STUDY
OF THE
PNEUMAT I C
CAISSON
FO
PISCATAQUA RIVER BRIDGE
BY
ROBERT T COLBURN
ERNEST N. GELOTTE
192-3
TABI.
Oi
rap-e
loreword ---------------------------------------3
Notation -nd refererces --------------------------
Case 3.----
4-20
Calculatior of neutral axi.- rd monent of
6-7
inertia ----------------------------------8
Calculation of weirht of cheerb------Calculation of weiTht of superstrtcture----9
Shear and moment curves-----------10-11
Determination of loads------------12-15
ibre stresses----------------6
treses--------------------------7
eri
18
Vertical rod -----------------------------19
Bond stre.sses -----------------------------Surmar
20
------------------------------------
Case 2.------------------------------------------21
~ener] theory (H"orizontal re-erorc-rent)--22-27
ricLticnal reitance-----------------------29
cp--------------------------------0
Irevsi:re
32
-----------------------Jolution of eruti
Fibre stresses in 'hcori zcrth xe-or'c rcerent-32-33
e-narcvn
3
Jtresses :nvertico
ctresses--------------------------------35-38
hoof
-
Case 3------------------------------------
39-40
Surierstructure ---------------------------------
41-43
Conclusion----------------------------------------44-46
Caissor charter of Piscatagua
-
iver Eridge-------late
Caisson superstructurc---------------------------Plate
DiagraF of section showir;
neutral axis--------
B
ure 1
FOREWORD.
Owing to the increased use of compressed air
work in deep foundations, and the very limited amount of
accurate knowledge on the subject at the present time,
we have chosen for our thesis, a study of a deep foundation using a pneumatic caisson. Rather than attempt to
design a caisson chamber, which, owing to the small
amount of available data, could be done intelligently
only by a person with experience in that line, we decided to take a design which had already been built, and
make a thorough investigation of it. This investigation
is a complete analysis of the stresses set up in the
caisson during critical periods of construction and
placing. We can thus check up the present methods of
design and can perhaps show where the design could be
improved. In doing this we learn all the principles of
design just as thoroughly as if we designed one of our
own, and furthermore we are able to study what is considered a good design, which has already been tried and
found to be safe. We are also able to study the practical
problems and difficulties which arise on an actual job,
which would be impossible in an artificial problem.
Through the kind offices of the firm of
Holbrook, Cabot and Rollins, we were able to obtain the
drawings for the reinforced concrete caisson used for the
piers of the new Piscataqua River Memorial Bridge, at
Portsmouth, New Hampshire. We are indebted to Mr. Rollins
and to Mr. Harkness of the same firm, for valuable data
pertaining to thesek particular foundations.
There were a number of practical difficulties
in this case which make it unique. The river bottom was
of gravel overlaying solid rock at a depth of ten to
fifteen feet. The water was about sixty to sixty-five
feet in depth making a total of about eighty feet.
Owing to the slight depth of the gravel, it was impossible
to drive piles with which to guide the caisson, and this
forced the use of special means. The caissons were built
on shore on ways, similar to a ship, and then launched
and floated into place, where they were anchored and sunk.
Owing to the great weight of the concrete caisson, two
sections of the wooden superstructure were built on top
of it before launching, in order to insure it's floating
in the water. Another difficulty was here encountered.
The water at the place whure they were built was shallow.
In order to prevent the caisson from touching bottom and
upsetting, it was necessary to lighten it in every way
possible. This was done by making the roof of the chamber
..............
........
...
..
only six inches thick before launching. When floated to
deep water, the extra three and one half feet were added.
Enough of the pier was also built to sink it to the
river bottom. It was then carefully lined up and anchored
by cables both ways, because the tide fbowed in both
directions. When in placeit was then sunk in the usual
manner, and the pier built inside. Plate A and B show
the complete caisson and superstructure with dimensions.
For a proper analysis of this structure, it is
necessary to consider three critical cases.
1. During launching when very considerable stresses
- are set up especially if some of the ways should
fail to function. It would normally be supported
by five ways.
2. During the sinking and when in place at the
maximum depth. In this case the air pressure
and hydrostatic pressure combine to set up
stress in the chamber.
3. The possibility of uneven bearing, as for instance
when a boulder obstructs one edge, causing most
of the weight to come at one point.
A fourth part which will be investigated, is the wooden
superstructure. Each of these cases will be taken up
separately and the stresses calculated in each case.
This will give a complete analysis of the structure and
show it'"s strong and weak points.
We must concede at the start, that this problem is a very indeterminate one, and certain assumptions
will have to be made, but in every case the assumptions
are explained and in our opinion justified, and coincide
as nearly as possible to ordinary concrete assumptions
used in practical work.
We feel that this problem will be of value
both as a study of deep foundations, and also as a
further study of the theory of concrete.
NOTATION.
Fs
Fs'
Fo
S
v
u
Tensile unit stress in steel.
Compression unit stress in steel.
Compression unit stress in concrete.
Total shear.
Shearing unit stress.
Dond unit stress.
Modulus of elasticity of steel.
Modulus of elasticity of concbete.
Es
n fEe
Be
Es
Ec
M
As
Zo
Q
Bending moment.
Area of steel.
Sum of perimeters of bars.
Statical moment about N. A.
REFERENCES.
"Applied Mechanics Vol 2"K
"Concrete Engineers' Handbook"
"Foundations"
"Beton und Eisen"
Fuller and Johnston.
Hool and Johnson.
Jacoby
and Davis.
Dec. 4, 1919.
Oct. 4, 1920.
CASE 1
This case takes up the consideration of the
stresses in the caisson chamber during launching. The
caisson will be considered under the two worst conditions
Case 1-A. Balanced in the center, acting as a canttlever, all ather ways having failed.
Case 1-B. Supported at both ends, acting as a simple supported beam, the center ways
having failed.
Theses cases are somewhat analagous to the "hogging"
and "sagging" of ships, and are calculated in somewhat
the same manner.
It is obvious from the start that these are
very extreme cases and that it is highly improbable
that they would ever be realized. Naturally, every precaution would be taken to have the ways all on the same
level, and to prevent any one of them from failing. It
is necessary, however, to investigate them to forestall
any emergency. In view of the fact that if an accident
should happen, the stress would be a maximum for only a
fraction of a minute while the caisson slid into the
water, it would be perfectly justifiable to allow a high
fibre stress for this case, as long as it came within
the elastic limit.
In this case we are really considering a concrete beam reinforced in both tension and compression,
and of very complicated cross section. As such it is
necessary to consider the maximum fibre stresses, shearing stress, and bond stress.
The assumptions that are made are the ordinary beam theory assumptions for concrete beams, and also
that the concrete takes no tension. While this last is
not strictly correct, it is very nearly so for high stress
and as it is used in most work in practice, it seems a
logical one to make.
