torsional properties of fabricated i-beam and box sections 1941

8/13/2019 Torsional Properties of Fabricated I-beam and Box Sections 1941

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Lehigh University Lehigh Preserve

Fritz Laboratory Reports Civil and Environmental Engineering

1-1-1941

Torsional properties of fabricated i-beam and box sections, 1941I. E. Madsen

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Recommended CitationMadsen, I. E., "Torsional properties of fabricated i-beam and box sections, 1941" (1941).Fritz Laboratory Reports.Paper 1234.h p://preserve.lehigh.edu/engr-civil-environmental-fritz-lab-reports/1234
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TORSIONAL PROP3RTIESOF FABRICATED I R ~ AND BOX SECTIONS

by I . E. ~ 1 a d s e n

1 - SYNOPSIS

This r epor t gives the r e su l t s of a se r ies of to r s iont e s t s on r ive ted and welded I-beams, and r ive ted and weldedbo x gi rders . Due to the s l ipping which occurs in the seams,the f a ~ r i c a t e dgi rde r s were ne i the r as s t rong nor as r i g i das the equivalent gi rde r sect ion without l ong i tud ina l seams.

On the bas i s of the t e s t s which were made i t wasfound t h a t a r ive ted sect ion was abqut oneth i rd as s t i f fin tors ion as a sect ion in which no s l ipping occurs . Des ign methods fo r computing the s t resses and twis ts of

bui l t -up girders are included in th is re p o r t .2 - INTRODUCTION

The s t resses an d twis t in a hollow tube may be predic ted f a i r l y accura te ly by the theore t i ca l f o ~ m u l a eproposedby R. Bredto. These formulae s t a t e tha t the average shears t re ss in the wal ls of t h e t w e due to torque i s :

\ i = -

2At

The angle of tw i s t per u n i t length i s :

e - M- GJ

to the polar moment of i n e r t i a and

J = 2 S.:J t

length and th ickness of each s ide .here s and t a r e the

i s the shearing s t r e s s in pounds per square inch , M i s thetwis t ing moment in inch-pounds, t i s the wall th ickness ofthe tuoe, A is the area of the surface oounded by the centerl ines of the tube wal l s , G i s the shear modulus about11,500,000 Ib per in 2 fo r s t e o l and J i s the to r s iona lconstant in in 4

J i s analogousfo r a hollow tube:

The above formulae apply to hollow tub es of a l lshapes which are bounded by one s ingle l i n e . The formulaeare approximate, but give close r e su l t s when the th icknessof the tube wall i s small in comparison with the dis tanceof the wall from the center of grav i ty of the tube . Forcrane. gi rde r s th i s approximation i s usua.lly smal l .- - - - - - - - - - - - ~ - * Ass i s t an t Research Engineer, Fr i tz Enginee ring Labora to ry

Lehigh Univers i ty, Bethlehem, Pennsylvania R. Bredt , V.D.I. Vol. 40, 1896, p.8l5


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The formulae are derived fo r one piece tubes, thusthey do not necessa r i ly apply to bui l t -up sect ions s inces l ipping may occur along the longi tudinal seams. The to r

s ional s t reng th of a bui l t -up se ctio n, lo osely b ol te d together, would be only the sum of the s t rengths of the .i nd iv id u al p ie c es . This s ~ ~ i s but a f rac t ion of thes t reng th of the sect ion as a t ~ e In a continuously weldedsect ion , on the other hand, no s l ipp ing can o ccur along theseams and the twis t ing s t reng th s ho ul d e qu al t h a t of theso l id tube as predic ted by the theory. A bui l t -up r ive tedor t igh t ly b ol te d s ec ti on should have proper t i e s somewhatl e s s favOl able than the welded or so l id tube s ince a l imi tedamount of sl1.p may occur.

This se r ies of t e s t s was made to determine how theactual behavior of bui l t -up box sect ions compared with tha tof one-piece sec t ions . In addi t ion , bui l t -up I-beams werealso t e s ted to compare t h e i r behavior with so l id I-beams,fo r which ra t iona l methods of analys is are avai lable .

