jkchL-:i^U 
 
 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 
 
 WARTIME REPORT 
 
 ORIGINALLY ISSUED 
 
 November l9'<-0 as 
 Advance Confidential Report 
 
 TBE EFFECT OF INITIAL DISPLACEMENT OF THE CMTER SUPPOET 
 ON THE BUCKLING OF A COIXJNK CCRTINUOUS OVER THREE SUPPORTS 
 By Eugene E. Limdqulst and Joseph N. Kotanchlk 
 
 Langley Memorial Aeronautical LaTaoratory 
 Langley Field, Va. 
 
 « 
 
 WASHINGTON 
 
 NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of 
 advance research results to an authorized group requiring them for the war effort. They were pre- 
 viously held under a security status but are now unclassified. Some of these reports were not tech- 
 nically edited. vAU have been reproduced without change in order to expedite general distribution. 
 
 L - 256 -;, 
 
u 
 
 THE ZJ?ZGT or INITIAL D ISPLACI^iZIIT C7 T^HE C^IT^IH SUPPOIl? 
 
 OIJ TEZ 3UCXLi:^G 0? ^ OjLUMIT C01'TI2TU0US C'.^E]x jKHSZ SUPFOIi^rS 
 
 3;- E-a.^;e::.G 3. L-undcuis t and Joscpli 1'. Zo'':anchik 
 
 A 1. :;,^ cc1l".t.;i c on'c ir.uous cvor throo suppci-t^ '..-as 
 tostud to d J t >..rT.ir;c its criticr-.l iof.d vhen thu GonGer 5"ap- 
 port WLis given var^'ing einounts of initi.?.! d icplac ^mcnt . 
 Duri::g oc.ch tost thic Zuiddlc si.-.pp::'t v;r.s hing-ici- so <"2 to Do 
 frse to :aove parallel to the cclumn axis during; "buckl in;r;. 
 
 
 
 
 rr. 
 
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 c 
 
 r 
 
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 Z. 
 
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 of 
 
 
 
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 ■I- 
 
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 en 
 
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 r^ 
 
 17 
 
 
 S 
 
 U'O 
 
 "JO 
 
 1" 
 
 t 
 
 
 w a 
 
 prsdicte^i froin Icad-def lee t i oj 
 for the MpT^er ana l0'\rei' spars, 
 tical load in each t;St -vas 
 ni'-, doflected -; o £.s to deepen 
 
 of the span and the smaller 
 eech test v-£,5 for the span th 
 as to straighten o'lt and re 
 urvG of the ST3an. Thoco odeg 
 
 c t i 
 
 wno' 
 
 r. e r t n e 
 T. 1- ,-. 
 
 .nit ial dcflo 
 tho loft 
 
 for 
 
 t h e 
 pre- 
 at , 
 verse 
 rva- 
 on 
 
 c r c n c "t- e t w e o n t h e c r i • 
 
 loadE predicted 
 
 for the iippcr and icv.'jr spans is lorcpor t i onal to the in- 
 itial deflection of the center sin;'Port. The o.ifforoncc 
 
 .on 
 
 hose tests 1 3 n c t 
 
 J .». '_j. ^ 
 
 .n 
 
 ;orm£ o;; errors -oor— 
 
 miisiol::; in -orac tical dcsiisn. 
 
 predicted c r i t 
 
 mdi scr irr. inato sini^le a",2p: 
 
 fact that a difference 
 .cal loads si^ggosts that an 
 
 the So"at]:woll method 
 
 . c a t i c n o ; 
 
 as presented in reference 2, or as modified in reference 
 1, can result in definite and measurahlc errors. 
 
 The average of the predicted critica-l loads for the 
 upper and lov/er spans is more correct than either pre- 
 dicted critici-l lo£id. This observation su^-gests that 
 
 v/natever i: 
 hi,;h in on, 
 to be lev; in 
 
 caus in^ 
 
 s- 
 
 ;nc 
 
 sredictod cri^ 
 
 ;al loaa 
 
 an also causer: the ■or-edicted critical 
 
 . o a 1 
 
 :n; 
 
 otner span. 
 
 The avorai,e of the predicted critical loads for the 
 upper and lo\;er spans i .^ reduced oy initial displacement 
 
 of the center support and thi" reduction t. 
 
 nC:'. 
 
 to i n c r 
 
 v; i t h 
 
 ahsolutc value of the initial displacement. 
 
 In 
 
t he re due t i on i 
 
 avera,:-e critical load 
 
 tncGCoOG 
 
 ca'':.sed oy inibial displ.;icen':3ut. of the csiiter sv.ppoi-t is 
 Ter7 sna?,l. [This fact ir.dicates th9,t the effect of cur- 
 -atiire dixe to "tendiii^ on the criticr.l load for the co~- 
 pretision flan,:;8 .-material of a dos oeani is prohahlj sjrall 
 aiad can "be ne^;lected in engineGrin§- design. 
 
 IHTROEUGSICK 
 
 1 
 
 n th 
 
 e c :■ V. 
 
