Rules and Regulations to be followed in the
SOM laboratory
All students must wear shoes during the laboratory practical classes.
Do not handle the machineries/instruments/tools/equipments inside the
laboratory without taking prior permission and instructions.
Keep your mobile phones switched off during the laboratory class.
Students must avoid unnecessary gossiping during the laboratory class.
All students must pay full attention in order to avoid any damage to the
machines and their accessories.
Students should not loiter inside the laboratory.
Students working with impact machine should never stand in the direction of
moving pendulum. Students should stand outside the safety fence.
Weights should be handled with extreme care in Brinell hardness test.
Do not handle the extensometer without permission of technical staff.
Anybody found violating the above rules will not be allowed to
continue the class and will be given absent for that class.
Your safety is more important.
Senior Technical Superintendent
Sanjib Sarma
Ph:2689
Faculty In-charge
Dr. Nelson Muthu
Ph:3440
INDIAN INSTITUTE OF TECHNOLOGY, GUWAHATI
DEPARTMENT OF MECHANICAL ENGINEERING
LABORATORY SHEET
NAME:
ROLL No:
DATE OF EXPERIMENT:
Gr. No:
DATE OF SUBMISSION:
EXPERIMENT: UNI-AXIAL TENSION TEST.
OBJECTIVE: To obtain the stress-strain relation of mild steel using a circular cylindrical
specimen and determine Young’s modulus (E), proportional limit (σp), yield stress (σy),
0.2% offset yield strength, ultimate tensile stress (σu), true fracture stress, and nominal
and true fracture strain and percentage elongation.
APPARATUS: The Universal Testing Machine (UTM) is a machine with which several
tests can be performed, namely, Tension, Compression, Bending, Buckling and Hardness.
The movement is controlled by rate of pumping of fluid into a hydraulic cylinder whose
piston controls the movement of the moving plate. The load ranges available on the
machine are 0-8 ton and 8-20 ton with resolution of 2 kgf and 5 kgf respectively. The ram
must be right down before the capacity is changed or the motor is switched off.
An electronic clip on type extensometer with gauge length 25mm and 50mm is used to
indicate the extension between the end points of the gauge length of the specimen to
which it is attached. It must be very carefully and should be used only for yield / proof
studies and not for specimen failure or breakage (i.e. it must be removed immediately
after yield point to avoid damage to the extensometer).
The specimen has a larger diameter at the ends with a smooth fillet connecting to the
reduced diameter of the central portion to ensure that the effect of the holding jaws is not
significant on the state of stress within the gauge length. The diameter at the middle of
the gauge length is reduced by about 20mm to ensure that neck forms in this region so
that a meaningful value of percentage elongation is obtained.
The machine frame consists of two cross-heads and lower table. The lower cross-head is
adjustable by means of geared motor. Tension test is carried out between lower and upper
cross-head. Sensing of the load is done by means of precision pressure transducer of
strain gauge type.
The loading unit consists of a robust base. The main hydraulic cylinder is fitted in the
center of the base and piston slides in the cylinder. The lower table is connected to the
main piston. This lower table is rigidly connected to the upper cross-head by two straight
columns. The chain and sprocket driven by a motor fitted in the base rotates the two
straight columns mounted on the base which enables movement of the lower cross-head.
The jaws inserted for tensile test specimen along with the rack jaws slide in the lower and
1
upper cross-heads. Jaw locking handle is provided to lock the jaws of the lower crosshead after the specimen is clamped. An elongation scale is kept sliding on the rod which
is fixed between the lower table and upper crosshead. The elongation indicating pointer is
fixed to the lower cross-head.
The control panel has two control valves to control oil flow in the hydraulic system, one
at the right side and the other at the left. The right side valve is a pressure compensated
flow control valve. The left side valve is a return valve, i.e. it allows the oil from the
cylinder to go back to the tank. Pressure compensation of the flow control keeps a
constant rate of straining regardless of the total load on the specimen.
PROCEDURE: Before testing, adjust the load range according to the capacity of the test
piece. Measure the diameter of the specimen. Mark the gauge length of the specimen.
Select the proper jaw inserts and complete the upper and lower chuck assemblies. Then
operate the upper cross-head grip operation handle and grip fully the upper end of the test
piece. Attach the extensometer to the specimen. Apply the load gradually and read the
extension from the extensometer at equal increments of load till yield occurs. Remove the
extensometer. Increase the displacement of the movable jaw till the specimen fractures in
into two pieces. Note down the maximum load applied. Measure the minimum diameter
of the necked section and final deformed lengths between the marked gauge points by
assembling together the fractured pieces.
LOADING / UNLOADING: The left valve is kept in fully closed position and the right
valve in normal open position. Open the right valve and close it after the lower table is
slightly lifted. Now adjust the load to zero by Tare push button. (this is necessary to
remove the dead weight of the lower table, upper cross-head and connecting parts from
the load). Operate the lower grip operation handle and lift the lower cross-head up and
grip fully the lower part of the specimen. Then lock the jaws in this position by operating
the jaw locking handle then turn the right control valve solely to open position, (i.e.
anticlockwise) until you get a desired loading rate. After this you will find that the
specimen is under load and then unclasp the locking handle. Now the jaws will not slide
down due to their own weight. Then go on increasing the load when the test piece is
broken. Then open the left control valve to take the piston down.
OBSERVATION AND CALCULATION:
Diameter of specimen d o =
Gauge length
Lo=
mm
mm
Maximum load, P max =
N
Load at fracture, P f =
N
Minimum diameter of the neck, df =
Undeformed Area Ao =
πd o2
4
=
m
m2
2
The load P (N) versus extension / displacement curve is obtained from the plotter. Slope
of the straight-line portion is determined from load versus extension curve as
In linear range, E =
∆PLo
=
Ao ∆δ
N / m2
From the computer plot, the loads Ppl, Py corresponding to proportional limit and yield
point are
Ppl =
N,
Py =
Proportional limit, σ pl =
σy =
Yield stress,
N
Ppl
Ao
Py
Ao
=
Pa
=
Pa
A permanent strain of 0.002 corresponds to the following displacement between the jaws
∆δ p = 0.002 L
Take the origin in the computer plot (load-displacement curve) at the point of intersection
of the straight line fitted to the data with displacement axis. From the point (∆δ p , 0 )
(where permanent displacement corresponding to 0.2% strain0 w.r.t. this origin, a line is
drawn parallel to the fitted line which intersects the curve at a load P1
P1 =
N
0.2% offset yield strength = P1/Ao =
Pa
Ultimate stress, σu= Pmax / Ao =
Pa
True fracture stress, σf = Pf / Af =
Pa
Final deformed gauge length, Lf=
m
Nominal average strain at fracture = (Lf – Lo) / Lo=
d 
True strain at fracture = 2 ln  o  =
d 
 f 
For Lo =
m,
and do=
Percentage elongation =
( L f − Lo )
Lo
m, we have for mild steel,
100 =
%
3
Percentage reduction in area = 100
(A − A ) 
o
f
Ao
2
df  
= 1 −   100 =
  d o  
%
Draw the sketch of the final deformed specimen.
DISCUSSION OF RESULTS AND SOURCES OF ERROR:
Lack of calibration of machine, improper alignment, initial curvature of specimen, error
in measurement of extension, etc., are the sources of error.
EXERCISE:
1. Draw nominal σ – ε relation for a ductile material and indicate properly in the
diagram E, proportional limit, yield stress, ultimate tensile strength σu, normal
fracture stress σf, 0.2% offset yield strength (0.2% proof stress), modulus of
resilience. For a stress level σ such that σy< σ < σu, show that the elastic part εo
and plastic part εp of strain.
2. Draw σ-ε relation for cast iron and mild steel in the same figure.
3. Classify the following into brittle and ductile: mild steel, C.I, rock, concrete, Al,
copper, Perspex, brass, brick wood, chalk.
