect of Quick and Slow Rates of Lourling on
the Strength of Test Bars. - Before deciding on the details
of the tests of the steel for the East River Bridge, ex
periments were made to determine whether the strength
of the specimens was affected by the rate of loading.
Nine test bars of steel, 1 inch square and 24 inches long ,
were cut from the same rolled bar, and these were used
without further preparation. Three test bars were
broken in periods of 3 minutes, three in periods of
6 minutes, and three in periods of 20 minutes. No
difference in ultimate strength was found which could
be attributed to the quicker or slower rate of loading: 1
The influence of time on the elongation has been dis
cussed in § 36. M. Barba has stated that in rapid
Mr. W. Denny appears to have made experiments leading to the
same result. See Hackney, ‘ Fornis of Test Pieces, ' Proc. Inst. of Civil
Engineers, vol . lxxvi.
U 2
292
TESTING OF MATERIALS OF CONSTRUCTION
testing the resistance is somewhat greater and the
elongation less than in slow testing. But this conclu
sion is certainly doubtful.
128. Form and Size of Test Pieces. The forms gene
rally adopted for test pieces have been described in $ 77.
Unfortunately no general agreement has been come to
as to the size to be adopted. The ordinary Admiralty
test pieces of plates are of the form d, Fig. 81 , p. 189 ,
and for all thicknesses of plates are of such a width
that the section is about 1 sq. in. The extensions are
measured in 8 inches. Other engineers adopt a length
of 10 inches for measuring the extension, and a constant
width of 2 inches for all thicknesses of plates. In the
recent German conferences it has been recommended
that the standard width for all plate specimens shall be
30 mm . ( 1.2 inch ), and the extension measured in
200 mm . ( 7.87 inches ). The French Admiralty com
monly adopt test pieces 30 mm . wide and 200 mm .
between gauge points. Undoubtedly plate specimens
13 or 14 inch wide, with the extension measured in
8 inches, would be very convenient, and the results
would be comparable with the greatest number of
earlier English, German, and French results .
For many cases very much shorter test pieces are
unavoidably used . Thus in the case of tyres it is neces
sary, and in that of rails it is convenient, to adopt much
shorter test pieces. Probably in such cases a diameter
of inch and a length for extension of 2 inches is the
most convenient size.
IRON AND STEEL
293
The criterion of ductility for practical purposes is
either the contraction of area at fracture or the exten
sion between the gauge points. One objection to the
contraction of area is the difficulty of measuring it,
especially in the more rigid materials ; another is the
probability that it is considerably affected by local
conditions of hardness and homogeneousness at the
point of fracture. The extension is less open to these
objections, but then the percentage of extension varies
with the form and proportions of the test piece. This
variation is almost entirely due to the variation of
length of the local contraction. If the extension is
taken , either ( 1 ) up to the maximum load before local
contraction begins, or ( 2 ) from the broken bar after
discarding the contraction in the neighbourhood of the
fracture, or ( 3 ) deduced from the contracted diameter
in parts not near the fracture, the variation of the per
centage of extension with different forms and propor
tions of test bar disappears .
In the discussion on Mr. Hackney's paper the
author suggested that the bar should be marked in
1 - inch or -inch lengths before testing, and the exten
sion measured, omitting the inch or two in which the
fracture occurred. In the appendix to the discussion
Prof. Styffe made the same proposal.
Professor Kennedy has made experiments on the
effect of varying the form of the ends of plate test bars
1 According to Barba, the extension up to maximum load is rigor
ously independent of the proportions of the test bar.
294
TESTING OF MATERIALS OF CONSTRUCTION
on the strength and elongation ." The most important
forms tried are shown in Fig. 115. With soft basic
steel, annealed , there was no difference of strength or
extensibility distinctly traceable to the form of the ends
FIG . 115 .
of the test bar.
Even form
II broke fairly in the middle,
I
and not at the
shoulder.
of common
Some pieces
wrought-iron plate, however,
ІІ
showed marked
differences
when tested in the forms II
and VII . Hard or inferior
material seems, therefore, to
VI
be affected by the form of the
ends.
VII.
129. Variation of Quality
in Pieces cut from the same
Plate.
Some
experiments
seem to show a more or less considerable difference of
quality in picces cut from the same plaie.
No doubt in
some of these cases the differences are due to errors in
testing. If the testing machine is not itself inaccurate,
still imperfect centring ofthespecimen in the machine, or
imperfect gripping of the specimen in the shackles, may
give rise to considerable apparent differences of strength.
But in other cases there appear to be real differences
in the quality of the material, and the limits of such
differences are not at present determined .
Proc . Inst. of Civil Engineers, vol . lxxvi .
Mr. Baker
79
24.93
16.93
Means
25.28
17.81
24:58
16.05
22.5
23.60
21.40
28.65
VII
15.75
28:18
29.12
iron
,VII
Wrought
Means
15.95
15:55
II
18:16
Means
,II
iron
Wrought
17.46
tons
pe
r
.n
isq
:0
14
14.0
14.0
14
:4
14.5
:2
14
5.7
15.6
15.7
15.5
5.7
6.7
5.5
4.7
:
4
8
6.7
4.6
26.7
25.8
23
:2
27.6
23.9
22.5
6.4
21
:3
20.8
21.8
Breaking
,in
stress
17.6
18.0
17.2
5.8
72
4.5
31.6
31.5
31.7
including
)of
fracture
51.2
9.3
44.5
5.0
22.0
:21
0
23
:0
6.7
8.5
20.1
18.9
21
:2
10.2
:0
11
51.3
51.0
44.5
Contrac
tion
of
area
,
. t
cen
per
44.5
i
nches
46inches
2
10
8 nches
Extension
ength
n
alcent
(.iper
lways
5
>
in s
ton
per
18.87
..in
sq
Limit
of
elasticity
,
VII
Basic
steel
I, I
Form
1}iPnch
and
thick
jinch
wide
lates
(.)about
K
(). ENNEDY
ENDS
EXCEPT
OF
FORM
IN
SIMILAR
‫ܕܙ‬
Hol
cornlow
ers
Square
corners
Hollow
corn
ers
Square
corners
TESTS
Two
U
STEEL
BASIC
NANNEALED
FOUR
,RESULTS
ND
WROUGHT
OF
PLATE
-IASTRIPS
RON
LL
IRON AND STEEL
295
--
296
TESTING OF MATERIALS OF CONSTRUCTION
has stated that entire bars, 16 feet long, 10 inches wide,
and 1 inch thick , gave an average tenacity of 19 tons
per sq . in .; while ordinary test pieces , cut from the same
bars , broke at a stress 35 per cent. , and even in some
cases 75 per cent., higher. An iron plate was cut up
in the workshops of the Compagnie des Chemins -de- íer
de P. L.M. into 32 test pieces. The strength length
ways varied from 20:32 to 29:21 tons per sq. in . , and
crossways from
20-32 to 23.50 .
The stretch varied
from 12.5 to 21.5 per cent. lengthways, and from 7 : 0
to 14.5 per cent. crossways.
HARDENING, TEMPERING , AND ANNEALING .
130. If steel containing carbon ,manganese, or phos
phorus in sufficient quantity is heated to about 1,450 ° or
higher, and then suddenly cooled by plunging into a
bath of cold liquid , it becomes harder, stronger ,and less
plastic. The more of the hardening elements in the
steel (up to a certain limit ), and the lower the tempera
ture, and the greater the power of absorbing heat in
the cooling liquid employed, the greater the hardness
produced. Water hardens steel more actively than
oil, and pure water has a greater effect than soapy
water .
In plunging the heated steel into a cooling liquid
the exterior loses heat first, and contracts on the
1 Proc. Inst. Civil Engineers, vol. lxxvi. p. 95.
2 Lebastour .
Les Métaux, p. 194 .
IRON AND STEEL
297
interior. There thus result tensions in the exterior,
which may exceed the elastic limit and cause per
manent stretching or even fracture. Afterwards, the
interior cools and contracts.
But it is now attached to
the stretched exterior, and in turn is put into tension.
Thus there may arise in hardening a condition of great
internal stress .
The cracking and twisting which often
occur in hardening are indications of this condition of
stress .
M. Caron has observed that the volume in
creases in hardening .
M. Considére states that if a
hardened bar is cut in two by a parting tool in the
direction of its length the pieces become curved, with
the concavity on the planed side.
By reheating hardened steel and allowing it to cool
1
slowly, the hardening previously induced is diminished .
This is termed tempering, or letting down the temper.
If the steel is raised to 1,300° or higher, the whole of
the induced hardening disappears, and the process is then
termed annealing.
In annealing the temperature must
be high enough, but should not approach the fusing
point or other changes occur.
The cooling must be
slower the larger the mass to be annealed, and in the
case of large masses requires days or even weeks.
Alternate hardening and annealing alter the steel,
somewhat in the same way as mechanical forging.?
The steel, originally coarsely crystalline, and with
| L’emploi de l'acier, p. 10 .
2 Colonel Maitland , R.A. , On the Treatment of Gun Steel . '
Inst. Civil Engineers, 1887 .
Proc.
298
TESTING OF MATERIALS OF CONSTRUCTION
small elongation, changes to a condition of finer grain
and greater toughness. The hardening is most safely
effected with oil .
Sir F. Abel has studied the chemical changes which
occur in hardening and annealing. He finds that in
FIG 116 .
*Tons per sq. inch.
35
619
d
re
e
rd
Ha
30
2.)
afterwards panneuled .
613-Herdet nedateand
d
ou , Avo
tr
.
20
5
15
10
5
1
2
3ins.
· Manganese Steel Bears.
Ertensions in 10 62.9
annealed steel the carbon exists almost entirely in the
form of carbide of iron of definite composition ( Fe,C) ,
uniformly distributed through the metallic iron . In
hardening, the sudden lowering of temperature appears
+
299
IRON AND STEEL
to have the effect of arresting the separation of the car
bon as a definite carbide. In tempered steel the condition
is intermediate between that of hardened and annealed
steel . There is less carbide than in annealed steel , but
1
what there is is of the same composition .
The autographic diagrams ( Fig. 116 ) show clearly
the changes in the condition of the material due to
hardening and annealing . They are diagrams from
three similar bars of manganese steel, one of which was
tested without preparation , the second hardened in
water, and the third hardened and subsequently an
The yield point disappears in the hardened
bar, the strength is increased, and the plastic clonga
' nealed .
tion diminished .
Annealing restores the steel very
nearly to its original condition , the annealed bar, how
ever, having a raised yield point and slightly increased
elongation .
Manganese stcel
Tenacity , in tons per sq. in .
Elongation in 10 inches, per cent.
Stress at yield point
Contraction of area, per cent.
llardened
Ilardened and
annealed
24.71
32.69
25:17
29.8
20 : 1
30 : 3
55.3
62.3
Original
state
18.76
1673
51.6
In the discussion on Mr. Strohmeyer's paper Mr.
Milton gave the following results of tensile tests of
plates, some of which were tested in their ordinary
state, the others after heating to red heat and quenching
in water at 30° : -1 Proc. Inst. of Mech . Eng ., 1885, p . 47 .
300
TESTING OF MATERIALS OF CONSTRUCTION
After heating and
Original state
quenching
Material
per cent .
sq . in .
Very mild steel .
.
Harder mild steel
steel
‫ני‬
25
29
35
24
23
22 1
35
22
2006
Tenacity, Elongation Tenacity , Elongation
in tons per in 10 inches, in tons per in 10 inches,
sq . in .
per cent .
38
43
50
43 2
The following results are given by Lebasteur on
32.5
24.8
10.0
8.4
5.2
28.83
57:47 | 67.31
28.6
12 :0
4 0
1 :0
. ut
ce
r
pe
stress
Hardened in water
.
cent
per
stress
20.83 29.72
28:32 | 44.77
43.69 68.00
Elongation
Breaking
23:11
| 30.48
43:31
44:39
54.61
Elastic
limit
0.150 11:57
0.490 14.61
0.709 19:56
0.875 | 20.83
1 :050 25.08
19.56
Hardened in oil
limit
Elastic
Original state
Elongation
Breaking
( The bars were 0.8 inch diameter and 7.9 inches between gauge points.
Stress in tons per sq. in. )
.
cent
Car
p, er bon
steel from Terre Noire, showing the increased effect of
tempering as the carbon increases :--3
19.0
2.5
30:48 | 49.53
2 . Broke intempering
Broke in tempering
A corresponding series of tests of steels containing
32.90
38.80
48-58
56.20
24.5
21 : 4
17.4
10.5
Elongation
Breaking
. rnt
ce
pe
Elastic
limit
stress
Elongation
stress
Elastic
0 : 521 | 16.70
0.060 | 19.81
1 : 305 | 26.16
2.008 30.29
Hardened in water
.
cent
per
Breaking
Hardened in oil
Original state
limit
Manganese
,
.
cent
per
different proportions of manganese was also made, the
other constituents of the steel being kept constant.
12 : 0
26.48 48-58
41.28 02.87
Cracked in tem
pering
| In 7 inches, and after annealing.
2 Quenched in soapy water.
3 Lebasteur. Les Métaux, p. 72.
301
IRON AND STEEL
A similar series of tests was made with steel con
taining 0.247 to 0.398 per cent. of phosphorus. The
action of phosphorus was similar to that of carbon or
manganese, but less energetic.
EXPERIMENTS ON THE TENSILE STRENGTH OF STEEL AT THE TERRE
NOIRE WORKS . I
(Diameter of bars, 0.55 inch . )
Percent
Material
carbon
Forged steel ( containing about
1
per cent. of manganese
and a trace of silicon)
oil
Cast steel, not forged (contain
about i per cent. of man
ganese and ì per cent. of
silicon)
The same, after hardening in
oil and annealing
Elonga
tion in
4 inches,
Elastic
limit
At
per cent .
Breaking
21:31
22.24
30.40
42:36
46.16
34.0
24.0
15.0
95
20.43
27.79
42.86
28:16
43.92
66.72
28.6
12.0
56.38
66.14
.875
13.08
16.51
19.00
24:42
27.85
26.98
40.00
40.18
.287
•459
750
.875
19.69
20.87
22.30
28.66
32.27
34.58
46.23
51:46
• 15
• 49
• 709
.875
C
• 15
The same, after hardening in
Stress, in tons per
sq . in .
age of
.49
-709
.875
287
459
-750
13.70
16.32
19.69
4.0
1 :0
8:8
3.0
3.5
15
24.6
19.2
14 : 3
3.5
.
131. Injurious Effect when Steel is worked at a ' Blue
Heat or Colour Heat. - It has long been known, in a
more or less vague way, that in cooling from a welding
heat steel passed through a condition in which it be
came brittle and dangerous to work . First, it should
be noted that there is a temperature at which the steel
is brittle and little capable of being bent. In 1881 the
1 Proc. Inst. of Mech, Engineers, 1880, p . 182 .
302
TESTING OF MATERIALS OF CONSTRUCTION
Board of Trade, in a Memorandum on Stecl, published
the result of experiments made at the works of the Steel
Company of Scotland. Forty -eight plates were taken ,
and strips cut from each . Half the strips were bent
cold to an angle of 180 ° round a bar of a diameter
equal to twice their thickness. The whole of the strips
stood the test. Corresponding strips were heated in
boiling tallow and bent at that temperature. Every
one of the strips cracked before the bending reached
180°. Second, a plate heated and allowed to cool is
no worse for the operation ; but this very curious
action appears to occur. If, while in cooling the steel
is at blue heat or colour heat, mechanical work by
hammering or bending is done on the then brittle plate,
it will be found when cold to be seriously injured in
quality.
Prominent attention was first directed to the in
jurious effect of working steel at a blue heat in a paper
by Mr. Strohmeyer .? The most interesting results were
obtained by the bending test. The test strips were
bent alternately in opposite directions till they broke,
and the number of bendings was taken to be an index
of the ductility of the material. The test strip was
clamped between a steam -hammer and its anvil, and
the projecting end was bent down by hammering ( over
a mould with rounded angle) through an angle of 45 °.
The test strip was then turned over and bent in the
2
opposite direction .
Mr. Strohmeyer takes ' blue heat
Proc. Inst . Civil Engineers, 1886.
303
IRON AND STEEL
as a convenient expression for any tenperature between
470° and 600 ° Broadly, it was found that while a test
strip bent cold would stand twenty to twenty -six bend
ings before cracking, if it was once bent while at blue
heat and allowed to cool , it broke afterwards with very
few bendings. The following table gives a summary of
the results :
Average No. of bendings before cracking
Conditions to which the strip had been
brought
Unprepared or annealed .
Bendings while at blue heat
Medium
Mild
hard steel,
Ž inch
steel,
steel ,
inch
inch
21
12 .
26
21
1:
3
2
Very mild Lowmoor
2.
iron ,
is inch
20
3
Bent at blue heat once and
cooled
Bent at blue heat twice and
11
12
1
}3
Bent once cold
twice
>
19 :
9.
8 :1
19
7 )
20
four times cold
eight
>>
10
‫ܪܺܐ‬
‫ܐ‬
‫ܝ‬-
3
cooled
19
13
15
13
11
2
The first two lines show that both steel and wrought
iron suffer much fewer bendings at blue heat than cold .
That is in accordance with the Board of Trade results
quoted above. Next, if a strip is bent once at blue heat
and allowed to cool, it is afterwards a quite different
material, much more brittle , and capable of suffering
very little bending. The last series of results show
that simple cold bending reduces the ductility much
more slowly, though iron reaches its limit of endurance
sooner than steel .
304
TESTING OF MATERIALS OF CONSTRUCTION
* All these results, ' says Mr. Strohmeyer, “ point
unmistakably to the great danger which is incurred
if iron or steel is worked at a blue heat.
The differ
ence between good iron and mild steel seems to be that
iron breaks more easily than steel while being bent,
when either hot or cold ; that iron suffers more injury
than steel by cold working ; but, if it has withstood
successfully bending when hot, there is little proba
bility of its flying to pieces when cold , as is almost sure
to be the case with mild steel. '
Mr. Strohmeyer thinks
that there is no foundation in fact for the opinion that
local heating of a plate sets up strains which may cause
fracture. But some qualities of steel are considerably
injured if made red hot or blue hot and cooled by
holding them with one edge in water. The following
table gives these results : --No. of bendings before cracking
Material
Medium
hard
steel
Very
Low
Mild
steel
mild
moor
steel
iron
26
12
24
10
---
Made red hot and quenched in ?
1
10
19
20
20
21
Made red hot and quenched in /
boiling water
3
8
25
27
3
6.
19
18}
Unprepared or annealed
cold water
Red hot.
Edge quenched in
water
Blue hot. Edge quenched in
}
water
The following experiments were suggested to the
author by Mr. Strohmeyer's paper. A plate of mild
27-ton steel was broken in the testing machine in the
305
IRON AND STEEL
ordinary way. The longer picce after this test was
heated to a temperature a little below redness , and
while at that temperature it was bent to a shallow curve
and straightened again. It was then tested in the ordi
nary way.
The results were these :
Second test,
after bending while hot
32.0
First test
Tenacity
27.0
+
Contraction
.
51 :0 per cent.
21.0 per cent .
These results seem to show that the tenacity is
increased at the expense of the ductility. Some test
pieces of the same mild steel were
heated to red heat, placed on a
V block , and quietly bent to an angle
FIG . 117.
Bent once
Rent turice
of about 15 ° at each end out of
straight. The bending pressure was
put on just as the redness disap
Thickness
peared.
The test pieces were then
1.655-39
642-578
straightened in the same way. Lastly,
they were tested by tension.
Fig .
1-729-513
117 shows the result obtained .
3101101
In
the place which was the middle of
the curvature in bending there is
1 SL8 +472
+2.3009 160
. 470
1613
350+ 1.306
scarcely any measurable contraction
of area, or extension . On each side
of the middle of the bar, where there
was hardly any bending, the material
is still ductile and draws down. The
figure shows the widths and thicknesses of the bars ,
The elongations in each inch length were as follows :
X
306
TESTING OF MATERIALS OF CONSTRUCTION
ELONGATIONS IN EACH INCH .
Bar bent once
Bar bent and
and straightened.
0.048
0.152
0.138
0.080
0.020
0.010
0.138
0.287
0.622
0.160
0.100
Heated part .
Break .
straightened twice .
0.120
0.154
0.156
0.064
Heated
0.000
0.002
0.082
0.174
Break .
0.610
0.232
part.
In the part heated and worked (by bending) the
steel is not weaker but it is stiffer.
The bar has been
rendered unhomogeneous, and consists of portions of
quite different extensibility. It is easy to see that by
locally treating a plate in this way it may be rendered
extremely treacherous, even without assuming that the
heating and bending has created a condition of internal
stress .
The results in the following table , obtained by Mr.
Webb, at Crewe, carry the same lesson of the gain of
strength with the loss of ductility. For convenience of
comparison the results for plates bent or hammered at
blue heat, and not annealed after, are separated from the
others. All were tested cold , except those marked as
tested hot.
132. Hammer Hardening and Cold Rolling.- It is
well known that ductile materials can be rendered more
elastic and harder by hammering, planishing, or wire
drawing cold, and this action is identical with that
which occurs in mechanical operations in many ways,
sometimes with useful, sometimes with prejudicial,
307
IRON AND STEEL
Elonga
Tenacity,
No. of
tion in
in tons
Condition of material
CO
CONCO
tests
Ordinary plate, annealed
Hammered while blue hot and annealed
Bent while blue hot and annealed .
per sq. in . 10 ins. p.c.
+
Bent red hot and cooled
Annealed plates bent cold
and annealed
Bent three times blue hot
Hammered while blue hot
Bent once blue hot
Tested while blue hot
1
2
.
3
2
.
23.6
23 : 8
22 : 1
30.96
30.26
30.74
31:05
32:42
30.60
22 : 5
12.5
23:03
38.04
35.24
31.95
38.80
4.3
10:05
7.5
11 : 4
Whenever a ductile material is subjected to
deformation by pressure at temperatures below those
results .
at which the metal is plastic, the strength and elastic
limit are raised , but the elongation at fracture is dimi
nished. The elasticity is increased , but the plasticity
is diminished .
The author has noticed that, in very
long rail bars, the colder end which passes last through
the rolls has a higher yielding point and strength, but
less elongation at fracture, than the botter end . The
following are some results from pieces cut from steel
rails rolled 150 feet long
Tenacity, in Extension in Contraction Work done per
in inch
tous per
sq . in .
Test No.
24 inches,
per cent.
of area ,
per cent.
cub . in.
tons up to
max. stress
36
37
38
40
Hot end
Cold end
46:37
45.03
46.73
49.84
22.0
26.0
22 : 0
17.6
49:17
54.63
46.85
33:17
5:15
6.72
5.45
7.07
The work done was measured from an autographic
diagram .
x 2
TESTING OF MATERIALS OF CONSTRUCTION
308
Many years ago an American process of cold roll
ing was introduced . Round bars passed through rolls
cold were straightened, polished , and rendered stronger
and stiffer. The following experiments by Sir W.
Fairbairn on a bar of good Dudley iron show how the
mechanical properties of the material were affected by
the process :
Tensile strength | Elongation in
Material
tons per sq. in. 10 ins. per cent.
Rough rolled bar, 11 inch diameter, in or
dinary state
The same, turned down to 1 inch diameter
in lathe
Bar, cold, rolled to 1 inch in diameter
}
26.0
20.3
}
26-7
22.4
38.4
8.0
The strength increased one-third , and the plastic
elongation diminished more than one- half.
The following results are given by M. Consi
dére :
1
Material
Elastic limit, in Tenacity , in
tons per sq. in . tons per sq . in.
mild steel in ordinary } 16:07
Very
state
Elongation ,
per cent .
26.99
26.5
22.67
28.32
17.0
18.80
33:34
18.0
26.92
34.61
11.5
14.48
23.75
15.0
26.42
29.78
7.0
The same , compressed by
hydraulic press at 32 tons
per sq . in .
Ship steel in natural state
The same, reduced by cold
rolling from 10 to 9:45
mm . thick
Iron plate , natural state
The same , reduced by cold
rolling from 8 to 7.1 mm.
thick
4A
1 L'emploi du fer et de l'acier, p. 148 .
IRON AND STEEL
309
The gain of ultimate strength is here not large,
but the rise of the elastic limit (probably the yield
point) is very marked . The diminution of plasticity,
shown by the ultimate elongation , is also marked .
Wiredrawing is a process similar to cold rolling, and
in wiredrawing the increase of strength is very con
siderable.
The effect produced by hammer hardening or cold
rolling is entirely removed by annealing ; and doubtless
it is to the removal of some effect of this kind , due to
rolling at too low a temperature, that the diminution
of strength by annealing, which sometimes occurs, is
due .
Mr. W.Parker's Experiments.- Mr. W. Parker has
recently shown that any mechanical deformation, such
as bending, has a similar effect to cold rolling or ham
mering. In the antographic diagram the yield point
disappears, and the true elastic limit is lowered . The
following table shows very simply the analogy in the
effect of hardening by sudden cooling and hardening
by mechanical pressure in the case of very ductile
material.
Similar bars of Siemens -Martin steel plate,
3 inch thick and 2 inches wide, were taken. No. 1 was
tested in its ordinary state. No. 2 was bent cold to
a radius of si inches , and straightened . No. 3 was
treated similarly at blue heat. No. 4 was heated, and
quenched in cold water . No. 5 was treated like No. 2,
and then annealed.
like No. 1 .
It gave a diagram almost exactly
310
TESTING OF MATERIALS OF CONSTRUCTION
No. Tenacity, in
COWOK
A
L7
of
Test
tons per
on Contraction
Yield point, tons Elongati
in 10 ins ,
of
.
per sq . in .
sq . in .
27.2
14.9
27.75
31.2
32.7
27.1
No yield point
15-3
aren,
per cent .
per cent .
27.8
25.7
20.7
17.6
29.2
53.6
52.6
50-5
32.0
53.5
Ordinary state
Bent cold
Bent hot
Quenched
Annealed
133. Local Hardening. — If a plate is sheared or
punched a very considerable lateral pressure is exerted
on the metal near the cut edge . The action diminishes
rapidly from the cut edge towards the interior of the
mass, like the stress in a thick cylinder subjected to in
ternal pressure. For about į inch from the cut edge
the metal is hardened ,and its power of extension greatly
diminished . M. Barba cut from a punched plate the
ring of metal surrounding a punched hole, and found
it to be extremely brittle and incapable of bending.
M. Considére has shown that a permanent condition of
compressive stress is induced in the ring immediately
round the hole.
That the diminution of strength of a punched plate
is due to the hardening of the metal round the hole is
now established .
M. Barba showed that rimering out
å ring } inch thick round the punched hole, or anneal
ing the plate, entirely removed the prejudicial effect of
punching. The punching is more injurious the thicker
the plate, and this is obviously due to the increase of
lateral pressure in punching thick plates. It is less in
jurious if the die- block hole is larger than the punch , for
that diminishes the lateral pressure.
Sheared strips of
IRON
311
AND STEEL
ductile material are known to be brittle when bent.
Mr. Baker has mentioned a case of a steel plate which
had been sheared which cracked in several places while
being straightened cold.
Some experiments of M. Barba showed that the
diminution of strength in a bar in which a hole had
been punched (reckoned on the net section ) was greater
the wider the bar.
Thus, some steel test bars 0:28 inch thick were
punched with a hole 0.68 inch in diameter . The
normal tenacity of the steel was 32 : 7 tons per sq. in .
The punched bars of different widths gave the following
results
Width of bars, in inches
1.28
Tenacity - cylindrical holes 27.1
‫לר‬
conical holes
317
2.0
25.9
28.3
2.72
25.3
26.3
3:44
22-7
22 : 4
4:16
24.3
22.9
4.88
23 : 1
23-7
Further experiments have been made by M. Con
sidére on a plate of Siemens-Martin steel , containing
0.34 per cent. of manganese and 0.22 per cent. of car
bon, and a plate of Bessemer steel, containing 0:38 per
cent. of manganese and 0.33 per cent. of carbon .
The
normal tenacity of these plates was 32 : 7 and 38 : 1 tons
per sq. in .
M. Considére first verified M. Barba's result, and
determined that the increase of strength in the narrow
plates was not due to the lateral expansion of the
narrow bar under the action of the punch. He then
tried bars with a punched semi-hole on each side, leaving
312
TESTING OF MATERIALS OF CONSTRUCTION
a strip of metal between them. The following were the
results :
Tenacity of war when distance between the
Material
holes was, in inches,,
Normal
tenacity
Martin steel
Bessemer steel
327
38 : 1
2
•24
• 32
• 56
1.2
2: 0
42.6
41 : 5
40.6
46.8
33.3
28.6
33.6
27.2
30.6
39.6
Here a new result appears. When the distance
between the holes is less than 1 inch , the punched bar
is stronger than the unpunched bar. For wider bars
the reverse is the case .
Part of the excess of strength
in the narrow bars is no doubt due to the suppression
of drawing- out, explained in § 33. By tests on plates
with drilled holes, M. Considére found that 5 tons
increase of strength in the 0.2 inch bar was due to this
cause .
There remains another 5 tons increase, due
directly to the punching. In this very narrow bar the
whole of the metal between the holes was hardened by
the action of punching, and the increase of strength is
that due to cold working. As the bar is made wider it
comes to consist of hard metal near the holes, and softer
metal, unaffected by punching, between. The , hetero
geneousness of the material involves unequal distribu
tion of stress. The bar tears at the rigid material, and
the tear doubly weakens the bar, partly by loss of
section, partly by the unsymmetry which results.
Suppose Fig. 118 represents at of the normal
stress-strain diagram of the material, and at Oe the
stress -strain diagram for the material hardened by
313
IRON AND STEEL
punching.
If the bar stretches an amount O a , the
stress near the hole will be a d, and that of the un
injured naterial a c.
The bar must tear at the edge of
the hole when the strain reaches the value 0 b.
The application of these considerations is far wider
and more important than the question of the deteriora
FIG . 118 .
tion of plates by punching. It
e.
has been seen that in many
c
ways the plasticity of the
material may be altered , so
that the yield point disappears
and the extensibility is greatly
C
diminished - by rolling at too
low a temperature , by sudden
cooling, by bending, hammer
ing, cold rolling, or by shearing
B
a
or punching. So long as such
an action is general, the only effect is that a more
0
rigid material is made out of a ductile one. But if, as
must often happen , the action is local, then the effect
on the strength, like that of the thin ring of hard metal
round a punched hole, is far more serious. To know
the danger, however , is sufficient. Either local harden
ing can be avoided , or, if unavoidably produced , it can
be destroyed by annealing .
134. Influence of Temperature on the Strength and
Ductility of Iron and Steel. — The results of experiments
on the influence of temperature on the strength and
ductility of iron and steel are somewhat discordant. A
314
TESTING OF MATERIALS OF CONSTRUCTION
paper by Sir W. Fairbairn in 1856 1 gave experiments
on wrought-iron plate and rivet iron for a considerable
range of temperature.
With plate iron there was no
well-marked effect of temperature till dull red was
approached , and then the tenacity rapidly diminished .
With rivet iron the strength was slightly greater at
- 30° Fahr. than at 60° .
With rise of temperature the
strength increased from 28 tons per sq . in . at 60° to
38.4 tons at 435º. At red heat the strength fell to
16 tons. Knut Styffe made similar experiments in a
more perfect way. He found the strength and extensi
bility of iron and steel were not diminished by cold. At
temperatures between 212° and 392° the strength of
steel is the same as at ordinary temperature, but the
strength of iron is greater than at ordinary temperature.
The results in the following table show no loss of
strength at very low temperatures. At about 300°
there is an increase of strength, greatest for the iron
with least carbon .
In steel there is no great difference
in strength or extensibility in the range of temperature
in these experiments .
Mr. Webster 2 made experiments on the tenacity of
iron, steel , and malleable cast iron at temperatures of
5° and 60°. He found almost exactly the same strength,
and nearly the same elongation, at these temperatures.
M. Papkoff > made experiments on soft steel and iron
| Report of the Brit. Assoc. 1857 , p. 405 .
2 Proc. Inst. of Civil Engineer's, vol . lx. p . 161 .
3 Proc. Inst. of Ciril Engineers, vol. lxxxiii . p . 513.
315
IRON AND STEEL
INFLUENCE OF TEMPERATURE ON THE STRENCTU OF IRON AND STEEL .
(STYFFE'S EXPERIMENTS . )
( Temperatures in Fahr. degrees. Bars of 0.1 to 0.13 sq . in . area. )
Percentage
Description of material
of carbon
Bessemer steel
1
Tenacity, in tons per sq. in.
At - 400
to - 130
1:14
At 500 to 600
At about
3000
62.92
51:37
61:17
58.49
>>
56.27
55.20
‫לל‬
0.68
0:33
0.33
steel
0.42
34371
63.28
29.59
34:59
33.29
59.33
7
>>
‫לל‬
+
97
iron
.
Uchatius
178
51:12
0.69
>
Cast steel (Krupp )
Pudůled steel ( Surahammar)
77
>
77
>
99
41.81
42.63
54.98
42.73
‫לל‬
99
0.21
0.21
0.21
0.21
22
Lowmoor iron
0.21
>>
>>
>
>>
‫לו‬
0.62
0.02
0.8
0.7
0.55
27:35
28.61
42.76
41.81
52.81
45.76
40.06
32.80
25.21
34.67
34:11
61.97
51.86
41.63
31:35
29.10
26.37
28.64
29:19
29.62
plates at temperatures of 63° and – 2° Fahr. There was
an increase of strength and of elongation at the lower
temperature. Mr. C. Huston ? made experiments on iron
and steel at ordinary temperatures, and at 572° Fabr, and
at 932° Fahr. They show generally a gain of strength
and decrease of elongation with increase of temperature .
A small hole in the test bar was filled with an amalgam
of known melting- point, and this was kept in a semi
fluid condition by a blowpipe . According to Barba,
steel has at 400° Fahr. an increase of strength of 30 per
cent. , and a decrease of elongation of 30 per cent. The
1 At 50 Fahr.
2 Proc. Inst. of Civil Engineers, vol. liii. p. 304.
Inst. 1878, p. 90.
Journal of Franklyn
316
TESTING OF MATERIALS OF CONSTRUCTION
maximum strength is reached at 572°, and for higher
temperatures decreases rapidly .
Amongst the most careful of the experiments on the
effect of temperature are those by Kollmann, at Ober
hausen . Three materials were used, the quality of
which may be judged from the following summary of
the properties when tested at ordinary temperature :
Tenacity , in tons Stress at elastic limit, Elongation,
Material
Fibrous iron
Fine-grained iron
Bessemer steel
per sq. in .
in tons per sq. in.
per cent.
23.5
25.4
37.8
17 : 1
174
24.5
17.5
20.0
14.5
These experiments show a regular decrease of
strength with increase of temperature in all cases. The
following table, calculated by Roelker,' gives the strength
at different temperatures in terms of the strength at
ordinary temperatures. For comparison the results of
some experiments made by the Franklin Institute are
added :
Temperature.
Fibrous
Fine-grained
Fahr.
wrought iron
iron
Bessemer
steel
700
1,000
100
100
97
92.5
81.5
26
100
100
100
98.5
90
36
100
100
100
98.5
68
31
1,500
10
0°
100
300
500
2,000
3.5
15.5
5
Wrought iron ,
Franklin Institute
96
102
106
104
92.5
36
12
5
Mr. Barnaby made some experiments on iron and
steel for the Admiralty, and these experiments are
1 Proc Inst. Civil Engineers, vol . lxvii. p. 437.
IRON AND STEEL
317
important, both as being recent and made on test bars
of reasonably large size. The bars were partly heated
in oil, partly in sand ; generally, however, they were
taken out of the hot bath and broken as quickly as
possible. The temperature was judged from the colour
of the fractured surface , or in some cases by observing
whether tin or lead melted when placed in contact with
the bars .
EXPERIMENTS ON THE INFLUENCE OF TEXPERATURE ON THE STRENGTH
AND ELONGATION OF IRON AND STEEL. By Mr. BARNABY.
(Elongations in 8 inches.)