P ilo t te s ts were made on a se r ies of small 2 by 3in . box sec t ions , 50 i n ~ o n gand made of l / 8 i n p l a t e .The s ec ti on s c on si st ed of welded and bol ted boxes as ShOivnin the drawing of Fig . These boxes were te s te d in a to rs ion machine of 24,000 i n - l b . capaci ty. Fig . 2 shows apic tu re of the bol ted bo x being twis ted in the tes t inG machine.

The b o lt ed g ir de rs were made to sim ulate the act ion

of a r ive ted gi rde r by using 1 Jo lt s w hi ch f i t t e d t igh t ly inthe ho les . Tests were made on the bol ted g i r d e r with thediaphragms f ~ s t n eon one, two, and three s ides , and withdiaphra.gm spacings varying from three to fo r ty -e igh t inches .

Pi lo t tors ion t e s t s were also made on two weldedboxes, one had diaphragms as sho IJI. Il in Fig . 1 , the other hadno diaphragms. Three t e s t s were made on the box with thediaphragms. I t was f i r s t tes ted with the sect ion shown inFig . 1, then i t was tes ted with.f18Jlge angles welded to thebox. to make the sect ion similal to a r ive ted sec t ion . Fina l l y, the top pla te an d angle wore burned off , leaving apla in rectangulo.r box, and the to r s iona l constant was againfound.

The welded bo x in the p il o t t e s t behaved as the theoryprodic ted , so fu r the r tors ion t e s t s were no t deemed necessaryon the welded sec t ions . However, the twis t and th o s t ressesin the bol ted box wero so much higher than tha t predic ted bytheory, i t Vl 2,S thought advisable to make add i t iona l t e s t s onr iv et ed s ec ti on s. Tests were made, therefore , on four I-beam - - - - - - * STRUCTURAL BEAMS IN TORSION Inge Lyse and Bruce G. Johns

ton, Transa.ctions A.S.C.E. , 1936, p.1389Bethlehem Manual of Steel Construct ion, p.279


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3

and three bo x sec t ions . The detai . ls of the I-beams are shownin Fig . 3 . The de t a i l s of the bo x gi rde r ca.lled T- 6 i s shovmin Fig. 4. The other bo x gi rde r s were s imi la r to T-6 exceptfo r the diaphragms. T- 5 had no diaphragms and T-6 had four i p l ~ g mequal ly spaced.

Since these specimens were too la rge to be tes ted inan ordinary tors ion machine, they were loaded by a spec ia lr ig at tached to a 300,000-lb. Olsen machine . Fig . 5 and 6show the de ta i l s of the loading r i g and also show gi rde r s T-2and T-6 being t e s ted .

The twis t in the girders was m ea su re d b y means ofl eve l bars . The s t r a in s , from v n ~ i c hthe s t resses were determined, were measured with a 2- in . Olsen and a 10- in .Whi t temore s t r a i n gauge on the outs ide of the boxes and ~ o t ; h::i0:; s of the I -be ams The s t r a ins : ~ l e r emeasured longi tudina l l y along the gi rde r and on stre. in rose t tes located on thewebs and f lange. The shear s t resses were found from thes t r a in r o se t t e s . So fa r as the author knows very few t e s t shave been made in which the s t resses have been measured inbo x oeams under to r s iona l loadso.

The s l i p in the seams of the gi rde r was measurea the Whittemore gauge Ii i th one end of the gauge on one sideof the seam an d the other end on the other s ide of the seam.The locat ions of the gauge l ines are shovm in Fig. 7 . Thegauge l ines marked 3, 6, 9, and 12 are a measure of thes l i p when corrected fo r the actual s t r a in in the elementsthemselves.

3 - TEST RESULTS

a . Pi lo t Tests _ Table I presents the r e s u l t s ofthe twis t ing t es t s on the p i l o t specimens. The tors ionconstants of the welded boxes agree with the theore t i ca lvalues of 2 .09 , in 4 The f lange angles an d outstanding port ion of the coverplate have l i t t l e e f f e c t on the r e s u l t sNeither did the diaphragms have any appreciable e ff ec t ,since in these gi rde r s no s l ipping oc curre d to br ing thediaphragms in to ac tio n.

