Part One. Secondary Moments in Building Bents Due to Column Shortening. Part Two. Primary and Secondary Moments in a Building Bent Due to Foundation Settlement Citation White, Merit Penniman (1932) Part One. Secondary Moments in Building Bents Due to Column Shortening. Part Two. Primary and Secondary Moments in a Building Bent Due to Foundation Settlement. Master's thesis, California Institute of Technology. doi:10.7907/592c-ed45. https://resolver.caltech.edu/CaltechTHESIS:09172024-160304878 Abstract No abstract. Item Type: Thesis (Master's thesis) Subject Keywords: (Civil Engineering) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Civil Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1 June 1932 Record Number: CaltechTHESIS:09172024-160304878 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:09172024-160304878 DOI: 10.7907/592c-ed45 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16736 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 17 Sep 2024 18:16 Last Modified: 17 Sep 2024 18:16 Thesis Files PDF - Final Version See Usage Policy. 9MB PDF (Plate 1: Computations of Bent Moments Hardy Cross Method) - Final Version See Usage Policy. 2MB PDF (Plate 2: Computations of Bent Moments Hardy Cross Method) - Final Version See Usage Policy. 2MB PDF (Plate 3: Computations of Bent Moments Hardy Cross Method) - Final Version See Usage Policy. 2MB PDF (Plate 4: Computations of Bent Moments Hardy Cross Method) - Final Version See Usage Policy. 2MB Repository Staff Only: item control page

PART ONE: SECONDARY MOMENTS IN BUILDING BENTS DUE TO COLUMN SHORTENING PART TWO: PRIMARY .AND SECOND-4.RY MOM.':;NTS IN A BUILDING BENT DUE TO FOUNDATION SETTLEMENT MERIT P. WHITE Submitted as a Requirement for the Degree of Master of Science in Civil Engineering California Institute of Technology Pasadena, California June 1, 1932 PRELIMINARY: The Hardy Cross method of distributing fixed end moments was employed. The directional convention of moment sign is used, that is, a moment which rotates a joint clockwise is positive. On the summary sheets, all lengths are in inches (unless otherwise specified) and all moments are in inch-kips. The first part of this paper contains the conclusions ang the summarizing sheets for both parts of this thesis as well as a copy of a discussion on 'Wind-bracing in Buildings' submitted to the 'Proceedings of the American Society of Civil Engineers' by v. A. Vanoni and the writer. of computation sheets. The second part is made up PART ONE SECONDARY MOMENTS IN BUILDING BENTS DUE TO COLUMN SHORTENING UNDER HORIZONTAL LOADS The primary purpose of this investigation was to determine for a particular building bent the importance of secondary moments due to column shortening. It was also desired to obtain criteria for predicting the probable importance of such secondaries. The twenty-story, three-bay bent analyzed in Bulletin 80 of the University of Illinois was selected for investigation. In this investigation the foundations of the bent were assumed firm, no settlement was considered. Any such movement would tend to increase the secondary moments. The second part of this dis- cussion deals with the effect of settlement of alternate columns of a bent. Starting with no displacement at the foundations the