 3r 5 
 
 e of 
 
 Greene 
 
 » "-■ 
 
 r Cor 
 
 rs 
 
 L i a 
 
 effect 
 
 of 
 
 curve 
 
 tu 
 
 re d 
 
 for th 
 
 e c c: 
 
 nprcE 
 
 si 
 
 on f 
 
 decide 
 
 d to 
 
 test 
 
 a 
 
 Ion 
 
 ports 
 
 ••;ith 
 
 the 
 
 r. i 
 
 d -^.i e 
 
 m J n t t 
 
 re 
 
 pre 3 
 
 nt 
 
 t he 
 
 3 h i n -if 
 
 in./. 
 
 In 
 
 th 
 
 t c 
 
 as to 
 
 DC f 
 
 r c t 
 
 
 
 nove 
 
 huckli 
 
 ilo. 
 
 It v; 
 
 a. 3 
 
 con 
 
 liTOUld 
 
 h a 
 
 2? C 0. S 
 
 onaljlc 
 
 pro V i d 
 
 Gd \ 
 
 7 the 
 
 r 
 
 i^E 
 
 a 0. i s c MS 5 i n v; i t h L t . Col. 
 ison Officer -fith the ITaCA, 
 no to D ending; on tliu critica 
 lan,_;e material of c, lox hcaii 
 V?, coliiran c cnt iniioiis OTor thr 
 
 sn.pT. o: 
 
 cur rat lire c 
 
 giyen an 
 
 initial di 
 
 l:if: in a s 
 
 st the aiddle support v/^-s hi 
 
 parallel to the coiv.mn ar.is 
 
 sidorod that this t7po of su 
 
 approxiij-.r. t ion to the t:-'pc o 
 
 01 
 
 1 1 
 
 » ~ 
 
 e - 
 
 spl 
 
 tre 
 
 n i: c 
 
 p;oo 
 
 1 F. 
 the 
 
 r... d. 
 
 t v/a; 
 s up— 
 ace- 
 s 3 :] ■ 
 a 30 
 rinr::: 
 
 roort 
 
 01 Zi-C 
 
 J o :■; 
 
 'AHATU 
 
 AIT! 
 
 
 
 
 .10 -COGt 
 
 PO t 
 
 -up is 
 
 s 
 
 dia 
 
 graramat ic 
 
 3ket 
 
 c h of t 
 
 h 
 
 
 T 
 
 h.; long 
 
 c on 
 
 t inuou3 
 
 
 3 / 4 
 
 -in 
 
 ch— dian 
 
 e t e r 
 
 steel 
 
 
 
 kni 
 
 f e 
 
 edges . 
 
 The 
 
 n:idile 
 
 
 por 
 
 tod 
 
 latera 
 
 117 
 
 b;- a st 
 
 i 
 
 end 
 
 of 
 
 th is 5 
 
 trut 
 
 vr as pi 
 
 >i 
 
 at 
 
 its 
 
 riiddlo 
 
 
 h c ax i s 
 
 
 int 
 
 r 3 c c t the 
 
 a:-: i 
 
 3 of '-.h 
 
 c 
 
 3 i'i 
 
 le 
 
 advers o 
 
 off 
 
 e c t s of 
 
 
 loc 
 
 " t i 
 
 on. Ta 
 
 e ot: 
 
 her end. 
 
 
 v/as 
 
 pi 
 
 n-joine 
 
 d to 
 
 a rigi 
 
 d 
 
 nan 
 
 r.cr 
 
 that t 
 
 he n 
 
 iddle o 
 
 f 
 
 dof 
 
 Ice 
 
 t Lorna 
 
 1 to 
 
 the i n 
 
 i 
 
 
 D' 
 
 uring c: 
 
 rch 
 
 test do 
 
 1 
 
 of 
 
 cac! 
 
 h span 
 
 V.' c r 
 
 taken 
 
 X 
 
 shovrn in figures 1, 
 
 t .■> p 
 
 she V,' n 1 n 
 
 : , and 
 ' i t^ur o 
 
 it 
 
 olunn used in the tests -.ifas 
 r 67-7/5 i n c h c s bet vr e e n the 
 f the continuous cclun.n --.'as 
 f strut 12-7/ S inches long. 
 Joined to the ccntinticus ccl 
 f this pin joint ■^ras riadc to 
 colT.-in 3:; as to re:r:cve :\r.y p 
 n eccentric p in Joint '^. t t h i 
 f the lateral supporting str 
 supporting structure in such 
 the continuous colunn could 
 i a i deflection. 
 
 a 
 
 n d 
 
 3 Up"^ 
 
 One 
 
 unn 
 
 ut; 
 not 
 
 iction readings at the nid:'.lc 
 ).- a fixed reference point on 
 the slotted tension rod of the testing nachine v;ith an 
 inside "licroneter caliiocr roadir.;; to thousandths of an 
 
m 
 
 he micr oir.et er caliper and its extension bar are 
 
 .0 -c 
 
 Fliovni in figures 1, 
 
 ana 
 
 In each test the specimen vfas loaded through the 
 same ran^e of leads. Therefore the sr.all errors in the 
 loaf-s indicated "by the testing machine cancel ;rhen com- 
 paring the results of one test ivith the r.-Rr.lt3 of an- 
 o t >- r tost. 
 