As this caisson has a very complicated cross
section, the only reasonable method of figuring is the
equivalent area method. This substitutes for the steel
an equivalent area of concrete. The caisson is 1-2-4
concrete and therefore n=4-15, and the equivalent area
area of.concrete is 15 times the area of the steel.
Figure 1. shows a cross section giving these qquivalent
areas for both case 1-A and 1-B. The roof in the center
can hardly be considered as acting as part of the beam,
inasmuch as the supports and most of the weight are on
the edges. It seems logical to use the Joint Committee
ruling for the width of tee beam flanges to determine
how much of the roof to consider.
Flange width (2 X s/ab thicknessjtidd
or I A-SPA N
of stem
This eliminates the central portion of the caisson from
the calculations (see fig. 1). The position of the neutral
axis as calculated by the equivalent area method, is
shown for both case 1-A and 1-B in fig. 1.
CALCULATION of the neutral axis and moment of inertia.
Let g:=distance from extreme compression fibre to
the neutral axis.
dedistance from extreme compression to extreme
tension fibre.
It is necessary to assume a trial position of
the neutral axis between any two sets of rods. If the
calculated value of y shows it to be in a different place
them a recalculation is necessary, using the new position
between a different set of rods. Only the correct calculation is shown here. To give the others would be merely
reptition.
For convenience the calculation is tabulated
in tables I and 2.
Col. A gives the areas or equivalent areas.
Col. B gives their distances from the neutral axis
in terms of d and y.
Col. C gives the statical moment of the areas about
the neutral axis, from which y may be calculated.
Col. D gives the squares of the distances in col. B
Col. E gives the moments of inertia about the N. A.
Table I gives values for case 1-A.
Table 2 gives values for case 1-B.
The values in columns A and B are taken from
figure 1.
Wid16
of /?af to consider as
-.
padrt of Beam
74
I
A
(d=
TA BLE /.
X=
qFEA
04
(C)
(a)
(A)
oJsrAjTcz
/OMa.
ANEV1.
AX/3
1,46 j
(E)
(D)
AX= SrATICAL
AfNwr
Ao,r0~~
N
AX/3
NE#T.
-60 y
-/6 y
04
/440 -- /65y
- 29 70 - 336y
'-
8700
/800
d-y -J
d .Y - 28
d-y -S2
/J-
/
Yb d-y -9
25340
/960
/2O
d -y -70
d-y -ae
d-y-94
JO
jo
JO
28
20
28
y- 3
y - 6
y -/ 6
20
y-Y
28
y-42
7
y
/120
460
2/82700
y0i,0/ar
.xg
Y
N.)
604000
8500
J7,000
65O
35M00
13800
2700
47800
/930
5970
170
tZ/40
t/oy
,ory?
8Z1
.)0
1,4800
5"
y
(I
3.ty
y
31~
40
*
41-4L /7/0
84 -23y
l 4 70
Y8,4
y
-/6 -26
190
24.4
- -04 +2d y
2/0
/44
e gy
-8-40
(0o
2.4
-//176 +2
-2772
__
75 7
2440
33
21.(=
14=
y
- 3y
-30
9730 -2
/0,00
4 41
tiZeMCT/A
/MENr
1N.) (/N.
60
Case I-A
49/~
;p *#4Tet
2/8'=
-4749~
trag
e
a
y= -
2/8)000
4/0
3
/Y
~X
CAI/cu/ate y
E4aating the Statical moment of +steel
-concr-ete
to that-of -s-teel and
297Ja-273:Y y
-2772
t.140Y
5, o 2 + -y
2iV2
=
y
4/J
, 0J2y' ,fyat
3
"
y= 444
=
TotA/
I = x
a/, 06 74
- 0,0.0
;740,00
w-
TAB E 2. (d-- /47")
(W)
(A)
4I4 A
DSrANCE
X v
ot
11v*
(_
g
'RON
N&117 AXIS
(N.)
.)2
y .-
4
d
d-Y -3
d-y -2
30
3
30
0
JO
3.
6
6T,
.
/4
(D)
AX = 374T/CAL
No/IET Aaour
2
NEI7
d-y-27
0
324
/'02
63=f
M-y
d- y -J/
y-2
26y -280
X
/45
/4 y-420
y-30
4__
425=
-1/2
J6y
y-
-
__ __ __,___ __ __
/01g000
87000
/8m
= C.0o
2/4
/.
2900
-812
.190900
223'
6yJ*
p
120000
795oo
2 &ir
/x4S
46800
22roo
750
?700
290
9"0 /400
-, '=
Iyr'2Z t
-3'.Y:6y /7 ,
8r 2060
d- yd,
-1$y
8/0
d-y-~93
99&0 -288.t y
toI
/60
4000
-3oy
-y3y
-JYy
2580
d-y.-T
2zO
d- y-75r 2/6
avINE/itrA
(11_)
O 3070
J'= /02
95qJ'= 9900 297000
7620 228,60o
87,F'
171,Ooo
$70
7,*.
-Jo y
-3 Yy
-3 y
-yg
4410
430o
3960
3600
2
foMdP/
N)
_3
d--y-39
y-
(E')
4x
(i
4X/3
N
30
30
(c)
Case I-D
/eey-/'2O
/
jr
49
260
/20,p
2
0o
358,00
____
__
__
____
____
___
____
Calculale y
Fgruating
the statical moment
of -steel -and - concrete
3y +/80y +1Z4y-3 -.Z41=
y*a+ 594.6y
y
7a / I = 2 X /,
ooo=
2996
___
__48330
of ,teel
-28,evy
445
O0;6
= ,0 , is4
to that
0
WEIGH/T OF CA.3OIV
CHAAN8ae/t.
A
A
COAXC)T
B
4
PA N
d~~X/X/279289
,4cd /X/8=28a
24Xfr
4Are-d
StCC77ION
,SiCdes
Cross
/1740
02 i&=/d/ M
A1
.178*~2s9,r~z/a,80 w
2Z
7,m2oe(2xr Z)'so2 7J-, rd
,zz(. xr xF//4J)(/rO)V
W
7 f0
S5ECT/CoA' z3
7iita
xY.r-xib.)0/6e
4t,
6.f
PCW7O
0
SECT/IOA/ A -f-S
s4
8=
7T07*,lL.
2O~roo#
,,p 7 4 ~ 9 ii
~ ~2#O ~
7
wz.
2XY2?44
#
4664jOO
;X4,4-00 -* ,
taA
8 Y27..A
~__
__
V
1
I-
.
'
2.r. 'I
2>v'-. /4'-
I
I
-I
no
tmtmm
9j4
28'
WEIGHT
OF
SECTION
WOODEN
5UPERSTRUCTURE
A
t/g.