cumulashorf,,.,;,,~ tive column~in each column at each floor was determined. The fixed end moments (bending moments which would result from differential vertical movement of the ends without rotation) of the girders were computed and distributed by the Hardy Cross Method. Summary sheet #1 outlines the procedure and gives all data necessary to obtain fixed end girder moments. All values are 2 obtained dir ectly or indirectly from Bulletin 80 (University of Illinois) . . "P~ is the column load in pounds, tension on one side of the center-line, compression on the other. Under !th" are given column lengths between floors, in inches. "A" is the column area in inches 2 4 I is the girder moment of inertia in inches. 2 2 L is the girder length squared in inches, while Mf is the fixed end girder moment in inch-pounds. Referring to the diagram on sum- I,nary-::sheet #2, t'd'Lds the cumulative differential column shortening at any story. "d t1 is the difference between the cumulative shorta ening (or lengthening) of columns "At1 and "B". cumulative shortening of column "B". pressions for !'~.~fa" and "Mrb" "d t1 is twice the b The computations give ex- in terms of I, L, P, h, and A. The fixed end moments thus obtained were applied to the gird~rs and distributed by the Hardy Cross Method, taking account of sidesway. Because of the proportions of the bent sidesway was con- siderable and seven cycles were required before satisfactory approach to equilibrium obtained. The final moments obtained were surprising to say the least, and at first very disappointing. In general their magnitudes were of the order of the probable accuracy of the computations. In other words the moments obtained were probably accurate within several hundred percent. The relatively largest final girder moment was only eleven percent of the original fixed end moment. w;..,J Summary sheets #2, #3, #4, give the primaryAmoments (not the fixed end moments) and the resulting secondary moments. · It must be remembered that these values are not exact and do no more than give 3 ( the order of magnitude of the secondary moments. The value of this investigation is not innnediately obvious. In fact it seems a waste of time to spend a term discovering that the secondary moments in a building bent are negligeable. V.A.Vanoni, making the same investigation on a different bent, found very large secondary moments, sometimes even greater than the original wind moments, and generally about half as great. Apparantly secondary moments are not always negligeable. The questton innnediately arises: Oan we know beforehand whether or not secondary moments require consideration? The present in- vestigation furnishes a clue to the answer. In the bent under discussion the colunm stresses on one side of the center-line of the bent are of the same sign, and the column stress and therefore the column shortening is roughly proportional to the distance from the center-line. Obviously when equilibrium is reached the bent will have moved a considerable distance sidewise but the girders will be nearly straight. In Mr. Vanoni's bent, on the other hand, the columns are alternately in tension and compression, so that the girders are subjected to considerable bending. Sidesway is small but column and girder moments are large. There is included a discussion submitted to the "Proceedings of the .American Society of Civil Engineers" by V.A. Vanoni and the writer. 