4. Draw the tensile flow curve ( True stress vs, True strain) from the load-elongation
curve during the tension test. Assume the displacement values from the loaddisplacement plot that was obtained using a 2” extensometer. Determine the work
hardening exponent for the sample tested.
5. What are the types of test that can be conducted on U.T.M.
6. What is the Bauschinger effect? Illustrate by σ-ε graph.
7. Why is the state of stress in the local neck formed in a uni-axial tension test of
cylindrical specimen of ductile metal neither uni-axial nor uniform?
8. Ductile metals in a uni-axial tension test have a cup cone fracture whereas brittle
ones have flat fracture surface. Why?
9. Percentage elongation of material has been quoted as 17%. What is wrong with
this statement?
10. Sketch on the same graph, σ-ε curves for uni-axial test of ductile metal for rate of
strain ε- very small, intermediate value, very large.
11. Sketch on the same graph, σ-ε curves for uni-axial test of mild steel at room
temperature and at temperature below the brittle-ductile transition temperature.
12. a) Define true strain εt (logarithmic strain) and obtain its expression in terms :(i)Lo & L (ii) Nominal strain ε.
b) Assuming volume constancy, relate nominal and true strains ε, εt to areas Ao
and A.
c) Which expression should be used to obtain εt before necking and after necking?
4
R 10 type
O 12.5
O 18
90
100
100
Tensile Specimen (Plain)
Material: 1) MS
2) Al
(Tensile test sample of MS was heated to 7300C and held for 45 minutes and allowed to cooled in the furnace)
All dimensions are in mm.
5
INDIAN INSTITUTE OF TECHNOLOGY, GUWAHATI
DEPARTMENT
OF MECHANICAL
ENGINEERING
LABORATORY SHEET
NAME:
ROLL NO & Or. No:
DATE:
EXPERIMENT:
Buckling Load of as Pinned-End Strut
SECTION 1.0 INTRODUCTION AND DESCRIPTION
Introduction
This guide describes how to set up and perform experiments related to the Buckling of Struts. The
equipment clearly demonstrates the principles involved and gives practical support to your studies.
Description
Figure 1 shows the Buckling of Struts experiment. It consists of a back plate with a load cell at one end
and a device to load the struts at the top. There are five aluminium alloy struts included in a holder on the
back plate Printed on the equipment are a number of equations and pieces of information that you will find
useful while using the equipment.
How to Set up the EQuipment
The Buckling of Struts experiment fits into a test frame. Figure 2 shows the Buckling of Struts experiment
in the Structures Test Frame. Before setting up and using the equipment, always:
• Visually inspect all parts (including electricalleads).for
damage or wear. Replace as necessary.
• Check electrical connections are correct and secure. Only a competent person must carry out electrical
maintenance.
• Check all components are secured correctly and fastenings are sufficiently tight.
• Position the Test Frame safely. Make sure it is on a solid, level surface, is steady, and easily accessible.
Important:
Never apply excessive loads to any part of the equipment.
The following instructions may have already been completed for you. If so, go straight to Section 2.
1. Place an assembled Test Frame (refer to the separate instructions supplied with the Test Frame if necessary) on a
workbench. Make sure the 'window' of the Test Frame is easily accessible.
2. On the Test Frame there are securing nuts in the bottom groove of the top member and the top grove
of the bottom member. In each member slide two of these to approximately
the positions shown in Figure 2
3. Lift up the STR12 unit onto the frame and have an assistant secure the unit to the frame using the
thumbscrews and washers provided.
4. Make sure the Digital Force Display is 'on'. Connect the mini DIN lead from 'Force Input l' on the
Digital Force Display to the socket marked 'Force Output' on the right-hand side of the unit
5. Carefully zero the force meter using the dial on the front panel of the experiment. Gently apply a small
load with a finger to the top of the load cell mechanism and release. Zero the meter again ifnecessary.
Repeat to ensure the meter returns to zero.
Note: If the meter is only ±l N, lightly tap the frame (there may be a little 'stiction' and this should
overcome it).
1
Runners fQr
sJld:<l<la$s~mbly
A(lJuslable
CrO$$l'Itiad
~o<1dI119
assembl)
Top fiXeel chuch
(remOVC,jl)lc)
BCoUoml"'''jhl.
chllr.:~
d cd
St,tZem'
«. tr :1
Figura
1 Buckling of SliUtS oxpOn'mCil{
2
~
t
sC.:lla
fest struts
Digl!AI
~
.
fOlef'!
c::JN
..
_-~.
Figure 2 Buckling of struts
3
SECTION 2 EXPERIMENTS
1: Buckling Load of a Pinned-End
Experiment
Compressive
They
members can be seen
Strut
ill many slructures.
worK, The struts provided have an /Ik ratio of between
520 nod 870 to show clearly t.he buckling load and the
ddlccled slwpe of the struts. In practice StJ'Ul.'; with an
Ilk ralio of more thnn 200 MC of little use in real
cnu form part of n fcsll1ework for instance in a
tl1lSS, or they can stand-alone;
•• wnler lower
roof
support is fin example of tbis.
Unlike 0 tension member which will g.cnerally (lnly
fail if the ultimme
tensile
stress is exceeded,
a
compressive member can 1':111 in t\VO ways. The fir~1 is
via rupture dllC to the direct stress, and the sec('lnd is by
an clastic mode of Failure called Buckling, Generally,
hort wide compressive
mcmber:Slhaltend
tmetureS.
\Ve willllse
trot:
10 fail by the
n~nt('rial crusbing <Ire cnlled columns. Long. thin
compressive ll1etllb~rs Ihat tenLl to [nil by buc.:klillg are
p. = Euler buck.ling load (N)~
l? =- Young'~ modulus (Nm-t);
I = Second moment of area (m,l);
= Length 1.)[ stHll (m).
cnlled struts.
'''bell bllckling occurs Ihe Mrul will no longer Clm)'
any more loao it will ~imply continue 10 Jispl;lce i.e. iL"
stiFfnes.s
then
becOJllc~
zero
and
it
d1e Euler buckling formula for a pinned
b
uscle~~
t
a~ u
R~f~rril1g co Figure 3. fit the bottom chuck [0 the
machine and fl'move th~ top chuck (10 give:? pinned
t.n.lctul"nll1lt:mher.
ends). Select the shoJ1~lil ~Irut. number
section using the vC:l'11icr
the cross
I, and Olt'asure
provided
and
cakullltC' the ~ccolld moment of area, I. for che su·uI.
Ad.iu~[ the position of the shcljl1~ cro,shend to <'lccept
the strut using (be lhurnbnuts
to lock off Ihe slid~r.
En~un: Ihill there i<; the maximum amount or Ir:wel
<Jvuilablc.OIl the llilndwhccl (hre<td to compress the strut.
Finally tighten the J()(.;king :,crew!>.
Carefully
back off the h:mdwheel ~o that the :-lnJl i~
rc,tint: in lht' notch but not lr(Hl~miuin!: :'Iny 10;1d: l'e7.cro
the forcemcter
lISlng Ihe front p~tncl control.
Carefu II)' <..tart to load the strut. ]f the SU1.Jt begins to
Place lest strul
in 'V' nolcl1es
lIdk: to lhe left, "nick" the slrut to the right 3nd vice
er,a
(Ihi" reduce!> any ",rrun. associ;ltcd with the
<;tr;lightnes~ of Lh\.'~lnil).'rUIll the 11Ilndwheei untillhcJ\~
is no fUrl her increase in load (the to:..u may nc.:Jk and
Ihell t1wp a~ it ,)cllk':, inlQ tlw notc:;hc.<i).
Record the liml1 IOl.lcl in Table I under 'buckling
load'. Ra;:rl<:!;'l with <.trUI number!'.~. 3, j and 5 'IlJjll~lil1g
lhe <:ro~:,"ead ;j~ r-::quired to fitlhe
"'11"\11. Takc
as thl; clifference!