 HIS'iJLTS 
 
 ti..;; 
 
 .^ -^r t ' 
 
 the 
 enc« 
 In : 
 cc-1 
 the 
 lo i 
 ploi 
 porl 
 
 ■Z'ha load-deflection readings taken duri 
 
 . t i n are given in t at 1 a s I to 711 i n cl u s 
 
 . o,r3 plotted ir. fif^iires 5 to 11 inclusiv 
 
 prodict2d loads are ohtainGd"" in the raann 
 
 : 1, xhcso predicted lo'ids are listed in 
 
 'i:,-urc 12 the difference bctv;aen the pred 
 
 load for the upper o,nd lov/er spans is plo 
 
 initial deflection of the center support, 
 
 ho avcra^AC value of the predicted critic 
 
 ted a^-ainst the initial r.rflection of th. 
 
 iv 
 e , 
 er 
 t 
 1 c 
 tt 
 
 this 
 
 e. T 
 
 f r n 
 
 of r 
 
 ahle 
 
 t e d c 
 
 ed ag 
 
 In f 
 
 load 
 
 c en te 
 
 mves- 
 h e 3 e 
 
 v.'hich 
 ef er- 
 
 VT T T 
 t X — ^ • 
 
 riti- 
 
 igurc 
 G is 
 r s up— 
 
 In each test "buckling- occurred --/ith deflection to the 
 right in the upper span o,nd deflection to the loft in the 
 lov;cr span. Hhe test for vrhich the initial deflection of 
 the center support v/as C.749 inch -ras the last test per- 
 for::;ed. In this test the column was loaded to '.cstruction 
 
 and 
 
 a:ciinum 
 
 , oad 
 
 o un 
 
 to 
 
 5 810 pounds. 
 
 i}:3c;ussio:t 
 
 loads 
 c n t f 
 critic 
 
 huckli 
 curve 
 in eac 
 s a s 
 curve 
 v.-hothe 
 to the 
 
 nsp 
 pre 
 r t 
 
 ,-.1 
 
 " £ » 
 of 
 
 .10 
 
 lo: 
 
 ; 'G 1 1 
 . c t e 1 
 up 
 
 01 
 
 ,t)l 
 
 to 
 
 C I 
 
 r t 
 
 r i 
 
 s-c 
 
 th 
 he 
 A'h 
 
 efl 
 
 C 3 
 
 r a i 
 
 c s 
 
 in 
 
 t o 
 
 per 
 in c 
 oc tc 
 pan 
 as f 
 gntc 
 pan. 
 it ir 
 r t h 
 
 om 
 
 and 
 
 ach 
 
 d S 
 
 an:l 
 or 
 n o' 
 
 ■t: 
 
 1 d 
 
 o 
 
 vii: 
 
 that the critical 
 
 loaa- 
 
 :i iecti 
 
 . :■! 
 
 ;e s 
 
 ? o 
 
 so 
 le 
 
 ■C vr ■ 
 
 to 
 
 S;n( 
 Sp.i 
 
 n d 
 
 CD 
 
 spans . 
 "or 
 i'pe 
 
 on readinj^s v;cro differ— 
 
 The larf^er predicted 
 
 + 
 
 d 
 
 Ml 
 
 n th 
 rcve 
 
 r, .-> T" -.r 
 
 zao Fpan that, on 
 the initial deflection 
 er predict el critical load 
 hat, on buckling, deflected 
 erse tiic initial deflection 
 ;ions held regardless of 
 the center support v;as 
 
Pi£:urG 12 shows vh."t tho .".if f oronc d "oot--;oon tin crit- 
 
 ic 
 vo 
 
 Tn. 
 of 
 
 ge 
 
 So 
 f i 
 er 
 th 
 dc 
 c iz 
 cc. 
 
 lcc:l r^rodict; 
 
 or 
 
 up"oc: 
 
 ar.d lov/er 
 
 3 '•:: an E is 
 
 '0- 
 
 lo: 
 
 e c. 1 X I :; r c r. C2 no 
 
 the initial cTcf 1 jr^ t ion .jf the center support. 
 . these tests iz not lo,r-?c in toriris 
 
 ~ oX! 
 
 "pcraiE s i ol> 
 ,sts : 
 
 m 
 
 prrcct icr-,1 
 
 : E 1 e:n , 
 
 ! r r o r G _ 
 
 - :f f ■ e r c ii c G o 'c i s t s i r. t h e p r o cl i c t e d critic r . 1 1 
 ;r; that .'.n indiscrir.iinnt c single r:.pT'li cr.t ion 
 . + Vi - '"• n :-. ■;, r e 3 e n t e d in i' o f e r i"- ■- r: a. P. n i 
 
 fact thf.t 
 rds sug- 
 
 t n e c. 
 
 a; 
 
 or 
 
 1^ .- o ti 
 
 lite 
 herGforc dosirr.ole to stuav the cause of 
 n the pre dieted critical loads in order to 
 
 . in refcro-.co 1, can result in definite and ir.easurab 
 rs. It is the 
 difference 
 
 -Zn to 
 o n s . 
 
 or. 
 