4 This discussion includes a diagram summarizing the results obtained by Mr. Vanoni. Thesis. The reader is also referred to Mr. Vanoni's '· 619.3 /44- 7 3/9f I/ " // ti ,, /9 140 20 43 ,, " /3 2057 ,, /4 15'79 ,, !5 /163 " /6 80.9 " ,, 17 521 ,, 16 300 12 2595" II 9 4.56/ /0 3856 8 5273 7179 1 6 // ,, 83~9 h Ph ~ L APh p J30j I 116623 24/39 90/!,6 /363!,5 1855 12"6 27.57 ll3ZSS.,. 237 " H II 159 ld627:. 5"19 186116 , , , 2 185597 8 .37 8.3 3d"6 1931 ldffb5" 1.1'0 I/ 42.26 .3!J63 179797 342 4227 l7S83? 4-713 53, 79 5.507 171607 640 ,, S"ll 166100 827 7667 /1312I 64-24 7/62. /60283 /037 ,, ,, 72. 42 9069 /4545.,. 1.571 ,, 83.S.5 /067'1- 127297 2163 ,, 92.fS ;5228 1031"92, 2tV3 I/ JI A A h A COLUMN A Ph B ~- T!h I'Diff. J;P I a L' GtRD£P M1 iz~?J I 4411 3'57/JI 71842 3717 ,, 23 4 6 50732 10238'3 17.1'6 S46'!JD I I 1410 J ll)e, :5"7469 I lt!J-'f:,1" 769 .59347 IJJ207 ,, ,, ,, ,, 6029~ 1lf820 2t:5 60i134 12f9SI 130 292 60166 12543/ 4 /. t>O .527 5~87~ 124611 ,, 4,4,39 I I 09 5857t 1212/9 ,, .57. 'J2 I 59 I .5'62.81 I 15326 ,, 6 7. 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II ,, ,, " " ,, ,, ,, " " II II 144 ,, " ,, 219.1'7 l21!Jo68 21934 120.n2 21&6 l20J32. 21723 11!)74<, 21479 11869? 21132 1171.1'6 20631" 114')3" 2O10.r l/2S62 J!J422 /09:380 ld714 I0S86a 17849 /0/4-64- 16919 96773 " ,, ,, " " ,, " ,, ,, ,, ,, I/ 15840 9/04" 202) 241f/ 8462? 3387 2490, 77.f'6i 3717 30755 613740 b ,, ,, ,, ,, ,, ,, ,, ,, ,, ,, II ,, " ,, " ,, II }!- GtRDE~ ~ 314/:J 31404 31337 31184 309}0 .30509 2993£ 293/3 28484 27570 26423 2sio1 237/D 36:J46 37075 45623 14.464 t?64 112,d 338SZ 33852 45d7 264 112.& 101.Jf 1013.r 23117 80Sd 696,6 /6D't, 21410 !305'8 46656222/9 ,, II I I 7!118 J8DIH 36950564I 17943 36166 630..1 211C,/ 55033 4317 293/f I 92. 12,444 192 ,, ,, 34899 23672 ,4<!,/0l!, 5°64/ /0.971 168 /0.3.l!J 17766 72799 3689 168 /03.8 5971 2-105,1. ~745" ,, ,, ,, ,, 3'3006 .533/ 293/Jj 51J979Jl6/ 15565' &,'3,4 3294 " 26204 .flJ770 516/ 9617 p COLUMN I 2. 3 4 5 "') ~ It" >-- .--- L d SLOP£ DEFLECTION EQUATION =6£K d L da = Z: ~4 - L 8s .:= C)A"' 6EL cl -rA. hA AA£ PRIMARY WIND MOMENTS AND SECONDARY MOMENT 5 DUE TO COLUMN SHORTENING A -18 42 B -141.5 -1 .9 (\J rt') -125.6 (\J (\J -135.0 00 l.f') ,.... 0 C\I r--- (\J (\J LO -1.5 co -1677 C\ifY'i I.() - ·~ f'--: LO ' <\i('j - I ~co ll) &O -1 .3 co -18 7.1 C\t ,-..: - t') r--- - 'o - 0 I (\J -.9 -203 .0 O') . - -226. 0 . - I. I r--- 1/) -184.4 (\J (0 -- ' coo ...: 0\ rt'! - -.I -287. 8 t') (\J I C\I C\I co ' -"" 0 1.6 -24 7.5 I - . 5 O?q -245 .0 C\1I ll) . C\ICO (\J 2 I '"'C\I t') 0 29 cO (OQ 0 I ()) 0 ~o It) (\J ,-..: 3 - r--- :: 3.4 -189.6 -1.5 ~ LO -171.7 C\tI "CO t') -o It) 4 -1.1 0)-: ~(0 -153.6 I I'--- 0 ~ 2.1 - -184.4 co • I (\J (0 -I.I -170.5 ' '. " I 5 . - ()) cO "-I" 4.6 -166.0 ~q Oco co • I I (0 I ""' . - 2.0 ~ t ' ). -152.0 N C\I (X) 0 6 - , • I ""' ·~ <t C\I r--: q I -N ~cri (\J (\J r--- I 0 (\J rt') I 22-0 II , ,, 9-0 I PRIMARY WIND MOMENTS AND SECONDARY MOMENTS DUE TO COLUMN SHORTENING A -I 4 -65 . 3 rtlM ' co 0 ' I ~~ ~~ -1.2 -rtl -73.4 I LI) (0 ~~ . . - -1.5 -68.6 ~ 0 I (\J ~-= ~ r"l ~-. . ·~ -1.2 -81.9 -1.5 -76.6 ~ l() ,-..: ~ 0 , I (\J 0LI) -~ ' -1 . 