60
500
530
22.39
27.15
26 : 3
13.28
10.93
10.15
60
450
490
21.75
24.6
22.6
9.3
6.24
60
490
500
21 : 1
24.4
23.2
27.6
550
850 to
900
60
420
3:12
15.62
Bessemer
23.95
8.38
12.5
plate
23.93
27.08
27 : 4
Tempe- Tenacity , Elonga
rature,
Fahr,
tons per
sq . in.
tion , per
6091
450
520
880
26.07
40.5
38.7
24.02
27:34
14.06
17.18
60
430
490
610
630
29.10
33.45
34 :5
30.83
25.78
14.06
18.75
18.7
18.74
60
430
550
580
28.49
38.4
33.08
18.56
21.87
18.75
17.18
250
cent.
26.56
M
Siemens
- artin
iron
Boiler
BB
60°
450
490
cent.
plate
fibre
Th
e
same
across
iron g
Bowlin
tons per
sq. in .
tion , per
Fahr.
rature .
-
lengthways
Tempe- Tenacity, | Elonga.
28.0
12.5
9.37
17.18
| 19 :3
18.75
24.8
30.3
23:43
21.87
COLLECTED TABLES OF TESTS OF IRON AND STEEL.
135. In giving tables of the results of tests of iron
and steel, the object has been to select some of the most
318
TESTING OF MATERIALS OF CONSTRUCTION
trustworthy results, on very various qualities of material,
and to give them fully enough to permit some judgment
to be formed of the range of quality in materials nomi
nally the same. A very large and valuable collection of
tests of iron and steel will be found in a treatise referred
An abstract of these tables, giving merely
mean values of very variable materials, would be of
to below. )
little use .
Knut Styffe's Rescarches. The following summary is
useful , as showing the general relation of the quantities
observed in ordinary testing in various qualities of iron
and steel. Knut Styffe's investigation is a very con
scientious piece of scientific work . His measuring in
struments were excellent, and the test bars were long,
so that the proportionate error is probably small.
On the other hand, he had perhaps the worst testing
machine ever used for so important an investigation.
Probably this in no way affected the accuracy of his
results , as care was taken to prevent any error, but it
increased very much the trouble of the inquiry. Then,
and this is a more serious defect, his bars were small in
section, varying from 0.2 to 0: 3 sq .in. in sectional arca.
In the following table Styffe's numbers for bars of
the same kind have been averaged . Where two values
are given for the amount of carbon , the earlier is the
estimate of the manufacturer, the second the result of a
special analysis.
Die Eigenschaften von Eisen und Stahl. Supplementband, Organ für
die Fortschritte des Eisenbahnwesens.
Wiesbaden , 1880.
319
IRON AND STEEL
TABLE I.
TENSILE STRENGTH OF STEEL AND IRON (STYFFE).
Description of material
Limit of Breaking
Contrac
Percent elasticity , stress, in
age of
in tons per tons per
carbon
89. in
sq . in .
tion of
area, per
Tilted Bessemer steel . 11.2-1.35
1.0-1.14
‫יי‬
9
0.9-1.05
)
>
0.0-0.68
99
23
99
0.3-0.33
iron
1.85
Rólled Bessemersteel
‫גי‬
77
‫ול‬
29
26 : 6
2:16
28.7
0.99
29.4
1.29
30.7
15 : 3
15.9
37.2
32.3
28.5
23 6
16 : 9
14.5
14 : 1
15.6
13.8
12.5
‫ܕ ܕ‬
Rollei Uchatius steel
‫יו‬
40-42
0:32
1.57
1:19
>>
0.69
Tiſted Krupp steel
Lowmoor iron
Cleveland iron
0.62
0.21
0.07
0:09
-
Dudley iron
Lowmoor engine tyre
Rail from Wales .
Motala puddled iron
Rolled charcoal iron
‫ܕܕ‬
Swedish iron
34.6
36.6
30.2
30.8
21 :6
0.2
0 :07-0.18
0.07
0.07
18.3
12.2
12.2
47:39
56.50
45.97
46.40
31:33
42.23
41.20
47.99
61.57
31.07
29.17
53.10
03.01
49.59
37:49
24.73
26.81
22:30
23.80
21:43
21.62
26.74
22.67
20.92
Elonga
tion , per
cent . in
cent .
5 feet
15
2.4
2 :9
3.4
4.2
7 :3
1 :4
3.4
3.8
4.8
16 :0
17.2
2.2
4.5
11 : 1
6 :0
19.6
173
8.5
41
56
36
62
2
4
4
24
53
59
7
12
33
53
53
42
20
34
11
12 : 1
47
14 : 1
16
63
70
6.6
7.2
18.4
21 : 1
136. Report of the Steel Committee, 1868–70.- The
Committee made a series of experiments of a very in
teresting kind. They were experiments on bars of
iron and steel of 10 feet length between the measuring
points, a very exceptional length for test bars . The
experiments were made in a chain testing machine at
Woolwich Dockyard. The specimens were placed in a
trough 11 feet in length, with cross diaphragms at 12
inches apart,having a level planed V groove to support
the specimen.
A V cap was fitted above and pressed
down tightly by screws. Sliding verniers were placed
on both sides of the bar , reading to todou foot.
It
320
TESTING OF MATERIALS OF CONSTRUCTION
is probable that, from the great length in which the
elongations and compressions were measured , and from
the use of two symmetrical verniers, eliminating to a
great extent the effect of initial bending, the measure
ments in these experiments were very trustworthy .
One important result of this mode of experimenting
was the observation, in a clearer way than previously,
of the remarkable behaviour of ductile bars at the
yielding point or breaking -down point.
The Committee arrived at the following important
conclusion from these experiments :
' It would appear from these experiments that
within the yielding point of steel the amount of length
ening from tension, or shortening from compression ,
produced by equal forces per unit of area, is nearly the
same, and also that the amount is rather less with steel
than with wrought iron .'
The experiments show also that the stress at which
the material yields or breaks down is nearly the same
for tension and compression.
There are two other points very worthy of notice .
The first is the great uniformity of mechanical pro
perties within the elastic limit for all the bars, however
diverse their mode of manufacture.
The other is the
much greater uniformity of the results of different tests
of the same material than in the more ordinary tests of
very short bars .
The compression and extension per ton per inch given
in the tables are the mean values before yielding began .
!
Η
W
S
LW
SLW
>
)
‫ܕ‬
‫ܕ‬
‫ܕ‬
3
steel
Cast
‫ܕ‬
‫ܕ‬
‫ܕ‬
Bessemer
steel
steel
cast
Crucible
steel
Bessemer
>>
19
steel
Crucible
steel
Cast
steel
cast
Crucible
Intended
use
TENSION
AND
axles
and
tyres
rolled
rods
piston
barnrels
gu
rods
piston
tyres
1
H
K
K
31
KB
Η
A
K
>
>
>
>
Α
Κ
HO
46
NB
NB
NB
SC
SC
Dark
Make
.II
TABLE
0· 00079
0
· 00079
000078
·000077
0
· 00077
0
· 00075
·000077
-000076
0
· 00077
0
· 00076
0
· 00077
0
: 00075
0
· 00075
0
· 00074
0
· 00077
000078
0
· 00076
000078
0
· 00077
000075
000075
0
· 00076
.000075
.000076
-000076
-000076
0
· 00075
inch
r
pe
Meann
exte
20:00
19:50
19.50
19:50
20.75
20.50
19.50
19.50
21:00
18:00
17.00
17.50
16.00
16:00
25.00
26.50
26.50
25.00
26.00
24.50
26.00
26:00
27:00
20:50
17:00
17.00
16:50
.isq
n
per
Yielding
Tension
53.74
53.33
51.21
52:30
46:00
54.74
43:48
41.85
40.54
38:11
39.61
)3779
37:05
35:47
35:01
35:26
35:34
33:05
34:44
34:09
34:10
34:33
34.30
33:07
33.27
34:05
33.66
.in
sq
per
tons
,in
stress
sion
tou
per
Ultimate
Ultimate
471
11:48
19.2
13.61
11.90
150
:41
2
2.02
0.89
11:13
9:03
13:01
7.95
1:12
4:13
2:9
1.3
2:
44
1.0
18.7
43
4.1
:
0
5.2
·000076
.
7:29
20
:0
.000073
-000074
0
· 00076
0
: 00076
-000070
0
· 00070
0
· 00074
·000076
-000076
0
· 00077
0
· 00073
17:00
18:50
18.50
27.00
24:00
22:00
20:30
21:00
17:00
15:00
16:00
15:00
16:00
19.00
26.50
26:00
26.00
26.50
27.00
25.00
25.00
26:00
18.00
16:50
16:00
16:00
21:00
.isqn
per
Meaning
Yield
com,ipressi
stress
per
tous
n
on
Compression
0
· 00075
·000071
.000074
-000076
-000077
-000076
0
· 00076
000074
0
• 00071
0
· 00073
·000071
-000073
0
· 00073
-000071
0
· 00073
inch
per
ton
5.29
inches
.
t
cen
per
elo
of
tionngation
5.7
cent
.
area
p
, er in
120
Contrac
COMPRESSION
STEEL
OF
COMMITTEE
(STEEL
).BARS
Mmade
.(1}i10
diameter
nch
easurements
and
extension
lcompression
aof
on
) ength
feet
IRON AND STEEL
321
.
)
2
>
KC
КС
KO
Yorkshire
Use
-
FR
FR
S.
C.
>
>
‫ܕ‬
Lowmoor
Make
I
FR
L
L
L
LS
LS
LS
•Mark
1
0
· 00078
000081
0
• 00083
·000080
12.50
11:50
11:50
13:50
0
· 00082
·000080
22:48
22.92
-000079
12:00
11:50
11:50
13:00
0
· 00076
22:48
17.50
.
17.87
·000077
>477
4:51
23:29
24:16
13.00
·000078
13:00
000076
23.62
13:00
.000078
11:50
24.07
12:00
0· 00078
.000079
10.50
0
· 00077
12.65
25.72
12.50
13.00
0
· 00075
.000078
13:50
0
· 00075
12:50
13:50
-000074
.000077
.isqn
per
tons
,in
stress
per
pression
Yielding
inch
per
ton
com
ean
,Mper
inches
120
area
24.60
48.8
7:01
. t
cen
per
Compression
11:00
29.33
14.00
·000077
5.9
cent
.
of
tion
in
ContracE
| longa
0
· 00078
29.53
14:00
0
· 00076
27.80
14.00
.isqn
per
stress
ton
per
,ision
stress
tons
n
.isq
n
. per
Ultimate
·000076
in
perch
Yielding
extenMean
Tension
Ediameter
(}ioot
in
nch
compressions
measured
length
a1and
0xtensions
.)-fon
bar
of
AND
TENSION
COMPRESSION
IRON
OF
(S). III
BARS
COMMITTEE
.TEEL
TABLE
322
TESTING OF MATERIALS OF CONSTRUCTION
-
1
2
323
IRON AND STEEL
137. Board of Trade Experiments on Iron and Steel .
- The plates were furnished by the Steel Company of
Scotland , as material suitable for ships and boilers.
The following table gives the mean results of tensile
tests of plates of different thicknesses . The elastic limit
recorded is properly the yielding stress. The plates
were tested lengthways and across the direction of
rolling, but in mild steel no sensible difference is found
in the strength, and only a small difference in elonga
tion and contraction . The large contraction of area of
the steel plates indicates great ductility , and in this re
spect steel compares favourably with iron. With regard
to the iron plates, the boiler plates are more uniform
than the ship plates , and contract and extend more be
fore fracture.
1 Memorandum issued by the Board of Trade upon the Use of Mild
Steel, 1881.
Y 2
TESTING OF MATERIALS OF CONSTRUCTION
324
TABLE IV. TENSILE STRENGTH OF IRON AND MILD -STEEL PLATES
( ' BOARD OF TRADE REPORT, ' 1881).
Thickness
of plates, in
inches
Direction of
stress
Stress at yield
point, in tons
per sq . in.
Tenacity,
in tons per
sq . in .
Elongation
in 10 inches, Contraction ,,
per cent .
per cent .
‫المبادراتهم‬
= + = + = + = +
‫لا‬
‫مماههرر‬
‫احمر‬
STEEL PLATES
=
Means
+
Means
19.0
19 : 1
15.8
15.7
15.8
15.6
14.9
14.8
31.0
3104
28.9
28.6
29.5
29 :1
28.0
28.0
23 :5
21.2
29.8
28.9
29.2
26.6
30.6
25.6
46.0
39.9
53.2
40.9
46.8
38.3
50.4
42.4
16 : 3
16.3
29.3
29.2
28.2
25.5
49.1
40 :3
24.00
22.62
19.42
70
6.7
3.6
6.8
47
4.8
22.01
5.7
5.4
21:20
19.03
21:40
18.67
20.86
9.0
2.7
10 : 1
3.8
9.8
17.74
3.1
12.91
4.28
13.30
5.08
13:00
3.87
21:15
18.48
9.6
3.2
13.07
4.41
‫سانحه‬
‫سهم‬
IRON SHIP PLATES
11
II
11
Means
0
Means
Means
+ = + = + =
‫سلام‬
‫سم‬
‫لد‬
‫لسعدممما‬
IRON BOILER PLATES
+
Tests of Iron Plates by Dr. Böhme.? — Table V. con
tains a very complete series of tests of material, chiefly
for boilers, made on similar test pieces. They are chosen
partly because the measurements were made with great
care .
1 Mitth . aus den K. Techn . Versuchs - Anstalten zu Berlin .
1884.
325
IRON AND STEEL
TABLE V. TESTS OF IRON BOILER PLATES (BÖHME).
( The test bars were 24 inches wide, and
to
Stress, in tons per
Thickness,
-
in inches
sq . in .,
at yield at maxipoint
mum load
inch thick. )
Elongation , per Contrac
cent.,
in 8
inches
in 4
inches
tion of
area, per
cent .
Tests in direction of rolling
2
3
.559
> )
2 )
77
7
8
.
.
9
10
11
,,
>
>>
398
12
13
14
15
>
)
1
sokun rmal
no
16
17
‫ܕ ܕ‬
0
77
18
19
.
> >
1
)
20
21
.
> >
.
>
7
Ship plate
0
>
79
29 Harkort
30
31 Wohlert
34 Boiler plate
35
36
37
11
>>
.
>
38
.
>>
39
40
42
43
44
•
.
41
>>
‫ܕ ܕ‬
413
14:50
394
· 413
•398
.433
.421
1744
15.75
14.78
413
449
.480
.476
15.60
1770
14:46
18.20
16:50
16.18
20.8
20.8
28.4
15.7
19.0
21 : 5
17-3
29.3
29.6
24.3
24.7
29.7
31 :4
23 : 8
35.4
33.2
28.0
25.7
22-5
21 : 4
15.4
17 7
26.95
25.25
26:40
24.74
23.00
25.80
25:35
24:35
25.05
25.57
25.57
25.70
24.55
24:48
33.6
33.9
26.9
29.4
25.6
23.6
210
19.2
22.2
21 : 0
24.2
15.2
25 : 1
23 :3
24.2
24.18
27:35
23.75
21:45
24.93
21 75
2175
23.60
24.23
22.95
22.90
22.83
22.3
29.5
257
26.7
15.0
33.1
5.6
6.4
114
7.2
5.7
9.6
5.7
6.9
19.3
21 : 3
21.3
18.7
18.7
12.6
7.5
6.4
8.8
6.2
7.3
25.0
27.9
27.8
23.4
24.2
40
5.3
40.2
45 : 1
33 : 4
29.0
22.9
11 : 0
19 :3
16 : 1
13.7
22 : 6
17.8
25.5
25.1
25.3
28.2
28.6
33.4
28.2
19.6
177
27.6
30.2
24.9
32.9
29.1
34.0
30.6
24.3
27.0
25.4
17.0
6:4
6.6
1
I 6
3
8
32
33
•461
.461
445
-449
•455
465
.465
425
465
315
•315
•472
.472
•472
•394
.295
-532
-521
516
•557
-569
-500
24:03
26:42
21.60
25:35
27.54
25:11
23:54
23.97
23:35
21.95
22.83
22.65
24.10
22.84
22:57
26.04
24.05
23:38
_
6
•520
•508
•516
516
543
539
-520
386
•406
14:10
15.62
14.08
16:15
17.14
17.00
13.64
14:21
13.70
14:27
13.70
13.83
14:52
13.90
14:08
16.68
15.72
16.00
15.66
17.82
15.82
11.95
13.20
15.22
15.60
15:40
15.66
15:40
18:14
17.70
13.76
16.18
16:36
16.06
1
1 Boiler plate
•563
14.9
326
TESTING OF MATERIALS OF CONSTRUCTION
TESTS OF IRON BOILER PLATES — continued .
Thickness,
1
in inches
at yield
point
45
Boiler plate
• 464
46
47
48
49
50
>>
472
-457
‫ܕ ܕ‬
464
-469
•469
•469
> )
>
51
7 )
Elongation, per Contrac
Stress, in tons per
sq. in .,
17:56
14:46
15:15
15:40
16:00
14.84
15.53
cent. ,
at maxi-
in 8
tion of
area , per
in 4
cent.
mum load | inchies inches
25:40
24.23
25.05
25.45
25.55
25.50
25.25
24.2
23 :5
22.7
23.9
23.9
23.4
22 : 1
29.1
30.9
27.6
29.8
28.8
28.2
26.5
29.2
31.5
27.6
30.8
31.7
30.8
27.8
Tested incross the direction of rolling
1 Boiler plate
(Nos . 7-9 above)
2
3
}
)
‫גל‬
-524
13.00
20:36
8 :8
10.2
16.8
• 524
.527
13.06
12.94
2175
19.46
12.8
15.9
15 : 1
4 Boiler plate
(Nos. 10-11 above)
394
13.45
20:16
8.4
9.4
5
6
394
394
14.08
14:46
19.84
21.82
7.8
8.2
464
13.76
21.05
7.2
84
-464
409
315
• 315
•472
13:35
15.02
14:33
15:34
15.34
14.70
20:18
21.25
21.95
23.27
20:42
22.82
74
15.2
7.4
6.8
44
7.1
7.6
17.0
7.6
10-2
14.9
7.7
10.2
1.7
6:1
>>
7 Builer plate
(Nos. 13-15 above)
8
‫גל‬
9
7. Iron plate
.
16
7
>
10
>>
• 394
10
9.6
5.0
7.5
TABLE VI. TENSILE STRENGTH OF BASIC STEEL (GILLOT, PROC. Inst .
C. E. , ' LXXVII. P. 304) .
Tena
Section of
Description
Section of
ingot
test piece, in
inches
Elongation , per cent.,
Con
in 8
traction
city, in
tons per
sq . in .
in 10
in 2
inches | inches
incles per cent.
1
Plate
Axle
Plate
12 "
15
12"
15 "
15 "
19"
x
x
x
x
x
x
12 "
15 '
12"
15 "
15 "
19"
2.015 * 46
1 " diam .
| 2-03 * •37
1.99 x 6755
2.035 x 59
1.52 68
25.89
22:29
24.96
23:00
24.16
23.92
25.0
31 : 3
35.0
30.0
27.5
28.1
27.5
34 1
37.5
31 : 3
30.5
34.2
59.4
1 " diam .
25.98
244
26.6
40.6
50.0
26.68
25.0
28.5
31 : 3
43.8
53 : 1
50.0
46.6
49.8
24.07
23.8
26.3
28.8
2476
28.0
30.6
53 : 1
55.5
53.1
53 : 1
62.5
02.5
55.8
62.9
62-7
63.5
56.5
58 : 3
Billet from
19 " x 19 "
axle
Plate .
.
Means
19 " x 19" 1.765 x .09
27 '' x 12 " 1.52 x 705
19 " x 19 "
20 x 565
26.68
48.9
327
IRON AND STEEL
TABLE VII .
KENNEDY'S TESTS OF LANDORE SIEMENS STEEL .
Description of plates
Limit of elas Tenacity,
Elongation
ticity, in tons in tons per in 10 inches,
sq . in .
per cent.
17.6
29.33
23.2
14.92
14.84
20.65
27.27
27.2
22 :3
21 :4
per sq . in .
inch plates , suitable for furnaces
(along fibre)
inch similar plates (along fibre)
( across fibre)
Rivet steel
26.93
29:12
TABLE VIII. TESTS OF STEEL PLATES, ANNEALED AND UNANNEALED .
Tenacity, in tons
Elongation in 8
Description of plates
per sq . in .
inches, per cent.
1 inch plate, hard steel, unannealed .
32.97
28.52
26.60
24.05
28.55
annealed
‫נו‬
1 inch plate, mild steel, unannealed .
annealed
+
inch plate, mild steel, unannealed
annealed
> )
26.95
>>
unannealed .
1. inchsteel boiler plate, annealed
28.25
25.75
16.65
24:12
24:32
29.87
25.05
26.90
21.25 1
28.751
>
The results on 1 inch and
inch plates are given by
Mr. W. Denny ; that on the thick plate by Mr. Traill.
138. The Testing of Rails.- The testing of rails is of
very great importance, from the extent of the manufac
ture, and the serious consequences which may follow the
use of unsuitable material. The ordinary tensile test.
so trustworthy for ordinary materials of construction ,
is comparatively useless, sometimes even misleading, as
a guide to the quality of rails .
For rails two require
ments have to be attended to, which are to a great
The rail must be strong and
extent antagonistic.
tough, for it has to carry great weights , and suffers
| Elongation in 10 inches.
328
TESTING OF MATERIALS OF CONSTRUCTION
severe shocks . But it also must be hard enough to
The
resist abrasion or lamination on the surface.
earlier tests adopted aimed chiefly at securing tough
ness , and led to the introduction of rails too soft to
stand the wear of traffic.
Tests of Rails . — The following table contains tests
of 30 steel rails, after use on the Furness Railway for
eight years ( * Proc. I. C. E.'vol . xlii . p . 74 ) , and of 36
mean values of tests taken weekly during the years
1869–70 ( Proc. I. C. E.' vol. xxx . ) :
TABLE IX . TENSILE STRENGTH OF STEEL FOR RAILS .
Furness rails
(Smith )
Means given by
Berkley
Tenacity , in tons
Elongation in 2
per sq . in .
inches, per cent.
37.5
3.0
Mean
50.4
30 : 1
354
Maximum
45.5
Minimum
Mean
33.8
40.5
Maximum
Minimum
29.5
No convenient direct test of hardness suitable for
rails bas as yet been found.
Indirectly, the bending
test gives indications of the hardness of the rail .
A
rail which will carry a heavy load with a high elastic
limit in bending is likely to be a hard rail. But if the
rail is too hard it is brittle. To control the bending
test a falling-weight test has been used . A monkey, or
ball, weighing 300, 600, or 1,000 lbs. , and falling 6, 12 ,
or more feet on the rail, bends it more or less ; the
number of blows the rail will stand before twisting or
breaking, or the deflection with one blow, is taken as
an index of its toughness.
329
IRON AND STEEL
Without attempting any complete account of rail
testing, the following suggestions, taken from Mr.
Sandberg's paper, may be made . Mr. Sandberg
advises ( 1 ) that the bending test should be severe, but
that no maximum of deflection should be stipulated for
—the rail should be required to carry a certain load
without sensible permanent deflection ; ( 2 ) the falling
weight tests should be regulated according to the
weight of the rail. The table below , prepared by Mr.
Sandberg, gives the tests he proposes , and the ordinary
deflections observed.
TABLE X.
PROPOSED TESTS FOR RAILS .
( Distance of bearings, 3 feet for all tests. Deflection and set measured on a 6 - foot
length of rail. In the bending test, the load A applied at the centre should produce no
permanent set. Deflection means temporary deflection .)
Bending tests
Impact tests
Weight
>>
26
28
30
13
1-1,5
> )
>>
‫ܕ ܕ‬
‫للنممسمصلارم‬
‫اده‬
‫مردراائ‬
‫ا‬
2-4
9
>>
7
2.5
-1 :
9
3.0
3.3
3.7
11
1.
> >
>>
>>
>>
31
>
51
>>
2 :0
20
,,
52
6
-13
45
48
50
inches
7
43
>>
; )
С
8
1-1
1
2
10
41
‫גל‬
22
23
24
8
13
15
17
19
21
23
‫ܕ ܕ‬
tion, in
feet
25
‫יו‬
22 09
>>
22
25
26
32
35
colon.com
Coleo
18
14
18
20
11
13
cwts .
73
75
80
85
90
95
100
> >
inches
02
65
70
0.125
inches
in tons
Usual
deflec
09
40
45
50
56
60
5
6
8
10
12
B
Usual Weight Height Con
Load , tion , in set, in of båll, of fall, stant,
‫اج‬
‫سا‬
‫ل‬
‫م‬
‫تمم‬
33
35
tion , in
in tons
inches
t
Load,
Usual
deflec
‫=تا‬
‫نداامشت‬
‫سلللمامسمطایاانه‬
A
yard
Usual
deflec
-chesi
of rail,
lbs. per
>>
> ‫و‬
40
4.2
4.4
4.5
4.8
50
| Proc. Inst. of Civil Engineers, vol . lxxxiv ., p. 387 .
9 )
>>
330
TESTING OF MATERIALS OF CONSTRUCTION
The constant C is weight of ball multiplied by
height of fall, and divided by weight of rail per yard .
Tetmajer has made a considerable number of tests
of rails, with a view of determining the connection
between the bending test and the hardness of the rails.
The pieces were 4 : 6 feet long, and were supported on
bearings 3.28 feet apart. The supporting knife- edges
and that of load-shackle were rounded to a diameter of
1 ] inch . The quantities determined were the elastic
limit in bending (or limnit at which there was no mea
surable set ) , the deflection with 35 tons load, the ulti
mate, or breaking, load ; diagrams were constructed
from which the work of deformation was calculated .
The rails varied from 67 to 75 lbs. per yard.
The
moment of inertia of the sections varied from 21 : 5 to
to 25 : 1 ( inch units ) . The table below gives the re
sults on some of the rails from the Swiss Central Line,
weighing 74 lbs . per yard, and 5:11 inches high .
Moment of inertia , 24.8 .
TABLE XI. EXPERIMENTS ON RAILS (TETMAJER).
67
Elastic limit in bending, tons 23 :0
Breaking load , tons
Deflection at limit, inches .
Deflection at 35 tons, inches
Deflection at breaking, ins.
Work of deformation up to
41.0
52
51
27.5
39.8
26.0
39.7
60
28.5
47.7
54
33.5
45.0
56
35.5
51.2
0.165
0.208
0.177
0 201 0.209 0-244
0.216
5.63
1.92
1.300
5.16
2.88
1.24
4.64
0.84
4.72
0.59
4:37
5.12
2.32
2.84
3.48
4.32
38.76
23.96
16:52
3.96
0.224
limit, inch tons
Work of deformation up to
35 tons, inch tons .
61-68 | 37:32
Stahl und Eisen, 1886, p. 408 .
vol. lxxxvii. , p. 480.
Proc. Inst . of Civil Engineers,
1
331
IRON AND STEEL
The variation of the deflection is much greater
than the variation of the tenacity in tensile tests , and is
therefore likely to be of service in determining hard
ness .
EXPERIMENTS ON SHEARING AND TORSION .
139. Let Fig. 119 represent a portion of iron or steel
plate, the large arrow indicating the direction of rolling.
FIG . 119 .
T
T
11||||||
IV
V
It
HIL
VI
Then there are six directions in which the plate can be
sheared, differently placed with reference to the struc
ture developed by rolling. In the course of an inquiry
into the causes of a boiler explosion at Hapburg,
Bauschinger experimented on the shearing resistance of
wrought iron in all these directions. The test - bar was
a rectangular block , fixed in the machine between two
cutting edges, and sheared in single shear. The shear
ing was sometimes sudden , with a loud crack , sometimes
more gradual. In directions I and II the sheared sur
faces were laminated , or scaly ; for the directions III
TESTING OF MATERIALS OF CONSTRUCTION
332
and IV, fibrous ; in the directions V and VI , irregu
larly torn . The following are the mean values ob
tained :
TABLE XII. SHEARING RESISTANCE OF IRON AND STEEL (BAUSCHINGER ).
Shearing resistance, in tons per sq. in ., in the
Description of plates
directions
I
II
III
IV
V
VI
Iron :
Plates from exploded
boiler at Augsburg
Puddled plate (Leon
Magis & Co. )
Puddled plate (Leon
Magis & Co. ) an-
16.50
16.64 | 18.91 | 19.80
17:18 | 16.25
20:20
19:10
8.46
8.44
10:30
10:33
18.36 | 17.84 | 19.68 | 19.68
8.89
9.20
17.78 | 17.30
9.20
8.06
9.17
10.15
nealed
Charcoal plate
20.16
20.00
German Lowmoor plate .
18.64 17.00 22:05 21.95 10:05
Rolled iron bar
22:15 | 17.16 | 22:55
19:00
11.70
Rolled iron bar,annealed 21.20 19.68 23.23 20-25 10:60 13-27
Plates from exploded
boiler at Wurtzburg,
15:42
15.06
17.62
17.68
6.95
7.23
14.40
14.38 | 17:26
16:28
5.20
4.76
16.00
16.38
19.90 | 10-01
9.58
from uninjured plate
Plates from exploded
boiler at Wurtzburg,
from injured plate
New locomotive plate
19.10
Cast steel :
Bessemer plate
‫לל‬
24:12 | 23:42 26.45 27.35 22.90 | 21:45
26.30 26:40 | 29.20 29.20 25.05 25.70
The resistance of steel in different directions is
much more uniform than that of iron .
The following are mean values of torsional tests,
made by Messrs. Platt and Hayward at the engineering
laboratory of University College. For comparison,
values of the tenacity and sharing strength from direct
experiments on tension and shearing of the same mate
rials are also given :
1 Proc. Inst. Civil Engineers, vol. xc. p . 382.
333
IRON AND STEEL
Wrought iron,
Crown best
Bessemer steel
Crucible steel .
}
.
sq
.per in
Ultimate
shearing
Material
fshear
, rom
stress
tons
,in
tests
ing
Tenacity
,in
tons
.sq
n
iper
Coefficient
of
irigidity
,n
n
iper
.sq
tons
inch h
lengt
Final
twist
in
revolutions
in
9
n
,itons
fracture
.isqn
per
Calculated
shear
at
stress
ing
Limit
elasti
,of city
tons
inn
sq
i.per
TABLE XIII . TORSIONAL STRENGTH OF IRON AND STEEL (PLATT AND
HAYWARD ).
25.2
8.90
5,714 21:00
18.76
44.64
42:30
3.84
4:36
5,750 | 52:20
6,098 52:10
35.21
33.30
10.20
29.85
7.85
5,834
28.40
23.00
10.36
28.87
6.90
21.21
8.99
20.28
19.36
Landore rivet steel,
0:18 carbon, 0 : 6
manganese
Crown rivet iron
10.40
34.7
4.15
6,116 25.01
5,822 | 38.04
Siemens-Martin steel
10-16
28.13
9.92
5,981 | 25.75
20.94
Wrought iron, S. C.
10.22
29.5
17:45
6,213
24.56
20.75
Steel cut from cast
27.00
ing
Crown
}
The apparently high shearing stress in the torsion
experiments is no doubt due to the false assumptions
involved in the formula for torsional resistance when
applied to stresses at rupture.
STEEL CASTINGS .
140. Steel castings are now largely used , sometimes
in place of cast iron, and sometimes instead of forgings.
Roughly, they are usually assumed to have nearly
double the strength of cast iron. Tests, however, show
wide divergence in the quality of different specimens,
both as to strength and ductility. The steel melts at
about 3,500° Fahr. , a temperature much higher than that
of cast iron. Consequently, the contraction of the cast
ings is nearly double that of cast iron. To obviate danger
+
334
TESTING OF MATERIALS OF CONSTRUCTION
from this contraction annealing is necessary, and in
some cases the casting is removed from the mould as
soon as set, and placed in an annealing furnace, kept at a
temperature of 1,700° Fahr., for not less than 24 hours .
Hardening in oil and annealing afterwards improves
the strength , and still more the ductility, of the casting,
the effect being similar to that of forging. Unannealed
castings may have a strength of 24 tons, with 1 to 5 per
cent. of elongation . Annealed , a strength of 27 to 30
tons, with 3 to 8 per cent. of elongation. Hardened
and again annealed, a strength of 27 tons, with 20 per
cent. of elongation, or 36 tons , with 12 per cent..
elongation . "
The amount of carbon varies from 0.25 to 1 per
cent. ; a small amount of phosphorus makes the casting
sounder. The manganese varies from 0.3 to 0.7 per
cent. Silicon , added just before casting, in quantity
depending on the amount of carbon , prevents ebullition
of gas during solidification.2
The following table, from Mr. Hill's paper, shows
the effect of annealing
TABLE XIV. INFLUENCE OF ANNEALING ON STEEL CASTINGS.
Tenacity, in tons per sq. in. Extension in 5 in. , per cent. Contraction of area , per cent.
Not annealed Annealed Not annealed Annealed Not annealed
24.01
32.80
36.60
32.30
28.40
30.08
12.00
4:16
1:00
22.00
14.60
15.00
13:00
21.90
8.16
2.90
2.80
1
33.79
32:10
Annealed
i Considére . L'emploi du F'er.
Proc. Inst. Civil Engineers, vol. xc. , p . 359.
2 Hill.
38.70
28.11
38.70
15.90
23:05
1
335
IRON AND STEEL
The following results were given by Mr. W. Parker
as to four specimens of a steel casting made at Terre
Noire :-1
Tenacity in tons Elongation in 5
Condition of material
per sq. in .
inches per cent.
32.07
33.70
16
17
38.60
17
41:10
15
First specimen , unprepared
Third specimen, annealed and tempered
Second specimen, annealed
in oil
Fourth specimen, annealed and twice
tempered in oil
Valuable experiments on the strength of steel cast
ings have been made by Mr. H. Foster, of Newburn
Steel Works :-2
TABLE XV.
PROPERTIES OF STEEL CASTINGS AS DEPENDENT ON
COMPOSITION (FOSTER).
Composition, per cent.
No. of test
Carbon
Silicon
Manga
Tenacity, in Elongation , Contraction
tons per
per cent. in of area, per
sq . in .
1.75 inch
cent .
31.0
30.4
39.0
24.0
24.0
24.0
22.2
21 :5
12.0
50
90
1 :0
1.9
33.6
31.0
38.0
35.6
2.0
1 :0
10
43 :8
43.8
41 : 0
410
37.1
16.8
6.3
12.3
1 :4
3.3
1 :8
2.2
0.8
1.8
nese
CON
LA
0.30
6
7
8
9
10
11
12
13
14
0.30
0.30
0.35
0.35
0.50
0.50
0.50
0.77
0.77
0-77
0.96
0.96
0.96
0.22
0.22
0.22
0.23
0.23
0:40
0.40
0.40
0.46
0.46
0.46
0.62
0.62
0.62
0.63
0.63
0.63
0.61
0.61
0.66
0.66
0.66
0.67
0.67
0.67
0.64
0.64
0.64
33.4
33.0
360
44.0
45.2
42.2
39.8
1 Journal of the Iron and Steel Institute.
Castings.
2 Proc. Inst. of Civil Engineers, vol. xc. , p. 365.
1 :5
On the Use of Steel
336
TESTING OF MATERIALS OF CONSTRUCTION
Some very complete experiments on steel castings,
obtained from the manufacturers in America , were
made by Mr. A. V. Abbott. The tests were made
on the test bars as taken from the sand without re
moving the skin . The dimensions of the test bars were
as follows :
For tension, 17 inch diameter, 10 inches between
gauge points. For pressure, 2 inches square and 21 feet
long. For bending, 2 inches square, 2 feet long ; loaded
at the centre. The average tensile elastic limit was 13.1
tons per sq. in. , and the elongation in 10 inches 9 per
cent. The mean coefficient of elasticity was 10,900 tons
1
2
2
3
4
6
7
9
9A
9A
10
12.9
11 :4
11 :4
10.3
9.5
13.9
16 : 0
15.8
17.0
170
7.8
Deflectio
in n
,
inches
lbs
.in
Transverse
., bs
lstress
load
,
breaking
limit
transverse
Elastic
for
..in
sq
Elastic
limit
in
STEEL CASTINGS.
compression
,
per
in
sq
.tons
Elongati
on
p, er
ins
.,i10n
cent
,tons
in
tension
stress
Breaking
TABLE XVI .