Vo/,me
No,
(47X22Xf)
Plan
Wa les
(47X/)
/5
24 (zz x r)
Stvds
ims/'(28sX i
Csj
Other 4cecessaries
InOS
WeigAt,
4r45-
/ ro0
J/#ova#
4JIf-
//90
18080
7;
ste n/oN
SEC TION A
P/an|
Wa les
StodS
Crdo
Bs.
i5
(59 X2X g)
(j9 x)
ZZ (2z x4
( 9 .)
4l.44
Toa4
1
/0
Othep accessoric3
Dr
7f'
JOro
l 1 - t 467
SECTION
TTAL
A-+B
62,8o
+-3;3orO
5ECTION (zzr: hisA)
=
279600 *
A
/0.
SHEAR AND MOMENT
A c tua/
Loading
0570
CURVE5.
CASE I-A.
Ate
&48
7040
Caison alone.
trueciare.
/Supers
3Aear
CAdmber a/one
Mh
4f
/omeni
=
=
I/874OX7= OJI2oA
2o4iQ
9if-,45400
7
00070
p5,erstrueture
An -2x6treoX7=
794040
NAl = 2xrror(wJe)#344 000
642tjao
607q 000
Lad
Considered
Uniform.
J2 7. 00
27;9600
CAamAer alone
Ma=327Yd0sx
Metnenet
=
ji/40:sA
AJuperstruetore
ANm =2X3.goXJ 424@W0
trror
(with
4,140-40
uniform
deadd)
-
.' In fgurming deflecions vse uniform load,
Cham her
IS4-e 1.
CA amr--- Juaperstractiure
"
Lsago oe
or
SA edJ46900
000
CA amber alo'ne
A/,4av //&74,OX7t &TyOot
--
204~~~7,
&t0/6*-24,e00
.t /#cim in
-fperi trvc tur-e
Xa= m Z;( 5*7,4X
Aote
Chamb~er a lone
p -. ers 1.*uc tore
7=
Af.
Ov ". all40p~4
zo(5204600 #
-80400
W.6 -2 xr7oj-o
x.54 S-T 3400ooa
-2 X82,doox,/8=/,94qaoo
+
,ON
'140 000
Cham7,be,I. L96 Oa A
CA a mhe,- * J Svpers tr-vc tvq-e
2'. 3.T0 0
ETERIJNATION OF LOADS.
Before it is possible to determine the fibre
stresses due to bending, it is necessary to ascertain
what part of the weight of the wooden superstructure is
carried by the caisson chamber. It is evident that the
caisson will not take the full weight, especially as the
superstructure is water tight, and necessarily must be
made very stout. Obviously it has some degree of stiffness itself, and will help carry part of its own weight.
To find what part this is, is a difficult Phing.
Any method will be more or less approximate,
but it is better than making an arbitrary guess.
The method which I will use is as follows.
Find the deflection of the caisson chamber and superstructure separately and under there own weights. The
ratio between the two, will give some idea of the % of
the load of the superstructure, which the caisson must
carry. To find either of these deflections accurately
would be impossible for such a complicated section.
Inasmuch as the deflection theory for concrete beams is
from 5 to 30 % in error, it seems justifiable to depart
from it for such a complicated problem as this. I am
therefore going to keep to my original ass ution of no
tention in the concrete and also use equivalent areas
of concrete for the steel. This reduces then, to a
homogenious beam 'f uniform cross section and will be
treated by the ordinary detlection formulas for each
case.
Given in Vol.2
General formula. EIv=Jidx.afJMdx.dx. Fuller and
Johnson.
In considering the superstructure it seems
that the studding and cross beams will add no material
amount to the stiffness of the structure, as they are
merely fastened to-gether at right angles to each other.
The plank itself is what gives it its stiffnessit being
very firmly built and water tight. The question comes up
as to how deep a section to take acting independently.
If we take a quarter of one section or 5.5feet, we have
good proportions for ordinary beams of the same length.
This method gives deflections for the caisson
chamber alone as follows.
Case 1-A..... 1/2"
Case 1-B..... 0'
These cannot be taken as exact, but we can probably say
that for case 1-A, the deflection is something under an
inch, and for case 1-B, it is under a 1/2 inch.
I
*
/I.
The deflection of the superstructure taking
a section 5.5 ft. high is as followos
Case 1-A.....1.3"
Case 1-B.....O"
Taking a whole section of 22 feet in height as acting
to-gether the deflection for case 1-A is only .162"
As this is so small it seems that the first is nearer
right. We can infer from these results that the deflection for case 1-A is under 2", and for case 1-B
from 1/2" to 1".
It is seen that very little confidence can be
placed in these results. However it seems obvious that
the tendency for the superstructure to deflect is greater than that of the caisson itself. From the results
it would seem that the caisson carries about 1/2 the
weight of the superstructure in case 1-A and,perhaps,
a little
less in case 1-B.
Recognizing the fact that this is only one
step better than an arbitrary guess, I am going to
assume that the caisson takes 1/2 the load of the superstructure as being the nearest to the correct one that
we can make. In order to make a more complete investigation, the fibre stresses for three different cases
will be calculated. The first case using only the weight
of the caisson itself, then using the full weight of the
superstructure, and lastly using the assumption of 1/2
the weight of the superstructure. The first two give..
the maximum and minimum values possible, and the third
gives a value between these which is probably more
correct than either.
The resulting fibre stresses indicate that
case 1- A is very highly stressed. The minimum condition
is not unsafe, but the condition when 1/2 the weight of
the superstructure is considered gives-stresses beyond
the elastic limit of both steel and concrete, and the.
maximum condition is decidedly unsafe. If tais case
of balancing in the center had ever occured (which
actually did not, and probably would not in any other
case) it seems certain that serious results would have
followed. We could allow stresses up to the elastic limit
for such an extreme case but it is hardly safe to go
far beyond this.
For case 1w-B, even the maximum posible
stresses are under the working stresses for both steel
and concrete by a wide margin. The probable stresses
are less than this. If this case actually,happened it
seems certain that the caisson is absolutly safe as far
as bending is concerned.
Following are the calculations resulting in
the determination of the fibre stresses.
47
O~PLECT/ON Of' cA1,5 ON
LOFF? ITJ5
OW4N
WEIGH-T
CA45E I-A870
"r-r
1hi3 caae
d erived( 1n k6Iff
Vi---
PvllerandS John,5on
CX 2 , 006OOOj
77,15
040
CA5E 4:
Eli
-4;,T/jzOmx */04,e7xt- /~fX4I?
EIS&W
*,
4br+3J4770/ - JA70X4 +
x
C, 4/40/2
CA
o(/8d
Mx~?
'
+fz/O9Oag4ood2J#08O/-40d
-q
ly
a, ado-864'#,oof
i
I
/5.