\\-1lh Ihe !ihorLcr ;;tnltS.
more c:ln:
l>Clw~~l'lI lhe
buckling
load and the lo[rd nccdcrl 10 obtam plastic
lh..rormatiOIl
i::.
'111lle 'il11rllL Try loading each "Inn
o,c\lcrdl lilTle~ ulIlil a consi~t~'nt re::.ull for ctll:h strut is
rlcbievetl.
d
Strut
5
;1
Figure 3 Expenmentaf
the
I
--
320
470
a20
520
370
Length
(mill)
{N} load
Buckling
:3
\\i.' \\.'ill I~};KJstrul~ unlil Ill!:')' buckle
In [hi." cxp<:rimem
inV~S(l~Wlinp
I numberends)
layout (pinned
eIFc •.:1 or IIw
Il'll);lh III 111<:,lfU!.
Tn
pn..:dkt the l>w:lling load .••.~ \\ ill u;,t: 111e Euler buckling
formulae. CriticLlI It' the LIS': (.rr till.! ELllel' fQnnuLl<:' i~ lhe
rnlio. \\hlch I'" Ihe ratio or lh~ lenglh ur lll.:
~lrul llJ ib n1diu~of g) ration tl/~). The Euler 10n11111,1I'
!;Jcndcl'ncss
Table 1 Results for Experiment
becum..: imtc.:cUt·ale Ill! "lrut:. \\'Ilh a (I/.. ratio 01 k:,,;, lhun
125 and thi~ ,houlcl
",allline
be: wken inln ac<.:ounl ill any dc"i~n
llppropriutc
4
[he ElIler huekling
parameter
1
cqUtlll11n
and ,dect
tll (;'~t.lbli~h a lincar
<In
relalion<;hi p
between the Ol.lckling IOJld and the length of the strut
(Him: remember rt, E and I arc ,III constan.ts).
Calculate Ihe\fuilles and enter t£lem into Table 1
Wilh an appropriate
tille. I'lot a graph to prove the
rcl.arionship is .linear. Compare your experimental value
to those c..'llclllaled from the ELller formula by entering n
theoretic<ll line OJllo the graph. Does the Euler formulu
predict the buckling load?
It wOllld be IIseful at Ihis stage to calculate the
gradient
of
the
experimental
results
for
use
ill
Experiment 2.
5
INDIAN INSTITUTE OF TECHNOLOGY, GUWAHATI
DEPARTMENT OF MECHANICAL ENGINEERING
LABORATORY SHEET
NAME:
ROLL No:
DATE OF EXPERIMENT:
Gr. No. :
DATE OF SUBMISSION:
EXPERIMENT: TORSION TEST.
OBJECTIVE: To obtain twisting moment-twist relationship of a mild steel specimen.
To determine shear modulus G, yield stress τy in pure shear, theoretical and experimental
ultimate torque based on elastic-perfectly plastic model of material.
APPARATUS AND PROCEDURE: Torsion Testing machine is used for conducting
torsion test on various metal wires, tubes and sheets. Mechanical machines have been
invariably used till now. To get more accurate results with convenience, electronic model
is utilized here. The torsion/ twist can be read on the read-out directly. The specimen is
held in chucks at both ends. The required torque is applied by the motor. Torque
transducer is fitted at the opposite end of the gear box. The angle of twist is obtained with
the help this assembly.
Suitable grips for the specimen should be inserted into the driving and driven chucks and
the specimen is griped. The ultimate torque shown on the read out is the maximum
capacity of the specimen.
OBSERVATION AND CALCULATION:
Diameter of the circular specimen D =
Length of specimen L =
m
m
The plot of T v/s θ is obtained from the attached printer.
In the linear elastic range, for small deformation, the twisting moment T, rate of twist
θ/L, shear modulus G and shear stress σxθ at radius r in a circular body subjected to pure
end torques is related by
σ xθ
r
=
T Gθ
,
=
J
L
J=
1
πR 4
2
=
πD 4
32
(1)
The shear modulus is obtained from equation (1), as
G=
32TL
=
θπD 4
Gpa.
For rectangular cross section shaft (a x b)
TL
kab 3 G
Where k is a constant which depends on the ratio a/b and is given below:
θ=
a/b
k
1.0
0.141
1.2
0.166
1.5
0.196
Twisting moment Ty =
2.0
0.209
2.5
0.249
kgf-m=
16T y
πD 3
=
4.0
0.281
5.0
0.291
10.0
0.312
Nm
∴τ y in shear =
Eq. (1) => For Ty, σxθ at R= yield stress,
τy =
3.0
0.263
Ty R
J
Mpa
Ultimate Torque Tu from experiment =
Kgf-m =
Nm
Fully plastic twisting moment Tp (also called as theoretical ultimate torque), for perfectly
elastic material is given by
R
T p = ∫ r {τ y 2πrdr} =
0
2πR 3τ y
3
=
Nm
Compute the ratios (Tp/Ty), (Tu/Ty) and (Tu/Tp)
Exercise:
i)
ii)
Compare τy from torsion test with τy from UTM test and comment on your
result.
Derive the analytical expression for torque v/s angle, i.e. T v/s θ for an elasticplastic (perfectly) material with torque lying between Ty and Tp i.e.
Ty<T<Tp
2
60 deg center hole (type)
O 7.1
14.2
10
35
120
35
Specimen for Torsion Test
Material: MS
(Torsion test sample is made from 10 mm sq bars of MS and Annealed at 7450C for 45 minutes and then Furnace Cooled.)
All dimensions are in mm.
3
INDIAN INSTITUTE OF TECHNOLOGY, GUWAHATI
DEPARTMENT OF MECHANICAL ENGINEERING
LABORATORY SHEET
NAME:
ROLL NO:
Gr. No:
DATE OF EXPERIMENT :
DATE OF SUBMISSION :
EXPERIMENT: Thin Cylinder apparatus
SECTION 1.0 INTRODUCTION AND DESCRIPTION
Introduction
All engineers need to know how to predict the effects of stress on common shapes. They can use this
information to decide the right type and thickness of materials for their own designs. This Thin Cylinder
shows students the strains in the surface of a, thin-walled cylinder when it is under stress from an internal
pressure. This arrangement is similar to many 'real world' applications, including
pressure pipes, aircraft fuselages and compressed gas cylinders.
The Thin Cylinder apparatus also teaches students about:
• A biaxial stress system.
• The use of strain gauges.
• Young's Modulus.
• Poisson's Ratio.
• Construction and use of a Mohr's Circle.
Description
The Thin Cylinder (SMl 007) is a thin-walled aluminium alloy cylinder. Inside each end of the cylinder is
a free-moving piston. The cylinder sits inside a sturdy frame, on the top of a steel box. The steel box
contains electrical equipment that works the electronic strain gauge display and circuits that can link to
1
TecQuipment's optional VDAS. VDAS will allow data acquisition with the use of a suitable computer.
Fixed to the surface of the cylinder is a set of electrical strain gauges. A digital display on the front of the
apparatus shows the strain measured by each gauge.
To apply internal pressure to the cylinder, students use a hydraulic Hand Pump to force oil into the
cylinder. A mechanical Bourdon type pressure gauge shows the oil pressure in the cylinder. Fitted as
standard to the pressure line is an electronic pressure transducer, for connection to TecQuipment's
optional VDAS. The Hand Pump includes a Pressure Control for the operator to control the pressure in
the cylinder and a built-in pressure relief valve to help prevent damage to the equipment. The body of
the Hand Pump is the oil reservoir.
Open and Closed Ends
A Hand Wheel at the end of the frame sets the cylinder for the open and Closed Ends experiments.
• When the user screws in the Hand Wheel, it clamps the free-moving pistons in the cylinder.