6 -85.0 ~ I -.~ (\J - (\J ~ - -1.3 -95.0 ~ LI) I (\J -: m. -LI) 0rtl rtl -1.2 -95.8 0 - ~"' -r-,.: (0 I t--,: (\J - " • LI) 0 I (\J (0 11 (\J 0 I -~CO I I 10 . . C\J0 -(\J 'o - I 2 .7 -106 .8 9 - 2.5 -107.8 8 -1. 8 -135.0 00 .~- - (\J I 4.2 -132 .5 - 1.7 -117.0 -0 <00 -= 0 3. 1 -87.5 ~LI) -1.9 -125.9 rtl (0 - . -1 .3 -92 .0 -r---: I ~ ~ I (\J -: l() -I C0 - (\J (\J 0 , 12 0 -~ • 'If ' I -1.3 ~(\J -91.1 ~~ (\J ' 3.0 -78.3 (\J l"q"' (\J ll) 0 I ,-co -982 .5.9 (0 0 ,- -C\J - I. 3 -89.6 rtl l() ~ 13 "' M I (\J :.: <t 28 B -69. 1 -1.6 <OCO -60 .8 7 (\J (\J I I C\J 4.2 -141 .5 6 -1.9 -125 .6 I 22-0 , " I 9-0 II - PRIMARY WIND MOMENTS AND SECONDARY MOMENTS DUE TO COLUMN SHORTENING A • 01-: (() 0 I (\J - «oo -1. 2 <.O ,..... ,· r--:: -13.4 ~~ , -1.4 -12.2 -- ~o t 2.6 B -5 . 5 -1.6 oco -5.3 -o 1- - ·9 -6.1 20 I 2.7 -13.6 I 19 l'-0> I co - I I (\J ,..... C\I • \0 (()a, -1.0 -22 . 1 2.5 -22.3 -1.4 I.() «o -20. r ,· r....: (\J 1V - I.() 0) u) - 0 , I (\J I.O v -0 i.nv -1.0 -31.0 2.7 -31.1 -1. 2 oco I.() -28.2 - 'rt') (\J . v. 0 (\J 0 I ' I.() - 2.8 ,- -40.5 -1. 2 -39.7 rt') . v. v (\J 0 - "q" v rtl - I. 2 -55.7 I v. ,. . _. ' I (\J (\J '° I 2 .8 v -59 .6 14 --in I I (0 ~~ -0> -(() CO - 1.3 -52 .8 rt') rt') 0 15 - 1.6 co~ -49. 6 I rt') "q" co rt') (\J 2.8 -q- -49.6 -48.7 0) (\J 0 I (\J ,o - I. 2 rt') " I ~<!) O>V co 16 -1. 6 ": ~ -36.4 I I.() -q- C\J I (\J 17 i.nv Q"q" - ,. I l("t') I.O I (\J 18 -1. 4 -65 .3 2.8 if) -69.1 - I. 6 -60.8 I I 22-0 II I CO I 9-0 13 I " WIND-BRACING IN STEEL BUILDINGS DISCUSSION A rather sketchy investigation disclosed only one reference to the subject of Secondary Stresses in building bents due to column shortening under wind-load. Bulletin 80 of the University of Illinois covers the subject in a paragraph. The shortening of the first story columns of the twenty-story bent is computed and the fixedend moments in the first story girders determined. These moments are small compared with the origi nal wind moments. However, it must be remembered that the effect of column shortening is cumulative from bottom to top , while the girder moments due to wind become smaller so that the effect of coiumn shortening should be much greater at the top than near the ground. In its discussion the Committee on Wind-Bracing states that in the case of a high, narrow building secondary moments require investigation. In the relatively high and narrow Wilson-Maney bent secona.ary moments ar e negligible. other criterion. Apparently there is an- The importance of secondary moMents depends upon the relative size of bays and upon the relative stiffness of columns and girders. In the Wilson-Maney bent both columns on one side of the center line have the same kind of stress under wind load and this stress and therefore the shortening is roughly 2 proportional to the distance from the center line . Since all the fixed-end moments in the girders due to column shortening act in the same direction, they will all be reduced by the resulting sidesway and the girders i n their final position (after equilibrium is reached) will be nearly straight. When we have alternate tension and compress ion in the columns , the girders are constrained and may therefore have large bending moments after equilibrium is