.isq
n
per
tension
,tons
per
No. e
of
sampl
Elastic
in
limit
per sq . in .
19.5
16.5
18.9
197
17.1
20.6
25.3
23.3
28.2
28.0
15.4
6.0
0 :4
0.8
6.0
10.0
2.0
10.0
9.0
29.9
20.5
8.0
15.6
14.0
10.9
11.9
13.2
16 : 1
12.0
9.1
6,000
2,500
2,600
3,000
3,950
4,000
4,000
4,000
8,000
3,870
3,950
4,181
5,720
6,259
5,480
6,810
72
45
4,010
.35
72
.88
• 15
.60
20
• 21
Some experiments by the author on steel castings,
turned to ordinary test bars about 1 inch in diameter,
gave
less favourable results, as shown in table XVII.
· Proc. Inst. of Civil Engineers, vol. lxxxiii. , p. 512.
337
IRON AND STEEL
below.
Fig . 120 gives autographic diagrams for some
of these bars.
Fig . 120 .
Cast Meer
L
99FA
SOSOA
N163
15
to
N776
4
ench
per
square
za
6
Sunt
n
JI
1
-51
Exterrorons we 8 inches
TABLE XVII .
TESTS OF STEEL CASTINGS.
Extension , per cent.,
Test No.
162
163
164
165
166
167
Tenacity ,
Diameter,
in inches tons per sq .
.997
.997
•620
• 615
.619
621
j2
1.5
in.
in 10 ins.
16.26
13.05
15.07
19.86
20.53
14:52
0.61
0.30
in 8 ins .
0.37
0.68
0.75
0.25
Coefficient of
Contraction
of area , per
elasticity ,
tons per sq .
cent .
in .
0.76
0:38
0.60
10,930
14,050
9,138
9,972
10,220
8,384
There were flaws in the fractured sections of 163, 164, and 166.
Mitis Castings. — These are castings of wrought iron
to which about 0:05 to 0 · 1 per cent. of aluminium has
Z
338
TESTING OF MATERIALS OF CONSTRUCTION
been added . The aluminium lowers the fusing point
of the iron 300° or 400°. The furnace used is a petro
leum furnace, and the iron is melted in crucibles of
plumbago or of fireclay. The tenacity is said to be
20 per cent. greater than that of wrought iron , and the
4:
ductility about equal to that of wrought iron .
339
CHAPTER XI .
COPPER , COPPER ALLOYS , AND MISCELLANEOUS TESTS
OF METALS .
141. Copper . This is a deep red metal of great duc
tility, and , relatively to most metals except iron , of great
tenacity. Its density is 8 : 6 to 8 : 9 when cast, 8.8 to
8.9 when rolle 1 .
It weighs on the average 546 to
552 lbs. per cubic foot.
Its fusing point is about 2000°.
Its tenacity when cast is about 81 to 12 tons per sq. in .
Hammering or rolling increases its strength at the ex
pense of its ductility, but the ductility is restored by a
process of annealing. Phosphorus is added to facilitate
casting, and the strength is greater the larger the per
centage of phosphorus used . The phosphorus reduces
the oxides formed in melting the alloy.
The table on next page gives some of the most
trustworthy results on the strength of copper..
The coefficient of elasticity of cast copper is given
as 4,460 to 6,700 ( Thurston ) ; that of hard drawn
wire as 7,650, and of annealed wire 6,680 to 7,650
tons per sq. in . (Wertheim ).
The coefficient of bending strength is 8: 9 to 17.8
z 2
340
TESTING OF MATERIALS OF CONSTRUCTION
Tenacity, in
tons per sq .
in .
Description of material
Cast copper
Forged copper
0.015 phosphorus
02
03
04
‫ور‬
.
> >
79
Ingot copper
Cast copper
.
+
Rolled copper
8.5 to 11.2
15.2
17.0
20 : 1
21 :4
22.3
11 : 6 to 13 : 3
6.5 to 9.2
Authority
Anderson
99
Thurston
>>
L
12: 9 to 14 : 3 Bauschinger
Rolled copper, i inch thick ?
13.3 to 14.2
26.0
20.0
Hard copper wire
Annealed
‫נו‬
Unwin
Wertheim
9‫و‬
tons per sq. in . for cast copper, and reaches 26-7 for
rolled copper ( Thurston ).
Fig . 121 gives autographic diagrams for copper.
The highest diagram is a normal diagram for rolled
FIG . 121 .
Cornier Plates
20.
Tons
rer
sa
inch
15
33
1
2 NS
N ° 63 N 63
10
Extorsion
copper.
in 412
The other diagrams are for the same copper ,
heated, and allowed to cool.
1 Contraction of area , 30 to 45 per cent.
2 Extension in 8 inches, 20 to 43 per cent.; mean, 37 per cent.
COPPER, COPPER ALLOYS, ETC.
341
Tin is chiefly valuable in engineering for alloying
with copper to form bronze. Its density is 7.3 to 7 : 4
( weight, about 456 lbs. per c. ft. ) . Thurston gives its
tenacity as ranging from 0.89 to 2:68 tons per sq.in . ,
and its coefficient of elasticity as ranging up to 3,125
tons per sq. in .
142. Zinc, known also as spelter, is used for alloy
ing with copper to form brass. It is malleable within
narrow limits of temperature, and can be rolled into
sheets for roofing. It fuses at 750° to 930°. Clean
iron immersed in melted zinc gets a protective coating ,
process being termed galvanising. The zinc being
electro - positive protects the iron from oxidation ,and its
the
own oxide is insoluble in water. If, however , sulphuric
acid is present, a sulphate is formed , and the zinc coating
perishes. The tenacity of cast bars is 2.0 to 2.9 tons
per sq . in . ( Thurston ) . The author found a tenacity
of 1 : 1 to 1.5 tons per sq . in .
Cast zinc breaks without
sensible elongation or contraction . Trautwine gives
for sheet zinc a tenacity of 7:14 tons per sq . in . , and for
wire 9.8 tons per sq. in. Wertheim gives the coefficient
of elasticity as 5,360.
Lead is a very valuable metal for certain purposes
from its great ductility. Its density is 11 :4 ( 711 lbs .
per c. ft.).
It fuses at 620° Fahr. In testing it con
tracts in section very much . Its tenacity is alout
1 : 1 ton per sq. in . , reckoned on the original area of the
bar .
143. Alloys.— The most complete and extensive
342
TESTING OF MATERIALS OF CONSTRUCTION
investigation of the properties of alloys is that made by
Professor Thurston , for the United States Testing Board.
Only a very brief account of the most useful alloys can
be given here. As to the general properties of an alloy
Professor Thurston says, “ The physical properties of an
alloy are often quite different from those of its con
stituent metals. In most cases, however, the hardness ,
tenacity, and fusibility will be greater than the mean of
the same properties in the constituents, and sometimes
greater than in either ; while the ductility is usually less,
and the density sometimes greater, sometimes less. The
colour is not always dependent upon the colours of the
constituent metals, as is shown by the brilliant white of
speculum metal, which contains 67 per cent . of copper.'
BRONZES .
144. Bronzes are alloys of copper and tin. With a
moderate amount of tin the alloy is tough and strong .
With more than 20 per cent. of tin it becomes weak and
brittle. Up to 171 per cent. of tin the elastic limit,
according to Thurston, lies between 0.5 and 0.6 of the
breaking strength . With 25 per cent. it rises up to the
breaking weight. With more than 40 per cent. it falls
again till it reaches about 0 • 3 of the breaking strength
in pure tin .
Gun -metal for bearings may contain 88 to 95 per
cent. of copper. Gun-metal for guns contains usually
1 Report of the United States Testing Board, vol . i. , 1878. Also Mate
rials of Engineering.
Thurston .
Part III .
343
COPPER , COPPER ALLOYS, ETC.
90 per cent. Bell -metal contains 72 to 82 per cent. , and
speculum metal 67 to 75 per cent. The following table
gives values of the tenacity with different proportions
of tin :
Composition
Tenacity,
Description
Copper
92.0
917
91 : 0
90.0
843
82.8
81 : 1
79.0
76.3
73.0
Tin
8.0
8 :3
9-0
10 0
15.7
17.2
18.9
21.0
23.7
27.0
Gun - metal
‫ܕ ܕ‬
Bell -metal
>
tons per
sq . in.
Authority
12.95
13.84
1473
16.96
16 : 1
15.2
17.7
13.6
9.7
4.9
Anderson
Mallet
>>
19
The following table gives a reduction of those of
Thurston's results which relate to the more useful
bronzes :
Coefficient
Coefficient
Composition 1
Density
Copper
Tin
96.27
92.8
92.5
90.0
87.5
86.57
82 : 5
80.0
3.73
7.2
7.5
10.0
12.5
13:43
17.5
20.0
ofstrength
bending of elasti-. Tenacity,
Elongation
tens per
in 5 inches
, || ticity , tons
tons per
sq . in .
per sq. in .
sq . in.
per cent .
14.83
19.52
17.26
22.05
26.96
6,132
6,368
6,063
6,255
5,568
14.29
30:32
25:32
6,762
5,938
14:29
12.74
12:46
11.99
13.88
13:14
16.16
14.72
A
8.65
8.69
8.68
8.67
8.65
8.68
8.79
8.74
5.53
7:43
3.66
3-56
3:33
0.71
0.40
The bars for bending were 1 inch square and 22
inches between supports. The test bars for tension were
about 2 inch in diameter.
1 From original mixing, not analysis.
344
TESTING OF MATERIALS OF CONSTRUCTION
BRASSES.
145. Brass is an alloy of copper and zinc, sometimes
with a little lead added . Ordinary brass contains from
66 per cent. copper and 34 per cent. zinc, to 70 per cent.
copper and 30 per cent. zinc. Muntz metal, which can
be rolled hot, contains 60 per cent. copper and 40 per
cent. zinc, or sometimes 66 per cent. copper, 33 per
cent. zinc, and 1 per cent . lead .
Mallet obtained the following values for the tenacity
of brass :
1
Copper
Zinc
90.7
877
85.4
83.0
50.0
9.3
12.3
14.6
17.0
50.0
Tenacity, in tons per sq . in .
12.05
13:37
14.28
13.83
8.93
The author obtained for ordinary brass used for
machinery a tenacity of 10:43 to 11:62 tons per sq.
in ., an extension of 13 to 22 per cent. in 8 inches ,
and a contraction of area of 16 to 27 per cent. The
·coefficient of elasticity is about 5,080 for rolled brass.
The table on next page gives a selection of Thur
1
ston's results for brasses . The test bars were similar to
those for the bronzes already described .
The great change in the character of the alloy when
the zinc exceeds 45 per cent. is best marked in the
tension results . The coefficient of bending strength is
calculated from the load which deflected the bar 31
inches , or which broke it within that limit.
COPPER , COPPER ALLOYS, ETC.
Coefficient Coefficient
of bending of elasti
Composition
strength , | ticity, tons
Density
Copper
82.5
70
65
60
55
50
45
tons per
sq. in .
Tin
8.63
8.00
8.53
8.44
8.37
17.5
20
25
30
35
40
8.41
45
50
55
8.28
8.29
per sq. in .
10:35
65,440
9.46
5,567
5,985
9.97
10.92
12.70
17.40
18.95
14.94
21.63
6,265
6,175
5,461
4,258
5,107
6,261
345
Tenacity , Elongation
tons per
sq. in.
in 5 inches
.per cent .
14.55
14:59
13.62
13.02
16.88
18:33
19.77
13.84
10-78
26.7
31.4
35.8
29.2
377
20.7
15.3
5.0
0.8
Fig. 122 gives an autographic diagram for brass.
146. Ternary Alloys of Copper, Zinc, and Tin .-
Thurston has made experiments on ternary alloys, with
FIG . 122 .
No 159
Brass Ta
N ° A32 Aluminium Bror Bar
inci
NO 432
suel
are
artmbs
157
2
1
Extensions .
No 159
No 432
35
ni Benches
10
a view to determining the strongest of the bronzes .
But these results are less completely given, and the
tenacities for most appear to be estimated from torsional
experiments . Thurston terms the bronzes of composi
tion lying between copper 58 to 54 , zinc 44 to 40, and
:
346
TESTING ( F MATERIALS OF CONSTRUCTION
tin į to 2 ), maximum bronzes. Some of these have
tenacities of 31 tons per sq. in .,and clongations of 47 to
:
51 per cent. The alloys appear, however, to be subject
to great variation of quality as ordinarily made.
Delta Metal.--- Mr. Dick has discovered a method of
obtaining copier -zinc alloys, combined with a definite
percentage of iron , which have remarkable strength and
ductility. Iron is dissolved in melted zinc till the zinc
is saturated . This iron-zinc alloy is then used in proper
proportions in making brass. To prevent oxidation in
remelting, and the resulting variation of quality, a
small amount of phosphorus is added, in combination
with copper. The density of delta metal is 8.4 ; its
melting point 1800°. It con be worked hot and cold .
It can be brazed . Cast in sand it has a tenacity of
about 21 tons per sq. in . Forged at a dark red heat
the tenacity is 33 or 35 tons per sq. in . Hammered
cold its tenacity is 40 tons per sq. in.
TESTS OF DELTA METAL, SUPPLIED BY MR. DICK (UNWIN).
Tenacity ,
tons per
limit, tons tons
sq . in.
per sq. in .
Elastic
Material
Elonga
Contrac
tion , per
tion of
arer ,
per cent .
cent. in
8 inches
Cast bar
7
72
Hexagon tilted bar
Rolled bar .
8.89
7:38
7:47
10.65
22.91
7.74
23.79
16.73
17.05
29.22
33.26
9.80
8.10
12:15
11:10
23:47
25.8
11.93
15:42
5.90
18:44
50.40
Coefficient
of elas
ticity;
tons per
sq . in .
5,052
5,503
7,021
6,423
5,945
Ring cast while rotat
ing
39.75
21.1
--
Ring cast while rotat
ing, hammered cold
COPPER, COPPER ALLOYS, ETC.
347
Aluminium Alloys produced in the Electric Furnace .
Messrs . Cowles have been engaged for some time in
perfecting an electric furnace, in which a temperature is
reached at which most of the more difficult metals are
reduced . A mixture of coarsely pulverised gas carbon
mixed with the ores to be reduced is introduced into a
fireclay retort, and subjected to the current from a very
powerful dynamo. The products at present obtained
are—aluminium and silicium bronzes, aluminium silver,
and alloys of aluminium with other metals.
The 10
per-cent. aluminium - copper alloy has a tenacity of
48.65 tons. per sq . in..
The 5 -per - cent. alloy 30.3.5
tons per sq . in . Copper with 2 to 3 per cent. aluminium
is stronger than brass . Boron in small quantity affects
copper much in the same way as carbon does iron . The
alloy has a tenacity of 22 to 27 tons per sq. in . without
loss of conductivity . A copper-nickel-aluminium alloy,
termed Hercules metal, broke without sensible elonga
tion at 44 : 6 tons per sq . in . Another alloy of the same
kind broke at 49 tons per sq . in . with 33 per cent.
elongation .
1
The following results on alloys made at the Cowles
Company's works were obtained by Mr. E. D. Self
at the South Boston Iron Works .
The test bars were
6 inches long between the shoulders :
1 The above data are taken from a paper in Am . Journal of Science,
1885.
Also Proc. Inst. C.E., vol . lxxxiii. p. 510.
TESTING OF MATERIALS OF CONSTRUCTION
348
Tenacity ,
Elastic limit, Elongation in
tons per sq. in . tons per sq. in . 6 ins., per cent.
Alloy
10 p . c. aluminium bronze
10
71
10
9
9
8.
73
9
8
97
7
97
79
‫ور‬
)
1 )
, ,
:)
.
40 : 8
41.3
43.0
34.4
32.0
32 : 1
27.1
32.0
25.8
26.7
38.0
23 : 1
19.6
20 : 3
1 :5
2.5
1 :0
9.0
G.O
28.5
6.0
8.25 1
12.5 1
A bar of aluminium bronze of a more ductile
character was sent to the author by the London branch
of the Cowles Company. This bar, about 1 inch in
diameter , gave the following results :
Tenacity
Elongation in 10 inches
36 ·78 tons per sq. in.
33:26 per cent.
39.87
Contraction .
Elastic limit .
‫לל‬
17.74 tons per sq. in .
In Fig. 122 the autographic diagram for this bar is
given, showing the great toughness of the material.
147. Effect of Temperature on the Strength of the
Alloys.- Old experiments by a Committee of the
Franklin Institute show that the tenacity of copper
diminishes with increase of temperature. The following
are some of the results :
Temperature.
Tenacity,
Temperature.
lahr.
tons per sq. in .
Fahr,
Tenacity ,
tons per sq. in .
1473
13.84
11:16
801
1016
2032
8.48
4.95
0 :0
122
302
545
1 These two tests were made at Watertown, and the elongations were
measured in 4 inches.
COPPER, COPPER ALLOYS, ETC.
349
In 1877 experiments were made, under the direction
of the Admiralty, at Portsmouth Dockyard, on the effect
of temperature on bronzes.
The test bars were heated
in an oil hath , and then quickly removed to the testing
machine and broken, the operation lasting only about
a minute. This is not quite so satisfactory as breaking
specimens in an oil bath. All varieties of gun-metal
in these experiments show a slow decrease of tenacity
up to a certain temperature , at which the tenacity
suddenly falls to about half its previous value and the
ductility is almost lost. The temperature at which the
change occurred was about 370° in series I. and 250° in
series II. Phosphor-bronze was less affected . Rolled
Muntz metal and copper did not suffer serious loss of
strength below 500°.
148. Influence of Mechanical Action on the Strength of
Bronze. — The specimens of bronze were 3 inches in
length and 0.077 sq. in . section. They were subjected
to the following preparation
I. Metal as cast .
II. Metal subjected to a continued tensile stress of
49 cwts ., which produced an elongation of 16.7 per
cent .
III. Metal subjected to a compressive stress of
15.87 tons per sq. in. for ten minutes before testing.
IV. Metal elongated 20 per cent. by rolling.
Experiment II. shows, in Major-General Uchatius's
opinion, that homogeneous bronze is susceptible of
1 Uchatius. Proc. Inst. of Civil Engineers, vol. xlix. 284.
1
1
Nil
Nil
265
250
4500
500
0.75
245
4009
°350
°
300
505 10
485 10
2500
525 11
200
°
505 10
°150
1009
spheric535
D
535
T
8.25
295
Nil
450
21
525
523 19
275
260
Nil
!230
Nil
2
250 2
260 2
495 17
515 16
531
255 3
500
10
265
0.66
295
Nil
530
152
152
5
)
TLD
T
25
435
23
435
18.25
26
440
1.2
Nil
257
360 6
15
580
420 5
380 4
424 5
470 7
12
575
0.66
615
620 5
2.5
650
5
670
390 6
415 6
3.75
420
600
2.25 6
430
2.25
650 6
430 6
430 7
440
685
3.9
605 18
445 4
2.5
680
720
3.9
465
460
.,: iam
d
in
2
7
,
rods
r
Coppe
2.5
2.5
D
614
17
25
609
700
17.5
TD T
38
Zinc
62 r
Coppe
610
18
D
Tin
7
0-5
Phos
2.5
.Ziuc
92-5
92.5
Copper
metal
rods
,
d
. iam
in
.74
25.5
450
19.5
26.25
460
440.
11
562 20
Tin
6
d
i
.1niam
Muntz
Phosphor
bronze
rods
,
48026
485
26
435 25
1{
D
T
D
15.5
550 18
T
460 9
8.75
16
D
Tin
2
Zinc
15
83
Copper
5
Tin
5
Zinc
10
527 14
525
8.75
575
8.75 525
D
385
5
12.5
575
T
Atmo
T
Tin
7
Zinc 2
Temperat
87-75
Copper
87.75 ure Copper
Copper
91
85
3
975
T
| Tin
in
9.75
Zinc
2.5
2
:5
2n
se
. td
4
5
Fahr
,
1
2
rods
-mdiam
Gur
etal
.,1inch
oTuctility
lbs
in
Loads
n
machine
D25
=
.CD
testing
of
,5lever
0onstant
figures
bactual
T
columns
.in
50-25
y
The
multiplying
by
found
is
samples
the
of
strength
tensile
DIFFERENT
TEMPERATURES
AT
METALS
OF
TENACITY
.
350
TESTING OF MATERIALS OF CONSTRUCTION
ō
351
COPPER , COPPER ALLOYS, ETC.
having its elasticity greatly increased by mere stretching
without compression.
A bronze with an elastic limit
of 15.75 tons and a ductility such that it elongates 37
per cent. was previously unknown.
Elongation per cent..
Breaking
Bar
stress in tons
Elastic limit
in tons per
per sq. in.
sq.in.
Ultimate
19 :4
21 : 1
24.8
32 : 2
2.54
15.75
3:17
10.79
50.0
I.
11.
III.
IV .
Atelistic
Density
limit
37 : 3
29.5
2.1
040
-478
-058
• 170
8.863
8.856
8.957
8.975
149. Strength of Screw Bolts. The metal in an ordi
nary bolt with screw thread and nut is weakened by the
removal of metal in cutting the thread.
At the same
time the apparent tenacity is diminished from the
cause discussed in 31 . The following experiments
by Major W. R. King are interesting as giving the
results of experiments on actual screw bolts of wrought
iron . Major King is of opinion that ordinary screw
threads are too coarse in pitch, and therefore he tried
both the standard pitch of six threads to the inch and
finer pitches.
The iron of the bolts in series I. had a tenacity
of 261 tons per sq . in. of original section. In the
case of the bolt with eighteen threads, the diameter
diminished with the stress so as to allow the bolt to
draw out without stripping the threads.
The tenacity
of the bolts has been calculated on the assumption that
the threads were of standard Whitworth section .
TESTING OF MATERIALS OF CONSTRUCTION
352
Tenacity,
Series
Diameter of
bolt, in inches
No. of
threads
to inch
1
Breaking lond ,
in tons
Elongation in
7 ins. per cent.
thrend, in tons
per sq . in .
22.77
22.98
26.30
27.26
26.21
29.62
35.00
34.21
41:50
42.07
6
1
12
6
> >
12
2
reckoned on
section at
bottom of
19
18
2.0
4.3
2.5
6.0
8 :0
150. Strength of Wirc.—Wire is stronger than the
material out of which it is made, in consequence of
the greater amount of mechanical work expended on it.
When in the condition in which it leaves the draw-plate
it is virtually cold rolled .' Annealing reduces this
excess of strength . Mr. Preece gives the following
table of the strength of various specimens of wire, when
annealed for telegraphic purposes :
Description of wire
Elongation,
Breaking
Diameter
per cent .
weight, Ils.
abt.0.171in
14: 6
14.5
1,379
1,266
15 0
1,461
14.9
1,449
15.2
16.1
12 :5
1,946
1,386
1,218
1. BB puddled iron
2. BB piled iron, puddled
Extra BB, puddled and Eng
‫וי‬
lish charcoal
4. Extra special BB, puddled and
77
English charcoal
5. English Bessemer
6. Swedish Bessemer
.
7. Swedish charcoal
77
The tenacity is about 22 tons per sq . in. for iron
and 30 tons per sq. in . for steel.
Mr. Preece gives the table on next page for
and silicium bronze wire .
1 Proc. Inst. of Civil Engineers, vol. lxxv.
copper
353
COPPER , COPPER ALLOYS, ETC.
per cent .
Tenacity ,
in tons per sq. in .
$ 15 : 1 :01
27.01
Elongation,
Diameter,
in inchies
>
Siliciun bronze :
080
2 :0 : 2:05
1 :5 : 10
29:37
47.41
50.07
29:02
27.47
nil
1.5 : 2.5
0.5 : 1 : 0
0.5
30:32
29.10
30.31
28.42
nil
059
044
036
nil
mil
$ 15 : 10
081
Copper :
081
082
0847
081
M. Albert Bonnaud gives the following results
of tests of three qualities of wire :-) . Iron wire ;
II. Martin steel wire ;‫ ܪ‬III . Crucible steel wire .
The
tensile tests were made on pieces 14 W.G.( .087 inch
diameter) and 16 inches long :
Firminy wire
Bigny
---
Mean tenacity, tons per sq. in .
Elongation, per cent.
Bendings at right angles before
charcoal
iron wire
No. I.
Iron
No. II .
Martin
steel
No. III .
Crucible
steel
46
57
0.37
86
0.91
102
0.75
19
20
0.30
18
28
breaking
The bendings were over the jaw of a vice of 0.4 inch
radius. Lest the high strength here shown should be
attributed merely to hard drawing , tests were made on
four pieces in each of the following conditions :-(a ) Rod
from rolling mill ready for drawing ‫ ( ;ܪ‬6 ) unfinished
wire, drawn down as far as it could be before annealing,
A A
354
TESTING OF MATERIALS OF CONSTRUCTION
and then annealed in the case of iron, and specially tem
pered in the case of steel ; (c) finished wire , drawn down
to : 087 inch diameter ; ( d) finished wire, annealed.
Firminy wire
Samples about 16 inches long ,
No. I.
087 inch in diameter
Iron
Tenacity, in tons per sq . in .
‫ני‬
‫ܕܕ‬
2 )
Elongation, per cent.
6
27.0
28.5
с
39.3
ca
31 : 1
a
a
b
7
>>
C
.
) )
)
Bendings at right angles
d
a
b
>
C
> )
7.5 to 16.8
22.0
0:31 to 0.74
20.6
8 to 11
20 to 22
21 to 29
d
7 )
31
No. II .
Steel
63.4
88.6
101.6
54.9
6.2
3.0
1.2
6.8
to
to
to
to
7.0
5.7
1.8
8.0
2
4
16
12
to
to
to
to
4
10
37
13
The iron wire retains an increased strength, due to
drawing down, even after annealing. The steel wire, on
the contrary, is weaker after annealing than the original
bar. To utilise the value of the steel fully it must be
tempered in such a way that a sufficient flexibility is
retained.
Mr. D. K. Clark gives the following values for
phosphor-bronze wire 1 :
Unannealed .
Annealed .
About 0·11 inch diameter
1
About 0.6 in. diameter
Tenacity ,
in tons per sq. in.
Lowest
43.6
Highest
71.2
56.3
Mean
Tenacity,
in tons per sq. in..
Extension,
22.6
28.8
24 :4
33
1 Rules and Tables, p. 629.
per cent .
47
39
355
COPPER , COPPER ALLOYS, ETC.
The following table gives a few miscellaneous tests
of the strength of wire made by the author :
Sq.in.
No. of
specimen
Description
Diameter
Brass wire .
112
113
Black cast - steel rod
124
Gilding metal (no tin)
Soft German silver
125
127
128
109
110
103
102
106
107
.
>
Black shear-steel rod
> >
Black soft-steel wire
• 1929
.191
• 191
.249
.249
.267
.267
• 194
• 192
• 196
196
Brighť hard -steel rod .
• 197
.198
Tenacity, Extension
tons per
in 8 ins. ,
sq . in .
per cent.
area
· 0290
0286
0286
0487
·0487
0560
·0560
·0296
0289
0302
0302
· 0305
·0308
25.23
62.04
62.44
20:17
20.62
29.89
29.10
50.90
52:52
39.17
38:07
51.96
51:45
25.5
4:12
5.76
6.25
8.7
47.0
477
70
6.25
11.25
15.6
7 5
6.5
Steel pianoforte wire has been produced with a
tenacity of 150 tons per sq. inch.
A A 2
356
TESTING OF MATERIALS OF CONSTRUCTION
CHAPTER XII .
EXPERIMENTS ON REPETITION OF STRESS .
ENDURANCE TESTS .
151. In 1871 was published a Report by Herr A.
Wöhler on the endurance of bars subjected to repetitions of
stress.1 It occurred to Herr Wöhler that most structures,
especially such machine parts as railway axles, springs ,
and piston-rods,are subjected to a continual variation of
stress , and that direct experiment in conditions imitating
those which occur in practice might afford useful infor
mation as to the limits of stress permissible in such
Herr Wöhler carried out a series of experiments,
extending over a period of twelve years , and undoubt
cases .
edly the results are of great importance.
It may be mentioned that Herr Wöhler's machines
were handed over to the Royal Institute for testing
materials in Berlin. Further experiments have been
made with them by Spangenberg , some of the results of
which have been published . Since Prof. Spangenberg's
| Uber die T'estigkeitsversuche mit Eisen und Stahl. Angestellt von
A. Wöhler, Ober-Maschinenmeister an der Königl. Nieder-Schlesisch
Märkischen Eisenbahn .
Berlin .
A good account of Wöhler's results
given in Enginecring, vol. ii . No other tolerably complete account has
appeared in English.
357
EXPERIMENTS ON REPETITION OF STRESS
death they have been used by Herr Martens, but the
later results obtained have not been published.
Wöhler's Machine for Repetitions of Torsional Stress
( Fig. 123).- The test bar was a simple cylindrical bar
with enlarged ends . An oscillating lever c, driven by a
connecting -rod, is attached by a link s to the lever l'
on the back end of the test bar .
The stroke of the
lever c can be adjusted by moving the connecting- rod
pin in a slot in the lever. At the upper end of the link
FIG . 123 .
h
I'
k
I '
To
f
f
сC
s there are nuts, which come in contact with knife- edges
on the lever W, and which give a further means of
adjusting the stroke of the lever h'. To ensure the bar
from being strained beyond the exact stress intended ,
the opposite or front end of the test bar is fixed in the
double-lever h .
This lever presses on the short ends of
the levers g, f, the other ends of which rest on the
bearing screws k, k, and which are held down by the
long springs f,f. If the torsion given by the lever h' is
in excess of a fixed amount, the lever h lifts either the
358
TESTING OF MATERIALS OF CONSTRUCTION
lever g or g' against the spring. By adjusting the
springs, the exact stress at which the levers g orglift
can be arranged. If the test bar is to be twisted in one
direction, only one of the levers g or g is required . If
the stroke of the lever l' is large enough it twists the
bar alternately in opposite directions, and then both
levers , I and g' , are used to limit the stresses.
When
working in adjustment, the stroke of his sufficient to
just lift one or both the levers g or g at each stroke.
Wöhler's Machine for Repeated Tensions (Fig . 124 ) .
- This consists of a wrought-iron bed -plate, at the left
T
FIG . 124 .
8
inte
in
PO
A
9
o
M
f
x
o
C
f
10 )
1 .
1
8
o
(2
hand end of which is a cast- iron standard , supporting the
knife-edge of the principal lever h. The test bar A is
held in a shackle attached to the lever ; the other shackle
is attached to an adjusting - screw b . The long arm of
the lever is connected by a link to the equal-armed
beam m . The centre of this beam is pulled down by a
lever worked by a connecting-rod, a bent spring g being
interposed to prevent shock . The other end of m rests
EXPERIMENTS ON REPETITION OF STRESS
359
on the short arm of the lever k, which has a bearing
screw and long spring f, as in the torsion machine. If
the pull on m exceeds a certain value the lever k lifts,
and by adjusting the spring f the tension can be regu
lated as desired . To facilitate the adjustment the rod d ,
by which the pull is applied to the beam m , is in two
parts , connected by a long coupling nut with right and
The rod d is continued down through
a bracket, and a nut under this bracket serves to limit
left hand screws.
the extent to which the test bar is relieved of stress .
In adjusting the machine to give a range of tension
between a fixed lower and fixed upper limit, the spring
f is first adjusted to the minimum stress.
The nut on
the end of d can then be adjusted, so that when d rises
it just keeps the lever k lifted . Then the spring f is
adjusted for the maximum stress , and the machine is
ready for use . As made by Wöbler the machine had
four sets of levers , so that four bars could be tested
simultaneously.
Wöhler's Machine for Repetition of Bending Stresses .
-For applying repeated bending stresses to bars, the
stress ranging between a fixed lower and upper liinit,
Wöhler employed the machine shown in Fig. 125. The
test bar A rests on knife-edges carried by pairs of links .
At a the links are suspended from a fixed bracket. At
b they hang from the short arm of the lever d . This
lever has a bearing - screw at its longer end , and it is
held down by a spring f. The bar is bent by the rod
1
2,
furnished with an adjusting coupling, and moved up
360
TESTING OF MATERIALS OF CONSTRUCTION
and down by a lever and connecting -rod. When the
bar is not to be entirely released from stress, but to
be strained between a fixed upper and lower limit of
stress, the screw m is used.
As the bar unbends it
comes in contact with m at some fixed amount of de
flection . To adjust the screw m , the spring f is set to
the desired minimum tension , and the screw m is then
FIG . 125 .
in
INTRO
a
re‫ܕܐ‬
7
coin
18
q
2.0
WOWA
MUDA
A
a
adjusted till it just lifts the lever d.
Then the spring
f is set to the maximum tension, and the machine is
ready for use.
Wöhler's Machine for Repeated Bending in Opposite
Directions. For repeated bendings in opposite direc
tions Wöhler used the very simple machine shown in
Fig. 126. It consists of a wooden frame carrying in
bearings the axle a , which is rotated by a belt. In the
ends of a are conical recesses, into which can be fixed by
driving two test bars . After being fixed, the test bars
are turned in the lathe so as to run truly .
At the ends
EXPERIMENTS ON REPETITION OF STRESS
361
of the test bars are fixed spring balances, which can be
adjusted to any required stress.
As the bar rotates
FIG . 126 .
аa
S
S
3
6
ő
152. Results of Wöhler's Endurance Tests.
The fol
lowing tables contain all Wöhler's more important
results. Table I. gives some ordinary statical tests of
the materials used in the subsequent endurance tests.
The elongation was probably measured in 8 inches, but
the length is not given .
why
railway axles.
wr
www
every fibre is subjected to bending alternately in oppo
site directions, precisely as is the case with journals of
362
TESTING OF MATERIALS OF CONSTRUCTION
TABLE I. STATICAL TENSILE STRENGTH OF THE MATERIALS
EXPERIMENTED ON BY WÖHLER.
Tenacity,
No. of
bar
Material
1
WROUGHT IRON :
Phoenix Co.'s axle .
2
3
4
5
7
8
Bar iron from Königshütte
Rivet iron (Berlin, Borsig )
Boiler stay iron (Borsig).
in tons per
sq . in .
Elongation ,
21 : 1
21.5
29.2
24 : 4
33.0
34.0
29.6
24.4
17.8
21 8
7.0
20.8
22.0
23.6
17.0
19.0
27.5
277
29.2
24.6
16.2
217
49.0
49.7
12.1
18.6
117
23.7
174
18.3
19.0
217
22 :3
per cent.
HOMOGENEOUS IRON :
9
10
Pearson , Coleman , & Co.
99
>>
11
CAST - STEEL AXLES AND BARS :
12
Krupp, steelaxles .
13
.
g )
14
.
>>
a )
15
16
17
>>
Bochum Company, steel axles
18
19
20
21
22
23
24
25
Borsig , steel axles
.
>
Vickers, Sons, & Co. , steel axles
)
Werner, hardened-steel axle
.
same axle annealed
Krupp, cast-steel rails
47.8
48.7
55.0
27
28
41.8
41.8
42.0
42.5
39-4
37.3
29.2
26 : 3
52.3
60.2
48.7
>>
26
49.7
Firth & Sons,'tool steel
19 :5
15.8
1 :1
2.2
27
15.8
15 :4
9.1
CAST- STEEL PLATES :
29
30
Krupp, I direction of rolling
99
31
).
32
33
34
.
-
79
|| direction of rolling
97
2 )
Borsig
99
+
33.9
36 : 3
32.0
36.3
377
33.0
12.2
10 8
10.2
9.5
22 : 0
22.3
Only a few endurance tests with the torsion machine
are given. These consist of some experiments with
EXPERIMENTS ON REPETITION OF STRESS
363
Krupp's axle steel , twisted in one direction only and in
opposite directions alternately.
TABLE II. WÖILLER'S EXPERIMENTS ON BARS SUBJECTED TO
REPEATED) TWISTINGS.
No. of
bar”
Stress applied ( at surface
of bar ) , in tons per sq . in .
Material
Maximum
Minimum
Range of
stress, in tons
per sq . in .