The frame then takes the axial (longitudinal) stress and not the cylinder wall, as if the cylinder
has no ends. This allows 'Open Ends' experiments (see Figure 3).
• When the user unscrews the Hand Wheel, the pistons push against caps at the end of the
cylinder and become 'Closed Ends' of the cylinder. The cylinder wall then takes the axial
(longitudinal) stress (see Figure 4).
2
Strain Gauges
Figure 5 Strain Gauge Positions
The Strain Gauges are sensors that measure the strains in the walls of the thin cylinder. Their use is
important to engineers that work with structures. Strain gauges are electrical sensors. Their electrical
resistance changes when an external force stretches or compresses them. This change in resistance has a
direct relationship with displacement (strain). Strain gauges are small sheets of metal foil cut in a zigzag
pattern. They are only a few microns thick so they are mounted on a backing sheet, for mechanical stability
and electrical insulation. Gauges are bonded to the surface of the structural part under examination. The
strain gauge stretches and compresses with the surface of the part that they are stuck to. To give a direct
reading of strain, the reading from a strain gauge is multiplied by a constant called the
gauge factor. This compensates for the slight differences in manufacture between each batch of gauges.
The gauge factor usually varies between 1.8 and 2.2. TecQuipment set the gauge factor into the electronic
circuits of the SMl 007, so you do not need to allow for it in your readings. There are six strain gauges on
the cylinder, arranged at various angles to allow the study of how the strain varies at different angles to the
axis (see Figure 5). The strain display on the front of the equipment shows the readings from each strain
gauge in ).1£ (microstrain). The display shows only four readings at a time, so you must use the 'Scroll
Readings' button to scroll up and down to see all six values. Note that
a negative reading is a compressive strain and a positive reading is a tensile strain.
Versatile Data Acquisition System (VDAS)
Figure 6 The VDAS Hardware and Software
3
Technical Details:
Notation:
This section only gives the basic information needed to do the
experiments. For full theory, refer to the textbooks
Noise Levels: The noise levels recorded at this
apparatus are less than 70 dB (A).
* Strain is a ratio of dimensions and has no units. The Thin
Cylinder display shows a traditional unit, the
‘µ€' (micro-strain) which is the strain value x 10-6.
Useful Equations
4
Theory:
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
SECTION 2: EXPERIMENTS
Experiment 1: Deflection of a Cantilever
Remove any clamps and knife edges from the
backboard. Set up one of the cantilevers as shown in
Figure 3.
Slide the digital dial test indicator to the position on
the beam shown in Figure 3, and lock it using the
thumb nut at the rear. Slide a knife-edge hanger to the
position shown.
Tap the frame lightly and zero the digital dial test
indicator using the 'origin' button.
Apply masses to the knife-edge hanger in the
increments shown in Table 1. Tap the frame lightly each
time you add the masses. Record the digital dial test
indicator reading for each increment of mass.
Repeat the procedure for the other two materials and
fill in a new table.
In this experiment, we will examine the deflection of a
cantilever subjected to an increasing point load. We will
repeat this for three different materials to see if their
deflection properties vary.
m
I:
2
I
Material
Width
b: d:
Depth
4
Nm
mm
mm
Evalue:
w
Mass
Figure 3 Cantilever set-up
schematic
0 and (g)
Actual
deflection
Theoretical
deflection
(mm)
(mm)
100
200
400
300
500
You may find the following table useful in converting
the masses used in the experiments to loads.
Mass (Grams)
0.98
2.94
4.90
3.92
1.96 (Newtons)
Load
Table 1 Results for Experiment 1 (beam 1)
Table 1 Grams to Newtons conversion table
I:
m
I
-2
Material
Width
Depthb:d:
4
Nm
mm
mm
Evalue:
As well as the information given on the backboard you
will need the following formula:
Deflection
WL3
3E1
Mass
0
(g)
Actual
deflection
Theoretical
deflection
(mm)
(mm)
100
400
300
200
500
where:
W=Load (N)
L = Distance from support to position of loading
(m);
E = Young's modulus for cantilever material (Nm-2);
= Second moment of area of the cantilever (m\
1
Using a vernier gauge, measure the width and depth of
the aluminium, brass and steel test beams. Record the
values next to the results tables for each material and
use them to calculate the second moment of area, 1.
Table 2 Results for Experiment
Page 3
1 (beam 2)
TecQuipment
m
Deflections
of Beams and Cantilevers:
I
4 -2
mm
Width b:
NmMaterialDepth
d:
mm
value:
Mass
Actual(mm)
deflection
Theoretical
(mm)
deflection
100
400
300
200
500
Table 3 Results for Experiment
Student Guide
On the same axis, plot a graph of Deflection versus
Mass for all three beams. Comment on the relationship
between the mass and the beam deflection. Is there a
relationship between the gradient of the line for each
graph and the modulus of the material?
Calculate the theoretical deflection for each beam
and add the results to your table and the graph. Does the
equation accurately predict the behaviour of the beam?
Why is it a good idea to tap the frame each time we
take a reading from the digital dial test indicator?
Name at least three practical applications of a
cantilever structure.
1 (beam 3)
Page 4
TecQuipment
Deflections
of Beams and Cantilevers:
Student
Guide
Experiment 2: Deflection of a Simply Supported Beam
In this experiment, we will examine the deflection of am
I:
simply supported
beam subjected to an increasing point
load. We will also vary the beam length by changing the
distance between the supports. This means we can find
out the relationship between the deflection and the
(g)
0
length ofthe beam.
As well as the information given on the backboard
you will need the following formula:
Maximum deflection =
4
Mass
mm
mm
Nm-2
Evalue: Depth
Widthd: b:
Actual(mm)
deflection
Theoretical
(mm)
deflection
100
200
300
500
400
WL3
48E1
where:
W= Load (N);
L = Distance from support to support (m);
E = Young's modulus for cantilever material (Nm-2);
1 = Second moment of area of the cantilever (m\
Table 4 Results for Experiment 2 (fixed beam
length variable load)
Part 2
Part 1
Using a vernier gauge, measure the width and depth of
the aluminium test beam. Record the values next to the
results table and use them to calculate the second
moment of area, 1.
Remove any clamps from the backboard. Setting
length between supports I to 400 mm, set up the beam
as shown in Figure 4.
Set up the beam with the length I at 200 mm. Ensure the
digital dial test indicator and load hanger are still central
to the beam, as shown in Figure 5.
r'o2rl
r--A
f-H.~
mm-I
f-o--200 mm-r---200
1= 400
tw
DDA
mm---"
A
Figure 4 Simply supported beam set-up and
schematic (fixed beam with variable load)
Slide the digital dial test indicator into position on the
beam and lock it using the thumb nut at the rear. Slide a
knife-edge hanger to the position shown.
Tap the frame lightly and zero the digital dial test
indicator using the 'origin' button.
Apply masses to the knife-edge hanger in the
increments shown in the results table. Tap the frame
lightly each time, and record the digital dial test
indicator reading for each increment of mass.
I
w
ADD
Figure 5 Simply supported beam set-up and
schematic (fixed beam load with variable length)
Lightly tap the frame and zero the digital dial test
indicator using the 'origin' button. Apply a 500 g mass
and record the deflection in Table 5. Repeat the
procedure for each increment of beam length.
From Table 4 plot a graph of Deflection versus
Applied Mass for a simply supported beam. Comment
on the your graph. Inspect the ruling equation of the
beam. What is the relationship between the deflection
and the beam length? Test your assumption by filling in
the empty column of Table 5 with the correct variable.
Plot a graph.
Page 5
TecQuipment
Length (mm)
Deflections of Beams and Cantilevers: Student Guide
Name at least one example where this type of bending is
desirable and one where it is undesirable.