 Ui- V 
 
 L 1 lU 
 
 )or-:ance in 
 
 ncme er : 
 
 aTjpl i- 
 
 foi; 
 
 m "■:ne one 
 v;in.:: va.lue; 
 
 v; e r .: 
 
 ■■/as ■ 
 
 c h t a i n c d 
 
 :arri:d to do 
 
 ; rue t ion, 
 
 the 
 
 ritic-'l load, upper cpan oS9? ITd 
 Predicted critical ioa.', lovror span 5757 lb 
 Avcrair:e preoicteif' critical load ?827 It 
 
 m 
 
 strnctior. t. 
 
 3310 11) 
 
 j!r or 
 
 . e s e re s i.\ 
 
 ts 
 
 rredictec-. cri-;ica. 
 
 ioa.C- : 
 
 er 
 
 up'oer and lovrer s'oaus is 
 
 Eore correct tnan ei 
 CD s e rvat ion s U::;go s t :-; 
 ed critical load to he h 
 
 predicted critica,l lop.d, 
 
 "n: 
 
 13. s 
 
 one 
 
 sps.n aj-so cautes tr.c 
 
 pre 
 
 . c t c d c r i t i c c , 1 
 
 CO u e .'- " 
 
 the ot: 
 
 rpan, 
 
 of t: 
 
 plac 
 
 tc i 
 
 plac 
 
 p red 
 
 the 
 
 indi 
 
 tho 
 
 a h 
 fine 
 
 It is 
 iT G "ore d 
 .■ncnt 
 .1 c r 3 a ri e 
 e Ik o n t . 
 i G t e d c 
 center 
 cates X 
 3 r i t i c a 
 :: D .3 a.u 
 J r i n t"' d 
 
 ;on 
 -ct 
 • t 
 ■>/ i 
 In 
 ■it 
 ;up' 
 lat 
 . 1 
 .s 
 
 i-ded fron fi-'u; 
 
 -■;u. 
 
 cri 
 
 lI loads 
 
 ; that the average Talue 
 reduced ty initial dis- 
 
 po 
 
 :al 
 rt 
 he 
 d 
 oh 
 
 ;enter support and this reduction tonds 
 ;he ah solute -trc iuj of the initial dib- 
 se test!? tlie ■ redact ion in the avsra,;;^8 
 load caused hy initial displacerrieut of 
 is, ho-./ever, very siiall. This fact 
 ect of curvature duo to hendini^ on 
 
 - -p. 
 
 the c orijjrcs s ion flange material of 
 
 ^Ol:r s n a 
 
 and can oe nei-'lectod in en- 
 
 ■ pcn , 
 
 _ fact tJ-.at ne,:ative initial di splCvCesent of the 
 center .^uxjport gave lov;or averajo predicted critical loads 
 
 iter 
 than corros 
 
 ■adin;i- poGiti" 
 
 initial displacenients indi- 
 
cates that • 
 and contrc.l 
 p G r £. p an a ], ', 
 to -;;he loft 
 
 hero ma;' h ?.'/•: 
 loading. Tho f ac i 
 ay^ doflcctou to t' 
 soers to sappn-t. z] 
 
 syrr.v.ctry ^1.r..:^. central load 
 
 .Hi 
 
 \f u ; 
 
 ^ lac!: of perfect synmetr^ 
 : 1: at, o n ''o v.c k 1 i ii ^^ , t h e up- 
 ) rii^lit and th.o lower span 
 ; 3uj£i;e3t icp- that pcirfsct 
 'e not achiovod. 
 
 
 
 
 I 
 
 J. 
 
 X !r 
 
 po 
 
 £ 
 
 r X 
 
 cl 
 
 
 
 
 t 
 
 n 
 
 a 
 
 z 
 
 d 
 
 it 
 
 i 
 
 on 
 
 c 
 
 in 
 
 th 
 
 3 
 
 t 
 
 v; 
 
 
 c 
 
 P 
 
 a 
 
 ^1 
 
 s 
 
 
 ia 
 
 T 
 
 ly 
 
 
 dof 
 
 lee 
 
 t 
 
 w I. 
 
 r* 
 
 a 
 
 'C 
 
 s 
 
 c 
 
 s 
 
 
 t 
 
 ha 
 
 
 tv; 
 
 
 
 
 ans 
 
 
 tc 
 
 a 
 
 :'. 
 
 X 
 
 f 
 
 
 
 ■** 
 
 • 
 
 e 
 
 ::i 
 
 J 
 
 tc 
 
 
 \l'.l 
 
 n d 
 
 
 
 fl 
 
 oc 
 
 J- 
 
 i 
 
 v- 
 
 n 
 
 » 
 
 
 d 
 
 of 
 
 X 
 
 ec 
 
 "G 
 
 ion 
 
 cv. 
 