No. of repeti
tions before
fracture
‫ܠ‬
‫ܢ‬
‫ܬ‬
‫ܘ‬
‫ܪ‬
‫ܐ‬
1. Torsion in one direction only
Krupp's
22.9
21 5
20 : 1
0
19 : 1
0
0
axle steel
18-1
22.9
21.5
20 : 1
19.1
18 1
198,600
373,800
334,750
879,700
[23,850,000 ]?
II . Equal alternate torsions in opposite directions
7
Krupp's
8
9
axle steel
+ 13.4
+ 12.4
+ 11 :5
+ 10.5
– 13.4
- 12 : 4
-11 :5
– 10.5
3
26.8
187,500
24.8
23.0
21.0
1,007,550
859,700
19,100,000 ]
For any given stress a certain number of repeti
tions of load produce fracture, the smaller the greater
the intensity of the stress. But below a certain limit
of stress a practically unlimited number of repeti
tions of load is required to cause fracture. Roughly
speaking, the stress for which an unlimited number of
repetitions is required to cause fracture is only half as
great when the bar is alternately strained in opposite
directions as when it is strained in one direction .
A bar strained in one direction will stand 24 million
repetitions of a stress of 18 tons per sq . in . , a much
larger stress than would ordinarily be considered safe.
1 Had previously suffered 286,000 repetitions of stress of 21.5 tons
per sq. in.
2 Not broken
8 Had previously suffered 1,070,000 repetitions of a stress of from 9 5
to 12 :4 tons per sq. in.
364
TESTING OF MATERIALS OF CONSTRUCTION
Table III. gives Wöhler's results on the endurance
of bars subjected to repetitions of tensile stress, the
stress in some cases varying from zero to a maximum
limit, in others from a minimum to a maximum value.
Two forms of bars were tried .
The bars marked A
had well - rounded corners at the point where the small
middle part joined the enlarged end. Those marked
B had square corners . It may be noted at once that
for any given stress the bars B broke with far fewer
repetitions of stress than the bars A. Thus, bar 5 of
form A stood 480,000 repetitions of a stress of 17:19
tons per sq. in. , while bar 9 of form B stood only 37,000
repetitions of a stress of 17.10 tons per sq. in. Bar 16
of form A was not broken with 13,000,000 repetitions
of a stress of 22 tons per sq. in. , while bar 21 of form
B broke with 35,000 repetitions of this stress.
The next most important point in Table III . is that
the amount of variation of stress, not the absolute amount
of the stress, determines the number of repetitions before
fracture. Thus, bars 7 and 8 endured nearly as many
repetitions as bar 6 , though in the former case the
maximum stress was 21 tons and in the latter 15.
But
then the load was not entirely taken off bars 7 and 8, and
the range of stress was only 91 and 114 tons.
Again,
bar 18 is not broken with 12,000,000 repetitions of a
stress of 38 tons per sq. in . , the minimum load being
19 tons per sq. in . ; but bar 10 broke with 19,000 re
petitions of a stress of 38 tons , the minimum stress
being zero .
EXPERIMENTS ON REPETITION OF STRESS
365
TABLE JII. WÖHLER'S EXPERIMENTS ON BARS SUBJECTED TO PEPEATEI)
TENSIONS BETWEEN DEFINITE LIMITS .
Stress applied, in tong
8
9
A
A
А.
А
А
A
B
10
A
11
A
А
А.
A
A
A
A
17
18
19
23
24
25
26
27
28
29
30
31
32
33
34
35
36
Minimum
0
0
0
0
0
+ 9:55
+ 11:46
0
38.20
33:40
28.65
0
0
28:14
0
0
0
0
22.92
21:01
19.10
17:19
17:19
15:28
11:46
9.55
17 10
38.20
33.40
28.65
26.14
23.87
22.92
21.95
14:33
800
106,910
340,853
409,481
480,852
10,141,645
2,373,424
[ 4,000,000 ] "
37,828
18,741
46,286
170,170
12:3, 770
473,766
1
А.
38.20
19.10
19:10
A
38.20
16.70
21:50
[1 2,000,000] '
23.89
21.97
20.08
0
0
23.89
21.97
20.08
19.10
17 18
15.29
B
21
22
22.92
21.01
19.10
17:19
17:19
15.28
+ 21:01
7. 21:01
17:10
Nuinber of
Range of
stress, in tons repetitions before
fracture
per sq . in .
(13,600,000]
(13,200,000)
(1,801,00011
112,100,000]
B
B
B
B
B
B
А
A
A
А.
A
A
А.
A
А.
A
axle
Krupp's
16
Maximum
23.87
22.92
21.95
+ 38.20
steel
12
13
14
15
+ 23.87
19:10
17.18
15.29
14:34
loco
from
iron
Cast
7
motive r
cylinde
6
PIron
axle
, hoenix
Company
А.
A
per sq . in .
Material
steel
axle s
Krupp'
No. Form )
of
of
bar bar
7.62
6.69
6.22
5.73
0
0
14:34
0
0
0
5.26
5.03
5.03
478
478
4.78
0
0
0
1 Not broken .
23,546
35,486
65,658
75,343
208,883
274,970
( 1,100,000]
7.62
3,140
6.69
4,000
10,342
45,028
78,682
27,885
35,599
208,439
6.22
5.73
5.26
5.03
5:03
4.78
478
478
[ 7,200,000]
17,600,000
1
1
366
TESTING OF MATERIALS OF CONSTRUCTION
This table contains some results on cast iron which
are interesting. Although this material is somewhat
more irregular in quality than wrought iron or steel, it
evidently behaves in the same general way.
In Table IV. are given the results of the experi
ments on the endurance of bars subjected to bending.
These exactly confirm those obtained with torsion and
simple tension. Further, as bending tests are made
more easily than other tests, and the deflections are
large and easily determined, these experiments are
numerous and very regular.
The stress given in the
tables is that of the extreme fibres, calculated from the
load, by the usual formula f = M/Z ; and of course this
stress, for all cases in which the elastic limit is exceeded ,
is greater than the real stress due to the load . It has
several times been alleged that this discrepancy destroys
the value of any deductions from these experiments by
bending. This view is put forward by those who hesi
tate to accept the conclusion that the breaking stress
with repetition of loading is so much smaller than the
statical breaking strength . It seems to have been over
looked that whatever error there is in the calculated
stress given in Wöhler's tables is in the opposite direc
tion, and that the bars broke, in fact, with smaller stresses
than those calculated and recorded in the tables. Bend
ing experiments are not less trustworthy than tension
experiments, and for stresses considerably less than the
statical breaking weight probably the error in the calcu
lated stress is not a large one .
EXPERIMENTS ON REPETITION OF STRESS
367
TABLE IV .-- WÖHLER'S EXPERIMENTS ON BARS SUBJECTED TO REPETITIONS
or TRANSVERSE STRESS (REPEATED BENDINGS) BETWEEN DEFINITE LIMITS .
Bars
Stresses applicd, in
tons per sq. in .
No. of marked
Material
Iron
for
axles
,
ened
Phoenix
by
made
geneous
Company
bar
H were
hard
Range of No. of repetitions
stress, in tone of load before
per sq . in.
26.25
6
23.87
21:50
19:10
17 18
15.28
7
14.33
0
26.25
23.87
21:50
19:10
17.18
15:28
14:33
38.20
33:41
19:10
19.10
14:31
0.
19:10
19.10
19.10
26.25
25.07
24.83
23.87
23:87
0
26.25
25.07
24.83
23.87
23.87
10
11
12
Bochum
13
14
15
16
17
18
19
-scast
teel
axles
9
Company's
8
iron
Krupp's Homo
3
steel
Krupp's
21
22
23
24
25
plates
IN
20
27
29
30
31
32
33
34
35
36
37
H
H
H
H
H
H
H
H
H
1 Not broken.
steel
spring
Krupp's
26
28
axles
steel
1
2
fracture
Maximum Minimum
33.41
28.65
26.25
23.87
23.87
21:50
0
0
0
0
25:07
23:15
23.87
22.93
28.65
26.10
0
0
52:50
481,950
1,320,000
4,035,400
13,420,000]
(48,200,000)
1
1
475,500
1,234,600
[34,500,000]
1
1,762,300
1,031,200
1,477,400
5,234,200
[40,600,000]
I
104,300
317,275
612,500
729,400
1,499,600
[43,000,000 ]
1
25.07
23:15
23.87
22.93
28.65
26:10
[4,100,000 ] 2
271,8002
0
52.50
47.75
54,600
0
42.95
0
47.75
42.95
38.20
35.85
35.85
33:40
33:40
33.40
28.65
33.41
28.65
26.25
23.87
23.87
21:50
169,750
420,000
0
2 Across direction of rolling.
38.20
35.85
35.85
33:40
33:40
33.40
28.65
175,300 ?
387,700 2
420,100 3
[ 3,600,000 ]" 3
76,300
200,100
339,150
330,750
389,200
293,300
455,700
268,900
[ 36,500,000 ]
3 In direction of rolling.
36S
TESTING OF MATERIALS OF CONSTRUCTION
TABLE IV . — continued .
Bars
marked
No. of
II were
bar
hard
Stresses applied , in
tons per sq . in .
Materia )
Maximum
38
39
steel
Krupp's
spring
ened
40
41
42
43
44
H
47
48
49
H
50
51
52
53
H
H
H
H
H
H
No. of repetitions
of load before
fracture
Minimum
4775
42.95
38.20
38.20
33:40
28.65
23.87
21:50
0
0
0
47.75
42.95
38.20
38.20
33.40
28.65
23:87
21:50
57:30
14:33
19.10
23.87
28.65
33.42
33.42
38.20
42.95
42.97
38.20
33.43
28.65
23.88
23.88
19:10
14:35
7.92
15.92
23.87
27.83
31.52
9.55
14:33
19.10
23.87
23:87
28.65
4.77
9.55
14:33
14:33
19:10
19:10
39.83
31.83
steel
46
Krupp'
spring s
45
Range of
stress, in tons
per sq . in .
27
‫נו‬
‫و‬
39,950
72,450
132,650
117,000
197,400
468,200
[40,600,00071
(32,942,000 ]
1
22,900
35,600
86,000
191,100
50,100
251,400
( 35,600,000 ]
33,478,700
1
--4775
54
55
steel
spring
Krupp's
56
57
58
59
60
61
42.95
7 )
7 )
02
63
64
38.20
65
66
7 )
2
67
08
69
70
71
7 )
>>
26.75
33:41
79
H
H
steel
spring
77 )
1Η
H.
S
76
77
78
Company's
73
74
75
Bochum
72
4.77
9:55
11.94
14:33
52:50
47.75
42.95
38.20
1 Not broken .
23.88
19.92
16:23
33:40
28.62
23.85
19.08
19.08
14.30
33:43
28.65
23.87
23.87
19.10
19.10
11.45
28.64
23.86
21:47
19.08
52:50
4775
42.95
38.20
62,000
149,800
400,050
376,700
[19,673,300 ]
1
81,200
156,200
225,300
1,238,900
300,900
[33,600,000 ]
1
99,700
176,300
619,600
2,135,670
[ 35,800,000
38,000,000 ]
[36,000,000 )
286,100
701,800
[36,600,000 ]
(31,150,000)
45,850
108,850
93,800
148,400
1
1
1
369
EXPERIMENTS ON REPETITION OF STRESS
TABLE IV.--continued .
Bars
Stresses applied, in
tons per sq. in.
No. of marked
84
85
86
87
88
89
90
91
92
93
94
H
H
H
H
Il
spring
steel
spring
Mayr's
Seebohm's
H
81
82
83
95
Range of
No. of repetitions
stress, in tons
per sq . in.
of load before
fracture
Maximum Minimum
47.75
33:42
31:04
28.65
23.87
62.10
57.30
52:50
47.75
45 35
steel
spring
80
Material
Seebohm's
bar
I were
hard
ened
42.95
38.30
33:42
28.65
26.25
23:87
0
47.75
39,800
33.42
212,700
31:04
28.05
23.87
0
62:10
57:30
52.50
4775
45:35
0
42.95
38.30
33:42
28.65
26.25
23.87
0
0
360,100
1
(30,500,000 ]
(26,260,000 )
1
28,350
45,500
46,550
141,750
190,050
80,850
154,000
210,000
471,800
538,850
1,105,500
Lastly, Table V. gives the results of experiments
on rotating bars subjected to bending. As the bar
turns round while bent in a fixed direction by the spring,
every fibre is alternately in compression and tension ,
and these are the only experiments of Wöhler in which
alternate opposite stresses of tension and compression
were obtained . The torsional experiments agree with
the bending experiments as to the effect of stresses in
opposite directions.
Wöhler tried three forms of bars in this research .
Two of these had square corners at the enlarged end .
These two forms were relatively much weaker than the
bars of the third form with rounded corners, and only
1 Not broken .
B
B
370
TESTING OF MATERIALS OF CONSTRUCTION
the results of these latter are given in the following
table :
TABLE V. Wöhler's EXPERIMENTS ON BARS SUBJECTED TO REPETITIONS
or TRANSVERSE STRESS (ROTATING BARS) BETWEEN EQUAL AND
OPPOSITE LIMITS OF STRESS .
Stress applied, in tons
per sq . in .
No. of
Material
1
2
3
Iron
for
,axles
Phoenix
Company
bar
Maximum
+ 15 :3
14 :3
13 :4
24
25
26
27
28
29
30
31
32
teel s
sKrupp'
-cast
7
iron
Homogeneous
5
6
Minimum
- 15 :3
11 :5
10 :5
9.6
8.6
7.6
14.3
13.4
12.4
11 : 5
10.5
9.6
8.6
7.6
+ 23.9
22.9
- 23.9
22.9
12 : 4
21.9
21.9
18.2
16 :3
14 : 3
13.4
12 : 4
18.2
16 :3
14 : 3
13 :4
12.4
11 :5
11 : 5
38
15 : 3
15.3
153
39
40
14.3
- 20 : 1
17.2
16 :3
15 :3
15 :3
15.3
14 :3
14.3
+ 17.2
- 17.2
16 :3
15 :3
16 : 3
15 :3
15.3
14 :3
14 :3
13 : 4
33
axles
34
35
36
37
53
16 : 3
-sCast
teel
,axles
14 : 3
Boch
&o. um
C
46
47
48
49
50
51
52
+ 20 :1
17.2
153
14.3
14 :3
13.4
12 :4
Range of
of repetitions
stress , in tons No.
before fracture
per sq . in.
12 : 4
1 Not broken .
30.6
28.6
26.8
24 :8
23.0
210
19.2
17.2
15.2
47.8
45.8
43.8
36.4
32-6
28.6
26.8
24.8
23.0
56,430
99,000
183,145
479,490
909,840
3,632,588
4,917,992
19,186,791
[ 132,250,000 ]
2,375
4,986
11,636
31,586
94,311
161 , 262
464,786
636,500
3,930,150
55,100
127,775
797,525
40.2
34.4
32.6
30.6
30.6
30.6
1,665,580
3,114,160
28.6
28.6
4,163,375
45,050,640
34 :4
32.6
342,850
30.6
30.6
28.6
28.6
26.8
24.8
1
642,675
127,775
627,000
20,467,780
2,845,250
[57,360,000] "
3,558,700
( 14,176,171]
EXPERIMENTS ON REPETITION OF STRESS
371
TABLE V .-- continued .
Stress applied, in tons
54
55
56
57
per sq . in .
ons
BSVickers
'&orsig's
cast
Dar
Maximum
14.3
axles
cast
steel
63
64
65
66
67
68
74
75
76
77
78
79
80
+ 16 : 3
15 : 3
14 :3
134
12.4
Firth
&
Sons
'tool
steel
09
70
71
72
73
+18.2
17.2
16 : 3
15.3
58
;;
‫ܕ ܕ‬
‫ܕ ܙ‬
Minimum
- 18.2
17.2
16 :3
15.3
14 :3
- 16 : 3
15 : 3
14 : 3
13.4
12 : 4
11 : 5
10 :5
11 : 5
+ 17.2
10.3
153
- 17.2
16.3
15.3
14 : 3
14 : 3
Copper
Range of
stress , in tons
Material
steel
asles
No. of
10.5
+7.64
- 7.64
7.64
6.69
6.21
5.97
573
478
7.64
6.69
6.21
5.97
5.73
478
No. of repetitions
before fracture
per se in .
157,700
364
344
239,875
553,850
32.6
30.0
1,373,225
28.6
1,023,625
32.0
30.6
28.0
26 : 8
24.8
23.0
21.0
51,240
72,940
205,800
278,740
564,900
3,275,800
[8,660,000 ]'
34 :4
32.6
30.6
370,975
694,450
233,700
28.6
1,528,550
15:28
15.28
13:38
12:42
11.94
11:46
9.56
30,875
67,725
480,700
663,100
798,000
2,834,325
19,327,460
153. Wöhler's Conclusions.-In certain structures the
whole load is a permanent, or dead, load . With such
cases Wöhler's investigation is not concerned .
But in
most cases a part or the whole of the load is occasional,
or varying. In those cases the engineer has to allow
for a practically unlimited number of repetitions of load.
Railway axles, for instance, may make 300 million
revolutions , involving reversal of stress, before being
put out of service. Now, with such varying conditions
1 Not broken .
B B 2
372
TESTING OF MATERIALS OF CONSTRUCTION
of straining action, safety depends, according to Wöhler,
not at all on the maximum stress, but only on the range
of variation of stress .
The following table gives the stresses and ranges of
stress which Wöhler considers to be the limiting values
which ,in the materials he experimented on, would only
produce fracture after an indefinitely large number of
repetitions :
TABLE VI.
LIMITS OF STRESS FOR UNLIMITED REPETITION Or Load
(WÖHLER ).
Maximum
Material
Minimum
stress, tons per stress, tons per
sa in .
Range of
stress
sq . in.
A. Bars subjected to simple tension, compression, or bending
+ 7.05
15.30
- 7.65
Wrought iron
7 )
9
2 )
12
Cast-steel axles
7
‫וי‬
Untempered cast-steel springs
97
7
,,
79
>>
,,
+. 15.80
+ 21:00
+13 :38
+ 23:00
+- 38.20
+23.90
+ 33.50
+ 38.30
+ 43.00
0
+ 11:50
- 13:38
0
+ 16.70
0
+- 11:50
+ 19:10
+- 28.70
15.80
9.50
26:76
23.00
21:50
23.90
22.00
19.20
14.30
B. Burs subjected to shearing or torsion
Cast-steel axles
‫ܕ ܕ‬
10.50
18.20
- 10:50
0
21.00
18.20
‫ול‬
154. Experiments by Spangenberg with Wöhler's
machines entirely support Wöhler's conclusions. If
the stresses are plotted as abscissä , and the number
of repetitions causing fracture as ordinates, curves are
obtained such as those in Fig. 127. These curves cut
the axis of abscissæ at the statical breaking stress, and
they are asymptotic to a vertical, the abscissa of which
EXPERIMENTS ON REPETITION OF STRESS
373
is the stress which the bar will carry if repeated an un
limited number of times .
155. Endurance Tests made by Mr. B. Baker . – Mr. B.
Baker has given the results of a series of experiments
FIG . 127 .
Pepetitions
urint 1000
4 300
4.000
!
3.500
.
5.000
Bendin
Trong)(
Azle
1
2.300
1
inelg)(
ndStemp
BeTi
BendIrinong)(
Pestphalia
8.000
1.300
1.000
ne
li
a
ph
800
Kr
Q
up
p
o
Stee
l
5
Stress
is
20
15
tonsper sq. in.
on iron and steel made with a machine like that shown
in Fig. 126. The rotating bars were 1 inch in diameter
1
· Notes on the Working Stress of Iron and Steel . ' Am . Soc. of
Mech. Engineers.
1886.
TESTING OF MATERIALS OF CONSTRUCTION
374
and the weight was hung at 10 inches from the fixed
The bars rotated 50 to 60 times aa minute.
end .
The
soft steel was fine rivet steel , with a tenacity of 26-8
to 28.6 tons per sq . in. , and an elongation of 28 per
cent . in 8 inches .
The bard steel was fine drift steel ,,
having a tensile strength of 54 tons per sq. in., and
an elongation of 14 per cent. in 8 inches . The iron was
best rivet iron, with a tenacity of 25.9 to 27: 3 tons per
sq. in . , and an elongation of 20 per cent. in 8 inches.
Some further experiments by Mr. Baker on simple
bending are also given :
EXPERIMENTS ON THE ENDURANCE OF ROTATING BARS
TABLE VII.
SUBJECTED TO BENDING (B. BAKER ).
No.
1
2
Material
Soft steel
7 )
3
>>
‫ܕ ܕ‬
7
9
22
8
>>
Hard steel
10
11
12
13
14
15
16
‫ܕ ܕ‬
> >
> >
17
18
19
20
Best
bar
21
iron
22
23
Maximum
Minimum
Range of
stress, tons
per sq. in .
stress, tons
stress, tons
tions to cause
per sq . in .
per sq . in .
fracture
+ 16 :1
16 :1
15.2
15.2
15.2
15.2
15.2
11.6
- 16 : 1
+ 29.9
29.1
23.9
23.9
20.8
22.8
18.1
15.2
- 29.9
+ 15.2
15.6
15.2
14.3
13.5
14.3
13.8
- 15.2
15.6
15.2
16 : 1
15.2
15.2
15.2
15.2
15.2
11.6
29.1
23.9
23.9
20.8
22.8
18.1
15.2
14.3
13.5
14.3
13.8
32.2
32.2
30.4
30.4
30.4
30.4
30.4
23.2
59.8
58.2
47.8
47.8
41.6
45.6
36.2
30.4
30.4
31.2
30.4
28.6
27.0
28.6
27.6
Number of repeti
40,510
60,200
68,400
92,070
107,415
128,650
155,295
14,876,432
5,760
7,560
14,600
16,300
26,100
32,445
157,815
472,500
108,160
110,000
141,750
389,050
408,000
421,170
480,810
i
EXPERIMENTS ON REPETITION OF STRESS
375
The following table gives results of experiments
on flat bars, some bent alternately in opposite directions,
the others bent one way only . The soft steel had a
tensile strength of 31.3 tons per sq. in ., and an elonga
tion of 20 per cent. in 8 inches . The iron was best
bar iron. The bars were 32 inches long, 1 inch wide,
and 1 inch thick .
TABLE VIII.
ENDURANCE TESTS. BARS SUBJECTED TO BENDING
(B. BAKER).
Stress applied, in tons per
sq . in .
No.
Material
Maximum
24
Soft steel
25
26
27
28
29
30
31
32
33
34
35
36
>>
‫לל‬
>>
+ 19.7
19.7
19.7
18.8
18.8
16 : 1
154
18.8
16 : 1
15 : 4
15.2
15.2
12.3
12 :3
15 4
Best
bar
iron
Minimum
-19.7
19.7
19.7
18.8
79
+ 15.2
15.2
15.2
Number of repeti
Range of
tions before
stress, in tons
fracture
per sq . in .
0
-15.2
15.2
0
39.4
39.4
39.4
37.6
37.6
32 :2
30.8
30.4
24.6
15.4
30 : 4
30.4
15.2
12,240
12,325
12,410
18,100
18,140
72,420
147,390
262,680
1,183,200
[3,145,020]
184,875
250,513
[3,145,020]
The bars 33 and 36 were not actually broken, but
when taken out of the machine were found to have
deep flaws.
156. Bauschinger's Experiments on Repeated Tensions.
- Table IX . contains a summary of all Bauschinger's
experiments on the endurance of a bar subject to re
peated stresses. He constructed a machine of the same
kind as Wöhler's, in which a bar could be subjected
to stresses ranging from 0 to an upper fixed limit in
376
TESTING OF MATERIALS OF CONSTRUCTION
He ascertained both the initial elastic limit and
tension .
the elastic limit acquired under repeated repetition of
stress ;
the initial breaking strength and the strength
after the bar had been broken in the Wöhler machine .
TABLE IX.
ENDURANCE TESTS.
BARS SUBJECTED TO TENSION
(BAUSCHINGER ).
i
Stresses in tension varying from 0 to an upper limit. )
Elastic limit, in tons
Endurance test
Material
Original
Acquired
during
repetition
of loads
6.84
Wrought
iron
6.84
plate
6.84
6.84
15.0
15.6
15.6
15.6
12 : 3
13.2
14 : 4
16 :4
19.4
18.0
200
16 :4
15.6
15.6
15.6
Mild -steel
plate
15.6
15.6
15.6
15.6
15.6
15.6
15 : 6
15.6
15.6
118
Bar iron
11 8
11 8
11.8
11.8
14 : 8
14.8
14 : 8
19 :1
19.0
19.0
19.9
16 : 4
Load
No, of
before
tons per
sq. in .
7.1
9.85
13 : 1
16.4
16.0
16 :0
16 : 0
16 : 0
19.7
19.7
23.0
23.0
23.0
23.0
23 :0
26.2
26.2
26.2
5:17
5:19
5.18
2.28
6.68
3.55
[ 11:03]
tion of
loads
25.2
25.2
25.2
25.2
28.5
28.5
28.5
28.5
28.5
28.5
28.5
28.5
28.5
28.5
26 : 6
26.6
26.6
26.6
26.6
26.7
26 :7
26.7
9:11
7.40
0.64
0.24
0.84
16:48
9.31
0.67
24.3
24.5
28.5
0.76
13.2
16.4
19.7
19.7
19.7
13.8
17.2
19.7
23 6
28.5
28.5
28.5
28.5
21 :4
10.7
10 : 8
10.6
10.9
16.3
18.6
11.9
Original by repeti
7:35
0:07
1:01
0:32
26.2
26.2
breaking
fracture,
in millions
11 : 5
153
After
applied , repetitions
0:16
0:44
0.62
0:34
0:49
0:07
0:11
0.04
20.0
16.9
15.9
12.3
Tensile strength , in
tons per sq . in .
per sq . in.
28.5
1
28.2
2
27.1
26.6
| Not yet broken in endurance test.
» Elastic limit rose to 167, and then fell near the end of the en
durance test.
EXPERIMENTS ON REPETITION OF STRESS
377
TABLE IX.--continued.
Elastic limit, in tons
Endurance test
per sq . in .
Tensile strength, in
tons per sq . in.
After
No. of
Material
Acquired
during
Original repetition
of loads
Thomas
steel axle
Thomas
steel rail
Mild - steel
boiler plate
..
17.6
17.6
17.6
17.6
17.6
20 : 4
19.0
19.0
19.0
19.0
240
17 :0
17.6
176
17.6
17.6
176
17.6
17.6
176
180
20.8
Load
repetitions
before
applied
breaking
Original by repeti
tion of
loads
fracture ,
in inillions
163
26.2
197
26.2
26.2
[9:58]
40 : 1
0.62
9.04
40 : 1
0.22
40 : 1
0.06
40 : 1
16 : 4
10:19
19.7
26.2
20.2
7.91
0.57
0:56
390
390
390
390
40 : 1
184
4.85
26 6
210
26.6
26 : 6
20.6
26.6
26-6
26.6
26.6
184
16 : 4
0:40
0:49
0.88
6:34
18.0
100
18.7
10.4
187
[6-54]
(4.871
21 0
21 :0
0:40
i
41 : 0
39.4
377
1
All the published experiments on endurance have
now been brought together and reduced to common
measures , because the subject of safe limits of stress,
especially in bridges, must before long be reconsidered ,
and because, while experiments of this kind take a long
time to make, it is the number and consistency of the
results which are most impressive . A few results of bars
breaking with comparatively small stresses might be
put aside as possibly accidental or abnormal.
But here
are four completely independent series of researches, by
different observers, with stresses of different kinds , on
| Not yet broken .
378
TESTING OF MATERIALS OF CONSTRUCTION
very various materials ; and the whole of the results
are very singularly consistent.
In all cases the number of repetitions of loading
the bar will bear diminishes with increased range of
variation of stress . Further , it is very striking how
regularly progressive the diminution of the number of
repetitions is as the range is increased . It is impossible
not to conclude that, whatever the cause of decreased
life of the bar may be, it is a cause which acts con
tinuously, altering in some way the structure or the
properties of the bar.
Undoubtedly it would appear likely that any gradu
ally progressive alteration or fatigue of the bar would
be manifested in some way in alteration of the strength ,
the elastic limit, or the elongation of the bar when tested
in the ordinary way. But this, so far, appears not to
be the case . A bar subjected to so many repetitions of
loading that it is known to be on the point of breaking,
or a piece of a bar already broken in an endurance test,
gives in the testing machine no indications that the
strength or ductility has been altered. Both Mr. Baker's
and Professor Bauschinger's results agree in this, and it
is in accordance with experiments on pieces of structures
long subjected to loading. Professor Kennedy has
given a series of tests of old rails, tyres, and other long
used material, and no one would guess from the results
that these test pieces were in any way different from
new material .
But this in no way gets over the fact
1 Prof. Papers of Royal Engineers, 1884.
EXPERIMENTS ON REPETITION OF STRESS
379
that material subjected to repeated loading is different
from new material. The material, after a certain num
ber of repetitions with a given range of stress, does
break with fewer subsequent repetitions . For some
reason the ordinary testing machine observations are
too coarse to detect the difference.
Whatever the alteration produced by repetition may
be, it certainly does not appear to be a loss of strength
( statical resistance ). If it is a loss of ductility or
power of elongation, then it must be a loss confined to
very short portions, or planes of weakness, in the bar,
for if not it would be shown in ordinary testing. In
certain cases flaws or fissures have been found to be
present in bars subjected to so many repetitions of load
that they were on the point of breaking. It is at least
conceivable that repetition of stress picks out sections
of weakness in the bar, and that the deterioration is
almost confined to such planes ; the deterioration
may be primarily a loss of power of yielding in the
particles near the plane of weakness, and not a loss of
tenacity . Such a loss of ductility at a section might
well show itself finally in a rapidly -spreading fissure or
crack. This explanation is purely hypothetical, but it
is at least in accordance with a very curious fact ob
served in the fracture of bars in Wöhler machines .
Such bars after fracture usually show no trace of draw
ing out, however ductile the material may be, when
tested statically. The bars break as if the material
was perfectly brittle. This peculiar fracture, without
380
TESTING OF MATERIALS OF CONSTRUCTION
indication of any plastic drawing out, is not uncommon
in fractures of tyres , axles, and other structures in
ordinary experience.
On what principle, then , is the limit of working stress
in different cases to be decided ?
As to structures
subjected to a purely resting load there is not much
practical doubt. There is no evidence that the deforma
tions due to ordinary dead loads on ordinary materials
increase with time, however indefinitely prolonged . Se
cular experiments, such as Sir W. Thomson is making
at Glasgow, will probably show that a structure may be
loaded with a considerable fraction of its breaking weight
and will carry it for a practically unlimited time without
sensible increase of deformation . What is exactly the
safe limit of stress in this case is not known , but pro
bably there is a limit of stress , such that smaller loads
are safe and greater loads unsafe.
157. Account of the Adoption of Fixed Limits of
Working Stress independent of the Conditions of Loading.Nothing has hindered so much the recognition of the
importance of Wöhler's researches as the existence of
officially sanctioned rules for the limits of working
stress, and the prevalence of opinions having no better
origin than the habit of working to such rules. It will,
therefore, not be out of place to indicate how such rules
originated . It will appear that they are rather the acci
dental product of momentary exigencies than the result
of any scientific induction . No doubt the ordinary
practice of engineers is to divide the statical breaking
EXPERIMENTS ON REPETITION OF STRESS
381
71
strength of a material by an assumed ' factor of safety
to find the proper limit of working stress ; and it has,
or had, come to be tacitly accepted that the ratio of the
working stress to the statical breaking strength measures
in all cases the margin of safety.
The so -called factor of safety has been supposed to
be required to allow for the following possible causes of
weakness :
1. Variation in the quality of the material.
2. Imperfections of workınanship , causing either
scant dimensions or unequal distribution of stress.
3. Corrosion, wear, and other deterioration arising
gradually with lapse of time.
4. Errors of calculation , or straining actions
neglected .
5. Vibration, shock , and other dynamical actions.
A margin of safety between the working and break
ing stresses is undoubtedly required to allow for the
contingencies thus enumerated .
But it would be im
possible, with these contingencies alone in view, to
explain the varying factors of safety which are adopted
in practice ; and, if Wöhler's results are true, it is
absolutely false to reckon as the margin of security the
difference between the calculated working stress and the
statical breaking stress .
Previous to 1819
18-19 2 no defined rule, recognised
1 Or, to use an American phrase, ' factor of ignorance.'
· See a very complete account of the Board of Trade rules, in a paper
on the “ Design of Girder Bridges, ' by W. Shelford and A. H. Shield .
Brit. Assoc. Report, 1886 .
2
382
TESTING OF MATERIALS OF CONSTRUCTION
officially, appears to have existed , limiting the discretion
of the engineer in the design of bridges and other struc
tures . In 1847 a Royal Commission was appointed to
inquire into the conditions which should be observed
in the application of iron to structures. The Commis
sion reported against fettering engineers by legislative
enactments. But they made some recommendations
with respect to cast -iron bridges which were adopted
as rules by the Board of Trade.
According to these
recommendations, the breaking weight of a cast -iron
bridge was to be six times the live load added to three
times the dead load. They also recommended that an
allowance should be made for dynamic action in bridges
of less than 40 feet span . A discussion arose shortly
afterwards as to the safety of the Torksey Bridge, and
then, for the first time, a proposal was made to limit the
stress in all wrought-iron bridges to 5 tons per sq . in.
The Torksey Bridge appears to have been finally passed
in a condition in which the working stress probably
reached 6 tons per sq. in . In 1858 a further dispute
arose as to the safety of the bridge over the Spey , ' built
by Sir W. Fairbairn .
An attempt was made to get the
Board of Trade to allow for wrought-iron bridges , as
for cast iron, a different factor of safety for the stresses
due to the dead and live loads .
But the Board of
Trade then formally adopted the rule that the stress in
wrought iron should not exceed 5 tons per sq . in ., and
1 It was in connection with the discussion about the Spey Bridge that
Sir W. Fairbairn made the experiment on the action of repetition of stress
on a wrought - iron girder.
EXPERIMENTS ON REPETITION OF STRESS
383
that without reference to the quality of the iron or the
character of the loading. Later, for steel bridges, a
limiting stress of 61 tons has been allowed , under certain
restrictions as to the testing of the material.
It will be seen that as early as 1847 the Railway
Commission recognised a difference between the action
of a dead and a live load . Unfortunately, they were
disposed to ascribe this difference entirely to the dyna
mical action of the live load causing increased deflection ,
and therefore increased stress . Since the publication
of Wöhler's results a quite different view of the differ
ence between the action of a fixed, or dea:1 , and a vary .
ing or live, load has been recognised by the more
thoughtful engineers. Although the official rules in
this country have remained unaltered, practice no longer
strictly conforms to those rules ; and in other countries
varying limits of working stress, depending on the range
of variation of stress, bave been boldly adopted .
Mr. Baker states that the short spans of the Elevated
Railway in New York were designed for a stress of
3.6 tons per sq . in . on the flanges , 3.4 tons on the web
bracing, and 2.0 tons for members subjected to alternate
tension and compression ; that a recent German bridge
over the Danube was designed for limits of stress vary
ing with the range of stress from 3 : 1 tons to 5.8 tons
per sq . in .; and that a Ilungarian bridge over the same
river was designed for stresses varying from 3 : 9 to 5
tons per sq . in . On the other hand, Mr. Baker estimates
that on the Conway Bridge, which carries the heavy
384
TESTING OF MATERIALS OF CONSTRUCTION
traffic of the London and North Western, and in which
the ratio of dead to live load is large, the stresses reach
the value of nearly 6 tons per sq. in.'
158. Bauschinger's Later Researches on the Variation
of the Elastic Limit.— It has been an obstacle to the adop
tion of rules based on Wöhler's experiments that they
stand apart as empirical results unexplained on any
theory of the resistance of materials.
The old view of the condition which fixes the limit
of safe stress was that, up to some definite stress , the
material was perfectly elastic. Any load producing
a less stress might be imposed and removed without
in any degree altering the material. The molecules
strained by the load returned on its removal absolutely
to their original condition. But a load exceeding the
elastic limit altered the material -the molecules after
straining assumed new positions. If it could be shown
that Wöhler's ranges of stress were ranges within which
the material was perfectly elastic, and that when those
ranges were exceeded a plastic or permanent deforma
tion occurred, then an explanation of Wöhler's results
would be found. For deformations, however small,
accumulating with repetition of the load, would ulti
mately cause fracture. But here two obvious and con
siderable difficulties have to be met :
1. A bar subjected to alternate pressure and ten
sion breaks after a sufficient number of repetitions with
a stress less than its primitive elastic limit.