DEFLECT/ON OP 3VPER3TRLCTVRE.
ir'S OWN WEIG/VT
UNDER
lDIII
CASE I-A
/.37;$
T= 2X4X(X2=
p/ coo
12
A'-= /, 6,00,000
Wy
= 3j-e
=3xA93/
W
E
ov
3J;0 (x(375"x/2)
-
8x
'4
,040O/9Xa
s#'
lx
2
X4X(
22
4"~
X2)t= /2,2 0aoa
12
W = 376X 7450
2:79;Ovotx
V= .-
279,040
(37~xIZ)
I000
ox / G0a0OX /2,20
i:980,
CA 5Z1-8
2oeoto+ 6280Ox-
-
EIr
d
+ 4/,400xz /47* +* C,
g5ox+.8Ogc37x4 + CX + C1
20q00o 1
/
-
=0O
=
S0c
C, = ,oqugoo - /43J0f/4-//
lr=4n
ax
Ef.r
=-- 2.T00/+4 72Y('- 2
2,6
J4+7/,-
O 3,4
O+24;O0 * JC0*
cz =o
+rg00if 5--/76/'+9to4
o
=-26:TOg3en
Et-
/9/
- ..
000
oc
/,beg0coX/2
. .....
....
..............
-/6a00
2(aooo0,OOOA/x
-
-
006r
= /&800
-
~
11
de
/6.
F bre
f3reasez,
41
A=k
* fj'=
(d-~J'~r
2~
A~l(~s-3)/J~~
I
CA.3E I-A
chamber alone
4 /40OX#44X/2,
3 77.4 oo
fJ=4, /490
,60%j
Kx4/X/2XRf
#/3O g
3,774000
chamber + supersfrvetwre.
6
-RAtio = //31400
f , /4400
fc
= r'9
Ab~ass
=
&5 X /2,140
cAfj
E
__244___7_
s upcrtratv fvre
e e
Ratiow b,/44uo+2,62oa
4
#
fe = ,43x&60
fs
= /,4X340o0
fs' = /
2Iwo
C A3Et /--5
chamber d/one,
=/,9oo4
Ae
3664
coo000 A.__
940 42.4X/2 x,
f
000
564
33240S
ck&AdIA i + superstye tfre
7/
Rafio =j72 4 00, fe = 7/X230
0f
Z Z7/ X 6
fs
7/ X 33240
fs' =
cAamber +
Ratio
/92.7ea
A4 sperstructfre
=/,3X
.9at7
/ -94 0o
fc
fs' =
As
/
X 2 O
3
3K
AT~
-X
3620
330
JT
h/D 04
-
1
P
i
___________________________________________________________
17
.3TRE356E.3
H1/EARING
The shearing stresses cannot be calculated ac.curately by the formula vr. V because this assumes that
all the tension steel is c ncentrated at it's center of
gravity. This is not the case and since it is distributed
over the section, the shear will vary. The value of b
is not constant either which makes variations. We will
go back to the homogenious beam theary using equivalent
areas.
V=
Derived in"Vol
'.
Fuller and Johnson.)
Q= Statical moment of the area obove the section
about the neutral axis.
S Total shear on the aes Men, cross section.
b Width at the section.
I= Moment of inertia.
One point of maximum shear is of course at the
fneutral axis. Where this does not come at the narrowest
section, as in case I-A, it is necessary to investigate
another section as XX.
Case /-A (at netiral axia)
Z(2973T-27j6444)-J{20
camioi alone ."197x32,3Td
-=r04
774#
-: X.Y
-,1-
t.j
i'
47z77
d'"
3
d
_
(sea tio,
S-
j
-ZA
92
.dd/P7462/00
=009.
rX)
ood -t0,y
/440 - I.y
202A-/roy
2/4/74
4
. 0412X 32);304 =
caissen? aer
*
=z/4/7
X
Z=377
-4g{5
= /
,oo/7
77 4
A-
Super .9d0/z7r6,4
*Z
,e62
46/s
97r
= Ad]4O
4
0eaA
Case ,-z9 (at neutr /dax5)
34200
b= A X,
=/
Tw .§44
Oo -2
"
ca9~o
issen~a/one
S
.000 78 2.8Zoa
suprY .
WA
0oo07dX
574200
,ooorax
007X2S4x0=
/
=oo
|,/9
226
=14&
While some of the stresses ruh over the present
allowable of the Joint Committee of 120#/sq. in., they are
not excessive in view of the fact that it has been debated
2 40jf/sq.in.
is not'"safe f or a working stress. In this extreme case therefore it seems perfectly safe in shear even
if the stresses are rather high.
Wv
~a
VERTICAL RODS WHICH IN THIS CASE ACT AS STIRRUPS.
These are 1" square rod.a, 6" c. to c.
As before we will keep to the assumption of no
sion in the concrete.
ket' Pz
tension in
ren-
stirrapoa
3 x dist. aptcrt
b
width of bedm
tf
rrotegt par-
P='vb3
Then
and
Civen in
0,afs As
aut P
. v(abI
.'
~//ep-and
.45A
fs
.( A,
C&se I-A.
{s ect xX)
,vXIzx6
Qr
&K
caisson aone
a * food.-.
i
pE
f=O/(20-
/
,-xyda
f, =7~X9=
7S
Case1-8 (sect N-4)
. vxI2 X
f5 ,XxXdz
4 =_ gr
caisson alone
* super
U
-)t
a
4, w4X
f~=to
/42
=.ZQ7
X2_9/ -__
fs POX.224
=L(S_
These values are the maximum values of the
&tress in the verticals and are seen to be within safe
values. Of course in positions where v is small, the
atress in the verticals willeless, and therefore could
have been spaced farther apart, as far as their action
as stirrups are concerned. However as they were put in pri
primarily to reinforce the cutting edge as a cantilever,
their use as stirrups in this case is only secondary in
importance. The other case will limit them and is treated
elsewhere.
1.9
BOND
J 7RE3.3.
As in the case of shear, the ordinary bond formula
is not correct. unless. modified, because all
u
the tension steel' is not concentrated at a point.
We will modify it to correspond to the shear formula
S'/4-w6
A/ow
s SStitv te for Lr, if>
9
a
S-= Xb
SQ
4Z
,61
.
Za=Zperimeter of rods outseide section.
Q0=Statical M of those rods about N. A.
S =Total shear.
As in the case of a rectangular beam, the greatiest
bond stress 1s in the tension steel and, since the most
stressed rode are the farthest from the neutral axis,
these will have the greatest fibre stress.
C4se /,4
Q= /20X /oY3;t-= /2,40
7'
e =418 =X2
Z ~ .! 77045'av7
12,440a
-
.00/033
"S X .7 7 40
caisso ai/ne
I
,
+)j,
?2?'/A =
.
OOpr
IO3Xt9d
A
j2i7
t0
2
=
S7
-48
.On/4'3/oo
Case I-B.
Q=
fOQ/2.5~=
(/.'V
=7-,44 ,0000
CI3Son
dIfloe ,o/
r, * A10 e,
Ii
IDZ
oopr-4
X.322?34
,a0/0fX467/O0 =
..