 -■» 
 
 re 
 
 
 
 z 
 
 
 
 
 n 
 
 3 
 
 
 y 
 
 or 
 
 2 
 
 c c 
 
 
 the 
 
 i"a 
 
 1 
 
 "■-' 1 
 
 al 
 
 
 .-> 
 
 e 
 
 f 
 
 1g 
 
 I 
 
 ns 
 
 p 
 
 c c 
 
 t 
 
 ion 
 
 Ox 
 
 
 ta 
 
 cl 
 
 c 
 
 Li 
 
 
 T 
 
 "7 
 
 
 t 
 
 ho 
 
 
 sa 
 
 "u 
 
 c i 
 
 ncr 
 
 C 
 
 r.-.e 
 
 nt 
 
 
 
 
 f 
 
 
 1 
 
 
 
 
 
 f 
 
 (I 
 
 ef 
 
 1 
 
 o?z 
 
 : oa 
 
 
 
 — t.'" 
 
 1 
 
 
 
 i 
 
 s 
 
 
 t 
 
 io 
 
 11 
 
 5 
 
 
 
 n b 
 
 ■ucic 
 
 J. 
 
 in 
 
 £■:. 
 
 
 d 
 
 •J 
 
 e 
 
 ';- 
 
 ^l 
 
 Of 
 
 i> 
 
 ho 
 
 
 spa 
 
 n. 
 
 
 ?h 
 
 e 
 
 
 
 ;r 
 
 i 
 
 <5 
 
 t 
 
 e 
 
 
 ef 
 
 i 
 
 cc 
 
 t 
 
 ior. 
 
 f 
 
 r 
 
 ■I, 
 
 V- ^ 
 
 
 ::. 
 
 
 Z 
 
 
 
 
 
 if 
 
 •P 
 
 or 
 
 c 
 
 11 cc 
 
 in 
 
 
 th 
 
 (^ 
 
 
 
 
 c . 
 
 d 
 
 i 
 
 i-> 
 
 a d i f 1 e r o n c c 
 vrh on 1 1" ^ ^ 
 
 ■h 
 
 in the Icadm. 
 center cupport is 
 
 c on- 
 
 i v: T — 
 
 he predicted critical loads for 
 
 on "b-achlin- 
 suan anc 
 
 Certainly a difference in loading 
 n-5, deepens the initial 
 strai-^htens cv.t and re- 
 cti o n c v.r T c f the 
 to YIZ incln.iiv 
 
 ad ?-?3^ , the largoi" increncnt 
 a 1 w ays o 1 1 a i n c d - ' h c n 
 
 other 3 70 an. 
 
 e h G v/ s that for 
 
 i n c r ' 
 
 t h d e f 1 e c - 
 
 ns the initial defl-^ction zv.vve 
 nee of different increnients of 
 increnent of load can only r.ecn 
 ■^; ccnditious for the tv;o spans. 
 
 Lan^-ley Memorial Aeronautical Labora^t or^/ , 
 
 iTaticnal Advisor;'' Comirittoe for Aeror.a-at i; 
 
 L angle y 
 
 ild, 
 
 1. L'undgnist, 3Uii;eno S.: G-on-iral iz :!d Analysis of Expori- 
 nontal Ob?, ervat icns in Proble^is of Elastic Stability 
 T.ll. tc. 558, ITACA, 1S38. 
 
 2. Southv;ell, P.. T 
 Observations 
 Froc . , P.or-al 
 
 : On the An:',ly3ij cf Z::7- er imcnt al 
 .n Froble:;.? of Elastic Stability, 
 j'ic.. A, vol. 135, 1952, pp. 6C1-S16. 
 
o 
 
 HACA 
 
 TABLE I 
 
 TaMes 1,S,3 
 
 Load-Def leotlon Data 
 Initial Deflection at Center Support Inches. 
 
 P 
 
 (lb) 
 
 Upper Span 
 Pi = 3000 lb, 
 yi = 18.191 In. 
 
 Lower Span 
 Pi = 3000 lb. 
 yi = 18.114 in. 
 
 y 
 (in.) 
 
 y-yi 
 
 (in.) 
 
 P-Pl 
 (IbO 
 
 y-yi 
 
 P-Pi 
 
 (in/lb) 
 
 y 
 
 (in.) 
 
 y-yi 
 
 (in.) 
 
 P-Pl 
 (lb) 
 
 y-yi 
 P-Pi 
 
 (in/lb) 
 
 3000 
 
 3200 
 
 3400 
 3500 
 3600 
 3700 
 3750 
 
 18.191 
 18.204 
 18.224 
 18.244 
 18.275 
 18. 350 
 18.451 
 
 
 
 .013 
 .033 
 .053 
 .084 
 .159 
 .260 
 
 
 200 
 400 
 500 
 600 
 700 
 750 
 
 0.0000650 
 . 0000825 
 .0001060 
 .0001400 
 .0002271 
 .0003467 
 
 18.114 
 18.104 
 18.083 
 18.064 
 18. 031 
 17.954 
 17.854 
 
 
 
 -.010 
 -.031 
 -.050 
 
 -.083 
 -.160 
 -.260 
 
 
 200 
 400 
 500 
 600 
 700 
 750 
 
 -0.0000500 
 
 - .0000775 
 
 - .0001000 
 
 - .0001383 
 
 - .0002286 
 
 - .0003467 
 
 TABLE II 
 Load-Deflection Data 
 Initial Deflection at Center Support 0.453 inches. 
 
 p 
 
 (lb) 
 
 Upper Span 
 Pi = 5000 lb. 
 yi = 18.556 in. 
 