1 ' Notes on the Working Stress of Iron and Steel. '
American Society of Mechanical Engineers. 1886.
By B. Baker.
385
EXPERIMENTS ON REPETITION OF STRESS
2. It has long been known that the application of a
stress exceeding the elastic limit raised the elastic limit .
In certain cases it appeared that the elastic limit could
be raised by strain nearly to the breaking stress . This
appeared inconsistent with the view that the safe limit
of stress could depend on the elastic limit.
A very important memoir by Prof. Bauschinger
1
throws some light on the difficulties thus raised .
Prof. Bauschinger's conclusions rest on extremely
delicate measurements of the behaviour of bars in ordi
nary testing, and are not likely to be generally accepted
without further and independent investigation. But
this may be said , that the memoirs of Prof. Bau
schinger represent an amount of scientific work in testing
materials to which there is no parallel in this country,
either in the extent and completeness of the researches
or the accuracy of the measurements. Prof. Bau
schinger believes that his measurements are minute
enough to determine definitely the true elastic limit
of a material , the limit at which proportionality of
the stress and strain first sensibly ceases .
Let it be
assumed for the moment that such a limit can be defi
nitely ascertained . Then , take this very simple point.
It is known that applying a tension to a bar greater
than its elastic limit in tension raises its clastic limit
in tension .
No one has cared to inquire whether such
1 Ueber die Veränderung der Elasticitätsgrenze und die Festigkeit des
Eisens und Stahls. Mittheilungen aus dem Mech. Techn. Laboratorium in
München
1886.
СС
386
TESTING OF MATERIALS OF CONSTRUCTION
raising of the elastic limit in tension affected the limit in
compression . Suppose that initially the elastic limits in
tension and compression were 10 tons per sq . in., and
that by a load of 15 tons the elastic limit in tension has
been raised to 15 tons—it has been universally assumed
that the bar would then be perfectly elastic from 10 tons
compression to 15 tons tension. But this is exactly
what Bauschinger's experiments appear to conclusively
disprove. The elastic limit in tension cannot be raised
without lowering the limit in compression , and vice versâ .
Even a moderate raising of the tension limit may lower
the compression limit to zero.
This furnishes a complete solution of one of the
difficulties in accepting Wöhler's laws. When a bar is
subjected to alternating compression and extension the
elastic limit cannot be raised .
Any attempt to raise it
in one direction lowers it in the other.
The law that
the elastic limit can be raised by stress does not apply
to a bar subjected to alternate stresses of opposite sign.
Why the elastic limit in this case is even lower than
the primitive elastic limit in most cases will be dis
cussed presently. At present, it is enough that under
alternating stresses we cannot expect that the elastic
limit will rise, and therefore cannot expect a bar to be
safe under a range of stress greater than that between
its primitive elastic limits.
1 One single exception should be noted . Prof.James Thompson, in
1877, stated that the common assumption that the elastic limit could be
extended both for compression and tension was unproved, and that the
determination of the point was a matter of importance in the theory of
elasticity.- Encyclopædia Britannica, “ Elasticity.'
EXPERIMENTS ON REPETITION OF STRESS
387
Next consider the case of a stress of one kind only.
Bauschinger's experiments, like earlier experiments,
show that under stresses of one kind only, the elastic
limit of a bar can be raised by strain nearly to the
breaking stress.
But they show, at the same time, that
these artificially produced elastic limits are extremely
unstable.
The following table illustrates these points .
TABLE X. BAUSCHINGER'S EXPERIMENTS ON THE CHANGE OF POSITION
OF THE ELASTIC LIMIT.
( Bar subjected to tension only. Tons per sq. in . )
Yielding
stress or
Treatment
Elastic limit
Greatest
stress
breaking-
imposed on
down point
bar
Bar of Bessemer steel , No. 939c :
1. Original condition .
2. One day after
3. Immediately after (2)
11.6
17 :4
24.8
27.0
28.3
32.4
22.6
26.8
28.3
29.6
340
18.6
24.0
21 :3
26.6
33.0
25.6
33.0
330
32.3
33.0
33.0
12.5
32.0
32.0
0
24.6
25.2
8.05
.
11
4. Immediately after (3)
5. One day after (4) .
Broke with 34 tons
Bar 9396.
Same steel :
1. Original condition
2. 69 hours after (1) .
3. Half
an
hour
120
20.0
after
(2) ;
straightened in the lathe
4. 68 hours after (3)
5. 3 years after (4)
6. 2 days after, and after being
vibrated by hammering on
end
7. After 2 years, and after heat
ing to cherry -red and cool
ing in water
4:05
6 :9
Broke at 35 :8 tons
It will be seen, in the case of the first bar, that
loading again immediately after stretching to the yield
ing point, the elastic limit is lowered from 11.6 to 8:05
tons .
In the case of the second bar, similarly strained
CC 2
388
TESTING OF MATERIALS OF CONSTRUCTION
but with a period of rest of 69 hours allowed , the elastic
limit is raised from 12 to 20 tons . But on reloading
immediately the elastic limit is lowered to 4:05 tons .
With a three years' period of rest it is raised to 33 tons,
just the load with which it had previously been strained.
But this artificially produced elastic limit is so unstable
that on hammering the bar on the end and reloading it
has fallen to 12.5 tons .
Now, to return to the case of a bar subjected to
alternate compressions and tensions. It was seen that
one of the difficulties of Wöhler's laws was, that the
limit of safe stress for alternate tensions and compres
sions is a stress less than the primitive tensile elastic
limit.
Bauschinger explains this by advancing the
view that the primitive elastic limit of many materials
is an artificially raised elastic limit. The material has
been subjected to mechanical operations in manufacture
which are equivalent to straining actions. Now, Bau
schinger found that alternate compression and extension
had the effect of raising an artificially lowered , or lower
ing an artificially raised, elastic limit. By subjecting a
bar to a few alternations of equal stresses, which are
equal to or somewhat exceed the elastic limits , they
tend towards fixed positions which Bauschinger calls
the natural elastic limits. The range of stress for which
a bar is perfectly elastic after a few repetitions of such
alternating stresses appears to agree very closely with
Wöhler's range of stress for unlimited repetitions of
alternating stresses
389
EXPERIMENTS ON REPETITION OF STRESS
TABLE XI .
BAUSCHINGER'S EXPERIMENTS ON ALTERNATING TENSION
AND COMPRESSION.
(Tons per square inch . )
Load imposed
Elastic limit
Time between the loadings
Tension
1 liour
5 minutes
20 hours
1 hour
46 minutes
137
.
14 : 5
14 : 5
14.5
14.5
14.5
17 : 3
17.5
127
-
175
.
6.35
48
15. 2 days .
6:35
16. 2 days .
7.15
17. 5 hours
7.15
6.35
7:15
7 15
7.95
18. Next day
19. 2 days .
20. 21 hours
21. 41 hours
22. 1 day .
6:45
6.45
7.25
7.25
4.8
2 hours
9 minutes
27 hours
30 minutes
14. 3 days .
145
1
9. 152 hours
Compression
13.7
Il8
8. 302 hours
10.
11.
12.
13.
Tension
4.8
9.65
12.9
11
3.
4.
5.
6.
7.
.
Wrought- iron bar :
1. Original condition
2. 6 days .
Compression
715
8.75
7.95
4.
.
8.75
8.75
23. 9 hours
9.55
1
7.95
Bessemer steel bar :
1. Original condition
3.24
1.6
4. 4 days .
5. 2 days.
5.55
6. 5} hours
7. 21 hours
8.85
8.5
8.5
10.5
9.65
11 : 3
11 :3
9.65
12. 23 hours
9.7
11 : 3
1
0
9.7
9.7
1
Il
1
8.85
10. 23 hours
11. 16 hours
24 : 3
24.0
4.85
8. 2 days.
9. 4 hours
24 0
17.7
2. 23 hours
3. 5 hours
9.65
11 : 3
1
The preceding table illustrates Bauschinger's attempt
to find the natural elastic limits by alternating stresses
in tension and compression . It will be seen that after a
390
TESTING OF MATERIALS OF CONSTRUCTION
succession of loads in tension which lower the limit in
compression , and of loads in compression which lower
the limit in tension , the elastic limit settles down - as
the loads are diminished towards an amount not greatly
exceeding the elastic limit—to a value not greatly dif
ferent in tension and compression , and below the initial
elastic limit .
Further, the limits thus obtained
about
8 tons for wrought iron and 91 tons for mild steel
differ very little from the stresses which Wöhler found
to be the greatest which a bar would bear indefinitely
when subjected to equal alternating stresses .
The tables given are only a sample of the numerous
tables in Professor Bauschinger's memoir. But these
may serve to show that the elastic limits of a material
are variable limits, restricted only by this , that the range
of perfect elasticity seems to be a fixed range. In this
a point of agreement is found with Wöhler's results .
Elastic Limit in Bauschinger's Endurance Tests.-- In
the endurance tests given in Table IX . the initial
elastic limit, which was determined from measurements
on a 5 -inch length of bar, and the elastic limit ac
quired during repetition of stress, are given . It will
be seen that the elastic limit usually rises with repeti
tion of stress to a point above the load applied. When
that is the case, the bar suffers a large number of
repetitions of load before fracture.
If the elastic limit
is very near to, or below , the load applied, the bar
breaks with comparatively few repetitions of load. As
far as the statical strength of the bar is concerned , it
EXPERIMENTS ON REPETITION OF STRESS
391
does not appear to be diminished by any number of
repetitions of load .
There is a small diminution in
wrought iron , and an increase in other cases .
159. Gerber's Parabola . – Suppose the ranges of
stress for unlimited repetition known for any material .
Then it has been shown that, if the ranges of stress
are plotted as ordinates, and the minimum stress as
abscissæ, the points fall on a parabolic curve.
Let fmax, ſmin be the limits of stress , and A =fmax
Ffmin be the range of stress. The upper sign is to be
taken if the stresses are of the same kind , and the
lower if they are of different kinds. Let f be the sta
tical breaking strength . Then Gerber's equation is
( ſmin +1 A ) + k A =f2 ;
where k is a constant for any material .
If the statical
strength f is known, and the value of fmin and was
for any one range of stress at which the bar stands
a practically unlimited number of repetitions before
breaking, then k can be determined, and the limits of
stress for all conditions of loading can be calculated.
The values of k have been calculated for all
Wöhler's and Bauschinger's experiments in which the
bars stood over 5 million repetitions of load, and from
the equations the parabolas in Fig. 128 have been
drawn. It will be seen that these quite independent
experiments give fairly consistent values for the ranges
of stress under all conditions of loading . Bauschinger's
results are specially valuable in connection with
30
U?
20
-10
O
10
IrVo
ug
Ironkt
Plak
e
20
Tvi
nni
,I ght
ron
n
bs iad suQ7
Minimum
Stress
in
square
per
inch
.tons
30
Bes Mil StASteel
sem d_s eexlle
e lR
stee Boi r eyail
l
.Ba p lPelr u
Ir r ie.ce te
o
s
40
emp
50
ere
d
Kru S
op' pfi
s
n
Hirl ste g
Steee . el
. l
Unt
BAUSCHINCERS
LINES
.
DOTTED
LINES
FULL
IM
RESULTS
WOHLER'S
BAUSCHINGER'S
.
TESTS
ENDURANCE
60
MATERIALS
1잃0
10
on
Burlj
WOHLER'S
AND
1
28
.FIG
TESTING OF
Range of Stress in
392
JIO
CONSTRUCTION
-
EXPERIMENTS ON REPETITION OF STRESS
393
Wöhler's , because in two of the materials used by
Wöhler the statical strength was exceptionally high.
The following tables give the values of fmax and
fmin for the most useful cases , recalculated from the same
equations. The last column is of course the experi
mentally determined breaking strength of the material
used :
TABLE XII . BAUSCHINGER'S ENDURANCE TESTS.
( Stresses requiring 5 to 10 million repetitions to cause fracture. Tons per sq . in . )
Opposite stresses
One stress zero
Similar stresses
Range
zero .
Ultimate
statical
Material
Greatest Least Greatest
Least Greatest
+ 7.15
+ 7.85
+ 8.65
0
- 7.85
8.65
14 :4
114
13.3
1575
13.2
8.55
- 10.5
- 9.7
+ 8.55
+ 10.5
to 9.7
0
0
15-70
19.70
14 : 3
200
0
18.4
- 8.65
+ 8.65
6
15.8
Least
Wrought- iron
plate
Bar iron
Bar iron
Bessemermild
.
steel plate .
Steel axle
Steel rail .
Mild - steel
.
boiler plate
7.15
13:10
strength
19.2
22.02
21.92
26.6
22.8
19.5
23.8
32 : 1
30.85
28.6
400
39.0
13 : 3
22:55
26.6
26.4
TABLE XIII. LIMITS OF STRESS, FROM WÖHLER'S ENDURANCE TESTS.
( Stresses, in tons per sq. in., for which fracture occurs only after an indefinitely
large number of repetitions. )
Opposite stresses
One stress zero
Similar stresses
Range
zero .
Ultimate
statical
Material
Least
Wrought iron
Krupp's axle
steel
Greatest Least Greatest
Least
+ 8.6
0
15.25
12.0
20 : 5
22.8
- 14:05
+14.05
0
26.5
17.5
3775
52.0
- 13:38
+ 13:38
0
25.5
12.5
34.75
575
8.6
Greatest
strength
Untempered
spring steel
"
394
TESTING OF MATERIALS OF CONSTRUCTION
CHAPTER
XIII .
TIMBER .
160. Unlike the materials bitherto examined, timber
has, in consequence of its organic origin , a remarkable
and definite structure, so that its mechanical properties
cannot be understood without reference to its mode of
growth. Nor is this all . The quality of timber is
largely influenced by the soil and climate, the age of
the tree and season of felling, and the duration of the
seasoning process . Hence, experiments on timber, to
be valuable, should be made on logs the history of
which is known , and should be directed so as to deter
mine the relative influence of all the circumstances
which affect its mechanical properties.
Timber is composed of vegetable cells, and, chiefly,
very elongated cells, termed wood -fibres, arranged
nearly parallel to the axis of the stem.
A stress
applied to a transverse section must break the fibres
across, while a stress applied to a longitudinal section
separates them from each other. The strength along
the grain depends on the strength of the fibres ; that
across the grain on their adhesion . Hence, in pine wood
the lateral strength is only one-tenth to one-twentieth
TIMBER
395
of the longitudinal ; in leaf wood , one- sixth to one
fourth. All the timber commonly used in construc
tion is derived from exogenous trees . In the section
of an exogenous stem there may be recognised the
pith, the woody tissue forming the greater part of the
section, and the bark . The growth of the stem occurs
by the addition, annually, of a ring of new fibres be
tween the bark and the already formed timber. Hence
most exogenous stems indicate , by distinct annual
rings , the age of the tree .
The timber is sometimes
broadly marked, so as to be distinguishable into two
portions — the heart-wood , and sap-wood ; and usually ,
but not invariably, the sap-wood is weaker and less
sound than the heart-wood . In some trees, plates of
cellular tissue extend radially from the pith towards
the bark. These are termed medullary rays, and are
planes of weakness in the timber.
From the joiner's point of view, timber is broadly
distinguished into soft wood and hard wood . The dis
tinction roughly agrees with a distinction between
timber derived from the needle-leaved trees ( coniferous
trees ), and timber derived from broad -leaved trees. By
far the largest part of the timber used in construction
is the soft wood derived from needle-leaved coniferous
In Europe the most important timber tree is
the northern pine ( Pinus sylvestris ), yielding timber
known as red or yellow fir, Memel, Dantzig, or Riga
fir, or yellow deal. Next to this, the spruce fir ( Abies
trees .
excelsa) yields the valuable timber known as white
396
TESTING OF MATERIALS OF CONSTRUCTION
deal. Similar timber , coming from America, the pro
duce of allied species, is commonly known as pine.
The yellow pine of the pattern maker, and the pitch
pine of the joiner are examples .
All timber, after
felling, requires to be seasoned, and in ordinary season
ing timber loses one-fifth to one-seventh of its weight.
When perfectly dried it may lose one -third of its
weight. During this seasoning it shrinks, and much
more in a transverse direction, and especially along the
annual rings, than longitudinally . A plank of oak may
shrink in width one -twelfth, and one of pine or fir one
thirtieth to one- fortieth. This shrinkage, which con
tinues a long time, is one of the determining conditions
in the arrangement of timber in construction. It is
during seasoning that the shrinkage causes the heart
shakes ( radial), or cup shakes ( along the rings ) which
often detract so much from the value of timber.
Till recently , nearly all tests of timber have been
made on comparatively small specimens. Such test
specimens are virtually selected, not average, specimens.
They are more homogeneous and better seasoned than
larger pieces, and are free from knots, shakes, and other
serious defects . Hence they give values for the strength
of the timber very much in excess of the strength of
large pieces. To furnish useful data for construction,
tests must of necessity be made on large pieces. Hence
few of the mass of tests hitherto made need here
very
be quoted . The following short table gives the general
relation of the strengths for a few of the more important
timbers :
397
TIMBER
PROPERTIES OF TIMBER, FROM SMALL TEST SPECIMENS.
Coefficient
Length of
Kind of timber
Coefficient Shearing
of elasti- | Tenacity Crushing
strength of bending resistance
city for
along
along
seasoning , tension
, fibre, tops along strength,
tonsper per sq. in . fibre, tons tons per fibres, tons
years
Yellow pine
Spruce
Red pine .
sq. in.
per sq. in .
0:27
0.29
1:03
2.60
4.91
3.71
5.27
6.92
4:46
446
4.69
2:08
3:00
4.40
7.18
.
$q . in .
2:41
.
White oak
Spruce
Ironbark .
Blue gum
1-6
4
3
4
Jarrah
.
.
1,071
4
1-2
13-18
1
111
Yellow pine .
Lignum vitae
Pitch pine
Whitepine
| |
British oak
Teak , Indian
Mahogany
714
750
656
871
910
317
5:54
5.80
6.70
6.70
5:51
870
8.93
5.44
6.87
714
5:09
5.10
7:12
8.97
1:31
2:59
4.40
5:36
3:30
2.81
2.88
4:51
3.99
2.24
4.54
3.45
3.20
3:03
8.15
5.80
4.13
161. Bauschinger's Investigation of the Elasticity and
Strength of Pine Wood .— By far the most thorough
and valuable investigation of the properties of timber
is contained in two papers in the 'Mittheilungen ,' of
the Munich Laboratory .1 In Bauschinger's earlier
investigation the object was to determine the condi
tions which should be observed in testing timber, the
relative value of different modes of testing, the in
fluence of conditions of growth, time of felling, and
seasoning on the strength of timber, and the rela
tions between the physical constants of the material.
Bauschinger immediately found that the amount of
moisture in the timber had a very great influence on
1 Mittheilungen aus dem
1883 and 1887.
Mech. T'ehn . Laboratorium
in München .
398
TESTING OF MATERIALS OF CONSTRUCTION
its density and strength , so that comparative values
could only be obtained by reducing experimental re
sults to a uniform standard dryness . He determined
the dryness for every test piece. At first this was done
by taking a few grams of sawdust, raspings, or chips
from the timber, drying them at 101° C. in a current
of dried air for about eight hours, and then reweighing
to determine the loss .
The percentage of moisture was
calculated on the original weight of the specimen. In
later trials the whole test specimen was dried in an
oven kept at 101 ° to 105 ° till it ceased to lose weight
The drying usually lasted two to four days. To deter
mine at all accurately the strength or density at a
standard dryness, it is necessary to experiment on
three test specimens in three stages of dryness. If the
results are plotted, a curve can be drawn giving the
relation of strength or density to dryness, and from this
the required value at standard dryness can be deter
mined .
Bauschinger takes 15 per cent. of moisture
as the most convenient standard dryness , that being
the condition most often reached by simple exposure
to air
The bending tests were made on beams about 20
inches square and 9 feet long.
These were broken
with a clear span of 98.4 inches. The tension tests
were made on small test bars of the form m shown
in Fig. 81 , and with the shackles shown in Fig. 74 .
These tests presented difficulty from the tendency of
the wood to draw out of the part in the shackles by
TIMBER
399
shearing along the fibres. The bar had to be well
bedded against its shoulders by driving the wedges at
the back, and the side screws had to be strongly tight
ened during the test. The elastic limit in tension almost
coincides with the breaking point. The coefficient of
elasticity was determined from the extension with a
load of about one- third the breaking load . Pressure
tests were made with specimens of the form shown in
Fig . 85 , and afterwards with simple square prisms,
about 3 to 4 inches length of side, and about 6 inches
long. Shearing tests were also made on radial planes
in the timber.
The tension results show very great differences, due
partly to the small section of the test pieces, which
allowed the greatest influence to original differences of
quality in the timber. The tenacity is very great, ex
traordinarily so if the large amount of vacant space is
allowed for which is observable in microscopic sections.
Pieces cut near the heart of the tree are much weaker
than pieces cut nearer the periphery ; and this is con
nected generally, but not always, with less density in
the wood near the heart. The strength does not directly
depend on the width of the annual rings. But it ap
pears to be more directly connected with the propor
tionate width of the summer zone of the annual rings
as compared with the spring zone. In tension experi
ments the influence of time of felling is not recognisable
a short time after felling. The coefficient of elasticity
varies very significantly with the strength, increasing
400
TESTING OF MATERIALS OF CONSTRUCTION
and decreasing with it.
The bending tests on beams of
the full useful section of the log showed generally that
the strength and coefficient of elasticity varied directly
with the density. The results were,however, influenced
by the presence of knots and other defects. The pressure
tests gave, on the whole, the most uniform results , the
section of the test pieces being fairly large , and a uniform
distribution of stress being fairly well obtained . But
the elastic limit and coefficient of elasticity are difficult
to ascertain accurately in pressure tests . The strength
increases with the density, but the heart pieces are
weak . In timber tested within three months of felling,
the winter-felled timber was 25 per cent. stronger than
summer felled .
But later researches showed that this
difference disappeared after a longer time of seasoning.
The strength increases in seasoning, but the increase
probably ceases after about one year.
Bauschinger concludes that when the question is
the average quality of a timber, as in inquiries with
reference to the influence of time of felling or seasoning,
or the influence of the soil or locality of growth, then
the pressure tests are the easiest and most trustworthy.
Discs about 6 inches thick should be sawn from each end
and the middle of the log, and these then divided into
four sectors. From each of these a square prism should
be cut, the height being 11 times the length of side.
The compressive strength should then be ascertained
for as nearly as possible the standard dryness ( 15 per
cent. of moisture) . The test pieces should be measured,
401
TIMBER
and weighed to determine the density. The CO
efficient of elasticity is best determined from bending
tests of a beam of the whole useful section of the log .
As this depends on the quality of the whole section ,
and is determined for stresses within the elastic limit,
it is probably a very valuable inclication of the structural
value ofthe timber. By plotting his results, Bauschinger
shows that there is a definite relation between the co
efficient of elasticity and the bending and crushing
strength , and that this can probably be expressed by a
linear equation . There is also a definite relation in
pine wood between the density and the strength , ex
pressed by the following equation :
B = 6:35 à – ( ) :633 ,
where ß is the crushing strength in tons per sq. in., and
the density at a standard dryness of 15 per cent.
The following are some of the results in the earlier
research , the timber being tested about three months
after felling :
TENSION EXPERIMENTS.
( Test pieces, 1.6 x 0:4 inch section . Mean values as tested . )
Summer felled .
Timber
Winter felled.
Tenacity,
Tenacity ,
tons per sq. in .
tons per sq. in .
Locality
Mleap
Cir
Heart
Cir
of
Cull)
terence
log
ference
Frankenhofen
6.67
0:16
1:46 5:01 4.76
1 :974.76 7.87
Regenhütte
6.54
Schliersee
6:44
2.60
1.84
cun
Me:11
Heart
of
log
의
Red pine
Spruce
‫ܕ ܕ‬
Lichtenhoff
5.24 | 6.10
3.39 3.68
1.84 | 3.78
2.19 5.97
1.90470
1:02 | 2.99
D1 )
402
TESTING OF MATERIALS OF CONSTRUCTION
PRESSURE EXPERIMENTS ,
(Test pieces, about 34 x 3 } inches , and 6 inches long. Mean strength, as tested , and
also reduced to a standard dryness - 10 per cent. of moisture. )
Winter felled .
Summer felled .
Compressive
Timber
Locality
As tested
Red pine
Spruce
Lichtenhoff
1.78 [ 19]
Frankenhofen 1:56 [20
1:49 (27
Regenhütte
1:03 [20]
Schliersee
.
‫ܕ ܕ‬
Compressive
strength, in tons
strength, in tons
per sq . in.
per sq . in.
Standard
dryness
As tested
2:37
2:13
2:41
1:41
2:03 [26]
3.20
1.99 (17)
2.50
1.78120
2.43
1.43019
1.89
Standard
dryness
The figures in brackets give the moisture per cent.
BENDING EXPERIMENTS ,
( Beams, about 74 x 74 inches, and 98 inches span. Mean values. The upper value for
each timber is for a summer, and the lower for a winter, felled tree. )
Coeffi
cient of
Timber
Locality
elasticity ,
tons per
sq. in.
Red pine Lichtenhoff
686
654
‫ܕ ܕ‬
Spruce
Frankenhofen
>
‫יו‬
Regenhütte
>>
‫וי‬
Schliersee
698
737
730
698
464
438
Elastic
Coefficient
of bending
Content
limit,
tons per
sq . in.
1.28
1:40
1:45
1.66
1:37
1:44
0.93
0.84
strength
, Density
to
ns per
sq. in .
3.00
2.86
2.66
2.86
2.64
2.83
1.87
1.63
of mois
ture , per
cent.
0.50
0.55
0.45
0.45
0:46
0:43
0.355
0.375
23
33
29
27
34
31
23.5
25
‫וי‬
These results are directly comparable with Lanza's
results, given below. These latter were also on pretty
large beams.
The influence of a longer time of seasoning is
shown in the following table :
403
TIMBER
AVERAGE CRUSHING STRENGTH OF WITOLE SECTION OF LOG.
( Ten per cent. moisture. Tons per sq. in . )
Time of felling
Lichtenholt
frankenhofen
Rogenshütte
Schliersee
А
B
А
B
2:34
3.21
2.15
2.86
2.37
2.81
1:40
2.04
3.03
2.83
2:51
2.95
2:39
2.83
1.89
2:13
A
B
A
B
Summer
felled
Winter
felled
A. Tested 3 months after felling.
B. Tested 5 years after felling.
162. American Tests of Timber, with Large-sized Test
Pieces. - It has already been stated that tests of large
test pieces give values of the strength of timber con
siderably smaller than those obtained from small test
pieces . Of tests with large test pieces the most im .
portant are those made in the United States , chiefly
under the direction of Prof. Lanza, of the Massachusetts
1
Institute of Technology .
Prof. Lanza appears to have failed to make satisfac
tory tension experiments on large specimens. He con
cludes that tie bars used in construction will always
give way in some other manner than by direct tearing
for instance, by pulling out the fastenings, and shearing
and splitting the timber. Tests of crushing strength
are much less difficult.
The following table gives a
summary of a series of tests of wooden posts, generally
7 to 10 inches in diameter, made for an insurance com
pany under Prof. Lanza's direction . In all these tests
1
Applied Mechanics. Lanza, p . 497. Also, ' Report on Strength of
Wooden Columns,' Lanza ; and Executive Document 12, Forty -seventh
Congress, First Session .
D D 2
404
TESTING OF MATERIALS OF CONSTRUCTION
the strength was simply proportional to the area of cross
section, the deflection laterally being insignificant.
TESTS OF Wooden POSTS AND BLOCKS, USUALLY WITH FLAT ENDS (LANZA) .
Crushing strength, in tons per
Approximate size
Coefficient of
sq . in .
elasticity ,
Form
tons per sq . in .
Length ,
feet
Section ,
Mean
Min .
Max .
.
YELLOW Pini
Round
Rectang
12
12
2
12
2
Round
1.97
2:10
1.63
1.82
1.93
2:18
1.61
1.90
1:34
1:40
1:56
2:10
2:05
30-65
45-61
49 -86
100
81-103
45-48
1.94
2:01
2.331
2:41
728-984
949
734-1091
WHITE OAK
Round
12
2
32-63
47--93
|
1:09
1.99
1:57
545-781
493-582
99
OLI) ANI ) SEASONED WHITE OAK
Round
>>
12
12
24
25
13
79-87
60-05
13
2.69
1.89
2.08
2:18
2.05
1:31
1.73
1:53
2.28
1:55 2
1.92
1.82
823-955
640-916
Another series of tests on large rectangular posts of
white and yellow pine timber was made with the Water
town machine.
The lengths varied up to 30 feet.
The
results are too numerous to give here, but they have
been plotted by Mr. E. F. Ely, of the Massachusetts
Institute of Technology, and from the plotting the fol
lowing rule is derived . The posts had flat ends , and the
load was evenly distributed .
Let l be the length, and r the least sectional dimen
sion . Then , the crushing stress f per sq . in. of section
in tons is as follows :
1 One end flat, one with rectang. pintle.
» Maple cap and oak base.
405
TIMBER
Yellow pine
White pine
0-10
10-35
35-45
45-60
f
1/4
f
1.116
.893
.609
.446
0.- 15
15-30
30-40
40-45
45--50
50-60
1785
1 : 562
1 : 339
1 : 116
.893
.669
163. Bending Tests.- The American bending tests
are not on so large a scale as those on crushing, but,
with the exception of those of Bauschinger already given ,
they afford the most trustworthy data as to the strength
of timber beams. They were made under Prof. Lanza's
direction . The beams were 2 to 6 inches wide, and 2 to
12 inches deep . The span varied from 4 to 20 feet.
Usually, in bending tests , the beam is supported at
the ends and loaded at the centre.
Let W be the load
at the centre ; b and h the breadth and depth of the
beam ; I the span of the beam ; the dimensions being
in inches, and the load in tons. Let f be the greatest
direct stress on the fibres furthest from the neutral axis ;
f,the shearing stress at the neutral axis, in tons per
sq. in . ; & the deflection at the centre, in inches. Then, so
long as the elastic limit for bending is not exceeded,
WI
3
if
2
W 13
1
al
4
; f=
1
612
W 13
E
i E
=
å 6 hs
ED3
1
(
. (
)
2
)
b72
W
W
fi =
3
4
.
6 h
(3 ) .
406
TESTING OF MATERIALS OF CONSTRUCTION
Equation ( 1 ) may be used to determine the dimen
sions for a given limit of stress ; and equation ( 2 ) to
determine the coefficient of elasticity of the timber,
from observations within the elastic limit. When,
however, W is the load which breaks the beam , the
value of f obtained from equation ( 1) is no longer the
real stress in the beam .
Since, however, it is a con
venient measure of the strength of the timber for
practical purposes, it may be called the coefficient of
bending strength. The coefficient of bending strength
is always greater than the real breaking stress .
From
the great weakness of timber along the grain , beams
give way about as often by shearing along the neutral
surface as by tearing the extreme fibres. Then the
shearing stress fs, calculated by equation ( 3 ) , bears a
similar relation to the real shearing stress that f bears
to the real tenacity of the timber.
The following summary gives the most important
results of Professor Lanza's bending tests :
Coefficient of
Coefficient of
bending strength,
elasticity,
tons per sq . in .
tons per sq. in .
Max .
Min.
Mean
Spruce beams.
3.910
1 : 337
2 : 180
>>
Yellow pine beams.
7 )
7 )
Oak beams.
Max .
Min. .
Mean
Max ..
Min .
Mean
.
>>
White pine.
>>
72
Max.
Min.
Mean
.
4
709
401
594
5 :071
1769
3.255
1,063
3.419
2.225
2.712
789
381
577
3.237
1.535
2 : 146
413
484
519
779
572
407
TIMBER
Beams which gave way by Shearing.-- In Lanza's tests
six spruce beams and five yellow pine beams gave way by
longitudinal shearing near the neutral axis. The intensity
of the shearing stress varied from 117 to 248 lbs. per
sq. in . in the spruce beams, and from 153 to 397 lbs. per
sq.in . in the yellow pine beams. The mean values were
Shearing strength,
lbs. per sq. in.
Spruce beams
Yellow pine beams
tons per sq. in .
0.0853
191
248
0 : 1107
On the beams which did not fail by shearing the
mean intensity of shearing stress was about the same .
Hence it may be concluded that, for soft wood timber,
>
beams give way by shearing at the neutral axis or by
tearing at the convex surface almost indifferently.
164. Direct Experiments on Shearing along the Grain .
- Direct experiments on the shearing resistance along
the grain were made at the Watertown Arsenal , and gave
somewhat higher values of the shearing strength . This
is probably due to the fact that, in shearing experi
ments, the timber is forced to shear at a selected section,
while in the beam experiments the shearing occurred
along the weakest of the planes near the neutral axis of
the beam . The specimens were also comparatively small.
SHEARING TESTS (WATERTOWN ARSENAL ).
Sbearing strength,
Ash .
Yellow birch
White maple
lbs. per sq. in .
458 to 700
563 >> 815
Red oak
367
726
White oak .
752
White pine
Yellow pine
Spruce
267
286
Whitewood
382
> >
647
999
966
366
415
374
253
‫ور‬
406
408
TESTING OF MATERIALS OF CONSTRUCTION
The greater shearing strength of the leaf woods is
noticeable.
165. Influence of Time on Bending Strength and Elas
ticity.-- Experiments by Herman Haupt, and more
recent experiments by Thurston ' and Kidder,” show :
( 1 ) That the deflection of a beam of pine under a
statical load increases with time, or the modulus cf
elasticity is less for a prolonged than for an immediate
loading ; ( 2 ) that the beam breaks in course of time
with a statical load a good deal less than that required
to break it immediately. In Thurston's experiments a
plank of yellow pine was selected. Bars 11 to 3 inches
square, and 40 to 54 inches long, gave a density of
0.75 to 1.0, a coefficient of bending strength of 4:91 to
5.36 tons per sq . in . , and a coefficient of elasticity of
1,005 tons per sq. in . Kiln dried, the coefficient of
bending strength increased one- fifth, and that of elas
ticity one -ninth . For a bar 1 inch square on supports
40 inches apart the centre breaking load was 375 lbs.
Nine bars of this size were prepared , three being loaded
with 350 lbs . , three with 300 lbs . , and three with
250 lbs. at the centre .
All the first three broke in less
than 43 hours ; all the second three in from 80 to 719
hours ; and all the third set, loaded with only 60 per
cent. of the immediate breaking weight , broke in from
6,000 to 11,000 hours . These experiments seem to
1 Proc. Am . Assoc. for Advancement of Science, 1881. Proc. Inst..
C.E. lxxi . p . 428 .
9 Journal of Franklyn Institute, 1882. Proc. Inst . C. E. lxxi . p. 431.
.
409
TIMBER
show that a statical load of 60 per cent. of the imme
diate breaking weight is not safe. When broken immc
diately, the ultimate deflection was about 1.8 inch ;
with 350 lbs . it was 2.3 inches ; with 300 lbs. 3 : 0
inches, and with 250 lbs. 2.5 inches.
Hence the de
flection is greater with a prolonged load . In Mr.
Kidder's experiments on dry spruce beams 13 inch
square, the deflection increased with time, even when as
small as isth of the immediate breaking weight. He
concluded that one-half the immediate breaking weight
could not be permanently supported.
LEATHER BELTING ,
The following few results may find place here :
STRENGTH OF LEATHER BELTS AND FASTENINGS.
1
Tenacity,
Dimensions, in in lbs. per
inches
inchi of
Authority
width
Single leather.
>
79
9
Max .
Min.
Meani
Max .
Min .
Mean
1,600
20 x 0.2
Riehle Bros.
700
1,280
1,272
2.5 x 206
616
964
2.5 x 314
2.5 x 203
31 x 21
1,110
Unwin
29
Double belt, copper sewn .
