advertisement

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 [email protected] 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, ~~ndor~~~W 1~l rsuewth thte cutl ~~Z S~. J. Of C t 3,the upward preur -i Opposinic thi's the-re s /M,1t 4; ft. -Slab at60 4 Al c'- 72/.r /440~ Pci 6 -) 6A~Wy 04'. QOO/O ?Ysena ~ec/,oz~ 6?4~ I I - - ~ Iz 41 Tr=- ~ A? ~ ~ -~- A04i c074;U3l Lao c/4'~/e ~/If e~'a(~~le/eo ec~ ZocyS/efl/e~~ -- "/75 cot 2 ~8O 17d 7 /2 /AI. C p-.0o.9.37 A ~40O7 60176 Z 2A .o4XZZ ./ - 56S40C # :/5z Goo =3.9, R=625 5*6 0063.94 X /{6-6 44 .d =/2g. 5 ~i.17 97 5 ec-n o o/ al/56/ -L /o a srip oa I.O c - /2* p-.0// 2XY70-901 -4o7X.85GX/ZX/6 2x7000 16 7030/ 3 .85SGX425X.5S S 6$94. 56 x 425 12 x. .46 2.5 S6 X 4 ca7 OtS-oOfm - CC 68 27 pe7- -oo 4/3O435SX 8557 16, 076 /.9 6 .eeoz s /AtVru CC A, 0/2,30 /- /2Soo . The value of tP-e 'I~ bre strsesco at the enas will obviousl -r b :nuc and since those at D ar not on t4he sfe siac those at ' will not be figured. .36, TIt czse 'a 0ii conu JzC T1/OAJ 4e7 r c53. df >& 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 fK Xi7.(7y x 4 144ax),= ---oxt.zo , /,Or-w = -16= Z .4XZ 14,0O X.?Y /2 - - IF ,YR-0 =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= Af Z (utiderilu$ lY2OX 2 1_ _4X - Az S= = i 4/2OXZ 4 2 X=4/.2o' O 4/2 X24 - /z X44' JTtvd's 12- 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+ -o- -2 W.; -A 2u Af,+4s+ Af - -- 2e9AM, -65s -oo -6a0'00 / 7,'OOO 4000 -t fGA000 Af 4 0 r *-2* I -,z I~pZ000 Nx 6 X s'. F 2 **&~v 4N /d M4 /JAf4 +t6O6b-t+/'k =-3Jor -you', /AMz +J' M, =-7~6-22w 4.d-2 +, ZLAI .454M -/12w -112 wj 26.Ms -/2 .......... .... .. a - 21e *2w.--!* Lr +2'' f 4.53 stad s (a t.) Afa 4JA-/ A [email protected] =W 42 ... 4- 43040 -4S.20 ,x $652ao / 74000/6 ,~ = 768,V0004. /2 x/-*- 664i 4 r 7660 -74/S J. J 4 Qw /141. ./J20~4/YO r-= ie o = Ma - 7, .yX3= a _ y G9Xe64 /08 Iongilvdinal Braces /niforn load= 4X4/20= /4460A /4so AA 2 + 4 IA 4 J44I4~LLLLLLLLLAJ 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./ I 3CALE ! ' - 3UPPONrED rkHE CA133ON WAS ON SWAY DURING TWO WOR4T LAVNCJING. CAJEZ TH1E TO CONSIDR APtE SJUPPORTING WAYJ FAIL T( T71 TWO CA3Z A5OVE AN IN ITACT5 aNetIrHICJ CON70IYON3 Wit A,3 A 5 EAMP -3E PAGE 6-7 FOR DiTERMIN COMPUTATIONS TO NEZUTRAL AXI3_ caeNCT!*4-2 -4 M.RUIVALENT AREA- nli- AXAs OF CA /3O.50N 3 TEEL TEQUIVALENT AREA3 OF CONCgETE CT/ON CRO33,5E 5 LONGITUDINAL JHOWING CENTER AND /T'S "WN-No" ' en 00 0o 0 II 0~l- ' .! " A N PLATE B ~qAcr~Iz7Iz ~4~z 31 14 0 I4 $$$$* to" PL..A N ev 375 U' ATAQ UA RUCTU/?E LOCATION 3CALE RIVER ,BRIDGE !ON CA3ODAL BUILT &DEPrH 46./* 0110mo * 1 111,