Deflection (mm)
380
320
260
560
500
440
Table 5 Results for Experiment 2 (fixed beam load
variable length)
Page 6
INDIAN INSTITUTE OF TECHNOLOGY, GUWAHATI
DEPARTMENT OF MECHANICAL ENGINEERING
LABORATORY SHEET
NAME:
ROLL No.:
DATE OF EXPERIMENT:
Gr.No. :
DATE OF SUBMISSION:
EXPERIMENT: HARDNESS TEST
OBJECTIVE: To determine the hardness of a given set of specimens by (i) Brinell
(ii) Vickers and (iii) Rockwell hardness testing machines.
APPARATUS:
1. Brinell hardness testing machine, 5mm and 10mm diameter steel ball
indentors, microscope.
2. Vickers hardness testing machine, diamond pyramid indentor, microscope.
3. Rockwell machine, loads and indentors: 1/16 inch diameter steel ball indentor and
diamond indentor 120o cone angle.
THEORY AND PROCEDURE:
Hardness of a material has been defined in various ways as the resistant of it’s surface to
plastic deformation, cutting, wear, scratching, abrasion, indentation or energy absorption
under impact. Hardness depends on crystal structure, dislocations, atomic bonds etc.
Indentation Hardness Test is one of the most frequently used non destructive tests for
quality control of machine parts or structural members to ensure that the specific piece
does have the material property used in design. It is a quick and inexpensive test and
information about yield stress. It is presumed that if the hardness is within certain bounds
then so are the other properties.
In Indentation Hardness Test, a pyramid, cone or ball is pressed into a flat surface by
gradual application of a load to produce a permanent indentation. Restraint of the
1
surrounding undeformed material means that most of the applied load merely developed
hydrostatic compressive stress which does not cause the metal to deform plastically. For
plain carbon and low steel alloy steels, the ultimate tensile strength (in Mpa) can be
estimated by multiplying BHN by 3.45. For other materials, relationship will be different
and may exhibit too much variation to be dependable. The most common indentation
hardness test are:
Brinell test: A 5mm or 10mm diameter (D) hardened steel or tungsten carbide sphere is
pressed into the flat surface of a test specimen under a load P of 250 Kgf, 500 Kgf,
700Kgf, 1000Kgf or 3000Kgf. The load is removed automatically after appliction or
preset time and diameter d of the indentation is measured by a microscope. Brinell
hardness number BHN is defined in Kgf/ mm2 as force per unit surface area Ac
P
2P
BHN=
(1)
=
Ac πD D − D 2 − d 2
[
]
P= 3000Kgf and 10mm steel indentor are used in a standard test. If a material is soft, load
(250 to 3000 kgf) and diameter D of ball should be adjusted to keep
d
within 0.3 to 0.5.
D
For BHN > 500Kgf/ mm2 , Tungsten cabide ball should be used. Nearest edge of the
specimen should be at a distance > 2.5d and thickness of specimen be > 5d to avoid
spurious side and bottom effects. The spherical indentor, unlike conical and pyramidal
indentors, does not provide geometrical similitude for indentations of different size d.
The BHN of a given material is not constant for all values of
d
D
due to the varying
inclination at the top of a spherical sector.
Vickers test: A diamond pyramid with a square base and a angle of 136o±0.5 between
2
opposite faces is used as an indentor. The Vickers Hardness value is defined by
V=
P 1.854 P
=
Kgf/mm2
2
Ac
dm
(2)
where dm is the mean diagonal of the square indentation.
Rockwell Test: A hard steel spherical ball of diameter 1.588mm (1/16 in) or a diamond
conical indentor (120o angle) is forced into the surface and the depth of indentation is
read on a electronic display. A minor load is applied to provide a firm contact with the
surface till display shows ‘SET’. The major (total) load is then automatically applied for
a preset time. To eliminate elastic effects the net change in penetration ∆ mm is measured
automatically after returning the load to minor value. The Rockwell hardness number
defined by the following equation, can be read directly from the electronic display:
R = C1- C2 ∆
(3)
Various scales use different indentors, loads, C1 and C2. The most common are the
Rockwell C (cone) 20-70 RC and Rockwell B (ball) 30-100 RB scales, used or hard
(or RB > 100) and soft metals respectively:
Table 1
Scale
Indentor
RB
1/16’’ or
1.588mm
Hard steel ball
Diamond
cone 120o
RC
Minor
(Preload)
Kgf
10
10
Major
(Total load) Kgf
Relation to Brinell
hardness BHN
100
RB= 130-500 ∆
RB ≅ 134-6700/BHN
150
RC= 100-500 ∆
RC ≅ 115-1500/√BHN
3
OBSERVATION AND CALCULATION
The captioned sketches of the three machines are given in Fig. 1, 2 and 3.
1.BHN:
Flat polished specimen.
Dia. of indentor D =
mm
The diameter d of the indentation for different loads P is tabulated in table 2 and BHN
computed by (1): The BHN vs load P is plotted in fig 4.
P kgf
d mm
BHN kgf/ mm2
P kgf
d mm
BHN kgf/ mm2
P kgf
d mm
BHN kgf/ mm2
If d/ D for P = 3000 kgf is in the range 0.3 to 0.5, then P1= 3000 kgf, else from table 2
choose a load P1 for which d/ D ≅ 0.4 and take three indentations corresponding to this
load :
P1=
kgf
mean d =
mm
kgf/ mm2
BHN for material ( from P1 and d ) =
Approx. ultimate tensile strength σu = 3.45 X BHN =
4
Mpa
2. Vickers: The observations for various materials are tabulated in Table 3
Table 3
Material to be
tested
Load : kgf
Diagonal dimension of
indentation
d1
d2
VHN
Mean
VHN
Mean
dm
3. Rockwell: The observations for various specimens are tabulated in Table 4.
Table 4
Specimen
Scale
Indentor
Rockwell hardness
(2)
(3)
(4)
(5)
(1)
5
Average
Write discussion and sources of errors:
EXERCISE : ( T o be submitted with the report )
1.Thickness of a strip is reduced in a cold rolling operation. How the hardness of the strip
is compared with its hardness before rolling and why ?
2. Why are hardness testing s used so frequently ?
3. Define BHN, Vickers diamond hardness number and Rockwell hardness numbers.
4. Why is it necessary to stipulate different loads P for finding BHN of two different class
of materials, say brass and steel ?
5. List the main advantages of Vickers diamond test over Brinell test.
6. Find Vickers diamond hardness number of Al if diagonal lengths of impression for
indenting load of 2.5 kgf are 0.363mm and 0.361mm. What size diamond impression
would be made in the same material under indenting load of 5 Kgf ?
7. What is the need and role of minor load in Rockwell test in contrast to the other
hardness tests ?
8. Why is the reading in the Rockwell test taken after removal of major load but when the
minor load is still acting?
9. What is wrong with the test result “Rockwell hardness of steel is 64”?
10. In a Brinell test on annealed Cu with 5 mm dia. ball, the reading of d are 2.2, 2.7 and
3.1 mm for loads of 125, 250 and 350 kgf. Find BHN. What would be the diameter of
impression for a load of 300 kgf?
6
INDIAN INSTITUTE OF TECHNOLOGY, GUWAHATI
DEPARTMENT OF MECHANICAL ENGINEERING
LABORATORY SHEET
NAME:
ROLL No.:
DATE OF EXPERIMENT:
Gr.No. :
DATE OF SUBMISSION:
EXPERIMENT: IZOD AND CHARPY IMPACT TEST
Objective; To study the toughness or energy absorbing properties of various materials
under two types of impact tests i.e. Izod and Charpy impact tests.
Theory and background: So far we have learned about quasi-static tests on materials
wherein load is so slowly applied that the inertia is ignored. Under dynamic test the rate
of application of the load is many times faster than in the quasi-static cases. The behavior
of the material may change substantially under these conditions of loading especially in
the presence of stress concentrations around notches and at low temperatures, i.e. a
ductile material (under static loading) may become brittle.