Single belt, ordinary laced joint
butt laced
99
>>
79
205
grip fastener
3.0 x 21
2.5 x 22
514
‫ܕ ܕ‬
07
Crowley's fastener .
3.0 x 21
> )
635
22
joint scarfed and
glued .
473
> )
hose riveted , 12, **
7.0 x 22
394
9
rivets in two rows .
242
Watertown
410
TESTING OF MATERIALS OF CONSTRUCTION
CHAPTER XIV .
STONE
AND
BRICK .
166. Building stone is derived from rocks of widely
different origin and very various age. The rocks may
be distinguished into volcanic or plutonic rocks con
solidated from igneous fusion, and stratified rocks
deposited under water. The former are crystalline in
the granites, less obviously crystalline in the traps, and
glassy in other cases. The stratified rocks, which show
more or less distinctly lamination or bedding, are some
times aggregates of detritus derived from denudation
of land surfaces , cemented by subsequent infiltration .
Sometimes they are precipitates from solution in water.
Sometimes they are of organic origin , and consist
largely of siliceous or calcareous skeletons . In some
originally stratified rocks a slaty cleavage has been
developed by pressure, which is more conspicuous than
the original bedding.
The value of stone for building depends on its
strength , its durability, and the facility with which it
can be worked. The durability depends partly on its
hardness and chemical composition, but also largely on
its power of resisting the absorption of water.
The most abundant constituents of the rocks are
411
STONE AND BRICK
silica, alumina, oxide of iron , lime, and magnesia .
Silica occurs nearly pure as quartz, flint, and sand, and
is almost universally present in combination with other
carthy bases. Alumina, combined with silica , occurs in
clay, and in mica and felspar. Magnesia occurs com
bined with silica in soapstone, augite, and hornblende,
and as a carbonate in some limestones .
Lime occurs as
a carbonate, nearly pure, in some limestones.
The most important building stones may be classed
as granite, clayslate, sandstone, or limestone.
Granite consists normally of quartz , colourless and
transparent ; felspar , opaque, red , yellow , or grey,
giving the prevailing tint to the rock ; and mica.
Hornblende and talc are sometimes associated with or
replace the mica . Granite is an extremely valuable
building stone. It is heavy, strong, non-absorbent, and
capable of taking a fine polish. On the other hand, it
stands fire badly, and is difficult to work. The horn
blendic varieties have great resistance to abrasion .
Inferior granites sometimes decay , either by decomposi
tion of the felspar, or by surface disintegration by frost .
Trap, Greenstone and Basalt have some of the
qualities of granite. They are compact crystalline
rocks, composed of felspar, hornblende, and augite.
They are strong, but difficult to dress.
Clayslate, composed of quartz and mica , is some
times a very compact rock, yielding a fine -grained and
strong building stone.
Sometimes the slaty cleavage is
so developed that it yields slabs and roofing slates.
412
TESTING OF MATERIALS OF CONSTRUCTION
Sandstones are stratified rocks, composed largely of
quartz grains, with a siliceous, clayey, or calcareous
cement. The fineness of grain varies greatly. In some
sandstones the cement is nearly pure silica , and these
are strong, durable, and non -absorbent.
The best
sandstones for building, in England, are obtained from
the millstone grit and coal measures, and from the new
and old red sandstone formations.
Limestones are of very various texture and quality.
Marble is a nearly pure carbonate of lime,hard enough
to take a polish . Granular and colitic limestones con
sist of grains of carbonate of lime cemented by a
calcareous or siliceous matrix . Some of these yield
excellent , durable, and easily - worked building stone ..
Generally , however , limestones are softer, more ab
sorbent, and less durable than sandstones . Shelly
limestones consist of shells embedded in a more or less
crystalline matrix , and some of these are useful as
building stone.
Magnesian Limestones, or dolomites, consist of car
bonates of lime and magnesia. When properly crystal
line in structure they yield a good , easily -dressed, and
durable stone. Steatite, or silicate of magnesia, is
valuable from its power of resisting fire.
167. Strength of Stone.-In most cases stone is used
in compression. A block of stone at the base of a pier
or in an arch ring is subject to a thrust due to the
weight of the structure, and , as far as the condition can
be secured, the thrust is normal to the faces of the block .
STONE AND BRICK
413
Generally the pressure does not reach 10 tons per sq . ft.,
though in some lofty structures it reaches 20 to 30 tons,
and possibly in some arch rinys 40 or 50 tons, per sq. ft.
Now, the crushing resistance of stone, tested in small
cubes, is seldom less than 250 tons , and often reaches
1,000 tons or more per sq. ft . Hence it has been
argued that the strength of stone is of little consequence ,
its lowest strength being in excess of what is required .
It must be remembered , however, that small cubes of
stones are selected specimens , more homogeneous and
free from defect than large blocks. The cubical form
is a stronger one than that of the blocks used in
building, and single blocks are stronger than aggre
gates of blocks. Further, it is quite impossible in any
actual structure to secure a simple condition of crushing
stress . Settlement, imperfect bedding, unequal compres
sibility of different blocks, and other causes, introduce
unforeseen and incalculable straining actions . Hence,
the real factor of safety is not nearly as great as the
nominal one.
168. Mode of Crushing in Rigid Materials. - In duc
tile materials like wrought iron the mode of yielding to
pressure is nearly the inverse of the mode of yielding to
tension, and the two resistances are not widely different.
But in cast iron and stone and other rigid materials, the
tenacity of which is suall compared with the resistance
to crushing , the mode of yielding is quite different. It
has been shown in § 9 that the stress on any oblique
plane in a prism subjected to a pressure p in the direction
414
TESTING OF MATERIALS OF CONSTRUCTION
of its axis may be resolved into a tangential component
p sin 6 cos 6 , and a normal component p cosa 0. On
a plane making 45° with the axis the intensity of the
shearing stress is greatest, and equal to } p .
Now
small cylinders of cast iron frequently give way exactly
as shown in Fig. 4 , and Coulomb inferred that the
action was then a simple shearing. But that this is not
an exact view of the matter is shown, partly because
the inclination of the plane of yielding to the axis often
differs a good deal from 45°, partly because the intensity
of the stress on the plane of yielding is usually con
siderably greater than the shearing strength of the
material when not in compression . Obviously , the
normal component p cos? O is not without influence on
the angle and intensity of stress at which the prism
breaks .
It produces a frictional resistance to sliding
which balances part of the tangential stress. But this,
also, is probably an incomplete account of the mode of
resistance of rigid materials . The axial pressure and
longitudinal compression correspond to a lateral dilata
tion and transverse tension ( $ 4 ) . In some cases stone
breaks up into nearly vertical prisms, splitting up at a
number of almost vertical planes .
In these cases it
appears to yield to the lateral tension.
Any cause
which increases the lateral tension readily produces this
kind of fracture, as will be seen presently.
In a square prism there are four symmetrical planes
similarly situated with respect to the axis . Hence such
prisms frequently yield simultaneously at these four
415
STONE AND BRICK
:
planes . Thus, a cube breaks into six similar and cqual
pyramids (Fig . 129 ; see also Fig. 132 ) . With a rect
angular base a prism breaks
FIG . 123,
similarly , but the upper and
lower pyramids are termi
nated by an edge instead
of a point . A cylindrical
prism shows , after fracture,
two cones with the sides split
off all round .
In an even
grained material like sandstone these forms are often
very regularly developed.
FIG . 130.
Fig. 130 shows a cube of cement concrete after frac
Here the pyramidal form of fracture is pretty
obvious, in spite of the irregularity of the material . The
ture .
416
TESTING OF MATERIALS OF CONSTRUCTION
middle part, near the apex of the pyramids, is really
loose and fissured . Fig. 131 exhibits a cylinder of cement
mortar showing very distinctly the conical fracture.
When the height of the prisms is greater than their
length of side, the two pyramids which stand on the
surfaces
at which the
FIG . 131.
pressure is applied are
often of unequal height.
169. Preparation of
Specimens for Crushing.
- The specimens re
quired for crushing may
be obtained by sawing ,
or by dressing with ham
mer and chisel.
It is
of the greatest import
ance that the surfaces at
which the crushing pressure acts should be plane and
parallel, a requirement sometimes too little attended to.
To obtain plane parallel surfaces a planing machine may
be used, with a black diamond for a cutting tool ; or the
surfaces may be ground smooth with emery on a plate
of stone or metal.
As these processes are troublesome,
especially when dealing with bricks, concrete blocks,
and other rough material, the author has adopted a plan
which is simpler and appears to be quite as satisfactory.
When the surfaces are approximately right, they are
covered with a thin layer of Parian cement or plaster of
Paris, which can be easily strickled so as to be plane.
417
STONE AND BRICK
This thin layer does not crusli under even the heavy
pressures required, and it does not yield or flow . It is,
for all practical purposes , a part of the block .
To avoid the trouble of getting parallel plane sur
faces ,it has been common to make crushing experiments
with a layer of pinewood , or learl,' or other weak material
interposed between the block to be crushed and the
cast-iron crossheads of the testing machine. The idea
has been that the wood or lead distributed the pressure
over the surface, and virtually annulled the inequalities
of surface. This, however, can be shown to be erro
neous. Any weak material may very greatly alter the
crushing pressure, and falsify the result of the experi
ment. It is important that the block to be crushed
should be placed directly between the parallel metal
surfaces by which the pressure is applied. The only
thing the author uses between is a sheet of hard mill
board . This is nearly as incompressible as iron , and is
not indented by the crushing pressure.
It does no
harm , and it is doubtful if it does any good . To neu
tralise , as far as possible , the effect of any want of
parallelism of the surfaces of the block and machine, a
spherical joint , like that shown in Fig. 105 , p . 226 ,
should invariably be used .
170. Diminution of the Crushing Resistance of Stone
when bedded on Leal.- Twenty years ago it was common ,
in experiments on crushing, to bed the test specimens of
rigid materials like stone on lead plates , with an idea of
* In some cases leather has been used, and in some a layer of sand.
E F
418
TESTING OF MATERIALS OF CONSTRUCTION
securing uniform distribution of pressure on the faces
at which the crushing pressure is applied . The author
has long had the opinion that to support blocks for
crushing on a plastic support is wrong in principle .
Hence, in experiments on the crushing of stone and of
Portland cement and concrete, he has adopted the plan
of preparing the faces on which the crushing pressure
acts with a thin layer of plaster.
This can easily be
worked to smooth and parallel surfaces, which receive
the iron plates of the crushing shackles directly, if
necessary ; but
sometimes a sheet of millboard is
interposed , which is a very hard and only slightly
compressible material. It seemed desirable to try what
was the difference of the crushing strength of blocks
supported in these two ways. Two series of 4 -inch
cubes of Portland stone and Yorkshire grit were obtained
of very uniform quality. The results of the tests are
given below . The great reduction of strength when a
thin plate of plastic material like lead is used on the faces
to which the crushing pressure is applied is interesting
both practically and scientifically. It will be seen
that the crushing pressure of blocks between lead plates
is in one case only three -fifths, and in another only
three- sevenths of that of blocks prepared with plaster
and crushed between millboard. One block was cemented
carefully between two rigid iron plates with parallel
surfaces, and this carried a little more, but only a little
more, load than the block prepared with plaster and
crushed between loose millboards. An examination of
419
STONE AND BRICK
the mode of fracture of the blocks shows why the lead
has so dangerous an effect on the strength. The blocks
crushed between millboards sheared approximately at
45 °, forming regular pyramids ; but the blocks crushed
between lead broke up into a number of vertical prisms .
The lead , flowing under the crushing pressure, pro
duced by friction a tension in the block at right angles
to the crushing pressure, and this, added to the tension
due to lateral expansion, tore the block in pieces , com
pletely altering the angle of fracture. The pressure
of fluidity of lead is from 11 to 3 tons per sq. in. ,
and these pressures were exceeded in the crushing
experiments .
CRUSHING OF STONE BLOCKS, 4- INCH CUBES ( APPROXIMATELY ).
Description of
Crushing load,
stone
in tons
Stress , in tons
per sq . ft,
Peiparks
Portland :
535
57 665
516.38
Between two mill
boards on each face
536
52.600
469.87
One plate of lead on
538
45.65
408.8
One plate of lead on
each face ,
inch
537
33.50
each face
smaller than face all
round
299.95
Three plates of lead
on each face
Yorkshire grit :
539
7972
712-08
542
80:05
716.86
Between two mill
boards on each face
between
Cemented
two strong iron
plates with plaster
of Paris
540
56.20
50443
One lead plate on each
541
35.90
322.27
Three plates of lead
face
on each face
The lead plates were 0.085 inch thick .
E E 2
420
TESTING OF MATERIALS OF CONSTRUCTION
The result seems
im
portant, because it is still
539
a common practice to use
lead , or deal, or some other
plastic
Or
compressible
material in crushing ex
periments, and it is not
generally known that this
has the effect of diminishing
the crushing resistance.
Fig. 132 shows three of
the blocks of the Yorkshire
540
grit series after crushing .
Block 539 , crushed between
1
. 32
FIG
millboards, has crushed in
the normal way, a central
wedge being formed , and
the sides shearing on the
four faces of the wedge.
But in the two other blocks,
supported on lead , the
541
shearing angle is completely
altered by the horizontal
tension induced by the
flow of the lead. The blocks
are
broken into a
series
of prisms or wedges ,the di
viding planes being nearly
vertical .
STONE AND BRICK
421
In a note in the “ Trans. Am . Soc. of Civil Engi
neers , ' 1872 , p . 192 , it is mentioned that the Commis
sion of 1851 on the Selection of Stone for the Capitol
at Washington discovered the remarkable fact that the
crushing stress of stone was reduced to about one-half
if pieces of lead were interposed between the stone and
the steel faces of the shackles .
171. Influence of the form of the Test Piece on the
Crushing Strength . — Building stone is most commonly
tested in cubes , and cubes of 4 inches length of side are
convenient. For some of the stronger stones, it may
be necessary to use cubes of 2 to 3 inches side in many
testing machines. Portland cement is often tested in
cubes of 4 inches length of side. For cement mortar
the author has used cylinders of 7 inches diameter and
10 inches height. Irregular artificial material like
cement concrete is best tested in the largest practicable
Cubes of 7 to 10 inches length of side are
blocks .
convenient.
It will be obvious, from the account given of the
way in which materials of this kind crush , that know
ledge of the crushing strength of different forms and
sizes of specimen is purely experimental. The first
attempts to examine precisely the laws of crushing
1
strength of such materials were made by Rondelet,
Vicat,2 and Hodgkinson. More recently, Bauschinger
has made a very much more complete investigation. A
1 L'Art de Bâtir, t. iv .
2 Annales des Ponts et Chaussées.
8 Mitth. aus dem Mech. Tech. Laboratorium . 1876.
1833
422
TESTING OF MATERIALS OF CONSTRUCTION
brief account of the results will here be given --partly
because test specimens are sometimes unavoidably of
exceptional form , and it is necessary to reduce the
results to those on a standard form ; partly because a
knowledge of these results is useful in applying the
results of testing in practice.
For test blocks of geometrically similar form , all
experiments show that the crushing strength varies as
the area of the surface on which the crushing pressure
acts . Thus , Rondelet experimented on cubes of 1.2,
1 : 6 , 2 :0, and 2.4 inches length of side, of three different
kinds of stone. The crushing pressures per unit of
area were, in tons per sq. ft. :
First series
246
Second series
107
50
Third series .
243
104
243
114
248
50
50
51
112
More generally this law may be stated thus : The
strength of geometrically similar test pieces varies as
the square of homologous sides .
The variation of the crushing strength of prisms
with the form of the cross section is less obvious.
Hodgkinson concluded that the form of the cross sec
tion had little influence.
But Rondelet found , with
prisms of circular, square , and triangular bases of
equal area, that the strengths were proportional to
1 : 0.93 : 0.86 ; and for prisms on a square base and
rectangular base, with sides as 1 : 2 , of equal area , the
strengths were as 1 : 0.95 . These numbers are nearly
STONE AND BRICK
423
in the reciprocal ratio of the square roots of the circum
ferences.
When cubes are used, placed on each other, the
strength diminishes with the number of cubes. Thus, for
columns of one, two, and three cubes of 2 inches length
of side, Rondelet found the strengths in two series of
experiments to be 1 : 0 : 61 : 0:54 , and 1 : 080
The strength in prisms of similar base but
heights diminishes as the height is greater,
for heights within the limit at which any
occurs .
: 0.75 .
different
and that
bending
Vicat concluded that for prisms of less height
than the cube the strength could be expressed by the
et
a
equation
=
a
+6 .
T
( 1 ),
where f is the strength per unit of area, and a and b
constants for each material,
Lastly, a single block is always stronger than a
compound block of the same form made of separate
blocks without cement. Thus, a cube made up of four
blocks of gypsum had a strength only 0.78 of that of
a single block of the same size. A block of eight small
cubes had a strength of 0.84 of that of a single cube of
the same size.
Bauschinger has found that all these results can be
expressed by the relation
s = (19)* (2+vVD
(2) ,
424
TESTING OF MATERIALS OF CONSTRUCTION
where A is the area of section of prism ,C its circumfer
ence, h height of prism , f strength per unit of section,
and a and v are constants for each material .
It gives at once the law that prisms and cylinders
of geometrically similar form have the same strength.
Also, that in prisms of the same height and sectional
area the strength varies inversely as the square root
of the circumference . Thus, prisms of circular, square ,
and triangular base, of the same height, should have
strengths varying as 1 : 0.94 : 0 · 88 . For square prisms
of different heights the equation becomes
f =i + ogo
( 3),
where s is the side of the square. According to Bau
schinger , this equation is valid up to values of h = 48
or 5 s .
This agrees with Vicat's formula . A series of
experiments on square and rectangular prisms of dif
ferent heights , varying from 0: 6 to 12 inches, of fine
Swiss sandstone, gave the following values of the con
stant ( f, in tons per sq. in .) -a = 239.5
v = 292.5 ,
when the axis of the prism was parallel to the layers.
In another series of experiments on prisms of the same
sandstone, crushed perpendicular to the layers, the
height, however, not exceeding that of the cube,
a = 283.5
V = 316 .
.
A third series of tests on rectangular and square
425
STONE AND BRICK
prisms of Perlmooser Portland cement, hardened ninety
days, gave
a = 139
V =
98.6 .
Tests were made on rectangular and cylindrical
prisms, of about 4 inches diameter or length of side and
very different heights, cut out of fine-grained Bunter
sandstone, and crushed parallel to the layers. These
gave
For prisms .
>
2 = 317
y = 111
337
105
327
107.5 .
cylinders
Mean
.
3
A series of tests with square and rectangular prisms
of different heights, having sides with the ratios 1 : 2,
3 : 4 , and 1 : 1 , also of a fine-grained sandstone , gave
a = 356.5
v = 97 .
Bauschinger shows that the agreement of the equa
tion with the results is throughout satisfactory.
Bauschinger made a further research on the crush
ing strength of cubes when on one
FIG . 133 .
surface the crushing load was con
fined to a portion of the area .
b2
Sup
a
pose Fig. 133 is the plan of a cube, d
IC
and that either by bevelling the edges ,
or by using a small steel pressure
plate, the load is confined to the
area of the small rectangle. If o is the centre of the
rectangle, and
ob = (1 ; 0 d = 12 ; oa = 1 ; 0c = d' ,
5
426
TESTING OF MATERIALS OF CONSTRUCTION
f = crushing pressure per unit of area when pressure
is uniform on whole face of cube ; fi = crushing pres
sure per unit of area of pressure-plate.
3
Then ,
fi = f
l' l'a
le
If A and a are the areas of the surface of the cube and
pressure-plate, then ,when the pressure-plate is central
CA
fi =fVAa
If two equal pressure-plates on both faces of the cube
are used, then the strength becomes that of the prism
of material between the pressure-plates, and is nearly
independent of the amount of material surrounding this
prism . It is easy to see, therefore, how much a block
of stone may be weakened by imperfect bedding .
172. Determination of the Porosity of Stone.-Speci
mens for this purpose should be cubes , and should be
well dried .
The stone should be brushed , weighed,
and then gradually immersed in water. The stone is
allowed to remain under water till saturated .
It will
become nearly saturated in twenty -four hours , but it
may ,
for certainty, be left for five days. It is then taken
out, care fully dried on the surface , and weighed.
gain of weight is estimated in
per cent . of gross
The
weight.
Sometimes the process is hastened by removing the air
pressure by an air-pump and allowing it to return .?
1 A similar research by M. Flamant is given in Ann , des Ponts et
Chausseés, vol. xiv. , and Proc. I. C. E. vol. xci .
‫ ܪ‬2 Hatfield . Trans. Am . Soc. of Civil Engineers, 1872, p . 145 ..
427
STONE AND BRICK
For strictly comparable results the specimens should be
of the same volume and surface.
POROSITY OF STONES.
Per cent. of
water absorbed
Granites (various)
Syenite
Porphyry
Granites
0.42-1.2
0:50
0.4-2.8
0.2-30
.
0
No. of
hours
iinmersion
Authority
125
Böhme
123
125
>
24
Wray
125
125
Böhme
1
Trachyte
2.0-4.5
-
:54-70
Slate
Roofing slate
05
售.
Sandstones (various) .
0.7-8.2
1 :0-70
1.6-3.8
6.0-10.0
3.0-80
8.0
Coal -measure sandstones
Old red sandstone
New red sandstone
Lias sandstones .
.
Craigleith
Kenton
Mansfield
+
.
9.9
.
1
10.4
2.6-4.8
99
Wray
24
125
Böhme
Wray
24
24
24
24
Royal Com .
24
24
24
24
Wray
1
Limestones (various) .
Portland
Ancaster
16.6
.
Box ground ( Bath )
Ketton
Chilmark
170
.
Roche Abbey
Oolitic limestones
Shelly
limestones (Purbeck )
Kent ra
g
Dolomite
0:31 -6.4
13.5
.
Magnesian limestone .
15 : 1
8.6
17.2
4.0-12.0
4.0-2.0
0.5
1 :5
3.5
125
24
24
24
24
24
24
24
Böhme
Royal Com .
‫ܕ ܐ‬
Wray
24
24
125
24
Böhme
Wray
The table on next page gives the density and absorp
tion of water of a series of 3 - inch cubes of English stone.
The blocks were weighed dry and then immersed in water
for from seven to fifteen days. The weighings were
carefully made for the author by Mr. H. M. Martin.
428
TESTING OF MATERIALS OF CONSTRUCTION
Per cent .
Material
Density
of water
absorbed
Aberdeen granite, red
grey
.
.
0
Clayslate
2.62
2.08
2.76
2.76
0.70
0.81
0.31
0.23
2:16
2.15
2.39
2.29
2.32
2:19
2.35
2.30
2:37
2.21
2:16
2.18
2.21
2:33
2:02
5.49
6.89
SANDSTONES :
Red Grinsell
.
White Grinsell .
Scotgate Head ( coal measure)
Corse Hill (new red) .
Robin Hood (coal measure)
.
Hollington
Red Mansfield
White
Red
.
Flag -rock Grinsell
Red Alton (new red)
Derbyshire grit
中
.
Billstone
.
Howley Park
Attleborough
.
.
Hansworth
2.32
2:12
Duston (ironstone)
Ispatria
Sydanope
.
Kenilworth
.
+
2:17
2.16
2.06
3:43
5.05
5:41
6:42
4:44
5.55
4.67
5.08
7.43
6.06
6:03
4.28
9:52
3.84
10:10
8.07
6:06
9.11
LIMESTONES :
White Portland
Portland
.
.
Brown Portland
Ancaster
Ketton
本
.
4.
售.
Stoke ground
.
1
C
Corsham Down
Westwood ground
身.
Caen
Box ground
Church Anson
Doulting
.
.
.
.
2.31
2.31
2.27
2:15
2.21
2.17
2:19
2.01
1.96
1.88
2.39
2:19
8.64
5.23
6.22
8:52
9.00
8.90
9.49
12-75
12:56
10:10
6.29
7.99
Resistance to l'rost . — The power of resisting frost
can be inferred to some extent from the porosity. It
is better, however, to saturate a stone with water and
then freeze it, repeating the operation ten or more
STONE AND BRICK
429
times. The percentage loss of weight is the measure of
the injury done by frost. Brard's test is to immerse
the stone for half an hour in a boiling saturated solu
tion of sulphate of soda, and then hang it up for the
absorbed salt to crystallize. The process is repeated
daily for a week . It is a test of doubtful value .
Resistance to Wear.-The only method of satisfac
factorily testing the resistance of stone to wear is one
devised by Bauschinger. A block of the stone, with a
face 4 x 4 inches , is placed on a horizontally -revolving
cast- iron plate at a radius of 18 inches .
The con
ditions are found to be most constant when the block
is loaded with 66 to 68 lbs. Emery is regularly
supplied between the block and plate and cleaned off.
The best rate of supply is twenty grams for each ten
turns .
173. Coefficient of Elasticity for Stone. — The measure
ment of the compressions and extensions of stone is
very difficult, partly from the limitation of size of
specimen, partly from the smallness of the deformations,
partly from the difficulty of securing uniform distribu
tion of stress . Professor Bauschinger appears to have
overcome these difficulties ' by the use of a modification
of his mirror apparatus . Plottings to a very large
scale of the stresses and deformations show that stone
has no elastic limit .
It takes permanent sets with
very small loads, and the deformation does not increase
1 Uber den Elasticitäts -Modul Baustein. ' Mitth. , anis dem Mec, Tech .
Laboratorinin in München .
1875.
:
430
TESTING OF MATERIALS OF CONSTRUCTION
at first proportionally to the loads and afterwards de
viate from proportionality. For very hard and dense
stone the compressions and extensions are indeed
initially nearly proportional to the loads, but this
remains so up to the breaking stress.
For all others,
especially for the weaker stones , the greatest departure
from proportionality is for the smaller stresses . The
greater the loads the more do the deformations approach
to proportionality. For sandstone and the less hard
granites , the compressions increase first more quickly
than the loads and afterwards less rapidly . Hence, the
stress -strain curve is at first convex and afterwards
concave to the axis of loads .
With repetition of load
ing the reversal of curvature gradually disappears .
In the later research on Bavarian stone in 1884 ,
Bauschinger had an opportunity of re-examining the
elastic properties of stone with somewhat more perfect
test specimens. He found for the hardest stone, and
especially limestone, that the coefficient of elasticity was
nearly constant, equal for tension and compression, and
very large. For most other stone the coefficient of elas
ticity for tension diminishes with increasing loads. For
pressure it sometimes increases with increasing loads,
but for the weaker kinds it diminishes at first and then
increases.
The stress - strain curves for tension and pressure
pass into each other at the origin of co -ordinates with
out forming a cusp. But three cases are distinguish
able : ( 1 ) If the coefficient of clasticity is nearly
431
STONE AND BRICK
constant, the two curves for tension and pressure are
nearly straight lines and inclined at nearly the same
angle to the axis. (2 ) If the coefficient of elasticity
diminishes with increasing loads in tension, the curve is
concave to the axis of deformations.
Then , ( a ) if the
coefficient of elasticity for pressure increases from the
beginning, or is nearly constant, the two curves form a
regular line always concave in the same direction .
But
if (b) the coefficient of elasticity for pressure diminishes
first and then increases , there is a point of contrary
flexure at the origin of co -ordinates . Bauschinger is
inclined to attribute this appearance to a disintegration
of the test block in dressing it by hammer and chisel.
The author has obtained measurements of compression
of stone similar to Bauschinger's.
It seems possible
COEFFICIENT OF ELASTICITY FOR STONE (BAUSCHINGER).
( Stresses and coefficients, in tons per sq . ft.)
Bending
Tension
Ata
Coefficient
E
Granite (Metten )
Ata
>>
(Passau)
Ata
stress Coefficient stress Coefficient stress
E
E
of
of
of
192,000 2-2 216,000 | 2 : 6
54,000 35
86
104,000 4 : 1 | 202,000 0.6
28,000 33
40,000 73
125,000
)
Pressure
264,000 27
244,000 460
113,000 1.4
| 199,000 410
Jura’limestone (Kelheim ). 315,000 1.5 175,000
13 310,000 1.8
71,500 12.5 185,000 172
27
Nummulite limestone
Bunter sandstone ( Phalz ).
(Würtzburg))
58,500
475,000
685,000
562,000
60,200 0.9
26,600 0.6
27,400 1.1
11,900
17,000 | 28
6 172,000 207
93,000 1 : 3 113,000 0 :6 137,000 0.9
35,600 | 19 165,000 340
35,600 57
Molasse sandstone (Kemp
ten )
173,000 1.1 116,000 2 : 2 153,000 1 : 4
Molasse sandstone (Kemp:
ten)
43,000
56
29,200 | 31
240,000 530
TESTING OF MATERIALS OF CONSTRUCTION
432
that, in a granular substance like stone, the action of the
pressure may be to bring the particles to a bearing, and
that this may explain the decrease of the coefficient with
increase of pressure.
174. Bauschinger's First Research on the Strength of
Stone ( “ Mitth . aus dem Mech. Techn. Laboratorium , in
München .? 1874 ) .—A few results will be selected from
this paper as giving very conveniently the relative resist
ance to different kinds of straining action. The pres
sure tests were made on cubes with accurately ground
surfaces, on which the cast-iron pressure- plates acted
directly. For the shearing strength, three directions of
shearing may be distinguished . The shearing plane
be normal to the laminæ , or beds, of the stone, and
is then distinguished by the symbol I ; or it may be
in the plane of the beds, and is then indicated by the
symbol 11. Bauschinger experimented in some cases in
may
a third direction also ; but these results are omitted .
The same symbols apply to the bending experiments ,
and indicate the position of the plane of fracture.
Bauschinger's Second Research on the Strength of
Bavarian Building Stones. In this series of tests paral
lelopipeds about 44 inches long and 10 inches x 8 inches
square were used for bending tests, with a span of
40 inches.
From one of the broken pieces a prism was
cut for pressure parallel to the laminæ . From the other,
a test piece for tension parallel to the lamina, and also
afterwards for shearing. Cubes were also obtained for
1 Mitth . aus dem Mech. Tech . Laboratorium in München.
1884.
>>
SANDSTONE
:
‫وو‬
DOLOMITE
AND
:LIMESTONE
>
►
+
Bunter
sandstone
)(Kronach
K)( onigstein
0
PLimestone
)( appenheim
1
gand
-red
rained
ertheim
)(Wfine
740
500
1,190
1,080
695
1,000
11
F F
IL
11
11
1
11
I
1
il
1
1
C
1 ubes
crusheil
not
with
this
.stress
08
17
14
12
39
29
47
1
1
Il
I
11
I
Il tit = y = + =
1
L
.
1
22
1
1
11
1
27
105
73
165
63
.84
89
84
4
14
9
25
25
20
25
40
30
pull
II
!!
L
L
of
tion
Tenacity
Direction
.,Direc
Tension
11
Il
.
II
1
53
54
13
61
40
64
NI
Il
1
192
136
tons
per
,f. t
sq
Ili Is
4
300
174
720
760
Keuper
,red
-gsandstone
fine
)(Wand
rained
urtemburg
580
420
,f). ine
rained
Cg(-white
oburg
290
240
bine
sandstone
lue
)(A-g,fMolasse
llgau
rained
465
中
1
1,460
820
400
83
61
II
1
72
55
52
1!
1
1
34
46
100
| 1
11
1
!1
1
=y =s
720
810
850
850
1
1
SWhite
Tyrol
nchlanders
),i(marble
Muschelkalk
W
)( urtzburg
K
)( ronach
725
750
9301
9401
820
.fper
t
sq
11
Yellow
ather
Pgfine
assau
)(-,rrained
SGotthard
-gt.
coarse
rained
)(Hard
white
and
Black
mean
of
Hcoarseness
)( auzenberg
Oberfranken
),i(S-gelb
grey
nrained
Coarse
frac
of
bending
of
plane
t
, ons
strength
ture
Coefficient
of
Bending
=
Dolomite
‫وز‬
gFine
- rained
yellow
>
Direc
Shearing
Direcof
t
stress
, ons
tion
sfsq
. thearing
per
pressure
I
"
>>
stre
ss
,
tons
per
.ft
sq
Shear
I
E =FE
GRANIT
E
:
Pressure
Crushing
1
STRENGTH
BUILDING
STONES
BOF
).( AUSCHINGER
STONE AND BRICK
433
Til
I
434
TESTING OF MATERIALS OF CONSTRUCTION
pressure tests parallel and perpendicular to the laminæ.
Some cubes were kept in water, and as opportunity
served taken out and exposed to frost. After being
frozen about twenty -five times, they were dried, and
crushed in a direction parallel to the layers .
strength
of
Crushing
bed
l,l
to
Tenacity
21:, 1
prism
!
Coefficient
bending
of
tbed
,Io
strength
STRENGTH OF BAVARIAN BUILDING STONE ( BAUSCHINGER ) .
( Stresses in tons, per sq. ft.)
Crushing strength
Shearing
of cubes
strength
Il to
bed
ll to bed
I to
after
bed
I to li to
bed
bed
88
93
9
55
19
freezing
Granite (Metten )
(Passau )
87
77
40
44
Jura limestone ( Kelheim )
30
137 226
>
830
850
1,210 1,380 1,230
1,290 1,310 | 1,230
210
Bunter sandstone (Pfalz ) | 30
560
286
455
213
l 460 )
32
435
435
525 .
7
331
37
23
63
40
710
970
780
835
63
35
Green sandstone (Kel-} 10
0
177
277
260
302
22
21
21
545
130
870
43
24
33
930
1,120
1,850
61
49
limestone } 115 58 1,220 1,320 1,200 1,240 95
73
(Wurtzburg )
Molasse sandstone 38
(Kempten )
Molasse sandstone) 62
( Kempten)
Nummulite
(Rosenheim )
Diabase ( Ochsenkopf)
2,340
1,700
Lyenite (Wölsau)
2,500
1,740
The following tests were made by Dr. Böhme 1 of
cubes about 10 x 10 x 10 inches of rubble limestone
The cubes were
masonry , set in different mortars.
three months old :
Mean crushing strength ,
Mortar
1 cement, 3 sand
1
6
97
‫נו‬
1 cement, 7 lime , 16 sand .
1 lime , 2 sand
+
in tons, per sq. ft .
123.4
69.6
64 :3
46.5
1 Mitt. aus der ks. techn. Versuchsanstalt zu Berlin. 1884, p. 86.
435
STONE AND BRICK
CRUSHING STRENGTH OF STONE.
Tons per sq. ft.
Description
Authority
GRANITES :
832
Mount Sorrel
Aberdeen grey (2-inch cube)
(cylinder, 23
1,412
inches diameter, 31 inches
high)
1,162
Fairbairn
Unwin
79
92
1,614
Aberdeen red ( 2 -inch cube)
, (cylinder,
1,357
inches diameter, 3} inches
high)
Quartz
9
23
99
1,270
Mallet
Penmaenmawr (2-inch cube)
1,086
Hornblendic greenstone
Felspathic
1,580
1,106
Fairbairn
Wilkinson
0
BASALTS :
12
SLATES :
Compact Welsh clayslate (3
inch cules )
733-1,052
Slate .
1,205
Valen
cia ( Irish) (1-inch cubes)
Killaloe
720
Mallet
Wilkinson
1,974
99
.
Unwin
SANDSTONES :
19
Giffneuk
Kenton
Morley Moor
Park Spring
Stanley
Runcorn (sixteen 4 - inch cubes)
> ‫و‬
267-443
(six 3-inch cubes)
(six 4 inch cubes)
York grit (3-inch cube)
>>
Red Mansfield
>>
White
Red Alton
(2-inch cubes)
(3 -inch cubes)
17
Sydanape
LIMESTONES :
White Italian marble
White statuary
Portland
1
.
>>
(4 -inch cube)
(2-inch cube)
Purbeck (14-inch cube)
11
295-416
427-514
712
609
327
337
309
490
1,400
206-389
239-292
516
250
587
Rennie
Roy. Com .
9 )
99
>
> )
9
‫ܕܕ‬
>
389
504
455
310
318
318
487
383
Bramleyfall
Craigleith (2- inch cube)
Darley Dale
Unwin
5 )
Roy. Com.
Unwin
Rennie
.
Unwin
Roy. Com,
Rennie
FF 2
436
TESTING OF MATERIALS OF CONSTRUCTION
CRUSHING STRENGTH OF STONE —continued .