 Lower Span 
 Pi = 3000 lb. 
 yi = 18.470 in. 
 
 y 
 
 (in.) 
 
 y-yi 
 
 (in.) 
 
 P-Pl 
 (lb) 
 
 y-yi 
 P-h 
 
 (in/lb) 
 
 y 
 
 (in.) 
 
 y-yi 
 
 (in.) 
 
 P-Pl 
 (lb) 
 
 y-yi 
 f-Pi 
 
 (in/lb) 
 
 3000 
 
 3200 
 3400 
 3500 
 3600 
 3700 
 
 18.556 
 18.576 
 18.605 
 18.635 
 18.677 
 18.796 
 
 
 .020 
 .049 
 .079 
 .121 
 .240 
 
 
 200 
 400 
 500 
 600 
 700 
 
 0.0001000 
 .0001225 
 .0001580 
 .0002017 
 . 0003429 
 
 18.470 
 18.461 
 18.444 
 18.424 
 18.585 
 18.269 
 
 
 -.009 
 -.026 
 -.046 
 -.085 
 -.201 
 
 
 200 
 400 
 500 
 600 
 700 
 
 -0.0000450 
 -.0000650 
 -.0000920 
 -.0001417 
 -.0002871 
 
 TABLE III 
 
 Load-Deflection Data 
 Initial Deflection at Center Support 
 
 -0.447 inches. 
 
 
 
 Upper Span 
 
 
 
 Lower Span 
 
 
 p 
 
 
 Pi = 3000 lb. 
 
 
 
 Pi 
 
 = 3000 
 
 Lb. 
 
 
 
 yi = 17.833 i 
 
 n. 
 
 
 yi 
 
 = 17.741 in. 1 
 
 (lb) 
 
 
 
 
 
 
 
 
 y 
 
 y-yi 
 
 p-Pi 
 
 y-yi 
 
 (in/lb) 
 
 y 
 
 y-yi 
 
 P-Pl 
 
 y-yi 
 
 
 (in.) 
 
 (m.) 
 
 (lb) 
 
 (in.) 
 
 (in.) 
 
 (lb) 
 
 P-Pl 
 
 (in/lb) 
 
 3000 
 
 17.853 
 
 
 
 
 
 
 17.741 
 
 
 
 
 
 
 3200 
 
 17.843 
 
 .010 
 
 200 
 
 0.0000500 
 
 17.724 
 
 -.017 
 
 200 
 
 -0.0000850 
 
 3400 
 
 17.863 
 
 .030 
 
 400 
 
 .0000750 
 
 17.691 
 
 -.050 
 
 400 
 
 -.0001250 
 
 3500 
 
 17.885 
 
 .052 
 
 500 
 
 . 0001040 
 
 17.660 
 
 -.081 
 
 500 
 
 -.0001620 
 
 3600 
 
 17.933 
 
 .100 
 
 600 
 
 .0001667 
 
 17.607 
 
 -.134 
 
 600 
 
 -.0002233 
 
 3650 
 
 17.985 
 
 .152 
 
 650 
 
 .0002338 
 
 17.547 
 
 -.194 
 
 650 
 
 -.0002985 
 
i 
 
I 
 
 KAOA 
 
 Tables 4,5,6 
 
 TABLE IV 
 
 Load-Defleotlon Data 
 Initial Deflection at Center Support 0.749 inches. 
 
 p 
 
 ( lb) 
 
 Upper Span 
 
 Pi = 5000 lb. 
 yi = 18.742 in. 
 
 Lower Span 
 
 "l = 3000 lb. 
 yi = 18.662 in. 
 
 y 
 
 (In.) 
 
 y-yi 
 (m.) 
 
 P-Pl 
 (lb) 
 
 y-yi 
 p-Pi 
 
 (in/lb) 
 
 y 
 
 (In.) 
 
 y-yi 
 (in.) 
 
 P-Pl 
 (lb) 
 
 
 
 y-yi 
 
 P-Pi 
 
 (in/lb) 
 
 3000 
 3200 
 3400 
 3500 
 3700 
 
 18 . 742 
 18.757 
 18.782 
 18.811 
 18.901 
 
 
 
 .015 
 .040 
 .069 
 .159 
 
 
 200 
 400 
 500 
 700 
 
 
 
 0.0000750 
 . 0001000 
 .0001580 
 .0002271 
 
 18.662 
 18.663 
 18.656 
 18 . 647 
 18.575 
 
 
 + .001 
 -.006 
 -.015 
 -.087 
 
 
 200 
 
 400 
 500 
 700 
 
 +0 . 0000050 
 -.0000150 
 -.0000500 
 -.0001245 
 
 TABLE V 
 Load-Defleotion Data 
 Initial Deflection at Center Support 
 
 -0.747 inches. 
 
 p 
 
 (lb) 
 
 Upper Span 
 Pi = 5000 lb. 
 yi = 17.605 in. 
 