(A) Fracture: Fracture is the separation of body under stress into two or more parts.
The fracture is considered brittle if the microcracks propagate rapidly with
minimum absorption of energy and negligible plastic deformation. In single
crystals brittle fracture accompanies cleavage along the weakest crystal plane. In
polycrystalline materials the fracture surface is granulated and rough in
appearance. According to Griffith, failure in brittle materials is caused by crack
propagation due to stress concentration at the tips of existing microcracks.
Ductile fracture occurs after considerable plastic deformation, accompanied by
slipping at intergranular boundaries. Such fracture begins with the formation of
voids in the materials, generally at non-metallic inclusions. Under continually
increasing loads these voids propagates to the surface and causes failure.
(B) IMPACT TESTING: The ordinary static testing is not satisfactory when we
want to determine the suitability of a material to resist sudden shock or impact.
Machines have been designed in which a specimen receives a simple shock and
the energy absorbed by the specimen is taken as the measure of the resistance of
the material to impact, or its dynamic toughness. The impact used in our
laboratory has the provision of carrying out two impact tests (i.e.Izod and
Charpy) by changing the support attachment and striker head. It has a swinging
pendulum with a fixed weight, with different starting positions for the two tests,
giving different initial potential energies.
1
(B1) IZOD TEST (Bending of a notched cantilever) : This test uses a 10mm x 10mm
Cantilever test piece of total length 75mm. A “V” notch is provided at 28mm
from one end, the depth of the notch is 2mm, its angle is 45o and its root radius is
0.25mm. The specimen is fixed vertically at the base; the cantilever portion above the
notch is 28mm long. The hammer strikes near the top of the specimen(6mm from tip)
and then moves further after the fracture of the specimen. The difference of the
potential energy between the initial and final positions of the hammer gives the
energy absorbed in the impact. A rotating pointer on the scale records this difference
directly.
(B2) CHARPY TEST: (Bending of a simply supported beam): The specimen used
for Charpy test, like the Izod test is 10mm x 10mm in section and has a 2mm wide,
5mm deep U-shaped notch. The length of the specimen is 55mm and notch is at its
center. The beam is supported horizontally by two standard supports and hammer
strikes it at the center from the notch less side. Thus tensile stresses at the notch tend
to open the notch and cause failure.
TEST DETAILS:
1. Temperature is a very important factor in the measurement of toughness. Most
materials show loss of toughness with the fall off room temperature. Reduced
temperature in many metals and polymers can lead to increase in yield stress
relative to fracture stress in tension. Hence the metal fractures like a brittle
material instead of like a ductile material. There are generally three regions. At
low temperature the materials give brittle fracture with little change in toughness
with temperature. This is low toughness low temperature region. Then there is a
transition range with rapid increase in toughness with temperature and finally we
have the high toughness high temperature region, showing little change in
toughness with temperature. The change from ductile yielding to brittle structure
can be quite abrupt and is referred to as the ductile-brittle transition temperature.
Conduct Charpy test for some material at room temperature and after cooling the
specimen to 0oC.
2. Brittle fracture and ductile fracture have characteristic appearances and can be
easily recognized.
3. Large value of stress concentration in marginally ductile material, particularly
notch-type concentrations can lead to brittle failure. The high rate of strain can
cause yield stress σy and the stress concentration can introduce hydrostatic
tension, reducing fracture stress σf in tension. Both effects promote brittle
behavior. Materials that are sensitive to this effect are called notch sensitive.
4
Accuracy of the notch is also an important factor. Small changes in the shape,root
radius and finish of the notch may create large difference in the test results.
5
Positioning of the specimen in the machine is important but is generally done by
a template.
2
OBSERVATIONS AND CALCULATIONS:
CHARPY1 and CHARPY2 refer to specimen at room temperature ,CHARPY3
refer to specimen at ice cooled and heated at100 oC respectively.
SPECIFICATION
Temp.
Material
Length
Breadth
Diagonal
Notch position
Notch angle
Root radius
Initial energy of
hammer
Final energy of
hammer
Energy absorbed
Type of fracture.
IZOD
Room
CHARPY1
Room(H)
CHARPY2
Room(A)
CHARPY3
……oC (A)
NOTCH IMPACT TESTS: Notch impact tests are used as quality
control/acceptance checks. These are relatively simple and are easy and rapid to
conduct. A fast moving hammer strikes a test specimen containing a milled notch,
and the energy absorbed in fracturing the test piece is measured. The ductilebrittle transition temperature is considerably higher for impact loading conditions
than for slow strain rate conditions. It is comparatively easy to determine the
transition temperature range under impact loading conditions, as there is a very
large difference between the energy required to cause ductile and brittle fractures
in this type of test. Another major use of notch impact test is to find whether heat
treatments have been carried out successfully.
DISCUSSION OF RESULT AND SOURCES OF ERROR:
EXERCISE
1. Which parameter of the notch geometry is most important factor influencing the
notch impact values?
2. Define clearly ductile and brittle fractures?
3. What are the main reasons for using notch impact test?
4. What is the major advantage of Charpy test over Izod test?
5. What is the basic difference between Izod and Charpy test?
3
1.00R±.07
1
10 +.1
-0
55 +.6
-0
Root Radius 1.00±.07
5
5
10 +.11
-.11
2
5
Specimen for Charpy Impact Test
Enlarged section of 'U' notch of
square specimen
Included angle 45°
Root Radius
0.25mm
10
10
8
10
22
28
Enlarged section of "V" notch of square
specimen
75
Specimen for Izod Impact Test
(Material: MS)
All dimensions are in mm.
4
INDIAN INSTITUTE OF TECHNOLOGY, GUWAHATI
DEPARTMENT OF MECHANICAL ENGINEERING
LABORATORY SHEET
NAME:
ROLL No.:
DATE OF EXPERIMENT:
Gr. No.:
DATE OF SUBMISSION:
PHOTOELASTICITY
1. Objectives
The objectives of this experiment are
1. To introduce a very fundamental and most important experimental technique to view the principal stress
components and directions of principal stresses– the photoelastic method
2. To use the photoelastic technique for the direct measurement of principal stresses for the plane stress
condition at any given point in the sample.
3. To view the map of principal directions at any given point in the sample.
2. Introduction
Photoelasticity is an experimental technique for stress analysis that is particularly useful for members having
complicated geometry, complicated loading conditions, or both. For such cases, analytical methods (that is,
strictly mathematical methods) may be cumbersome or impossible, and analysis by an experimental approach
maybe more appropriate. The name photoelasticity reflects the nature of this experimental method: photo
implies the use of light rays and optical techniques, while elasticity depicts the study of stresses and
deformations in elastic bodies.
The essential feature of this method is that one can visualize the distribution of principal stresses and
their directions at all infinite number of points of the sample under study. Moreover, this technique provides
quantitative evidence of highly stressed areas at which most of the failures usually originates. On the other hand,
often equally important, it also shows the areas of low stress level where structural material is utilized
inefficiently. This technique has been widely used to aid in development of correct analytical methods for
complex stress analysis problems.
3. The Polariscope
The most common equipment for photoelastic studies of engineering components is the polariscope. Polariscope
utilizes the properties of polarized light. There are two basic types of polariscopes, plane polariscopes and
circular polariscopes. The polariscope used for this laboratory can be configured as either. However we use
circular polariscope for laboratory work.
4. Photoelastic behavior
The photoelastic method is based upon a unique property of some transparent materials, in particular, certain
plastics. This property is known as birefringent property. Consider a model of some structural part made from a
photoelastic (birefringent) material. When the model is stressed and a ray of light enters the sample two
phenomena takes place due to change in optical properties of the sample
[1]
At each point of the stressed body the light wave is resolved into two mutually perpendicular
components lying in the planes of the principal stresses occurring at that point.