Description
Tons per sq . ft.
Ancaster (2- inch cube)
150
114
1
Barnac
Ketton
164
312
9
(3-inch cube)
Ketton rag ( 2 -inch cube)
Bath, Box ground (2-inch cube)
Bolsover (2-inch cube)
Bramham Mvor ,,
Brodsworth
Cadeby
‫ܕܕ‬
>>
>>
>>
Unwin
Roy. Com.
1 )
3 )
>>
>>
295
.
2 )
)
.
•
>>
Roche Abbey
中
)
f
Tottenhoe
>>
Caen (3-inch cube)
.
104
409
259
278
278
250
124
198
19
>
)
97
Huddlestone
Park Nook
Roy. Com .
> )
Chilmark
Hamhill
577
95
484
380
Authority
12
‫ܕ ܕ‬
)
)
29
> >
99
)
)
Unwin
BRICKS .
175. Bricks are made from clays, loams, or marls
containing silicate of alumina, mixed with sand, oxide of
iron, and carbonates of lime and magnesia. The plastic ,
strong, or pure clays contract very much in burning,
and do not vitrify, so that the bricks are not durable.
Sand diminishes contraction , and permits partial vitri
fication in burning. Iron acts as a flux, facilitating
fusion of the silica, and, in many cases, determines the
Lime diminishes contraction ,
colour of the bricks .
and acts as a flux ; but lumps of lime become quick
lime in burning, and slaking afterwards cause the
brick to crack . The following short summary gives
the composition of some clays : 1
1 Notes on Building Construction. Part. iii . p. 88.
1
437
STONE AND BRICK
Burham
London
brick clay
Loam
Marl
clay
633
5.0
18 : 9
83.8
77
937
1 :3
0.5
0 :1
5 :1
43.0
3 :0
40.5
3.5
Material
Silica and alumina
Oxide of iron
.
Carbonate of lime
Carbonate of magnesia
1.4
Malm is clay mixed with chalk in a wash mill.
Bricks are either hand -moulded or machine- moulded .
In the latter case the clay may be wet and plastic, or
dry or semi-dry. Hand-made bricks have usually a
cavity, or frog, on one side, which is supposed to afford
a key for the mortar.
Wire- cut machine -made bricks
have necessarily no cavity or frog. Some pressed
bricks have frogs on both sides .
Bricks are either
The weight of
bricks varies a good deal. London stocks weigh about
6.8 lbs. Pressed bricks and blue bricks may weigh
10 lbs. Ordinary red bricks weigh about 7 lbs. , while
6
clamp burned ' or ' kiln burned . '
some of the lightest weigh only 5 to 6 lbs . The
absorption of water by bricks also varies. Staffordshire
blue bricks absorb 2 to 6 per cent. of their weight;
ordinary stocks and red bricks, 7 to 10 per cent.; and
the softer and more porous bricks 20 per cent.
The following table gives the crushing strength of
a sufficient variety of bricks. It may be added , how
ever, that Mr. Ward gives some tests of bricks of
exceptional strength." In these tests, Staffordshire blue
bricks carried 630 to 1,064 tons per sq . ft., and bricks
made of slate débris 1,056 tons per sq . ft.
1
| Proc. Inst, of Civil Engineers, lxxxvi. p. 24.
438
TESTING OF MATERIALS OF CONSTRUCTION
CRUSHING STRENGTH OF BRICKS (Unwin).
per
ftons
t
.sq
Colour
inches
London stock .
2 ‫و‬
99
.
2
> >
Crushed
,at
Dimensions, in
Description
>>
tons
sq
per
.ft
aCracked
,t
( Single bricks. Faces made smooth and parallel by plaster of Paris. Crushed between
two millboards, or the iron pressure-plates of the testing machine.)
0
9
Aylesford , common .
pressed
Rugby, common
4.6 x 4.1
4.6 x 40
9.2 x 41
8.9
4.2
8.9 x 4.25
x2.4 128
x 2.45 133
x 2.8
x 2.3
x 2.5
8.9 x 44 x 2 :7
177
181
129
Yelluw Half -brick
>>
‫גל‬
‫ܕ ܕ‬
113
>>
103
79
183
Pink
Red
8.9
x 44 x 27
48
111
9.1
9.5
* 4.3 x 27
71
228
141
x 2.9
158
190
x 42
Remarks
‫לל‬
Deep frog
Between
pine boards
90 x 42
120
x 3.0
Lodge Colliery,Notts 90 * 4-2 * 3 :4
9.0 x 42 x 3.25
127
55
159
122
‫יל‬
Digby Colliery,Notts 9.3
x 4:1 3-25 248 ( 353)
414
4.6 x 42 x 3.2 414
‫ܕܕ‬
Ruabon, pressed
> ‫و‬
8.8
* 4.3
x 27
361 [ 361]
83
Grantham, wire cut 9.2 x 4'4 * 3-2
Leicester, wire cut .
)
>
115
149
337 Pale red Half- brick
308
79
‫לל‬
229
>>
>>
181
Half-brick ,
)
x 2.5
165
237
8.8 x4.3 x 2.8
8.7 x 41 x 3.0
44 x 42 x 2.5
8.7 x 41 x 2.9
80
111
381
173
145
4.4 x 41 x 2.6
4.3 x 41 x 2.6
9.06 4.2 x 2.8
4.7 x 46 x 2.5
251
109
ů
Cranleigh, pressed
Notcrush'd
Half-brick
Notcrush'd
frog
4.6 x 46
>>
Half -brick ,
72
frog
Candy, pressed
Gault, wire cut
.
9
79
>>
>>
19
Staffordshire
4.5
x 4.3
3.0
216
464
4.3
4.2
x 3.0
152
386
8.9
Half- brick
ラク
x4.3
3.1
240 ( 353]
7
72
17
Notcrush'd
blue,
pressed
C
Glazed brick
.
9.0
4.3
3.1
88 x 44 x 3.3
8.9 x 44 x 2.9
275
69
166
166
174
Reà rubbers, three
in column, bedded
in putty
9.0 x 4.5
x 8.0
6 sq. ins .
Terracotta block
>>
0
15
15
6
>
Blue
blue,
common
Staffordshire
Half-brick
blue ,
cominon
Staffordshire
‫לל‬
169
blue,
common
Staffordshire
119
White
‫לל‬
‫و‬
25
168
139
17
267
104
Frog
439
STONE AND BRICK
176. Strength of Brickwork. — Comparatively few
accurate tests have been made of the strength of brick
work masses .
The following results of tests of brick
cubes, with different mortars, were made at Berlin by
Dr. Böhme.
The brick cubes
were approximately
10 x 10 x 9.5 inches, and were three months old . Two
kinds of brick were used :
Mean
Crushing
crushing i strength
Condition strength , of single
in tons brick , tous
per sq. ft . per sq . ft.
Crushing
strength of
mortar ini
cules, ton !
per sq . ft.
116.2
130.4
11 :4
420
3. 1 cement, 6 sand
Dry
Dry
Dry
4.
Wet
141 : 9
5. 1 cement, 3 sünd
Dry
1588
6.
Wet
169.8
Mortar
Beneckendorfer brick :
1. 1 lime, 2 sand
2. 7 lime, 1 cement, 16 sand
‫ול‬
2032
139.4
112 :4
192-9
‫ܕܐ‬
Hertzfelder brick :
7. 1 lime , 2 sand
8. 7 lime, 1 cement, 16 sand
9. 1 cement, 6 sand
10.
Dry
Dry
Dry
Wet
>
11. 1 cement, 3 sand
Dry
12 .
Wet
700
73.3
932
874
1007
104.6
1009
,
!
11 :4
420
112.4
192-9
This gives for the ratios of strength of brickwork to
strength of single bricks:
For mortar of 1 lime, 2 sand .
7 lime, 1 cement, 16 sand .
1 cement, 6 sand
>
>
‫ܕ ܕ‬
79
‫رد‬
>
1 cement, 3 sand
0:44
0:48
0:55
0.03
The following experiments on bricks and brickwork
pillars were made by Curioni .' The bricks were placed
flat. All the bricks were of the same clay. The mortar
1 Proc. Inst. of Civil Engineers, lxxiii. p. 385.
440
TESTING OF MATERIALS OF CONSTRUCTION
consisted of equal parts of Casale Monferrato cement
and fine sand , and was allowed fifty days to set : -Crushing stress, in tons per sq. ft.
Machine-made bricks
Description
Hand
made
bricks
Single bricks, between lead
First
Second
pattern
pattern
119.8
2149
142.7
2378
282.6
150.0
1271
114.3
211.2
142.6
Single bricks, with faces made even with
mortar
Pillars of 2 bricks, mortar faces
)
3
4
1426
86.9
>
17
>>
The reduction of strength by using lead is obvious.
If we take the length of a brick to be twice the width
and 4 times the thickness, Bauschinger's formula for
pillars of this kind takes the forin
f= a +
12
where f is the strength per sq. ft ., n the number of
bricks in height, and a and b are constants .
The formula agrees pretty well with the results, if
the following values are taken :
225
Hand-made bricks .
f = 13 +
12
225
Machine-made bricks ( 1st) f= 58 +
22
136
(2nd ) f = 75+
12
which at least seems to show that the diminution of
strength is due to form , and not to influence of the
mortar joints.
441
CHAPTER XV .
LIMES
AND
CEMENTS .
177. Limes and cements are of the greatest impor
tance to the engineer, and , being artificially manufactured
products, they vary in quality according to the care
exercised in the selection of the materials of which
they are made, and the skill and attention with whichi
the processes of manufacture are carried on .
To secure
a uniform and trustworthy cement, the cngineer has
been driven to test regularly the cement supplied. To
Mr. Grant is largely due the credit of establishing sys
tematic tests of cement, with the result that, from the
pressure brought to bear on manufacturers, and the
knowledge gained of the conditions on which the
strength of a cement depends , there has been achieved
a very considerable and general improvement of
quality. In large works, like the Metropolitan Main
Drainage, it was perceived that a considerable sum
might economically be spent on systematic and regular
tests of the quality of the cement supplied .
A com
paratively large sum spent in testing formed but a
small percentage on the value of the cement, and as the
quality of cement may vary through very wide limits,
442
TESTING OF MATERIALS OF CONSTRUCTION
from qualities absolutely trustworthy to qualities abso
lutely dangerous, the cost of testing was fully repaid
by the greater value of the cement obtained, and the
thorough confidence with which after testing it could
be used .
The cementing materials ordinarily used are classi
fied thus :
1. Rich or fat limes .
2. Poor limes .
3. Hydraulic limes.
4. Hydraulic cements.
The rich or fat limes are produced by the calcination
of nearly pure limestones, and they consist of lime
nearly free from other ingredients. Such lime, when
mixed with water, slakes violently, and afterwards sets
or hardens extremely slowly, if at all, by the absorption
of carbonic acid from the air.
weak mortar.
Such lime makes very
Poor limes contain 10 to 40
sand or other inert matter .
per cent. of
They slake much less
violently, or even imperfectly, and also make a very
weak and very slowly setting mortar.
Hydraulic limes and cements are those which contain
ingredients capable of combining and hardening apart
from any absorption of carbonic acid from the air.
They will , therefore, set under water.
The hydraulic limes contain a large amount of pure
lime, so that they slake . But they contain also clay,
silica, or other ingredients in a condition capable of pro
ducing chemical action in the presence of water.
LIMES AND CEMENTS
443
This action results in the setting of the lime, which
hardens and becomes insoluble. Feebly hydraulic lime
makes mortar which hardens enough to resist a finger
nail in a month .
The Lias and Mountain limestones
yield limes more actively hydraulic.
Artificial hydraulic limes or cements are mixtures
of lime and clay in proportions which produce eminent
hydraulic or setting properties. The mixture is calcined
to clinker at a suitable temperature , and then ground
to a fine powder. Such a cement hardly slakes at all ,
but sets with great rapidity, becoming in course of
time extremely hard. The name Portland cement ,
given to the first successful artificial cement of this
kind , has become a general name for all artificial cements
formed by calcining mixtures of chalk or limestone
and clay.
178. Portland Cement. — About the year 1850 there
was first produced a new cement, which from its resem
blance to Portland stone when set was called Portland
cement. It has the properties of setting rapidly and
setting under water, and it slowly hardens to a condition
in which it is nearly as strong as natural stone. In
hardening , it has the very important quality of altering
extremely little in volume. It rapidly established its
superiority as a constructive material to Roman cement,
and it bids fair, in spite of its greater cost, to largely
supplant hydraulic lime. It can be kept with little
deterioration and shipped to distant countries . Its use
has extended till its manufacture has become one of the
444
TESTING OF MATERIALS OF CONSTRUCTION
most important industries in this country, in Germany,
in France, and in the United States .
Success in its manufacture depends on careful judg
ment and the rigid observance of essential conditions.
It may be produced from a great variety of natural
rocks, but, broadly speaking, it consists of 72–79 per
cent. of chalk and 28–21 per cent. of clay .
Experience shows the exact proportion of the natural
materials used which is most suitable .
These materials
must be so mixed that the cement is absolutely homo
geneous and invariable in composition. At first, the
chalk and clay rere ground together with a large
volume of water into a liquid slip. Now, it is found
that grinding with only 35 per cent. of water is
not only economical, but prevents the segregation of
materials which took place in fluid slip . With some
materials no water is used in grinding. The mixed
materials are then calcined to a clinker at a temperature
just short of that which produces fusion or vitrification .
Underburned clinker is weak, and overburnt clinker is
an almost inert cement. Lastly, the clinker must be
broken up and ground to a powder, so fine that the
cement particles expose a maximum surface at which
chemical actions may occur, and are not too large to
fill the smallest interspaces in the sand with which the
cement is mixed in use.
According to Michaelis , the hydraulicity of a cement
is due to the silica, alumina, and oxide of iron. In a
good cement the sum of these should be about one
445
LIMES AND CEMENTS
third 1 of the total weight, the rest being chiefly lime.
The calcination removes carbonic acid and water, and
leads to the formation of calcium silicate, calcium alu
minate, and calcium ferrate.
In the setting and harden
ing of a paste formed of the cement, there is probably
a hydration of the silicates, and perhaps the formation of
double hydrated silicates.
The composition of a Portland cement varies more
or less , but generally lies between the limits given in
the following tahle : -ler cent.
20-26
Silica
.
Alumina
.
Oxide of iron
Lime
+
5-10
2-6
.
}
67-58
0.5-3
Magnesia
179. Ordinary Cement Tests for Strength. --The ordi
nary test is a tensile test of a small briquette of neat
cement, made in a brass or gun -metal mould, left twenty
four hours to harden in air, and then placed in water.
The cement is tested in seven days, and , if possible,
at later dates also. At least five briquettes should be
tested at each date, and the mean result taken .
The form of the briquettes has a considerable in
fluence on the strength.
Fig. 134 slows some of the
forms which have been used.
Form a, used in all the
earlier tests , is a very bad form , the square corners
producing unequal distribution of stress with a rigid
material.
The most common forın now is
C,
known
1 In the French rules a cement in which the ratio of silica and
alumina combined to lime is less than 0.44 is regarded as doubtful.
446
TESTING OF MATERIALS OF CONSTRUCTION
sometimes as Grant's, and this is universally used in
Germany . A few engineers use forms like f and g . A
small metal plate is placed in the holes at the ends, and
a knife -edge of the shackle passes through each hole.
In some of Mr. Grant's tests, briquettes of the same
cement gave strengths ranging from 280 lbs. per sq. in .
for form a, to 460 lbsper sq.in. for form e, at seven days
after gauging. For some time briquettes with a sec
FIG . 134 .
ISET
X83
tion of 21 sq. ins. were used, but it is far more usual
now to make the section 1 sq. in. The smaller bri
quettes are more easily moulded, and give more uniform
results .
The briquettes are broken in small lever testing
machines , of which there are now many in the market.
It is very important that the load should be applied at
a regular rate and without shock . Adie’s machine is
a single-lever machine with a rolling weight. Reid
& Bailey's machine is a single-lever machine, with a
LIMES AND CEMENTS
447
cistern at the end which fills with water to apply
the stress. In Michele's machine, a bent or pendulum
lever is used.
Mr. Faija has designed a neat single
lever machine with a spring balance at the end. A
worm and sector, acting on the spring balance , regu
larly increase the load . The ordinary German ma
chine is a double-lever machine, and is loaded with
shot.
Precautions in Gauging Briquettes.--A sample of the
cement should be taken from every twenty -five or fifty
barrels or sacks ; the samples should be mixed, an !
a portion taken for gauging. To obtain the best re
sults , the gauging must be done with the smallest
amount of water which will make a smooth stiff paste.
Preliminary tests must be made, to ascertain exactly the
quantity of water necessary .
A small quantity of the
mortar, dropped from the trowel at a height of 20
inches, should leave the trowel clean , and retain form
without cracking. It should be capable of being
moulded into a ball by hand which can be dropped
20 inches without cracking.
Having ascertained how
much water is necessary ( 18 to 25 per cent. of the
weight of the cement usually ), the cement and water
for gauging should be accurately weighed.
The cement is generally gauged on a slate or marble
slab with a light trowel, and the more rapidly this is
done and the moulds filled the stronger are the bri
quettes . Usually mortar to fill five or six moulds is
gauged, six ounces of cement being necessary for each
448
TESTING OF MATERIALS OF CONSTRUCTION
mould . The mixing with the trowel should take five
minutes, and then the moulds, placed on a glass or slate
slab, are filled and rammed and shaken. It is important
that the operation should be finished before setting
begins.
Mr. Faija has introduced a very convenient cement
gauges the cement in less time and more
uniformly than it can be done by hand .
gauger, which
The briquettes are removed from the moulds when
set, and in twenty - four hours they are placed in water.
The temperature during all the operations should, if
possible, be 15 ° to 18 ° C.
In testing the briquettes, the load should be applied
at the rate of 100 lbs . in fifteen seconds .
Briqucites of Sand and Cement. — Briquettes of sand
and cement give far more trustworthy indications of
the value of a cement than neat cement tests.
The ce
ment is always used in construction mixed with other
materials, and the cement which is strongest neat is not
always strongest tested with sand. The gauging of the
briquettes also is easier, and the results are less affected
by small variations of procedure. On the other hand,
the briquettes must harden twenty -eight days before
being tested, and this is in many cases a longer time
than can be allowed .
The greatest difficulty of the sand test is securing
an identical quality of sand for all tests which are to be
compared.
A sharp pit sand is best, which should be
carefully washed and sifted .
The sand used should be
449
LIMES AND CEMENTS
the portion which passes through a 20 -mesh, and
remains on a 30 -mesh, sieve. In Germany, a special
sand has been selected, and washed and sifted portions
of this normal or standard sand are sold by the Go
vernment laboratories. In France , a standard sand is
obtained by crushing quartzite, and sifting through
sieves of practically the same sized mesh as is given
above.
In the ordinary sand test , the mortar is gauged
with one part by weight of cement and three of dried
sand . The water required is about 12 per cent. of the
weight of cement and sand. The sand and cement are
mixed dry, the water added, and the mortar is gauged
for five minutes. The briquettes are placed in water
twenty - four hours after gauging.
180. Increase of Strencjth in Hardening. Initial
Strength, and Rate of Gain of Strength.— The construc
tional value of a building cement depends on two quite
distinct elements -- on its power of setting into a rigid
forın soon after it is gauged , and on its power of at
taining in course of time a considerable strength. In
the actual process of building, especially building under
water, it is important that the cement should set
rapidly, and gain strengtlı enough to keep its form .
But, generally, it is only after the lapse of months, or
even of years, that the structure is called on to exert its
full strength . Hence any strength acquired by harden
ing during that time is advantageous.
Consequently, in judging of a cement from tests of
GG
450
TESTING OF MATERIALS OF CONSTRUCTION
its strength, both the initial strength acquired in a
short time and the rate of gain of strength with age
require to be considered.
Now, suppose experiments have been made, say,
at seven days, four weeks, and twelve weeks.
One
would still like to be able to predict the strength at
a greater age, and even in judging of the data in
hand some difficulty arises from the discrepancies and
anomalies incident to such experiments, and due to the
difficulty of making the experiments numerous enough
to get true average values. If anything were known
of the law of increase of strength with age, if we could
put our results in a formula, their meaning would be
much clearer.
Now beyond the first week , and up to a period at
which the full strength of the cement is reached, the
rate of hardening follows very approximately a simple
law . For ordinary tension briquettes, for instance, the
gain of strength is nearly proportional to the cube root
of the time of hardening, and that both for neat cement
It is possible, therefore, to repre
sent the results of a series of tests in a simple formula,
and cement mortar .
the constants of which indicate the character of the
cement with very great clearness.
Let y be the strength of a cement, or cement mortar,
in lbs. per sq. in. , at an age of 2 weeks after mixing.
From some preliminary tentatives the author found for
the relation between x and y the expression-,
y= a + b 2
( 1),
451
LIMES AND CEMENTS
where a , b, and n are empirical constants .
In this
form the equation would not be very convenient to use ,
for it would require at least three sets of experiments
at three different ages of the test pieces to determine
the three constants ; and a still greater number would
be required for satisfactory results in consequence of
the discrepancies which occur in cement testing.
It appeared , however, that for any given kind of
cement, and any given kind of straining action , n had
a constant value. Further , by a modification of the
formula, a might always be the strength of the cement
at seven days ' age. Consequently there would remain
only one constant to determine.
The formula then is
(2),
y = a +1 ( x - 1 )"
where
y
is the strength of a cement or mortar, at a
weeks after mixing, the initial strength of which at
seven days is a lbs. per sq. in. The constant n has
values which can be assigned beforehand , and only the
constant b remains to be determined by experiments
on test pieces more than one week old . It will be seen
hereafter that, though b varies , its variation is not
within very wide limits, so that when the characters of
cements are better known it may be possible to assign
for it a probable value, even if experiments are wanting
in any given case.
Now since in this equation a is the initial strength
of the cement, and b a constant, varying with the
rate of increase of strength with time, the two con
GG 2
452
TESTING OF MATERIALS OF CONSTRUCTION
stants exhibit very clearly the character of a cement .
If their values are determined for any given cement,
and inserted in the equation, a numerical equation is
obtained which may be termed the characteristic equa
tion for the cement .
181. Application of the Characteristic Equation to
Tension Tests. — To examine the applicability of the for
mula, let the constants be determined for the series of
tests of Portland cement briquettes extending over seven
years given in Mr.Grant's first paper. Mr. Grant's table
gives in each case the mean strength of ten briquettes,
24 sq. ins. in section. In one series the cement was
gauged neat ; in another series the cement was mixed
with an equal weight of clean Thames sand . Mr.
Grant's numbers, reduced to lbs . per sq. in. , are as
follow :
Strength per square inch
Age
7 days
1 month
3 months
6
9
.
29
> >
12
0
.
2 years
3
.
Neat cement
1 cement + 1 sand
363
415
470
525
542
547
590
585
157
202
244
285
307
320
351
350
Now, for Portland cement in tension, n = } ; the
constant a has the values 363 and 157 for the two series,
1 Minutes of Proceedings Inst. C.E. vol. xxv . p . 89 ;'also vol. xxxii .
p. 280 .
453
LIMES AND CEMENTS
and it only remains to determine the most probable
value of l in the equation
y=a+b
-1.
This is best done by calculating b for each of the
experiments, except that at seven days, and taking the
mean of the values so found .
Thus
NEAT CEMENT..
6
Age
Strength
X
?
1
4
13
26
39
52
104
156
Strength
a
y
y - a
Gi
Y
1
by formula
363
303
431
36
47
56
53
52
107
162
415
470
525
542
547
590
585
Mean
179
184
227
49
471
503
525
541
48
588
48
.
1 CEMENT + 1 SAND .
b=
Strength
-
Age
Strength
ya
y-a
Y
1
4
13
26
39
52
104
156
208
260
157
202
244
285
307
320
351
350
363
365
37
87
31
38
128
44
150
163
194
45
44
41
36
45
193
y
1
by formula
157
214
249
274
292
305
345
372
40
Mean
Hence the characteristic equations for this cement
and cement mortar are
Neat cement .
Cement mortar
.
y = 363 + 48
y
x - 1
157 + 40 YX
1
454
TESTING OF MATERIALS OF CONSTRUCTION
Hence, the sand reduces the initial strength of the
cement by rather more than one -half ( from 363 to
157 lbs. per sq. in. ) , and the gain of strength at any
age is less for the mortar than for the neat cement in
the proportion of 40 to 48. By comparing the calculated
and observed values of y, it will be seen that the formula
FIG . 135 .
LOS 650
600!
NEAT CEMENT
500
1
1
1
I CEMENT
1
1
o
-
-
1
400
1
3 SHND
300
200
100
10
20
40
60
80
100
120
140
WEEKS
agrees closely enough with experiment for practical
Mr. Grant's figures show that the neat
cement reached its maximum strength in one hundred
purposes.
and four weeks, and the cement and sand in one hun
dred and fifty -six weeks. Hence values of 6 are cal
culated from data up to those dates only.
In Fig. 135 the experimental values are shown by
455
LIMES AND CEMENTS
small circles, connected by a broken dotted line, and
the calculated values lie on the curves .
In the case of cement mortar the briquettes gain in
FIG . 136 .
LBS
850
o
800
700
o
o
.
A
600
500
400
300
200
100
0
10
20
30
40
50
WEEKS
strength up to any period to which experiments are
usually extended . But with neat cement briquettes
a maximum strength appears to be reached, often in
456
TESTING OF MATERIALS OF CONSTRUCTION
about three months, after which the strength remains
constant or slightly falls off. For example, in the ex
periments given by Mr. Grant on the relative strength
of briquettes made on an impervious slab, and on a
porous (gypsum) slab,? the strength slightly diminishes
after thirteen weeks. Hence, for such results the value
of b must be deduced from experiments before the maxi
mum is reached, and the formula ceases to apply beyond
the maximum .
The following characteristic equations
deduced for these experiments from the results for
four, eight and a half, and thirteen weeks.
NEAT CEMENT.
Impervious slab
Gypsum slab
449 + 161 3
- 1;
257 + 164 3 x - 1.
Impervious base
Gypsum slab
2
Weeks
y
1.0
40
8.5
13.0
26.0
39.0
52.0
?
y
Observed
Calculated
Observed
Calculated
449
449
687
765
808
731
746
718
681
257
454
765
034
819
626
620
655
257
493
577
631
608
These results are plotted in Fig. 136 .
182. Values of Constants for different Cements. First
some data have been selected from the Table XLVII . ,
p. 169, of Mr. Grant's paper.
The only principle of
selection adopted was to take those cements for which
the completest series of data are given . The following
1 Minutes of Proceedings Inst . C.E. vol . lxii. p . 142.
457
LIMES AND CEMENTS
table gives the characteristic equations obtained for ncat
cement briquettes, the constants being in all cases de
duced from the strengths given at one, four, and thir
teen wecks . In none of these cements did the strength
increase beyond that period,
CHARACTERISTIC EQUATIONS FOR MR. GRANT'S CEMENTS.
( Units, lbs. per sq. in . , and wecks. Gauged neat. )
No.
1
12
13
Water Setting
Initial
used , time, in Characteristic equation strength
per cent. minutes
18.5
22 :5
20.0
Slow
15
600
21.2
15
19
22.5
20 : 0
22.5
22.5
y = 558 +
‫נו‬
480
> )
>>
96
422 +118
614 + 91
610 + 91
520 + 112
626 + 50
576 + 140
422 + 188
9-1
>
>>
>>
> >
Strength at
13 weeks
Strength
at
52 weeks
Obsery.
Calc .
558
422
815
744
778
825
614
846
840
692
824
094
813
779
772
718
785
747
610
520
626
576
422
783
824
833
793
820
780
755
896
852
The tests of cement which form the most complete
series are, however , to be found in the publications of
the Engineering Laboratories of Munich and Berlin .
In the Mitt, aus den Mech . Techn. Laboratorium in
München ,' for 1879, there is a remarkable series of ex
periments on the tensile strength of cements, by Pro
fessor Bauschinger. In Table II . are given no less
than three hundred and sixty results , each the mean of
ten separate experiments. Ten different cements were
used, and these were made into test pieces of 72 sq .
cms. ( 11 sq. ins. ) section . From these results the
author obtained the following equations, those for
neat cements being deduced from results on test pieces
one week to sixteen weeks old , and those for cement and
TESTING OF MATERIALS OF CONSTRUCTION
458
sand from results on test pieces one week to one hundred
and nine weeks old .
The extreme regularity of the constants for a great
variety of cements and their limited variation in value
is remarkable . The comparatively low initial strength
may be partly due to the cement being fresh, partly to
the size of the test pieces .
CHARACTERISTIC EQUATIONS FOR TENSILE STRENGTH OF BAUSCHINGER'S
CEMENTS .
( Units, lbs. per sq. in. , and weeks.)
Cement Setting time,
minutes
mark
А
80
49
195
136
B
C
D
13
F
G
H
R
T
416
9 to 17
14 ‫ و‬26
344
146
Neat cement
y
1 cement + 3 sand
y =
1 cement + 5 sand
y =
199 + 40 3 - 1
81 + 29 3x - 1
43 +31
121 +49
199 + 95
199 + 53
185 +42
256 + 37
227 + 64
227 + 36
299 + 61
227 + 61
46 + 36
26 + 30
78 + 37
80 +46
136 + 37
114 + 28
60 + 28
67 + 38
67 + 33
50 + 36
105 + 31
71 +24
Mean 54
Mean 40
Mean 33.5
108 + 40
53 + 61
85 +40
112 +41
91 +40
- 1
37 +47
The French official standard of strength for neat
cement briquettes is a minimum of 284 lbs. per sq. in.
at 7 days, 498 lbs. at 28 days, and 640 lbs. at 84 days
after gauging. This agrees nearly with the equation
y = 284 + 155 % 2-1.
The strength is taken to be the mean of the three
highest of each set of six tests .
183. Values of the Constants in Shearing Tests . - Parts
of the briquettes used in Bauschinger's tension tests
.
459
LIMES AND CEMENTS
given above were subjected to shearing. The following
are equations for a few of them :
Neat cement
y
1 cement + 3 sand
A
270 +43 3-1
112 + 4935-1
B
142 + 67
412 + 57
242 x 92
46 + 53
187 + 55
131 +43
Cement
mark
R
T
1 cement + 5 sand
y
y =
60 +52 0-1
31 + 57
131 + 61
105 +44
184. Characteristic Equation for Tests ofother Cement
ing Materials . - Some experiments by Dr. Böhme on
hydraulic lime have also been examined. These are
not very extensive , and they were carried to an age of
thirteen weeks only. However, they agree well with a
formula of the same general form with n = 1 . The
equation is therefore
y = a + b (x - 1 ) .
The following were deduced from the data :
Tension ; 1 lime + 1 sand,
y = 20 + 11 (2-1 ) .
Tension ; 1 lime + 3 sand ,
y = 31 + 17 (2–1 ) .
Compression ; 1 lime + 1 sand,
y = 97 + 44 ( x - 1 ).
Compression ; 1 lime + 3 sand,
y = 122 + 22 (x - 1 . )
185. Fineness of Grinding.
The greater part of the
improvement in the quality of cement which has been
effected in the last ten years has been due to the dis
460
TESTING OF MATERIALS OF CONSTRUCTION
covery of the importance of grinding the clinker to ex
treme fineness. The amount of surface the particles of
cement expose increases inversely as the diameter of
the particles . A cubic inch of cement would have 150
sq. ins. of surface if the particles were spherical and 25
inch in diameter, and 600 sq. ins. if they were TỚo
inch in diameter ; so that the area on which chemical
action occurs increases as the cement is ground more
finely. But probably this is only part of the explana
tion of the greater value of very finely ground cement.
If cement is taken and sifted through a sieve of fifty
meshes to the inch , the residue on the sieve of particles
larger than the holes in the sieve will not adhere to
gether sufficiently to form a briquette. They are almost
absolutely without cementitious value.
But if these
same particles are reground, they are converted into
valuable cernent.
The extremely small value of these larger particles
in the cement was not for some time perceived . For a
long time all tests of the strength of cement, or nearly
all , were made with neat cement, the reason being that
tests of this kind can be made more rapidly than any
others. Now, a good cement will bear the addition of
a certain amount of inert matter without any sensible
reduction of strength ; indeed, with a certain gain.
Hence it happens that in neat cement tests a somewhat
coarsely ground cement gives results higher than a
finely ground one. But cement is never, in fact,used
neat ; it is used mixed with three to seven or more
LIMES AND CEMENTS
461
times its weight of the cheaper material, sand or gravel .
In the German laboratories , therefore, it was thought
desirable not to test the cement neat, but to test it in
the condition in which it is used in practice, mixed with
sand ; and directly this was done, it was found that the
cements which were strongest tested neat were by no
means always strongest tested as mortar mixed with
sand . There may be more reasons for this than one,
but the principal reason is that the more finely ground
cement will bear a considerable addition of sand with
less loss of strength than the coarsely ground cement.
The coarse cement has, in fact, a proportion of matter
as inert as sand already mixed with it.
Suppose a cement has 10 per cent. of inert matter ;
then , when mixed with sand in the proportion of 2 : 1 ,
the true ratio of cement to inert matter is 1 to 2:33 ;
but if the cement initially contains 40 per cent. of inert
matter, then, when mixed with double its weight of
sand, the true ratio of cement to inert matter is 1 : 4 .
It may also be noted that the cement and sand test is
to some extent a test of adhesion , the neat cement test
being a test of tenacity only .
The fineness of grinding is determined by careful
sifting through copper or brass wire sieves with square
meshes, and these should be carefully and accurately
made. Obviously, in specifying the sieves to be used,
1
it is necessary to state not only the number of meshes
to the inch but the size of wire used. The following
are the sieves most commonly used in cement -testing : --
TESTING OF MATERIALS OF CONSTRUCTION
462
No. of meshes
to in .
Diameter of
wire
No. of meshes
to sq . in .
inches
25
For cement
0
‫ور‬
50
74
100
120
180
20
28
.
.
.
79
1
For sand .
.
79
625
012
·005
0044
· 0031
2,500
5,476
10,000
14,400
32,400
0146
0123
400
774
FIG . 137 .
35. 750
700
600
w$
UN SISTEO
500
D
LBS 450
SIFTED
400
400
SIFTED
NEAT CEMENT
300
300
LBS 300
200
200
200
SIFTEA
UNSIFTED
100
100
100
ICEMENT J SAND
UMSIFTED
50
50
SO
SANO
ICEMENT
10
20
30 WEEKS
0
10
20
30 WEEKS
10
20
30 WEEKS
The best German cements are ground so fine that
they leave a residue of only 3 to 10 per cent on a
76 -mesh sieve. English cements are more commonly
1
The German standard for fineness is that not more than 10 per
cent. remains on a 76-mesh sieve, the wire of which has a thickness equal
to half the width of mesh ; alb . of cement is used for this test.
LIMES AND CEMENTS
463
specified to pass entirely through a 25 -mesh sieve,
and to leave not more than 10 per cent. on a 50-mesh
sieve.
Fig. 137 shows the results of a series of tests by
Messrs. Dyckerhoff, given in Mr. Grant's paper. The
same cement was used in all the tests ; but in one
series the cement was used as manufactured, in the
other after sifting through a fine sieve. The former
left 10 per cent. on a 50-mesh sieve ; the latter all
passed through a 180- mesh sieve.
The equations corresponding to the curves in the
diagrams are as follows :
Neat cement.
Neat unsifted cement
353 + 122 V
Neat sifted cement
y
- 1
y = 346 + 36
-1
1 cement + 3 sand.
Cement unsifted
y = 75 + 69 % c - 1
Cement sifted
y = 252 + 53 $ x - 1
1 cement + 5 sand.
Cement unsifted
y = 31 + 46
Cement sifted
- 1
y = 136 + 47 Val.
A series of experiments, given in Mr.Elliot Clarke's
very interesting Report on the Boston Main Drainage
464
TESTING OF MATERIALS OF CONSTRUCTION
Works, shows the effect of fineness of grinding still
more strikingly. An English Portland cement was
taken and divided into portions , which passed through
a 50 , 70, 100, and 120 sieve. Briquettes made with
these and with different proportions of sand were tested
at different periods, from one week to fifty -two weeks.