4
.*4
z
tr5s
All these values are below the working boni
of a0,/sq.in. for plain rods recommended by the Joint
Committee. It seems that the caisson is safe as far as
bond stress is concerned.
I
_J
11
or RiE5ULT3.
SUMMA/RY
J T/
Z333
IN Lo. PE?
sQ. //V,
CA S4E /-A
F'
F
A.
L Oad
v (C.k)
44.V
/Z,/6o
OaJsi*J Ja4ae 46(0 3000
/rp0 .rpJre 244dd
, + sp~er;
42410 /7T3
'0 /3'
e
1 +4$
Load5
COWDw alone
S osper
-+
A
2y3O
92
CASE
-6
Fs
F'
v6MA.)
8104
Y320
6.700
JIaI 29/
40
29
3.94
3/0
//
/6QdO
vtxX)
2470
3AO
293
ve)-t. Iods
A-
34
4Z
40
/200
2 JDO
/ 50O
ert. rods
9720
4
/62
MA.
CASEI-iB
-
-
#.1~-
-'
I
/
N.4.
-
CA W I-A
7
-
I
-
I
I
I
/73400
'T
E
'i:.
|
mR
33
DjAGRAMA.
.
:
-.
:
.
.
2/
CASE 2.
The purpose of this investigation is to make an
analysis of the probable stresses in the working chamber,
when the cutting edge is at elevation 25. This was the
elevation to which the structure was sunk, and according,
ly, the stresses under possible conditions at this elevation
will cause the maximum fibre stresses.
The first condition is that due to the sudden
dropping of th pressure in the working chamber, which
acts as a blo n the top, causing the structure to sink
against the f iction on the sides of the caisson. This
method as well as loading the structure is used in practice
to overcome frictional resistance.
However, in case the air compressors should cease
to be in operation, or in case the material through which
the structure was being sunk should be of such a consistenby that it caused a blow out, so that the compressor
would not be able to furnish enough ai:b, then the structure
would be subjected momentarily to a pressure almost as high
as full hydrostatic pressure.
To facilitate the investigation under these
conditions, the analysis will be divided into three parts
as follows,
1. The calculation of the fibre stresses in the horizontal reinforcing, when the pressure is dropped
so as to allow the caisson to sink.
2. The calculation of the fibre stresses in the vertical reinforcing under the same conditions as in 1.
and also the stresses under the condition of a
blow out.
3.dAn investigation of the roof.
In the first part , the slope deflection method
shown in Section 10 of Hool and Johnson's "Handbook on
Reinforced Concrete", will be used to derive the necessary
formulas for the moments at the corners and connections
of the cross bracing.
In patt 2 the ordinary formula for the figuring
of a cantilever beam will be used, while in part 3 the
slab and beam formulas will be used.
/
r
-
-
-
-
OOI/o*
-
-
-
-
-
-1-
ce
6
8
9'/
is
Deflectiona
about B3.
-4/
7)~
SZ
A
le
+_
g
.t
.1af
E5,z
3 is
6
~ciu~
I
.~o ~ ~ ~oz.
.
6EZ
E[-7'
7A
v /
.3
-~
XfAJ
a~LZ'
Y2/
Difference in slope between the two tanxents at
equal to the area of the moenerve.
(e~-o~)
=
mN
8 .I
z ez
AZ
zez
i/4Mi6#
+2
Jx
,f2
6c
A and
2zz
from equations I and 2.
Eliminating
equation 1 by 3 and equation 2 by 2-.
11(,-a,
[M,,
0a
Multiplyin6
4
7t"
Subtracting equation 4 fromn 3.
f-7
2
2
O~f
by
Multiply both sides of the equation by 2 and divide
49
M
In
74
a
.
n
Ez
= 2/(E(zO+e-se)7+ j
the saue nannor
E-
/-
6
Applyint, this tua the end section
ABC and assutaing theC two the tvo
corners 2 and 3 to be fixed.
The deorrmation a ases~aed to be
A C
as&shown in tne ske~ ye
Then the angles
h lueoRisequl
proxiately to the deormtion
C
due
th
appii
o
trally applied lod of wl/2
4of
Then:..cu-
IZX;'Z3
7
Z 4X 56
variable thIckness of te caisson wall.
X
Zo equivalent area of concrete for two one inch square
rode when n 15.
p
Deformation:
(z4X+56)
(24x+-56.)E
Substituting in equations 5 and 6
~ZE413
-1
S(-3
) -. /*
*7
4X4 f56
/Z X
7.
/2
x
Ora
/Z
26
/
If, however we assume that the corners B and C are
not fixed and that relatively they hold the same position
after the load is applied the value of R is zero
Then
and the deformation will be as shown in the
accompanying sketch.
7
Then:
a -
/2
la"
also
Shear at A and B.
/*
/2
i w/2
2
_
12
.8
L
..............
. ..
.......................
. ...............
j
N/ 0
na7pee3
or
e
Pei
C
.8C
0
10
/
/7'
/
Since in equation 9 the ament at A is the saae as
that for a beam fixed at the ends, we can assume that
A and F are fixed, and concider the structure shown by the
full lines.
It
is
also assumed that the ends G H I J are
fixed.
Then the equations for the moment at each end of the
members can be written:
Mo
6
m
Ny
a
zE,
(,+-
= zR,
a>.2
aG)
G,+, 742
)
7 Me2I'E~
2,+,3
e,+
x ,(Z
MA
BC
MIT
Mp
M
-0
zE4
Me, -9~
,
~ O'
+-3IV,)
(9n3
Z
EX
z=209
29/G)
)+' /2
.Z
oIents at iJny joint equal zero
Since the sum of the
"
Als"
O
Le
=
0
From which we Set:
G(4,
4k,4,+kG-k
19a
.
(6x, 4ks
9,
/
)+zt2* , sz R,2-*,r>&
0, (k
k,
- A- 1/
c
7%K)+z
ks
74,44
c2
kZ 9,-6
7 Q/ 0
coI (
A0 - 6 AG ' al=
of
Also the sum of the moments at the top ard bttm
slazar multipIl
. by the height.
columns are etqual to the
86
C
D/
66
YU.0
But
/
2
4X,'4Agf4 ZXk
2K
.3
2
4
5
6K+4X
-
+-z4no'-o
MaConsA
67
K
K/r>
/2
'/eayE.-
/2
Z-k
KZ
2K
z
/WO
/C
/
4K
ZX-5_Z
4/g4W t,4k -6
/
-24r>
Using these general equations it is possible to solve
'tre'e at
and the moments and fib'e
izna
4 ections of the struc-
for the values of
the various pointo
The same type of general equations as are shown on
can be derived for the case when the points B and
page
E-are assumed to be fixed. Figure
I
I
2
/
I
2
-I----,/
AZ
K,
/
/
N
L~
/1~74~
lop
8
+ ,
/
~1/
I
I
a /8 zC.