reached. I n such a case sidesway will increase certain girder moment s and decrease others. The committee does not consider the possibility that the secondary moments as first obtained may require correction. For example, i n general (not always) the secondary moments in the girders will be opposite to the primary moments. If the s econdaries are large, say 50% of the primari es, the resultant moments will be one-half of the original. But the secondaries wi ll also pro- duce column short ening which will cause more secondary moment s, ordinarily of the same sign as the primary moments. If the first secondaries are 50% of the primary moments then the second secondaries will be about 25% of the primary moments which will make the resulting moments 75% of the original moments instead of 50%. In general the f'irst secondary moments will give results which, for girders, are on the unsafe side. Calculations were made on two bents; one, the twenty story Wi lson-Maney bent , gave negligible secondary moments. The other bent, which was obtained by adding twenty-two foot bays to the 3 upper ten stories of the Wilson-Maney bent, gave very interesting results. Under wind loads the columns of this bent were alter- nately in tension and compression. The accompanying diagram gives the ratio of the first secondary to the ori ginal wind moment :~ ( lower figure), and. the ratio of the secondary moment after t wo corrections (algebra ic sum of secondary plus first correction plus second corre ction) to the origina l moment. V. .A. Vanoni, .Junior Member, .Am.Soc.C.E. Graduate Student, Calif. Inst. Tech. M.P. 1-filh ite, Assistant in Civil Engineering, California Institute of Technology RATIOS OF FIRST SECONDARY MOMENTS AND CORRECTED SECONDARY MOMENTS TO WIND MOMENTS -.35 _,46 co (\J 1-'n -.72 ~~ -:56 :;: + _,21 O?::::: -.26 I I .. -.. +.40 ~~ +.50 ++ rt>O - .32 C\J C\J -.25 ~~ -.12 IO<O j bI ~ _,..._ (\J I ' 01() N C\J I ' 1I ' I <DCO I I I I co <O oo. I' I (\J C\J C\J (\J +.21 oo. +.17 ~ + I C\J (\J - .08 + + -.09 I7 I -.08 C\J-:10 o0 -.08 + + •.15 +.12 -.05 C\J C\J 00 +.09 00 -.06 + + -.01 +.11 00 +.09 + + 00 -:07 -- -.:,..: + . + . . . - .05 +.OB -o ?,q -- +.05 -- -.03 QQ -.06 -.03 0.I I . -.03 00 rt)~ + QQ -- C\JC\J -.02 00 • i -.02 00 +.03 C\J~ -.03 0 0 -.02 ~Q -O.Q -.01 I -00 +.02 -oo -.01 oo I' ,. -.01 oo -.01 ~Q +.02 00 oo +.02 .00 00 ..00 OQ .00 oo ~Q .00 .00 .00 .00 -t= + +.04 I '?- .. - .01 ~ I b ' 0o ~q .00 22·-<f - -- I3 ' 2 + + -.01 • I <D 4 00 +.04 QO. +.03 + +.02 22'-o" - - 5 I + ... -.04 +.07 00 00 . .. +.07 -- -.02 oo + + -.02 -:04 0 0 -.0.3 I +07 ++ +.07 ,· r I 00 -.04 --.06 Q0 ~" QQ 6 -- -+.07 00 +.08 ++ -.04 ++ 8 -C\J +-+ +.II 00 ' oo ,. ,· -.06 I 00 00 rt) cO , -+ ,.: rt) (Y) -:13 0Q -.11 + + C\J rt) +.12 00 + + +.15 I j I -.II Q~ -.13 + ... I ,, I 9 +.30 C\J C\J 00 +.17 ~~ +.20 QQ -.05 j' + +- .18 rt)~ ~~ I' ,. ~IO I I ~IO -.15 00 -08 -.11 I ' + -t- +.40 +.24 0Q -.06 1' II -.19 oQ -.15 + + ,-... <D \ ' rt) •. so (1') 00 rt) rt) O,Q -.06 I -~ =O) I' I'-- O> I I ~24 -.30 ~~ 00 I 71 :.:~ +.23 +.29 ++ . -.15 0,. rt) <O - .61 SYM.ABT. ~ -.77 R +1.14 'lit co +.90 +.88 +1.12 ' .00 .00 9•-0·· - PART TWO PRil{I.ARY AND SECONDARY MOMENTS Ilf A BUILDING BENT DUE TO FOUNDATION SETI'LEMEW.1' In connection with the first part of this