1
[2]
The linear velocity of each of the components of the light wave is retarded through the stresses
specimen in direct proportion to the difference in the principal stresses.
These facts are the basis of the photoelastic method stress analysis. This phenomenon is called double refraction
or birefringence, and is the same as exhibited by certain optical crystals — but in photoelasticity the double
refraction is artificial, being controlled by the state of stress or strain at each point in the body.
4. Isoclinic and Isochromatic lines
Once the state of the stress at each point of a stressed body is available, many visual interpretations of the
various aspects of the available data can be made. For example, the points of algebraically equal principal
stresses regardless of their sense, when connected, provide a map of stress contours. Thus any point lying on a
stress contour has a principal stress of the same algebraic magnitude. Similarly, the points at which the
directions of the minimum principal stresses form a constant angle with the x axis may be connected. This
means that the direction of the maximum principal stresses through the same points also forms a constant angle
with the x axis. The line so connected is a locus of points along which the principal stresses have parallel
directions. Such line is called an isoclinic line. Similarly a line that is a locus of points along which the
difference in principal stresses (σ 1 − σ 2 ) remains constant is called an isochromatic line. Basically we can
visualize the isoclinic lines and isochromatic lines of a stressed member using polariscope.
5. Photoelasticity terminologies
a. White light: Light from a source that emits a continuous spectrum with nearly equal energy for every
b.
wavelength.
Monochromatic light: Light of a single wavelength such as light emitted by sodium vapor lamps.
c.
Plane Polarized light: Light that is restricted to vibrate in a single plane
d.
Plane Polarizer: Optical element that generates polarized light along its axis of polarization. Light
waves perpendicular to axis of the polarization are absorbed.
e.
Analyzer: It is also a plane polarizer except that it is near the user or analyst and hence its name. The
Polariscope consists of a polarizer at the source of light and another polarizer at the user or analyst side.
f.
The one that is at the light source is termed as polarizer and the other one is termed as analyzer.
Quarter-wave plate: A wave plate is an optical element which has the ability to resolve a light vector
into two orthogonal components and to transmit the components with different velocities. Specifically
if the phase lag is by an amount of one quarter of the wave length then the wave plate is termed as
quarter wave plate. Quarter wave plates are employed in polariscopes in order to condition the light.
6. Circular polariscope
The setup of the circular polariscope is illustrated in Fig. 1. Figure 2 shows a schematic diagram of the circular
polariscope. The circular polariscope contains four optical elements. The first element following the light source
is the polarizer. It converts the ordinary light into plane-polarize light. The second element is a quarter wave
plate set an angle 450 to the plane polarization. This quarter wave plate converts the plane polarized light into
circularly polarized light and hence the name circular polariscope. The second quarter wave plate is set with its
fast axis parallel to the slow axis of the first quarter wave plate. The purpose of this element is to convert the
circularly polarized light into plane polarized light vibrating in the vertical plane. The last element is the
analyzer (another polarizer) with its axis of polarization horizontal (opposite to the axis of polarizer see Fig. 2)
and its purpose is to extinguish the light.
As a result of photoelastic effect the light exits the stressed sample with two light vectors E1 and E2
parallel to the directions of principal directions at that point with a phase shift. These rays finally passes through
2
the analyzer (after crossing quarter wave plate) which allows only the components of light parallel to the axis of
polarization and thus permit them to come to optical interference. Due to photoelastic effect one of the rays of
E1 and E2 is retarded relative to other by an amount directly proportional to the principal stress difference at that
point. If the relative retardation N is 0, 1, 2, 3,... cycles, the waves reinforce each other, and the combined effect
is a large light intensity. If the phase difference N is 1/2, 3/2, 5/2, 7/2,... cycles, the amplitude of the two
interfering waves is everywhere equal and opposite; destructive interference ensues, and the light intensity
diminishes to zero (extinction)
Fig. 1 Basic set-up of circular polariscope
Fig. 2. Schematic diagram of the circular polariscope.
Intermediate intensities are developed for intermediate values of N. Thus, a photoelastic pattern of dark and light
bands, such as shown in Fig. 3 (typical), is formed as follows: the locus of points at which N = 0 forms a dark
band: the locus of points at which N = 1/2 forms an adjacent light band; another dark band is formed by rays
traversing the photoelastic material at points where N = 1; and successive dark and light bands are formed for
increasing values of N. In the nomenclature of optical interference, these bands are called fringes. These fringes
which are formed due to interference of two different velocity waves are known as isochromatic fringes. Thus
Fig. 3 shows the locus of points along which the difference between the two principal stresses remains constant.
It should be noted that if the bands corresponding to N = 0, 1, 2, etc., are dark then band corresponding to
N=1/2, 2/3 etc must be light. This arrangement is called as dark field arrangement.
3
Fig.3 A typical isochromatic fringes
7. Analysis of Isochromatic fringe pattern
Let us view a plane-stress model in a circular polariscope. A pattern of dark and light bands (Fig. 6) forms in the
viewing screen when external forces or loads are applied to the model, and the number of these bands increases
in proportion to the external forces.
Fig.6 Formation of isochromatic patterns for increasing loads.
The isochromatic pattern is related to the stress system by the stress-optic law. Namely
σ1 − σ 2 =
f
N
t
(1)
where f is the stress-optical coefficient (Kg/cm), a constant that depends upon the model material and the
wavelength of light employed, t(cm) is the model thickness, and N is the relative retardation of rays forming the
pattern. The term N is also known as isochromatic fringe order. The fringe order, N, is defined as the number of
cycles of relative retardation between two components of a light beam passing through the stressed model.
Equation (1) states that the relative retardation, N, at each point in the model is directly proportional to the
difference of principal stresses σ 1 − σ 2 at the point. Thus isochromatics are locus of points at which σ 1 − σ 2
are constant. However we also know that the difference σ 1 − σ 2 is equals to two times the maximum shear
stress at that point
σ 1 − σ 2 = 2τ max =
f
N
t
Thus isochromatics are also locus of constant maximum shear stress points on the stressed model.
4
(2)
8. Difference between plane and circular polariscope.
Quarter wave plates are absent in plane polariscope. You can see only isochromatic patterns in circular
polariscope. Plane polariscope provides both isochromatic and isoclinic lines such that it is difficult to
distinguish them. Therefore, generally plane polariscope set up is used to determine the principal stress
directions at different points in the stressed sample. In order to find the magnitude of principal stresses circular
polariscope is used. Both the set-ups can be obtained using the present polariscope.
9. Monochromatic light and white light source
One can use either monochromatic or white light for viewing the isochromatics/isoclinics. Monochromatic light
produces dark and light bands a single color. It is very easy to distinguish dark and light bands (and hence
determination of fringe order N) of a single color and hence monochromatic light is generally employed in
photoelastic studies. Since the white light contains wavelengths of entire spectrum, isochromatic fringe patterns
appear in different colors. It is relatively difficult to estimate the fringe order from the colored isochromatic
fringe patterns. With white light, isoclinics appear in black color.
10. Experimental procedure
Fig. 7 A simply supported beam
In order to understand the principles of photoelastic method the following laboratory experiment will be
conducted
1.
A simply supported beam subjected to two concentrated forces placed at equal distance from the
supports as shown in Fig. 7.
2.
The direction and magnitude of principal stresses at any point within the beam can be computed if the
applied loads and cross-sectional properties are known.
3.
4.
Turn-on the monochromatic light switch and wait for 20 minutes
Adjust, analyzer and two quarter-wave plates to form a circular polariscope
5.
6.
Keep the specimen at the center of the loading frame
With no load observed the beam. No isochromatics can be identified as the difference between
principal stresses is zero everywhere.
7.
Place 1, 2 and 2 Kg of weight in the weighing pan in order. Observe formation of fringes with
increasing load. You will also see some dark fringes at the supports and loading points.
8.