 Lower Spa.T 
 Pi = 3000 lb. 
 yi = 17.490 in. 
 
 y 
 
 (in.) 
 
 y-yi 
 (m.) 
 
 P-Pl 
 (lb) 
 
 y-yi 
 p-Pi 
 
 ( in/lb) 
 
 y 
 
 (in.) 
 
 y-yi 
 
 (in.) 
 
 P-Pl 
 (lb) 
 
 y-yi 
 
 (in/lb) 
 
 3000 
 3200 
 3400 
 3500 
 3600 
 5650 
 
 17.605 
 17.614 
 17.635 
 17.662 
 17.719 
 17.818 
 
 
 
 .009 
 .03,0 
 • 057 
 .114 
 •213 
 
 
 200 
 400 
 500 
 600 
 650 
 
 0.0000450 
 
 .0000750 
 
 .0001140 
 .0001900 
 . 0003277 
 
 17.490 
 17.463 
 17.422 
 17.381 
 17.309 
 17.226 
 
 
 -.027 
 -.063 
 -.109 
 -.181 
 -.264 
 
 
 200 
 400 
 500 
 600 
 650 
 
 -0.0001550 
 -.0001700 
 -.0002180 
 -.0003017 
 -.0004062 
 
 TABLE VI 
 Load-Defleotlon Data 
 Initial Deflection at Center Support I.OI3 inches. 
 
 
 
 Upper Span 
 
 
 
 Lower Span 
 
 
 
 
 Pi = 5000 lb. 
 
 
 
 Pi = 3000 lb. j 
 
 p 
 
 (lb) 
 
 
 yi = 19.010 i 
 
 n. 
 
 
 yi = 18.902 
 
 in. 
 
 y 
 
 (in.) 
 
 y-yi 
 
 (in.) 
 
 P-Pl 
 (lb) 
 
 y-yi 
 f-Pi 
 
 (in/lb) 
 
 y 
 
 (in.) 
 
 y-yi 
 
 (in.) 
 
 P-Pl 
 (lb) 
 
 y-yi 
 prpl 
 
 (in/lb) 
 
 3000 
 
 19.010 
 
 
 
 
 
 
 18.902 
 
 
 
 
 
 
 3200 
 
 19.037 
 
 .027 
 
 200 
 
 0.0001550 
 
 18.897 
 
 -.005 
 
 200 
 
 -0 . 0000250 
 
 3400 
 
 19.080 
 
 .070 
 
 400 
 
 .0001750 
 
 18.880 
 
 -.022 
 
 400 
 
 -.0000550 
 
 3500 
 
 19.111 
 
 .101 
 
 500 
 
 .0002020 
 
 18. 856 
 
 -.046 
 
 500 
 
 -.0000920 
 
 3600 
 
 19.169 
 
 .159 
 
 600 
 
 .0002650 
 
 18.804 
 
 -.098 
 
 600 
 
 -.0001633 
 
 3650 
 
 1 
 
 19.254 
 
 .244 
 
 650 
 
 . 0003754 
 
 18.739 
 
 -.163 
 
 650 
 
 -.0002508 
 
fv 
 I 
 
 HACA 
 
 Tables 7,8 
 
 TABLE VII 
 Load-Defleotlon Data 
 Initial Deflection at Center Support 
 
 -1.020 inches. 
 
 p 
 
 (lb) 
 
 Upper Span 
 
 Pi = 3000 lb. 
 yi = 17.393 in. 
 
 Lower Span 
 
 P]^ = 3000 lb. 
 yi = 17.274 in. 
 
 y 
 
 (in.) 
 
 y-yi 
 
 (in.) 
 
 P-Pl 
 (lb) 
 
 y-yi 
 P-Pi 
 
 (in/lb) 
 
 y 
 
 (in.) 
 
 y-yi 
 
 (in.) 
 
 P-Pl 
 (lb) 
 
 y-yi 
 P-P, 
 
 (la/lb) 
 
 3000 
 3200 
 3400 
 3500 
 3600 
 3650 
 
 17.393 
 17.396 
 17.416 
 17.450 
 17.499 
 17.566 
 
 
 .003 
 .023 
 .057 
 .106 
 •173 
 
 
 200 
 400 
 500 
 600 
 650 
 
 0.0000150 
 .0000575 
 .0001140 
 .0001767 
 .0002662 
 
 17.274 
 17.241 
 17.193 
 17.150 
 17 . 075 
 16.996 
 
 
 
 -.033 
 -.081 
 -.124 
 -.199 
 -.278 
 
 
 200 
 400 
 500 
 600 
 650 
 
 -0.0001650 
 -.0002025 
 - . 0002480 
 -.0003317 
 -.0004277 
 
 TABLE VIII 
 
 Summary of Critical Loads 
 Predicted From Load-Deflection Data. 
 