= (2
/
1-
~2{2~JO~r3~e)
.(ZOc.4 OOL cv-e
t.Z
=zx,
A7DC ~2EX
N,,R,
p1 ,e
/2
(2O9,,-yQ)
w2EKJ
29D+9,)
-jtZ
A~wix
Also*
If,+
z Ek, (
4zx, (z 0,
,
-0
7,,-C
,,-a
,1=o0
zEX
4K z,+,3)zE
=6--2
z,9-
0
.........
1
2
2i'WA3
fVl 5
5 e c /1 *0
r."
MeMoe/6
464F
BC CD
I
o~'
D
B6C/D/*1-,
5c/1*
.
5.
228
55>Z6
-6/(3,
447 *
z5lz
,,/7c he.5
4412
ZA4X
Covo03/
.zI
5 I
cof7s/a
&
52
/66
/Z258.96
6.77
/66
216.4
1162
.304
575-2
31L
F89 .0Qo.52q
.5ec/,or, /Alcc cro-ll>-ac1?,
3o4
*Ot-eco5eaa
.4roae"
5 75.2zI
6-9 1.oo-2.9
I/.3c
e /L
Pa,?e4d~ ize
0aI0,oo one/boc.
Q4 o',A OsecA 'o.'j:.
-
the
te~i
der'i~the
lw
uaitreatl
Before cl
horzotalcet~;, i
pressLare on the cilsson.
.i .
u n~mryto
/3/ro
7.
-37
c~n~7Z
Area of-" VoIo
1-.7t.94
"9'
'Fle Y.Ot,
/30
3010
-17Ar
~I
v/e-
Li plac- ,31,, e: er in wtr
I
on
O/Q 4
Z4x
6 7 rec7 0/' sw'/ace
6 7 3$QmZIy
6 01//om.
31v ale /0~ OC7.rl C/ocv CAC
3~do
.77A5
-9 4 - zx
.
ii ., /( "12 550 -#4
a5.9.4 x55o
~ /0
'C/
472 67o#i
n
C CZ"Crl0/,
p"/Oe1
so
4726~7o
7o-lal I/*oae/.
76053,9ZO
wve.,9 A
A'r'17-e
cc
(j
/Ae
COC':t*
Wvez7
otwe4
A/ o~
9
C012AtCZ /00/?
c/r,~,
~5415oo
22"5eimon Odewooa/es-7 3cvoePa al oirn
Z7~A 4oo&
7
i6.14eo 0,0/ cve/ 124/ 0//'O0O/' ad /edW a Ac4rZ445X4ZGX-9S-W
('' S. -)
/OU.0C,4i;1.
CV'
252d/~/~O
~4~/weig/
0 1A cc/.
-,Z
Xq3.4)
0%//0 o
-1e
4
.h IYo
10r
3/i, 3cc
eV/
3~ZZJe7
o~
/po/ur
G.94Z74
34
I
From to difference in weight and displacement it
would seem that the caisson would have a tendency to r
is
in
the actual case was not true, for in placing the
pair in alignment enou
weight was added to
tracture
ie
at high tide so that the cutting ecies were arely off th
bottomn and when ta
proper location.
ime wen
p ie
duwn t.
na
n
It
It is safe to assume thrfore
that t 1 e only drop in
pressure needed is that necessary to over come a frictional resistance of 472,670 .
To arrive at a rational estimate of the ressure
drop necessary to sink tho structure, concider the amount
of water that should be allowed to enter the c"isson to
make it sink under its own weight.
Pneozi re
a/b o
472
G 706
the working chamber.
,Theoretically water should fill
2'/ev.
C&6/er' w oa/Y! tv'e /o
PpeavcJ('c afsec
W
af
C7/
N:o/er-
cl7
o Eom&er 7(52o v
wor^CA 2
w
=70
2.
. 7375
B=
.32
oa 47 (.5z--zG)X
2.5 -375#/sy./Ed
?.d
4.eA.
A difference in pressure of 375 # per sq.
equal to a drop in -age pressure of about 2.6
ft.
is
# which is
about that used in actuaal practice.
ubstitutin
we can sol ve f~
....
.....
....
..
......
these values in
the equations for
thnbending moments and fibre stresses.
....
..
............
..........
.............
11
t 1hus in to tabuiur f orm so wn on pag ZG
o
t-.
The vrluc of a will b
of w at
zero inice there can not be any horizontal movement of the
structure when it is symetrically loaded.
Subs ti~
with the 'v
Values of 9 for section A.
L9a
_____on
5.72
/3.:5*4
3
/A.-54
£1.72
S
2
I
e
is4
32
2.6
54.7 roz
o4.
-.
/
44.556
/
4
-4.2/7
/
/
.3
/e
4.18
-2.37
+'.o oOO 4
4.55$
/
4,928d
/
/
.Za/
4
/
4.18
4 - >C315
-oo4
SuLstitutinG
9 in the first
tion, however,
zero.
2000:z
cs
Ioc2.4
6
Yales oIG
62Z5
/3.54
13.72
13.54
-.
Cons3/anl
--.
4
5,
$
-o0o1Z
.00
-- ocooxi
Aolr
+,o 004/6a
Aoo4-
In the e 1ution
on page 45 te values
fo
assumption can be calculated,.
An inspecshow thmt bh 9 at C and D are equl to
The vjal e of the m ets for the several points can
can now be found for sections A and
arid are tabalated
with the fibre stresses on page.3Z
g5
/
Z
3
4
I
4I7Z
/3. S4
-. o 377
r35
61/.72
/3. 54
/3. f4
5<,.7'Z
4.555
/
/
f4
/
55
3,
+. oo 37
'.ooooCG
.238
/
Coa 3 /cO$
s
13.54
.7
/3.54
/
Go
O4
Ga
6qgoa~/on
/
-oaoz 7
48
A-000
2'/Q4-1
/
3'
-ooo/57
.237
4 55
/
/
'-a4 328
4'
4olue o 0
/N
6'
foooozj-:oooo
422
37
3i 2o
320
2.9z2o0
a3o
/2500
z 4 _34r 0
z35 2/1Q
So
295
27
Soo o
7.3 3G
397
S9Zo
2/ I00
422
31 20
12 900
51
7.96
7oo
54o
3600
3370
2 Goo
2600
G6
540
7oo
75
790
3600
S06 oo
.o675
5930
D3,38 /:5S1
2or,7
P
V.00007
D 4 340
/3,ooo
C,
f.ooa76
en/
3 5.ooo
/7 36
8
8
4./8
o oo
fAootoo/G
C
CO
-.
93.95
:ooo7
--.000 067
.Z31
/
c
0
?.3Goo
75
6e
6/
3370
The moen
at A witt
will not b~e f'i4ured eInec
hor
uL
e a
mtion that B nde
ta
the moments at the other pont
caees less than
0..0, i all
3
/
5.4C.