The following equations give the results :
EFFECT OF FINEN ESS OF GRINDING ( Boston) .
Percentage which
would not pass
1 cement + 3 sand
1 cement + 5 sand
through a 100 sieve
55
33
28
18
8
0
y = 39 + 28 % *; -1
92 +42
97 + 45
117 +44
123 + 50
154 +44
y = 19 + 19
-1
-
43 + 32
47 + 35
65 + 35
73 +36
86 + 35
186. Heaviness of Cement. — It was early discovered
that heavy, well-burnt clinker produced better cement
than the lighter under-burnt clinker. Hence for a long
time it was prescribed in all specifications that the
cement should have a certain weight per bushel.
To get uniform results the cement is sifted through
a very coarse sieve, and allowed to fall through a
funnel 18 inches to 3 feet high into the standard
measure .
The cement is strickled off, and the measure
weighed without shaking. The size of the measure
must be defined, as the cement packs closer in a large
than in a small measure. Bauschinger found 13 per
cent. difference between the weight of cement in a 50
litre and a 1 -litre vessel..
But another influence affects
465
LIMES AND CEMENTS
the result. A cement ground coarsely will give a
heavier weight than the same cement ground finely, so
that the weight test is a premium on coarse grinding.
Since this has been understood, the weight test has been
generally abandoned.
The weight per cubic foot of the same cement of
different degrees of fineness was determined at Boston ,
with the following results :
Per cent, retained
Weight per
on 120 sieve
cubic foot
0
10
$
牛
20
30
40
75
79
82
86
90
.
FIG . 138 .
PER CENT
LEFT ON
120 SIEVE
401
30
20
10
0
LBS .
75
80
A
85
WEIGHT PER CUBIC
90
95
100
FOOT
Fig. 138 shows these results plotted in a curve.
It
is still, however, convenient to know the weight per
1
' Boston Main Drainage.
By Elliot C. Clarke.
p . 115 .
H H
466
TESTING OF MATERIALS OF CONSTRUCTION
cubic foot, and if the fineness is taken into account it
affords some indication of the quality.
The French official weight test is free from the
objections to the ordinary weight test. The cement is
sifted through a sieve of 180 meshes to the inch, and
only the sifted cement is used for weighing. This is
filled into a litre measure.
The weight of 1 litre
must be within 100 grams of that of a litre of cement,
of similar fineness ground from specially selected heavy
clinker produced at the same factory.
187. Influence of the kind of Sand used in making
Cement Mortars. — The sand used with cement in making
mortar is commonly directed to be clean, sharp, siliceous
sand. It is usually specially directed that the sand
should be free from clay. Experiment seems to show
that a percentage of clay does not really harm the
cement. But leaving this question aside, and suppos
ing we have got a clean siliceous sand , tests will give
very different results, according to the quality of the
sand . For instance, experiments given by Mr. Grant
with Berlin standard sand and a coarser sand give the
following equations
Standard Berlin sand. Briquettes pressedy = 73 + 31
Standard sand.
- 1
Briquettes not pressed
y = 89 + 19 % & - 1
Coarser sand
y
172 + 28
- 1
467
LINES AND CEMENTS
The ex
These experiments extended over a year.
periments are plotted in Fig. 139 .
Fig. 140 shows some experiments on a Portland and
American ( Rosendale) cement,' made with a sand un
sifted (marked mixed on the diagram ), and on portions
of the same sand of different degrees of fineness obtained
by siſting. It will be seen that the coarser sands give
FIG . 139 .
lbs
300
300
200
200
100
13
8'2
th
13
26
WEEKS
39
52 1
82
39
26
WEEKS
52 1
100
13
82
26
WEEKS
39
0
52
briquettes of greater strength ; but the unsifted sand is
nearly as strong as the coarsest. For use on works the
mixed sand would be good, but for comparative experi
ments sand of a definite size is preferable.
By coarseness of the sand we mean , primarily, size
of grain . Large-sized sand is good for exactly the
! ' Boston Main Drainage. ' Clarke .
p . 123.
II 1 2
468
TESTING OF MATERIALS OF CONSTRUCTION
inverse reason that fine cement is good. Fine cement
coats a large surface, and fits well into the interspaces
of the sand. Large-grained sand has less surface to
coat, and its spaces are more casily filled with cement.
Now, uniform size of grain may be obtained by sifting.
Standard Berlin sand is passed through a 20- and is re
tained by a 28 -mesh sieve. But sands of uniform size
FIG . 140 ,
los
400
THS
9 MON
300
2 5
10
1
P
MONTHS
Is S.
10
R7
200
2 WEEKS
2
P.
10 .
R.
IC
S
.
la S
4 WEEKS
IŹ S
, WEEK
100
IC
0
Very fine
Fune
Medinin
Very Coarse
Mixed
of grain do not make equally good mortar. Two sands
sifted through and retained on the same sieves give
different tests .
There is something in the form of the
grains and the kind of space between them - possibly
even something in the chemical condition of the sand
which affects the initial strength and rate of hardening
of the briquette . These different qualities are shown
very clearly in the following characteristic equations,
469
LIMES AND CEMENTS
deduced from experiments by Mr. Amold, at the
Harbour Works at Wilhemshaven .
The tests are 1
cement to 3 sand, the same cement used throughout :
Wilhemshaven blue sand , fine-grained and sharp
y = 101 + 22-1
Dangast normal sand , sifted in the same way as
Berlin normal sand , not very sharp
y = 124 + 23
-1
Dangast common building sand
y = 165 + 13-1
Wangeroog , coarser, clean and sharp
y9
= 193 + 41 X - 1
Berlin normal, clean sharp quartz sand ---34 = 250 +44 NX - 1
188. Influence of Proportion of Sand on the Strength
of the Mortar.– Cement mortars are weaker than neat
cement, probably because the adhesion of the cement
to the sand is less than the tenacity of the cement.
The larger the proportion of the sand, the weaker the
mortar .
It appears that, even with a proportion of
1 cement to 3 sand, the whole of the interstices of
the sand cannot be filled with cement, and as the pro
portion of sand increases the proportion of unfilled
space must increase, and therefore there must be a less
section to break .
From a series of tests, by Mr. Elliot Clarke, of
about 500 briquettes , all made with the same cement
$
470
TESTING OF MATERIALS OF CONSTRUCTION
(the tests extending over two years ), the following very
uniform series of equations are obtained :
PORTLAND CEMENT MORTAR, WITH DIFFERENT PROPORTIONS
Neat cement
1 cement + 1 sand
1
1
or SAND (Boston ).
1
y = 303 + 613x-- 1
160 + 57
126 +44
95 + 36
55 +26
+2
17
1 )
+3
+5
)
1
)
‫ܕ ܕ‬
Below are given the results of experiments by Dr.
Böhme on the influence of the addition of various sub
stances to cement .
Some of these, such as gypsum ,
have been added at times with an idea that they im
proved the cement ; others have been added occasionally
as adulterations.
Slacked lime has sometimes been
used with cement in very cold weather. It will be seen
that , with the exception of sifted cement, every one of
these additions reduces the strength of the cement :
PORTLAND CEMENT WITH VARIOUS ADDITIONS (BÖHME) .
( A, Cement ; B , Siſted cement ;‫ ܪ‬C , Fine sand ; D, Slag ; E , Brick -dust ;
F, Slack -lime.)
Mixture
100A
90A + 10B
90A + 100
90A + 10D
90A + 10E
90A + 10F
50A + 50F
Neat
y = 583 + 8832-1
498 +
526 +
469 +
452 +
514 +
262 +
93
69
77
107
71
88
1 cenient to 3 sand
y 199 + 4893-1
213 + 45
128 + 65
128 + 59
137 +58
155 +48
82 + 44
189. Determination of the Setting Time.--The roughest
means of determining the time in which a cement sets
is to observe when a flat pat can no longer be indented
by the finger -nail A more accurate method is to use a
.
LIMES AND CEMENTS
471
loaded needle or wire. Perhaps the French standard
test is as definite as any. The cement paste, as soon
as possible after gauging, is filled into a metal box
1
inch deep and 3 inches diameter.
Over this is
suspended , by a pulley and balance weight, a needle of
10 ] oz. weight, with a square section of 1 sq. mm. ( side
of square, 0.04 inch ) . The cement is said to bave taken
initial set when the needle fails to penetrate the whole
depth if lowered gently on it, and final set when its sur
face just supports the needle. A cement commencing
to set in less than 30 minutes , or setting finally in less
than three hours from commencement of gauging, is re
jected . For certain purposes quicker cements are useful.
In America a needle iz inch in diameter, loaded with
1 lb. , and a needle 24 inch in diameter, loaded with 1 lb. ,
are used to determine setting time.
Effect of Time of Setting on the Qualities of a Cement.
There is a prevalent opinion that quick -setting cements
do not continue long to gain in strength, but reach a
maximum , and then fall off , or diminish in strength.
This curious diminution in strength, often shown in
experiments, may be due to minute and imperceptible
cracks , but perhaps it is rather an error of testing
than a real loss of strength . The cement, no doubt,
gets more brittle, and that has the effect of making the
test more difficult, and increasing the chance of break
ing the briquette with a load rather less than the real
tenacity.
Mr. Grant has given a table of tests of quick and
:
472
TESTING OF MATERIALS OF CONSTRUCTION
slow cements, which give the following characteristic
equations. Mr.Grant does not say, but I believe these
are 28 -day tests of mortar gauged 1 to 3 of sand :
Set, in
Set, in
Quick cements
minutes
10
20
30
45
Y = 7+
953x - 1
34 + 113
83 + 86
23 + 90
Slow cements
hours
5
7
10
11
Y = 166 + 80V 3 - 1
101 + 94
143 +70
140 + 67
These results show that the slower cements have
very much greater initial strength than the quick
cements , but the quick cements in this table are some
what exceptional. The means of four series of tests on
quick cements and four on slow cements, from Bau
schinger's tables, give the following equations :
Gauged neat
.
1 cement to 3 sand
Quick cements
Slow cements
y = 183 +487 x - 1
y = 220 + 55.3 * - 1
y = 88 + 473x - 1
Y = 76 + 363 x - 1
Here the slow cements have greater initial strength
and greater rate of gain with age than the quick cements,
but the difference is not so great as in Grant's table.
At any rate, the opinion is general that the slower
cements are more trustworthy. The German manufac
turers propose different standard tests for quick and
slow cements , the standard being higher for the slow
cements ,
190. Influence of Quantity of Water on the Strength of
Neat Cement and Cement Mortar . — A certain quantity of
473
LIMES AND CEMENTS
water must be used in gauging cement or cement mortar,
which varies with the character of the cement..
The
finest ground and quickest cements require most water.
Now, unfortunately, every drop of water added beyond
what is necessary weakens the cement, and this is the
chief source of the discrepancies which occur in cement
testing . In purely commercial testing it is naturally
FIG . 141 .
LBS.
500
1
YEA
R
NEAT
MON
6
THS
PORTLAND
"
H
W
O
N
I
400
I WEEM
THIN
CROAT
GROUT
SOFT
DAMP
100
STIFF
PASTE
200
DAMP
SLIGHTLY
300
0
20
25
30
5
15
35
40
PER
CENT
and not unfairly desired to get the best result possible
out of the cement .
In this country the briquettes are
moulded on an impervious slab of slate or marble or
glass . The cement is gauged neat with the least amount
of water which will permit moulding, and the very stiff
paste into which the cement is formed is pressed into
the moulds as rapidly as possible. To get uniform
results the water used must be very accurately measured .
!
474
TESTING OF MATERIALS OF CONSTRUCTION
It varies from 18 to 25 per cent. of the weight of
cement .
In Fig. 141 are shown the results of some experi
ments at Boston , on the same cement, mixed with
different proportions of water. The greatest strength
is obtained with between 20 and 25 per cent. of water.
The proportionate difference of strength as the time of
hardening increases is less ; so that it is for short, one
week tests that the quantity of water makes the greatest
difference.
191. Test for Soundness . - One of the most dangerous
qualities of a cement is a tendency to blow or crack
after setting, in consequence of expansion due to the
chemical actions which are going on. Expansion of
this kind, producing cracks, is commonly due to the
presence of unslacked lime in the cement ; gypsum
added as an adulteration is open to the same objection .
These substances are the more dangerous that they
rather add to than detract from the strength of the
cement, and hence escape detection by the ordinary test.
That Portland cement does expand in hardening
may be shown easily by filling lamp glass chimneys
with the cement, and placing them for hardening in
water.
With both neat cement and cement and sand the
chimneys invariably crack about the third day, and in
the course of ten days the glass is cracked all over.
The ordinary test for soundness is to make a pat or
cake, 2 or 3 inches in diameter and i inch thick, with
thin edges , and place it in water. If the cake, in
1
LIMES AND CEMENTS
475
hardening, sbows any tendency to crack or contort,
the cement is dangerous .
often extremely important to determine the
It
soundness of a cement in a shorter time than this pro
cess requires. Now , heat accelerates greatly the harden
ing process , and hence sometimes the pats of cement
are placed on an iron plate heated by a gas jet . Then
any tendency to crack shows itself in a short time.
This
may be called the baking process . Tetmajer re
commends that a pat 4 inches diameter and 3 inch thick
should be baked in a drying chamber at 120 ° C. for
three or four hours .
A still better process is to heat the pats in a steam
bath. Mr. Faija makes a convenient apparatus , consist
ing of a double bath with regulated gas jet . The water
in the outer bath is kept at 110°, and the pats are placed
at first on a slip of glass in the steam, in the inner bath ,
in vapour at about 100°.
After five or six hours the
pat is hard enough to be placed in the water, and may
be kept cooking for twenty hours .
If at the end of that
time the pat is still adherent to the glass, and without
cracks, the cement is perfectly sound.
German
Standard
Test.
The
minimum tensile
strength of briquettes of 1 cement to 3 sand by weight,
after hardening 1 day in air and 27 days in water, is
227] lbs.per sq. in . The crushing strength is 2,275 lbs .
.
192. Measurement of Erpansion of Cement.-- Bau
schinger took cubes of cement of 4.8 inches length ofside.
476
TESTING OF MATERIALS OF CONSTRUCTION
Twenty-four hours after mixing, a small brass plate,
about 4 inch diameter , was fixed into two opposite
sides of the cube, by cementing. After forty -eight
hours' hardening, the accurate measurements between
the brass plates were commenced . The cube was placed
in a measuring instrument, having a spring touch -lever
on one side and a micrometer screw on the other.
The
touch -lever ensured the constancy of pressure between
the measuring points and the block to be measured .
The pitch of the screw was very accurately determined ;
and as a perfectly constant temperature cannot be insured
in experiments lasting a long time, a correction for the
expansion of the cement blocks by heat was determined.
Neat cement briquettes hardened in air sometimes
showed a small expansion at first, but all ultimately
shrank in volume.
Neat cement briquettes hardened
in water all showed a very small expansion, generally
less than : 05 m . in 120 mm . length in sixteen weeks.
With briquettes mixed with sand the changes of volume
were of the same kind , but smaller.
Quickness of Loading.-- I believe Mr. Faija first
pointed out that the rate of loading a briquette affected
the breaking weight. The quicker a briquette is loaded,
the greater the load which can be got on before it
gives way. In some definite experiments, Mr. Faija
found a difference of 23 per cent. in the breaking
weight of exactly similar briquettes, broken quickly
and broken slowly. It is now generally recommended
that the weight should be added at the rate of 100 lbs.
1
LIMES AND CEMENTS
477
in fifteen seconds.1 Mr. Adie has devised an ingenious
arrangement for regulating the speed of loading. Mr.
Deacon, I believe, puts half the probable breaking weight
on the briquette, and leaves it twelve hours, and then
coinpletes the test.
193. Tests by Pressure. — Almost all that has been
said thus far relates to the ordinary mode of testing
cements and cement mortars by tensile stress. That mode
of testing was adopted for mere reasons of convenience .
The cement has only about one-tenth the strength in
tension which it has in compression . Hence, for tension
tests a small, cheap, easily managed testing machine can
be used. For compression tests, the testing machines
must be much larger and more costly. But as a matter
of fact cement is but little used in positions in which its
resistance to tension is in play.
The most important
works in which cement is used are expressly designed
to avoid tension in any part. If, indeed, in some
positions structures are exposed to the possibility of
tensile strains, due to failure of foundations or backing,
still the tensile stresses so developed are small com
pared with the normal crushing stresses for which the
structure is designed .
Tension tests having been adopted, and being con
venient no doubt , find defenders. Broadly speaking,
a cement with high tenacity will be strong to resist
crushing ; but the correspondence in the resistance to
1 The German rate of loading is į lb. per second , the briquettes being
0 : 775 sq. ins. section.
478
TESTING OF MATERIALS OF CONSTRUCTION
the two kinds of stress is far from exact . Bauschinger
has found that the ratio of resistance to crushing to re
sistance to tension varies from eleven to one to seven to
one ; and that the order of merit for cements tried for
tension is not the same as the order for crushing. It
has even been said that crushing tests are useless and
inaccurate. If they have proved so, it is only because
the proper conditions of accurate testing have been neg
lected . In Bauschinger's tests of 5 - inch cubes , the
results are considerably more uniform than the tests of
the same cements in small briquettes by tension.
In proper crushing experiments two conditions
must be fulfilled, which have hitherto been too much
neglected in crushing experiments . ( 1 ) The faces of
the block on which the crushing pressure acts must be
plane parallel surfaces. (2 ) The crushing pressure
must be uniformly distributed on those surfaces.
In moulded blocks of cement or cement concrete
the surfaces are hardly ever as parallel as is desirable.
The surfaces are generally more or less rough, and more
or less warped. By striking over the faces a thin layer
of gypsum or Parian cement, which sets immediately,
perfectly plane and parallel faces can be obtained, with
out in any way altering the strength of the block.
Weak as these cements are, thin layers stand the crush
ing pressure perfectly. To ensure the equal distribution
of the crushing pressure on the faces it is only necessary,
in a properly constructed testing machine, to interpose
a spherical joint between the block and the face of the
machine.
479
LIMES ANI) CEMENTS
It may
be useful to examine if the rate of hardening
in pressure tests can be expressed as simply as that in
tension tests . In Bauschinger's paper already referred
to there are a series of pressure tests of the same series
of cements as that used in the tension tests .
The test pieces were cubes of 144 sq . cms. ( 22 :3
sq . ins., or 4.75 inches length of side) . Either from
the large size of the cubes , or the nature of the stress,
or someother cause, it is necessary to take n = 1 in the
general equation, instead of its value for tension. With
this change, the equation fits the compression results
satisfactorily. The equation for compression is there
forem
y = c + d 2-– 1,
where y
is the compressive strength in lbs. per sq . in.
at x weeks after mixing:
The equations obtained from Bauschinger's results
are as follow , the equations being all applicable to an
age of two years at least :
Cement
mark
Neat cement
Y
1 cement + 3 sand
Y
1 cement + 5 sand
Y=
A
B
1,877 + 206 / x - 1
953 + 299VX - 1
469 + 299/ x - 1
953 + 227
313 + 248
o
1,991 +490
1,770 + 327
1,592 + 341
2,404 +299
1,582 +270
1,436 + 334
2,631 +441
1,038 + 313
1,920 + 455
782 + 270
711 + 270
1,507 + 341
1,024 + 313
199 +199
740 + 305
284 + 313
356 + 263
540 + 284
483 + 249
341 + 256
995 + 341
626 +227
Mean 339
Mean 312
Mean 274
D
E
F
G
H
R
T
427 + 412
668 + 320
825 + 334
1
69.73
5
51.30
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63.32
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64.68 43
60-51 35
80.21 28
99.51
23
92.4
20
106.33 17
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moulding
Date
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7
8
9
of
No.
block
Load
at
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Alean
Mean
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.
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nDitt
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Remarks
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cement
top
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,not
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Badly
an
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cem
on
top
face
; ent
crus
n[ ot hed
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not
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.)block
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Deacon's
Mr.
from
taken
are
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second
the
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hen
(in
480
TESTING OF MATERIALS OF CONSTRUCTION
>
9
"
LIMES AND CEMENTS
481
Here the first constant, which can be obtained by
tests lasting one week only, varies a good deal; but the
second constant has no very great range of variation
If the initial strength of the
cement is known therefore, the strength at any age up
to two years can be inferred with a certain degree of
about its mean values .
approximation.
Strength of Concrete . — The table on opposite page,
from the Report of Mr. G. F. Deacon on the Vyrnwy
Masonry Dam , gives the strength of a series of nearly
cubical blocks of Portland cement concrete, made at
various dates during the progress of the work.
The following summary gives a general view of the
average strength at different ages :
Age of block ,
Main strength ,
in months
in tons per sq. ft.
32-36
over
284-29 ,
17-25
2-5
1-2
180
162
159
102
0
.
114
The blocks prepared with Parian cement to ensure
a plane face give rather bigher crushing pressures than
the others. Some blocks cut out of the work itself gave
crushing pressures somewhat greater still .
Detection of Adulteration . — The means of detecting
adulteration of cement have been examined by Drs . R.
and W. Fresenius. Adulteration by lime is shown by too
low a specific gravity, great loss by ignition, high alka
linity of aqueous solution, and too great absorption of
II
482
TESTING OF MATERIALS OF CONSTRUCTION
carbonic anhydride. An adulteration by slag is shown
by slightly lowered specific gravity, lowered alkalinity,
and by the large amount of chamaeleon solution which
may be added. The details of the methods of testing
are given in a paper abstracted recently for the Institute
of Civil Engineers.
1
4
INDEX .
BOH
ABB
TT, experiments on steel
ABBO
castings, 336
Abel , Sir F. , on hardening and
annealing , 298
Adamson , testing machine, 139
Admiralty experiments on effect of
temperature on strength, 349
Adulteration of cement, 481
Alloys, 341
Aluminium alloys, 347
Annealing, 296 ; tests of plates,
327 ; tests of steel castings, 334
Askenasy, deflectometer, 245
Autographic diagrams, time curves,
Basic steel, tests of, 326
Bauschinger, on yield point, C5 ;
raising of elastic limit, 98 ; in
fluence of rest after loading, 101 ;
shackle for wood , 183 ; mirror
extensometer, 220 ; change of
elastic limit in successive
load
ings, 250 ; in bars loaded beyond
yield point, 258 ; strength of
steel , 286 ; shearing tests of iron
and steel, 331 ; experiments on
repeated tensions, 377 ; variation
of elastic limit, 384 ‫ ;و‬alternate
tensions and pressures, 389 ;
87 ; effect of removing load, 99 ;
endurance tests, 393 ; strength
elastic diagrams, 239 , 242 ; time
extension curves, 243 ; of iron
of timber, 397 ; influence of form
on crushing strength , 421 ; elastic
constants for stone, 429 ; strength
and steel, 281 ; of hardened and
annealed steel, 298 ; of steel
castings, 337 ; of copper, 340 ;
of brass and bronze, 345
Autographic recording apparatus,
228, 243
of stone, 432 ; of cement, 457 ;
expansion of cement, 475 ; crush
ing strength of cement, 479
Bell- metal , 342
Belting, leather, strength of, 409
Bending and temper test, 163
Bending strength , of cast iron , 268 ;
of rails, 329 ; of copper, 339 ; of
ine, 152and
, testi
BAILEY
perforated
onmach
B. , ng
Baker,
brass and bronze , 343, 345 ; of
timber, 402 , 405 ; of stone , 433
nicked plates, 83 ; variation of
Bending stress , 35
Blue heat, influence on strength of
strength in pieces cut from one
plate, 294 ; endurance tests, 373 ;
on limits of working stress, 383
Barba's law , 75 ;
on
effect
of
punching, 310
Barnaby, influence of temperature
on strength of iron and steel , 317
steel, 301
Board of Trade, tests of iron and
steel, 323 ;
experiments
0
punched plates, 77
Böhme , tests of iron plates, 324 ;
of limes, 459 ; on addition of
484
TESTING OF MATERIALS OF CONSTRUCTION
BOH
various substances to cement ,
470 ; on strength of masonry,
434 ; strength of brickwork , 439
DUP
Clay, on the effect of, in reworking
iron , 288
Coefficient of bending strength ,
Bottomley, hardening effect of
270 ;
long-continued stress, 90
Bramah testing machine, 109, 125
Brasses , 344
bronzes, 343 ; for brasses , 345 ; for
timber, 402, 406 ; for stone, 433
of elasticity, 20, 246 ; for
different materials, 251 ; for
iron and steel, 252, 287 ; for
bronzes, 254, 343 ; for steel
castings, 337 ; for brasses, 345 ;
for delta metal, 346 ; for timber,
402 , 406 ; for stone, 429
Breaking stresses, 7
Brick , 410, 436
Brickwork, strength of, 439
Bronzes, 342
Buckton & Co.,testing machine, 132
for cast iron, 271 ; for
of volume, 29
YALIBRATION of testing ma
chine, 167
Carbon, in iron and steel, 259 ;
in cast iron , 261 ; influence on
steel , 285, 300, 319 ; in steel cast
ings, 335
Cast iron , extension and compres
sion of, 248 ; definition of, 259 ;
composition of, 261 ; properties
of, 264 ; tensile strength , 265 ;
crushing strength , 268 ; trans
verse strength , 268 ; shearing
strength , 272 ; resistance to tor
sion, 273
Cathetometer , 210 ; differential,
218
Cement, 441 ; tests for strength ,
445 ; form of briquettes, 445 ;
gauging briquettes, 447 ; sand
and cement briquettes, 448 ; rate
of hardening, 449 ; characteristic
equation of, 450 ; shearing tests,
459 ; fineness of grinding, 459 ;
heaviness, 464 ; influence of kind
of sand used, 466 ; proportion of
sand , 469 ; setting time, 470 ;
quantity of water in gauging,
472 ; soundness , 474 ; expansion,
475 ; pressure tests, 477 ; adul
teration , 481
Clarke, Elliot, on cements, 403, 469
of rigidity, 28, 253 ; determina
tion by torsion , 35 ; for cast iron ,
274 ; for iron and steel, 333
Cold rolling, effect of, 306
Compression of lead, copper, and
iron, 94
Concrete , tests of , 480
Considére , stresses in hardened
bars , 297 ; effect of cold working,
308 ; experiments on punching,311
Contraction , local, 281 ; relation to
elongation , 84, 278
Copper, 339
Cowper, extensometer, 214
Creusot testing machine, 127
Cross-breaking, machines for, 162 ;
shackles for, 186
Crushing strength of cast iron , 268 ;
of stone, 435 ; of brick, 438 ; of
cement, 479
Curioni , strength of brickwork , 439
EFLECTION of a beam , 40
DET
Deflectometer, 245
Delta metal, 346 .
Drawing out, 68 ; distribution along
bar, 72 ; suppression of, 77 ; in
bars broken by repetition of
stress , 379
Ductility , 18, 293 , 302
Dupuy, extensometer , 217
485
INDEX
LOA
ELA
ASTIC ity,
O. limits of,2466 ;
EL"LASTIC
Cconstants,
Elastic
raised
by stress, 98 ; influence of rest
after loading, 101 ; change in suc
cessive loadings, 250 ; modeofde
termining, 254 ; variation of, 384
Emery testing machine, 152 ;
shackles , 179
Endurance tests, 361
Ewing, time curves, 87 ; auto
graphic arrangement, 231
Expansion of cement, 475
Extensions and compressions of
cast iron , 58 ; of steel , 60 ; of
indiarubber, 61 ; in bars of dif
ferent lengths, 75 ; of stone , 429
Extensometer, 205, 206, 208
enttesting machine,
JA ,cem
FAI477
; gauging machine for
cement, 448 ; test for soundness
of cement, 475
Fairbairn , testing machine , 126 ;
on cold rolling, 308
Fairbanks, testing machine, 120 ;
autographic apparatus, 232
Fineness of cement, 459
Flow of solids, 47 , 96
Foster, tests of steel castings, 335
Frankel, extensometer, 243
Friction grips, 174
Friction of cup - leathers, 108
Frost, resistance of stone to , 428
447
UGerber's briquettes,
GAAUGING
parabola, 391
Grafenstaden testing machine, 122
Granite, 410
H
AMMER hardening, 306
Hardness, determination of,
187
Hardening of cement, 449
of steel , 296
Heaviness of cement, 464
Henning & Marshall, extensometer,
206
Hercules metal, 347
Hill, strength of steel castings , 334
Hodgkinson , experiments on cast
iron , 58 , 247 ; relation of stress
and strain in cast iron , 264 ;
crushing strength of cast iron ,
268
Hydraulic limes, 442
NDIARUBBER ,
stress - strain
curve of, 61
Ingot metal, 260, 276
Isotropy , 24
,
stress - strain curves, 67 ; tor
sion shackle, 185 ; lever extenso
meter,
216 ;
mirror
extenso
meter, 220 ; autographic appara
tus , 240 , 242 ; on form of test
bars, 294 ; tests of steel , 327
Kortum , rope shackle, 183
LANZA,experiments on strength
Grant on cement testing, 441 , 446,
Lead , 341
Lebasteur on tempering iron and
452, 456, 466
Greenwood & Batley, testing ma
chine , 123
Gun - metal , 342
Limes, 441
Loading , influence of rate of, in
testing, 291 , 476
steel, 300
486
TESTING OF MATERIALS OF CONSTRUCTION
STE
MAI
MAILLARD: testing machine,
123, 150 ; shackles, 180
Maitland, Col. , influence of time in
testing, 89 ; on oil hardening, 297
Malleable cast iron, 274
Mallet, tests of heavy forgings, 290
Manganese in steel, 277 , 286, 300
Martens, testing machine, 120
Masonry, strength of , 434
Measuring instruments , 192 ; for
strains , 199
Millar, strength of cast iron , 270
Milton , effect of quenching on
steel, 299
Mitis castings , 337
Modulus of section , 42
Moment of inertia , 42
Monge balance, 163
Morin and Tresca on bending , 37
AILS, tests of, 327
Repetitions of load, 356
RA
Richard, ineasuring machine, 199
Richard's experiments on perforated
plates, 80
Ricketts on malleable cast iron , 274
Riehle, testing machine, 122 ;
wedges , 177
T. CHAMOND testing machine,
ST.
127
Sand , standard, for cement-testing,
449
Sandberg on rail tests , 329
Screw bolts , strength of, 351
Screw micrometer, 194 ; extenso
meter, 205
Self on aluminium bronze , 347
Sensitiveness of testing machine,
111 , 169
OLSEN, testing machine, 142
effect of bending
PARonKER,W.,
strength of steel, 309 ; on
steel castings, 335
Phosphor bronze, 354
Phosphorus in steel , 277 , 301 ; in
copper, 339
Pin grips, 172
Pipes, testing of, 165
Plasticity, 17 , 45 , 53, 96
Platt and Hayward , on strength of
cast iron , 273 ; on iron and steel ,
332
Poisson's ratio , 20
Polmeyer, autographic apparatus,
231
Porosity of stone, 426
Preece , strength of wire, 352
Pressure of Huidity, 46, 52
Pressure tests of cement, 477
Proportionality , limit of, 256
Punching, 47 , 78, 310
Shackles for tension , 171 ; for
crushing, 184 ; for torsion , 185 ;
for shearing, 186 ; for cross
breaking, 186 ; for indenting, 187
Shearing stress , 25 ; tests of iron
and steel , 331 ; of cement, 458
Sieves for cement and sand, 449
Silicon in cast iron , 262
Spangenberg, endurance tests , 372
Steel , extension and compression
of, 249 ; composition of, 277 ;
castings, 277 ; influence of car
bon , 285 ; hardening, tempering,
and annealing, 296 ; influence of
carbon, manganese, and phos
phorus on properties, 300 ; in
jurious effect of blue heat, 301 ;
influence of
of temperature on
strength, 313 ; Styffe's experi
ments, 319 ; Steel Committee's
experiments, 319 ; Board of
Trade experiments, 323 ; shear
ing strength , 332 ; torsional
strength , 333
也t
487
INDEX
STE
UNW
Steel castings , 333
Steel Committee's experiments, 319
Stone, 410 ; influence of bedding
on
crushing
strength,
416 ;
strength of stone, 412 ; porosity,
426 ; Bauschinger's experiments,
433 ; crushing strength , 435
Straightedge , 192
Streinitz, differential cathetometer,
218
Stress-strain curve , correction of, 91
Stress-strain diagrams, 56 ; for
brittle material, 58 ; for elastic
material, 60 ; for ductile material,
See also Autographic
63, 94.
diagrams
Strohmeyer, experiments on per
forated plates, 79 ; roller extenso
meter, 223 ; on influence of blue
heat, 302
Styffe, definition of elastic limit ,
255 ; on properties of iron and
steel, 285 ; influence of tempera
ture on strength, 314 ; experi
ments on iron and steel, 318
Superposition of stresses, 23
Tetmajer, tests of rails, 350
Thalen on elastic limit, 255
Thomasset, testing machine, 121 ,
148
Thurston , extensometer, 205 ; tor
sion machine, 229 ; on copper ,
339 ; on bronzes , 342 ; on brasses,
344 ; on other alloys , 345
Timber, 394 ; strength of small
specimens, 397 ; elasticity of ,
397 ; tensile strength of , 401 ;
crushing strength of, 402 ; bend
ing strength of, 402 ; American
tests , 403 ; strength of posts,
404 ; of beams, 405 ; shearing
strength , 407 ; influence of time
on strength, 408
Time, influence in testing, 291 , 476 ;
on strength of timber, 408
Tin, 341
Torsion, 31 ; machine, 161 ; shackle,
185 ; of cast iron , 273 ; of iron
and steel, 331
Touch micrometer, 212
Tresca on plasticity, 46
Turner on cast iron, 262
Sweet, Professor, micrometer, 196
TANGYE, testing machine, 162
Tempering steel , 296
Temper test, 163
Temperature, effect on strength of
iron and steel, 313 ; on alloys, 348
UCHATIUS
, strength of bronze,
349
Union Bridge Company's testing
machine, 143
Unwin , extensometer , 208 ; touch
micrometer, 212 ; mirror extenso
instrument
Test bars , 188, 292 , 446
meter,
Testing machines, . 106 ; types of,
119 ; Woolwich machine, 125 ;
single -lever machines, 128 ; com
139 ;
pound-lever machines,
Union Bridge Co.'s machine,
measuring compressions , 225 ;
autographic apparatus, 235 ; elec
222 ;
for
tric semi- autographic apparatus ,
238 ; change of ductility in steel
when worked hot, 304 ; experi
143 ; manometer machines, 148 ;
emery machines, 152 ; special
ments on steel castings , 337 ; on
machines, 161 ; cement-testing
machines, 446
Tests of cement, 440 ; of pipes, 165
bronze, 348 ; on wire, 355 ; on
strength of stone, 417 ; on porosity
delta metal, 346 ; on aluminium
of stone, 428
488
TESTING OF MATERIALS OF CONSTRUCTION
ZIN
VER
I
Woolwich testing machine, 125
ERNIER calipers, 193
Vicat on strength of stone
blocks, 424
Work done in tension and compres
sion, 21 ; in plastic deformation ,
54 ; measured from stress-strain
diagram , 104
Working stress, 9 ; history of limits
adopted, 380
Viscosity of solids, 100
, testing machine, 127 ;
Dstrength
WAADE
of cast iron, 268
Wrought iron , composition of, 276 ;
Watertown testing machine, 152
tenacity, 278 ; effect of reworking,
288 ; effect of cold rolling, 308 ;
Wear, resistance of stone to, 429
Webb on working steel at colour
heat, 306
Wedge gauge, 204
Weld iron, 261 , 276
Werder , testing machine, 123, 128
effect of temperature, 314 ; tensile
strength , 318 ; tests of, 324 ;
shearing strength, 332 ; torsional
strength, 333
Wertheim on elastic limit, 255
Whitworth measuring machine, 198
,
Young's modulus, 20 ; deter
mination by bending, 44
Wicksteed , testing machine, 120 ;
autographic apparatus, 233 ;
shackles, 175
Wire, strength of, 352
ZINC, 341
Wöhler's experiments on repetition
of stress , 356
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NEWMAN (Curlin l).— WORKS BY. NEWMAN (Curdinal).-- WORKS OF :
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