The values of the tors ion constants ; as shovm inTable I are quite v aria ble fo r the bol ted gi rder. Theyare much l e s s than tha t given by Brod t s theory fo r a box. - - - - - - - - - - - TORSION TESTING ~ H I N EOF 750,000 INCH POUND CAPACITY

Briice G Johnston, Engineering News-Record Vol. 114,N o . 9 , p .3 l0 , February 28, 1935

o TORSION OF RECTANGULAR TUBES W i l l i ~ nHovgaard, Journalof A pplied Mechanics, September 1937, p. A-13l


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This i s due to the s l ipping which occurred along the seamsof these gi rders . s the t ab le shows the diaphragms hadan important e ff ec t on the twis t ing of the beam. V{hen thediaphragms were fas tened on three s ides they were much moreeffec t ive than when fastened on two s ides . Secondly increas ing the number of diaphragms when bol ted on threes ides increased the s t i f fne s s of the gi rders .

Fig. 8 gives the r e su l t s of the tors ion t e s t on thewelded box. The s t r e s s e s as measured are about fo r ty percent grea te r than the theore t i ca l as computed by B r e d t stheory. The t w i s t checlrs c lose ly. Fig. 9 gives a s imi la rcurve fo r a bol ted g i r d e r. Two computed shear s t resses areshown in t h i s f i g u r e . The lower s t r e s s curve marked 1 i stha t given by B r e d t s theory while the higher value marked2 includes the shear s t r e s s due to the twis t ing of eachside of the box. This second fac to r i s small fo r a box withno s i i p and can be sa fe ly neglected . I t i s l a rge howeverin the p re se nt ca se .

Fig . 10 gives the r e su l t s of the to r s ion t e s t on thebol ted gi rder with the diaphragnls spaced a t 24 in . I t showsin de t a i l the act ion of the g i rde r. When the gi rde r i s f i r s ttWisted as shovm in the curve marked F i r s t Run the bo x i si n i t i a l l y very s t i f f due to the f r i c t i o n of the seams. How-ever as the load i s increased the jo in t s s l i p and thef r i c t i o n i s gradual ly broken. The por t ion of the curve marked shows the twis t which takes place while the bo l t sare s l ipp ing . Most of the t o t a l twis t occurs in th is range .At point D the bol t s s t a r t to bear an d the por t ion of thecurve beyond D shows the increased r e s i s ~ n eto s l i p whichr e s u l t s At po in t F the load was re leased and the sec t ionFH on the curve shows the e ff ec t of the r e t ~ ~ nf r i c t i o n inpreventing the gi rder from untwis t ing . I f the t e s t i ngmachine had been b f such a type tha t the bo x could havebeen twis ted in the reverse di rec t ion i t i s expected tha tthe r e su l t an t curve would have a l a rge hys te res i s loop.

Fig. 11 shows the var ia t ion in the to r s iona l s t i f f -ness as the number of diaphragms i s increased.

b . I ~ e a mTests - The t e s t r e su l t s on the I b e a ~ swere qui te s imi la r. T-l and T- 2 were iden t ica l in sec t ionbu t T-2 was welded and T-l was r ive ted . T-3 an d T- 4 weres imi la r to T-l and T-2 except t h a t the sect ions of the formerwere 3/8- in . th ick an d the sect ions of the l a t t e r were 1/4in . th ick .

Since T-2 and T-4 were welded l e s s s l i p could occur.Therefore the s t resses an d twis t s in these gi rde r s shouldbe l e s s than those of gi rde r s T -l and T-3.


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Fig. 12 compares the twis ts of the four I-beam g i r -ders under a torque load.. The ro ta t ion given i s the averageof the ro ta t ion of the f langes and the webs except fo r T 3fo r which the top twis t i s given. The top twis t of T 3 i ssomewhat l e ss than th e av era ge s ince the web usual ly twis ted a i t t l e more than the f lange. The values fo r the to rsion c on sta nts a re a pp rec ia bly l e s s than the theore t i ca lvalues fo r the equivalent so l id I-beam.