Add 5 Kg of weight in the weighing pan and observe the formation more isochromatic fringes with
N=0 fringe at the center of the beam i.e., neutral axis.
9.
Determine the fringe order of the dark fringe at the sample point 1 on the beam (a red mark is placed on
the beam sample). This fringe order corresponds to 6 Kg weight in the weighing pan.
5
10. Add 6 more Kg of weight gently to the existing weights. Observe the formation of more number of
fringes on both tensile and compressive side. However you can see always a fringe at neutral axis
which represent N=0 fringe.
11. Determine the fringe order of the dark fringe at the two sampling points 1 and 2 on the beam. These
fringe orders correspond to 13 Kg weight in the weighing pan.
12. Obtain the stress-optical coefficient, thickness, dimensions of the beam and dimensions of the lever (to
which weighing pan is attached).
13. Calculate the experimental values of principal stresses at the sampling points 1 for the loads
corresponding to 6 Kg and at sampling points 1 and 2 corresponding to 13 Kg. Note that the weights in
the weighing pan are not equal to the applied forces Ps on the simply supported beam (Fig. 7).
14. Calculate using elementary beam theory the principal stresses at the sampling points 1 and 2 for
different loads and compare with experimentally obtained values.
15. Turn the quarter-wave plates for plane polariscope set up. Switch off monochromatic light and wait for
10 minutes. Switch of the fan. Turn on the white light. You can see now the colored isochromatic
fringe pattern due to the white light and isoclinic lines simultaneously. Turn the front knob to see the
changing isoclinics.
16. Prepare the following tables of results
17. All neat and systematic calculations for filling up the following tables must be attached with this
manual.
Table 1: Properties of simply supported beam
t (cm)
h (cm)
I (cm4)
L1 (cm)
L2(cm)
P value for 6 Kg in weighing pan
P value for 13 Kg
Distance from the neutral axis of
Sampling point 1 (y1)
Distance
from
neutral
axis
of
f ( Kg / cm)
of
Sampling point 2 (y2)
Optical
constant
stressed sample
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Table 2: Fringe orders at the sampling points for different loads
Sampling Point
Fringe order N at
5 Kg
13 Kg
1
2
----------------
Table 3. Comparison of theoretical and experimental results
Sampling
5 Kg
13 Kg
Point
Theoretical Experimental Theoretical Experimental
results
results
results
results
σ1
σ1
σ1
σ1
( Kg / cm 2 )
( Kg / cm 2 )
( Kg / cm 2 )
( Kg / cm 2 )
--------
---------
1
2
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INDIAN INSTITUTE OF TECHNOLOGY, GUWAHATI
DEPARTMENT OF MECHANICAL ENGINEERING
LABORATORY SHEET
NAME :
ROLL NO :
GROUP NO :
DATE OF EXPERIMENT:
DATE OF SUBMISSION:
EXPERIMENT: Bending stress in a beam experiment in the structures frame
SECTION 1.0 INTRODUCTION AND DESCRIPTION
Introduction
This guide describes how to set up and perform Bending Stress in a Beam experiments. The equipment
clearly demonstrates the principles involved and gives practical support to your studies.
Description
Figure 1 shows the Bending Stress in a Beam experiment. It consists of an inverted aluminium T- beam,
with strain gauges fixed on the section (the front panel shows the exact positions).
The panel assembly and Load Cell apply load to the top of the beam at two positions each side of the strain
gauges. Loading the beam in this way (rather than loading the beam at just one point) has two main
advantages: It allows a gauge to be placed on the top of the beam. The constant bending moment area it
creates gives better strain gauge performance and avoids stress concentration close to the gauge positions.
Strain gauges are sensors that experience a change in electrical resistance when stretched or compressed.
Strain gauges are made from a metal foil formed in a zigzag pattern. They are only a few microns thick so
they are mounted on a backing sheet. The backing sheet electrically insulates the zigzag element and
supports it so it does not collapse when handled.
1
The T-beam has strain gauges bonded to it. These stretch and compress the same amount as the beam, so
measure strain in the beam. If you look carefully at the equipment you will notice there is another set of
strain gauges. These are called dummy gauges. The dummy gauges, and how the way they are connected in
the electrical circuit, help reduce inaccurate readings caused by temperature changes and thermal
expansion. The Digital Strain Display converts the change in electrical resistance of the strain gauges to
show it as displacement (strain). It shows all the strains sensed by the strain gauges, reading in micro strain.
Look at the reference information on the unit. It is useful and you may need it to complete the experiments
in this guide.
How to Set up the Equipment
The Bending Stress in a Beam experiment fits into a Test Frame. Figure 2 shows the Bending Stress in a
Beam experiment in the Frame. Before setting up and using the equipment, always: Visually inspect all
parts, including electrical leads, for damage or wear. Check electrical connections are correct and secure.
Check all components are secure and fastenings are sufficiently tight. Position the Test Frame safely. Make
sure it is on a solid, level surface, is steady, and easily accessible. Never apply excessive loads to any part
of the equipment.
The following instructions may already have been completed for you.
I. Place an assembled Test Frame (refer to the separate instructions supplied with the Test Frame if
necessary) on a Work bench. Make sure the 'window' of the Test Frame is easily accessible.
2. There are two securing nuts in each of the side members of the frame (on the inner track). Move one
securing nut from each side to the outer track (see STR 1 instruction sheet). Slide them to about the
positions shown in Figure 2. Fix the two supports on to the frame in the same position.
3. Slide two nuts into position to hold the load cell. Fix the load cell leaving the screws slightly loose.
4. Lift the beam into position and level the ends of the beam with the frame.
5. Position the load cell so the hole in the fork reaches the hole of the loading position, and it is vertical.
Tighten the load cell using the 6 mm A/F hexagonal key. Secure the fork using a pin.
6. Make sure the Digital Force Display is 'on'. Connect the mini DIN lead from 'Force Input l' on the
Digital Force Display to the socket marked' Force Output' on the left-hand side of the load cell.
7. With no load on the load cell (the pin should turn), use the control on the front of the load cell to set the
reading to around zero.
8. Make sure the Digital Strain Display is 'on' and set to gauge configuration I . Matching the number on
the lead to the number on the socket, connect the strain gauges to the strain display. Leave the gauges for
five minutes to warm up and reach a steady state.
2
3
SECTION 2.0 EXPERIMENTS
Ensure the beam and Load Cell are properly aligned. Turn the thumbwheel on the Load Cell to apply a
positive (downward) preload to the beam of about 100 N. Zero the Load Cell using the control. Take the
nine zero strain readings by choosing the number with the selector switch. Fill in Table I with the zero
force values. Increase the load to 100 N and note all nine of the strain
st
readings.
dings. Repeat the procedure in
100 N increments to 500 N. Finally; gradually release the load and preload.
Correct the strain reading values for zero (be careful with your signs!) and convert the load to a bending
moment then fill in Table 2.
From your results, plot a graph of strain against bending moment for all nine gauges (on the same graph).
4
What is the relationship between the bending moment and the strain at the various positions?
What do you notice about the strain gauge readings on opposite
opposite sides ofthe section? Should they be
identical?
If the readings are not identical, give two reasons why.
TABLE 1:
TABLE 2:
5
TABLE 3:
Calculate the average strains from the pairs of gauges and enter your results in Table 3 (disregard the zero
values).Carefully measures the actual strain gauge positions and enter the values into Table 3.
Plot the strain against the relative vertical position of the strain gauge pairs on the same graph for each
value of bending moment. Take the top of the beam as the datum.
Calculate the second moment of area and position of the neutral axis for the section (use a Vernier Caliper
to measure the exact size of the section) and add the position of the neutral axis to the plot.
• What is the value of strain at the neutral axis?
• Calculate the maximum stress in the section by turning the strains into stress values (at the maximum
load).Compare this to the theoretical value.
• Does the bending equation accurately predict the stress in the beam?
6