IfoI
A6
6q
6
55
/,-
/2 X +38
qB
E
omen'
/35,6o5
425
comnp
3/3o
38'7
72
Lntiria
.6$Zo
3800
5her,
Tae corner A will have the :aaxi(mu
invetisat~e t11at secio.G
at we shll
<w/
~onuula U
.3ec. OPA
"2
.~7 5X/9.~Z
2
325
.5525
/2 ~ /0.4.3
4A10.43
.Yec.
88
G .x /3.4.
2
/ op- 2 776
~06
GOG
GdOG7
I.
i ,:ac~i~cerwt
ch~rberone foot wl1 d
a-wswnend t.3 be
th ctyoi
C
C/
c
.1
Fo~t/Y 0/c2 Ad-m
//oo/ q' Yo0k>n3on
L
L7,aeer3//&B
Coi-cle
FWS e4 ~zPay
-I7-=o
34
Akjco AVO 4oyo// ?/C eyuiv-
Y/n
c/e
=h735
0 44
2X65611/
C
.2/GX.934XIZ
4/
G7.O
-.
5leqrt
34"X-.9567,
-a6
7
/5A~6X2G5j
-o
34e."
Me rb, qC al
laooe -7Z2
c 0 mo.a
o n o1 o. ( ' a
/e~
/ 1?
caip
Aa.,e
/'9omenA
'~~
2/00
A2 .9.34 x 3
Th c)lio
vestI~~~atc
o
s~x
2
~~ j 0/ CO3
o A
2/00 -#
A
the
~
O
>i~v!
I jcJu
6tos uiide t L.ctdt~orfll~abo
A~
.5
N/ev.
of co///n
5e
eo07 e
/00
Ppe ssure o/-32 -4-250
P7
Fre
a40e /0
oafrm' /oao/ 0f 41250
s/resses ae
/o
/3
7
//G,
57
of' /06 257
/06 Z57ZX /Z X
G X94zz/2
XC
X3 44x. .95G7
/000
- 54 Soo
Yer/c
,/t
VZ. 75o-/4,35o=
in resist
retLsio
corr-p.
o/
stress es
3A..
c orrop r'oo
/5400#
oo'~o
Ip"-hecEzra:_Ireabv
In the investigallon o~ tone stresses in the root it
will be concidered that ':m six inch slab is ofec tive
in resisting the upward pressure, and the concrete above
act onl; as de~a veicht.
the
However-, vin
t- e
wrn in the;:working is reccd,
concete atove the slab will be assumed to be self austaining.
It was shown on page tha6 the difference in the weight o f
the structure and the displaceneent was 7,884,00c. 6,947,150
per.
or 936-850 1 which was bullt up in sol
Thisacting
ivin/
evation 45.
ta
over an area of 816 sq./ft.
fills the pter solid to about el-
Actually however the concrete was filled to about elevation 57.
e2yat~1v,
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CASE 3,
This case takes into account unequal bearing.
If we take the case of a boulder obstructing one edge,
we will have the worst. case. Undoubtedly, if this -boulder
were considered as located either at the extreme end or
in the center of one side, we have the worst condition.
Die 4
tWag
Z;
Diag 3
These diagrams illustrate the results due to
this cause. Owing to the fact that the caisson is supported laterally on all sides by the material through which
it has penttrated, it seems almost impossiblu for there
to be any tilting of the structure. This means that the
assumption is made that vertical lines remain vertical
after deformation. This gives us the case of a fixedended beam. In diagram 1. we have a fixed-ended beam with
uniform load, and the supports on different levels. In
diagram 2. we have the same but with the end supports
on the same level, and an extra support in the canter
on a higher level.In the latter case we have bending in
a direction perpendicular to the paper also if the stone
comes only under one edge.
This particular case is not very serious if we
werely consider the boulder as having a vertical reaction.
When sunk as deep as this, the chamber including a four
foot roof, as well as the pier itself and three sections
of the superstructure, will act as the beam. Moreover,
the friction on the sides &f the caisson is, according to.
reliable data, about 600#/sq.tt. and would thus support
a large part of the vertical load. I beleive then that
merely taking a vertical reaction of the boulder will
not give high stresses. In practice too, it would be a
simple matter to remove a boulder of this type and reduce
it's effect to nothing.
This case becomes serious, howevmr, if the
boulder or ledge has a slanting surface and has a tendency to crush in the cutting edge. It is this horizontal
concentrated thrust which is dangerous. Diagram 3
illustrates. It would be a very difficult thing to remove
an obstruction of this type, because it would be
necessary to get behind the cutting edge, and this is
almost impossible.
This last case will be calculated,thenas it
is the worst possible condition.
Fro,~,
CaseZZ
Case ff
/~j.
~
we have
we
,F
=
e
c =
/1-;' (b
c,,da,. <.9?W7'
7.Y4
odd
.2/( X;
Al = rA'X7X ;/.
,
2AA
,z'
rf_
. aaorI.Af~l= .a651
x- q934
X3w
?-AF,4/
Y)~. 1
lYf-x
('d
t7
2%':'
IIl
d
b
93'4 X /-
A/ax
tpCC
ZX
-x
c-#it
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x 4
144ax),= ---oxt.zo
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=
-16=
Z .4XZ
14,0O
X.?Y
/2
-
- IF
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=4Jre-o A
It.4e tensjen streel limnits and
7 TAjs
is
can centfraited /Odid
t~ze m8.zimom
doci
7pof talVe into dac,007t' rAe horizobtal itel
whicA would vndoobtedly r-arry 30ome of the load.
741.;j, ~A owi
....
..
....
..
tha f
0-
00
WOODEN SUPERSTRUCTURE ABOVE CHAMBER.
While the wooden superstructure is entirely
separate from the concrete caisson chamber as far as
design is concerned, it seems worthwhile to investigate
it, in order to complete the analysis. It is readily
seen that it is a very important part of the caisson as
a whole and would have to be figured carefully. It can
be figured to a greater degree of accuracy than the
chamber itself.
There is some uncertainty as to just how much
bracing was put in. The main braces are shown in PLATE B
at the first of the thesis. There were however a number
of auxiliary braces placed after part of the pier was
built, which braced agr.st the pier. The number of these
is uncertain and their* f uncertain depending on how
tight they were placed. They would certainly add to the
strength and cut down the stress in the braces. We will
figure it as if only the main braces were in place and
modify the results to take into account the auxiliary
braces. The load will be taken as full hydrostatic
pressure as there is a possibility that this may occur.
The following calculations show the stresses
in the plank, studs, longitudinal bracing, and cross
bracing. If we take 1300#/sq.in. fibre stress and 120#/sq
in. longitudinal shear as the safe working stresses we
can compare the results. The studs and plank are within
safe values with the exception of a high shear stress in
the studd. The braces, however, are decidedly unsafe
if the effect of the auxilliary braces is omited. We must
therefore assume that enough braces were added to reduce
the high stress in the main braces to safe values.