Fig. 13 gives the magnitudesof the shear s t ressesin the web and co ve rp la te o f the four I-beam g i rde r s . Thisf igure shows tha t in the sanle g ir de r s ec ti on as fo r exampleT 3 and T-4 the measured s t resses in the r ive ted sec t ionare about twice tha t of the welded sect ion. This i s the res u l t of the g re ate r tw is t of the r ive ted g i rd e r. The shears t re sse s in the f lange are grea te r than those in the web.Theoret ica l ly disregarding s t ress concentra t ions thef la ng e s he ar in g s t resses should be twice the web s t ressesfo r the gi rde r s tes ted since the f lange i s twice as t h i ~as the web.

Table gives a comparison of computed a nd m ea su re ds t resses fo r the 40 OOO-in-Ib. load. The shear s t resseswere computed by the formula t G 6 where i s the shearing s t r e s s an d t i s the thickness o f the sect ion considered.This formula comes d i r ec t l y from the formulae fo r twis t an ds t ress of a narrow rec tangular sec t ion . The web s t ressescheck closely as shovm by the t ab le . The f lange s t resses arel a rger than the web s t resses but smaller than the t h eo re t i c a l .This shows tha t some sl ippage i s ta ki ng p la ce end t h a t thef u l l thickness of the flange can not be assumed to be act ingas a u n i t .

Fig. 14 gives curves fo r th e var ia t ion of the s l i pwith the twis t and the moment fo r girders T-l and T-2.Similar r e su l t s were obtained fo r T- 3 and T-4. The s l i pgiven i s the t o t a l of the s l i p s in a l l the se l S around theg i rde r. t should be noted tha t fo r T- l the twis t i s propor t iona l to the s l i p The s l i p s fo r T 2 are much smal lerthan fo r T- l . Trle v l ~ s f o rT 2 are not ac tua l ly s l i p ss ince the seam was welded but since the w eld ing was i n t e r -mit ten t the welds are s t ra ined higher than the adajacnt

pla tes-and th i s r e su l t s in a r ela tiv e s tr ai n between thep l a t e s .

Secondary longi tudinal d i r e c t s t resses are se t upin a twisted I - sec t ion or bo x as a r e s u l t of the tendencyof the f ib er s f ar th es t from the center of twis t to belengthened. In Fig. 15 are plo t t ed the curves of d i r ec ts t r e s s i n T-I as actual ly mec.sured.Table gives a com-par ison between computed values of the s t r e s s and them e a s ~ e dvalues a t th e 40 OOO-in-Ib. load. These s t r e s s e s


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- 6

are q u it e a pp re ci ab le . The formula fo r the d i r ec t s t r e s sin the I-beam was der ived in a manner s imi la r to tha t whichTimoshenko uses fo r the rec tangle in to r s ion . t should benoted t h a t the s t r e s s increases with the square of the twis t .Since the bui l t -up beam twis ts more than the so l id beam,these d i r ec t s t resses are much more im po rta nt th an in theso l id beam. The computed s t r e s s in the webs checks f a i r l ywel l with the theory but the s tre sses in the f lange do no tcheck as wel l . This 1s probably due to the s l ipping whichoccurs, as indicated by the f a c t t h a t t he s t r e s s a t theedge of the cover pla te and a t the edge of the f lange anglei s qui te d i f f e r en t , showing a re l a t i ve s l i p

c . Box G ird er Tes ts - The three bo x gi rde r s wereal ike except fo r diaphragm spac ing . T- 5 had no diaphragms,

T-6 had one diaphragm in . each end, and T- 7 had four diaphra@ns equally spaced. After T- 7 had been t e s ted the f i r s ttime, the seams were welded with in te rmi t t en t welds to prevent sl ippage and the girder r e t e s t ed . This t e s t wascal led W-T-7. .

Very l i t t l e difference was found in the t e s t s on thethree boxes, so apparent ly the diaphragms were of i t t l e eff e c t in the e l a s t i c range . These d ia ph ra gm s w er e r ive tedonly to the webs as i s the usual prac t ice a.nd thus are r e l -atively ine ffec t ive in prevent ing s p ~ Since the r e su l t sfo r a l l girders are so very much a l ike , the t e s t r e su l t sw i l l bo given only fo r T-6.

In Fig. 16 i s plo t t ed the twis t of the box as themoment was increased. In Fig. 17 i s shovm a number ofcurves showing the measured s l i p and measu re d s t resses inthe box.