 Initial 
 Deflection 
 at Center 
 
 Support 
 
 (in.) 
 
 Per 
 Upper 
 Span 
 
 (lb) 
 
 ^r 
 Lower 
 Span 
 
 (lb) 
 
 ^cr 
 Average 
 
 (lb) 
 
 ^cr - ^cr 
 Upper Lower 
 Span Span 
 
 (lb) 
 
 
 
 .453 
 -.447 
 
 .749 
 -.747 
 
 1.013 
 -1.020 
 
 3858 
 
 3868* 
 3773'* 
 
 3897* 
 3727" 
 
 3890* 
 3737" 
 
 3850 
 
 3789*' 
 3830* 
 
 3757'* 
 3831* 
 
 5733*' 
 3872* 
 
 3854 
 
 3829 
 3802 
 
 3827 
 3779 
 
 3812 
 3805 
 
 8 
 
 79 
 -57 
 
 140 
 -104 
 
 157 
 -135 
 
 •Deflected on buckling so as to deepen the initial deflection 
 curve of the span. 
 
 ••Deflected on buc.-.llng so as to straishten out and reverse the 
 initial deflection curve of the span. 
 
HACA 
 
 rig.i 
 
 Pigura 1.- Tett 
 
 ■9t- 
 
 up ihowing col- 
 umn with ini- 
 tial deflection 
 at center sup- 
 port of 0.749 
 inch before 
 loading. 
 
 300,000 -POUND 
 
 HYDRAULIC 
 
 COMPRESSION 
 
 TESTING 
 
 MAC MINE 
 
NACA 
 
 rigur« 2.- Test 
 set- 
 up showing col- 
 umn with ini- 
 tial deflection 
 at center sup- 
 port of 0.749 
 inch approach" 
 ing critical 
 load. 
 
 Pig. 2 
 
 3OO.000 -POUND 
 
 HYDRAULIC 
 
 COMPRESSION 
 
 TESTING 
 
 MACHINE 
 
VACA 
 
 Figure 3.- Test 
 eet- 
 up •howlog col- 
 umn with ini- 
 tial deflection 
 at center sup- 
 port of 0.749 
 inch at, or 
 past, maximum 
 load. 
 
 Fig. 3 
 
 300,000 -POUND 
 
 HYDRAULIC 
 
 COMPRESSION 
 
 TESTING 
 
 MACHINE 
 
IJACA 
 
 Fif'.4. 
 
 CM 
 t 
 
 k1 
 
 Positive deflection 
 
 Eef ersnce 
 line 
 
 l\ 
 
 Deflection 
 readings | 
 taken at thid 
 point in 
 upper span | 
 
 I 
 
 I 
 
 l/'-i h 
 
 Pin 
 joints 
 
 Initial 
 deflec- 
 tion at 
 center 
 support - 
 
 Rigid 
 supporting 
 structure 
 
 Upper 
 sup-Dort 
 
 ! / 
 
 Deflection 
 readings 
 taken at thii 
 point in 
 lov/er span 
 
 -it - 
 
 y 
 
 stiff 
 strut 
 
 1/2 h 
 
 i 
 I 
 
 Center 
 support 
 
 3/4 h 
 
 r-V- 
 
 h ~ 67 7/8 ii 
 
 ..-V 
 
 Position with 
 no deflection 
 
 LovvTir 
 support 
 
 Figure 4,- Diagraminatic sketch of test specimen. 
 
CM 
 
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 NACA 
 
 Figs. 5, 7, 11, 
 
 
 
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 Figs. 6, 8, 9, 10. 
 
 
 
 
 
 
 
 
 • 
 
 
 
 
 ction data, 
 at center 
 
 
 • 
 
 « 
 
 
 
 
 
 
 
 ction data 
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 support, 0.^ 
 
 
 
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 support, -0. 
 
CM 
 I 
 
 1-^ 
 
 NACA 
 
 Figs. 12, 13. 
 
 -^oo 
 
 -.8 -.4 .4 .8 
 
 Initial deflect ion at center support, in. 
 
 Figure 12.- Variation of difference in predicted critical 
 load with initial deflection of the center 
 support. 
 
 
 
 
 
 
 1 
 
 \ 
 
 
 
 
 
 3840 
 
 
 
 
 
 / 
 
 \ 
 
 \ 
 
 
 
 
 
 
 
 
 1 
 
 
 \ 
 
 
 
 
 ~ 3SB0 
 
 
 
 
 / 
 
 
 
 
 
 ~~~^ 
 
 \ 
 
 
 
 
 
 / 
 
 
 
 
 
 
 N 
 
 3800 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3780 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 -a -.4 .4 .8 
 
 Initial deflection at center support, in. 
 
 Figure 13.- Variation of average predicted critical load 
 with initial deflection of center support. 
 
UNIVERSITY OF FLORIDA 
 
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