We can therefore conclude,that with sufficient
extra bracqing,that the superstructure is safe.
4Z
The
of spans and,
a 12" lap, it
a 1
plank is a continuous beam over a number
as it is securely fastned at the ends with
can be considered as fixed at the ends,
*
12."
I'
2'
2.V
'
2'
2
/yo'rostat i c presspre
P= -"O
1=
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=
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The studs are vertical, continuous
beams with five spans (1 section).
As they are vertical they are subjected to a uniformly varying load as
the hydrostatic pressure varies with
the depth. It will be close enough for
this calculation to take an average
load on each span.
The beam is solved by the use of
the three moment equati~n.
4F
A);
+4#x+A&y= -Zui-2mi.
A,2+
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-A 2u
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+, ZLAI .454M -/12w -112 wj
26.Ms -/2
..........
....
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a
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Lr
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f
4.53
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t.)
Afa
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43040 -4S.20
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74000/6
,~
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x/-*- 664i 4
r 7660 -74/S
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/niforn load= 4X4/20= /4460A
/4so AA
2
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4 1 i 141
,"
1141
4 4 4 it 411
9'
Kq4braces
q'
I
IMxA
f
are continuous beams and may be
These
cons idered as uniformly loaded, as the studs are only
two feet c. to c.
From Hool and Johnson "Concrete Eng. Handbook."
we have that the
/2 ,oooF?*=|/4 ###i.
ax A = - /0r x /648OX 9'
IX123, /72a
/2.
= .f2J0
/728
S
A- X /540eX-9= 8 4OAe'w
Ja
72x3 = 2/
69A0X2'6
/2 X/728
1''
"
0
Crosj Brace
9X4.4/A.
4 Leaad-
/44 000
*x- 722..
Acteal
(~AR.F.A.
1
F. //oo(/-,37= 7o 710
AlowaYe 4 =
if
//po~A
6
Aowever tAere is
Ma x allowa4le a- 2/ c
Sum maty
race in center
A. A E.A,
Pc
ri-a n r1
4sny' Dra ces.
Feorinv
963.
X4 Y
ae
F
-
/
d4
CONCLUSION.
Having calculated the stresses in this caisson
under the worst possible conditions that it would ever
be subjeeted to, we are now able to point out both the
strong and weak places in its construction, and suggest
improvments in the design.
Inasmuch as the stresses in nearly every case
which has been considered are below the elastic limit of
the material, and in view of the fact that these maximum
conditions in all probability would never occur, it seems
justifiable to say that the caisson is within safe limits.
In looking over the results, however, it is possible to
poimt out the good and bad features of the design. This
will be done for each case separately.
Case 1.
The results in this case seem to me to be very
satisfactory. In case 1-B the stresses are within safe
working values even under the absolute maximum condition.
Sn case 1-A the concrete and tension steel have rather
high stresses, but owing to the remote possibility oft
this case ever being realized and then only momentarily,
it would be justifiable to allow a higher stress.
Referring to the diagrams on page
it will be
seem that the stresses in the steel which comes between
the positions of the neutral axis in the two cases is very
small. It would seem that it would be better to have bunched
the rods at the top and bottom where thbir maximum strenghh
could be utilized. This point is further emphisized in
case 2, where the same conclusion is reached.
It is not possible to criticise the section of the
caisson which acts as a beam because the section is determined for an entirely different purpose, and this case
is not the limiting one.
CASE 2.
It is seen from this analysis that the fibre
stresses in the horizontal reinforcing due to the pressure
drop necessary to sink the caisson, are well on the safe
side and this in spite of the fact that no account was
taken of the resistance that would be offered by the vertical reinforcing.
In fact , the rods at section B and one or two
below this section might well have been omitted.
In the calculation of the stresses in the vertical
section, assumed to be under full hydrostatic pressure,
it was found that the stresses in both the steel and the
concrete are excessive, but here again, no account was
taken of the horizontal rods. The later will have a tendencyto resist the deformation and so help by carrying some of
the load. Even under this improbable condition of full
hydrostatic pressure, which could only last an instant, the
combined resistance of the horizontal and vertical reinforcing would probably be strong enough.
Under this condition, if we assume that the horizontal reinforcbmgnt takes the the pressure necessary to
sink the caisson, against friction, the stress in the
vertical section will be those shown on page3Y. However,
it is fair to assume that the horizontal reinforcement will
carry a greater percentage of the total load, thus reducing the stresses in the vertical sections.
The analysis of the sides of the working chamber
seem to indicate that even under the severesttconditions
it would not fail.
In the analysis of the roof, no real satisfactory
results were obtained when the six inch slab was considered.
Undoubtedly the mass of concrete above the slab resists
the upward pressure by punching shear or arch action.
Assuming that it resisted this upward pressure in shear
at the perimeter of the working chamber and allowing
40#/sq. in., the area necessary would be the total upward
pressure of 936850+5760 or 163/sq." ft. This gives a depth
of concrete of about 1.22 ft. with'the perimeter equal to
133 ft.It is on the safe side then as far as punching
shear is concerned. No analysis will be attempted on the
probable arch action, but it does seem to the authors,
that it would be possible to design an inverted arch above
the working chamber, which would have withstood the upward
pressure. This it seems,could have been done by placing
the curved rods in position before pouring the skeleton
caisson.
Case 3.
This case is extremely important as it one which
is often met with. It is not very easy to determine the
value of the load in this case, and it seemed better to
Find the maximum load which the caisson could stand concentrated on the cutting edge in this manner, and then
use our own judgement as to whether this was a value large
enough to be safe. While it is difficult to say what load
it ought to carry, the loads obtained seem to be as high
as it would seem possible to obtain actually. This load
is carried by both the cattilever and the horizontal reinforcing rods and would thus be even safer.
General Conclusion.
It seems to the authors that the value of this
analysis, is not simply the determination of the stresses
in this particular caisson, but rather an introduction to
the methods used in deep foundation work, and an insiht
into the difficulties encountered with the methods of
overcoming them. The fact that this particular caisson
was shown to be a safe structure is reatively unimportant,
but the conclusions which were obtained which would be of
use in designing another similar structure, are important.
This problem has necessitated the study of the
theory of concrete to an extensive degree, not only relative to foundation structures, but involving a number of
other subjects as well. As a study of the concrete theory
then, this thesis has been of great importance, even if
incidental to the main object.
. ...
...
..
.
.........
...
........
............
.....
...
CA J5E /-A
CA13501N 3UPPORTED IN
CENTER
CAOEI-8
CA1530N iUPPORTED AT
BOTH END3
FIG./
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ON SWAY
DURING
TWO WOR4T
LAVNCJING.
CAJEZ
TH1E
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T71 TWO CA3Z A5OVE
AN IN
ITACT5
aNetIrHICJ CON70IYON3
Wit
A,3 A
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