investigation it was decided to find the effect of column settlement. Because of the short time avai1ible a very simple bent was selected, the upper six stories of an interior bay of the Insurance Exchange Building in Los Angeles. This building is of reinforced concrete. All essential dimensions are given ort the summarizing diagram. Fixed end moments resulting from one-quarter inch settlement of alternate footings were calculated and distributed by the Hardy Cross Method. The assumption of one-quarter inch differential settlement is certainly pessimistic, but is not an impossibility. In any case the effect would be proportional to the displacement. The final moments thus obtained are much greater in the center than in the exterior bays. Dead load moments and wind load moments (assuming thirty pounds per square foot) been determined for this bent. had previously In the exterior panels the mo- ments due to footing settlement were about equal to dead load moments and to wind load moments, but in the interior panel the moments due to settlement were from two to three times the dead 2 load or wind load moments. The next step was the calculation and distribution of fixed end moments due to column shortening. The final moments obtained by this process of course are correction moments for the original moments. They are of opposite sign and therefore, if neglected, constitute a factor of safety. They vary from about eight per- cent at the bottom to about thirty-five percent at the top of the bent. Unlike secondary moments due to wind loads, moments due to footing settlement and the resulting secondary moments do not depend on the characteristics of the bent for their importance (except that they increase directly with stiffness of members). They are primarily a linear function of the settlement. PRIMARY AND SECONDARY MOMENTS DUE TO FOOTING SETTLEMENT MOMENTS IN INCH-KIPS -90 240 A oo ~ K= 181 Ol,qN 0 I oo O>N -220 (\I I (0\0 (0 t--- - N (\I II II (\I <( ~ <{ ~ - ,.,, <ON I 00 II K=240 o,q- ,.,, U") rt) 11 ' rl II ,q-r-,. -,qI • I IO 00 =N ~ I I <O ,q- t--- tnCO II <(~ II II K=240 <OIO ' -- -• ~,qII K-= 240 <00 (0 I 00 \00 II K:240 N_ ,q- ,.,, (0_ co rt) II II <{~ ,, II 3 K=205 I I 00 460 -3130 -280 00 1840 <Oco I (0 2 K=205 I 00 O)rt"I I C.0 270 -3250 -140 00 ,q- co 1840 I t--- I K=205 II <(~ I , 23-7 I 00 ,q- co I , I Olt'l <(~ co I CON 11 t--- U") t--- co 0,.,, &I') rt) -110<(~ 1430 00 4 K=205 -,qI -410 oo (\It"-1860 -<O t II I 840 -2710 00 (\I~ r-,.. 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Cele bate aes eee aoe (9,5) a ® a OCIS SPaiee|eiNom/8)s's) be Tel mm ces BA ieee BEAR ges) numer! | pemwn, ch: coo ena T f a Q Tat Lee : rj se 9 2m aid NS coe ic ee St 2 a7 eh Seal if aE Tat a 1S g = Ae e Le git 18 ia] Lots 3 ee i ey na [Z| te T Ta ACRE SS i 100 D.19 |. z a ee aril | fo te\| | | ia mh 3G ah Seal € bea es Path any yt t Or] | z iz a ol sr ae Zz +f | ai + £ i j_} —4—-4 SL/L ¥/'9[ 9) Neale /S bal om SiSi | sini S/S si SSI8 ; 7 rey dl Lay \e ro o M s = cs ga = = 2h | mat cae Ed | Ss ed AC ‘a Eisai YT fal eed le as u SI ; Boma a oft rs Sele sal! rlel. 4 fe SN sho Ie brs dod | o dels cde xt Oe ny hen mu Sse Pee | StI ge] FITS A ole B/E EIN) wo) 9/3 lee 1) [Sage (ay . 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