The measured shear in tho f lange and web are f a i r l yclose to the t h eo re t i c a l . The theore t i ca l shear curvemarked 1 i s the s t ross as found from B r e d t s formula. Theother theore t i ca l curve marked 2 i s the sum of the s t r e s sfrom Bred t s theory and the s t r e s s due to the twis t ing ofthe elements of the box.

The shear curves are computed from the s t r a in r o s e tte data an d are the shears act ing on the cross - sec t ion ofthe gi rde r p e r p o n d i ~ u rto the long i tud ina l ax i s . Therose t t es in the por t ion of the webs an d f langes forming thebox showed tha t the d i r ec t s t resses on these cross - sec t iona lplanes were neg l ig ib le .

In the rose t tes on the outstanding port ions of thecover plates and f lange angles outs ide the box sec t ion , themeasured shear s t resses were l e s s than the t h eo r e t i c u l sheu rs t resses in the box. The d i r e c t s t resses determined by theserose t tes were apprec iable , showing tha t these sect ions weren ot s ub je ct ed to pure shear. STRENGTH OF M TERI LS Vol. 1, S.Timoshenko, p.89


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The d i r ec t s t ress a t the edge of the f lange asshown in Fig . 17 i s apprec iable fo r high loads but in theworking range th i s s t ress i s zero . This s t r e s s i s a sec

ondary s t r e s s an d increases with the square of the twis t .The s t r e s s in the diaphragm i s ra th er la rg e. This

s t ress was taken on a gauge l ine 45 with the hor izon ta ls ince i t was thought tha t the s l i p in the gi rder woulds t ress the diaphragm with a tWist ing moment. However t h i smeasured s t ress i s much l a rger tl1an any which were computed.

The s l i p in the gi rder i s qui te appreciable . Thes l i p did not s t a r t with the i n i t i a l torque but a t a torqueload of about 45 000 i n ~ l b I f an i n i t i a l tension of 32 000Ib per sq in . i s assumed in the r i ve t s an d a coe ff i c i en t off r i c t i o n of 0.2 i s assumed to be act ing between the p l a t e sthe load a t which s l ippage w i l l occur i s 44 000 i n l b .

In making these t e s t s one has to be careful tha tthe torque i s a pp li ed e qu al ly to the vn10le g ir de r s ec tio n.The t e s t on T- 5 was made with the torque appl ied to thewebs. Fig. 18 shows tha t the top f lenge and web did nottwis t equal ly. The average ro tQt ion however i s about thesame as t h a t fo r T 6 and T-7.

The t e s t r e su l t s for T 7 a f t e r the seams were weldedare s h o ~ ~in Fig. 19 . I t i s seen tha t th i s gi rder i s thenmuch s t i f f e r . The shear curves also check the t h eo re t i c a l

computed f rom Bred t s formulae because thereW

no addedtwis t due to s l i p .

4. IS USSION OF RESULTS

Pi lo t Tests The p i l o t t e s t s on the bo x girdersshowed tha t the ac tua l twis t in a weld ed bo x agreed with thet h e o re t i c a l an d tha t Bred t s formula gives a good value fo rthe tors ional constant . These t e s t s also showed t h a t thef lange angles an d outs tanding edges of the cover p l a t e hadl i t t l e e ff ec t on the to r s iona l constent .

Theshear s t resses

onthe outside of the box were

about f o r ~ per cent grea te r thpn the theore t i ca l averagevalue from Bredt s formula. This may be due to the eccent r i c appl ica t ion of the load t h r o L ~ hthe f i l l e t weld. Sincethe pla te i s th in and the box sect ion very sm all th i s e f~ e c t i s e ~ p h a s i z e din th is t e s t an d i t would be picNed up the c o n ~ a r a t i v e l ylong 2 - in . Gauge len g th of the s t r a i ngauge. Since th i s e ff ec t was not no t i ced in the l a rg e rspecimens i t may be a p ecu l i a r i t y of the small specimen.


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The p i l o t t e s t s on the b ol te d g ir de rs probably haveno prn.ct ical s igni f icance by themselves. Their chief valuei s the t they exaggerate and emphasi ze the eff ec t s d.ue to

s l ip pin g in the seams of a r iv et ed g ir de r.As

shown by Fig.11 the to r s iona l s t i f fne s s of the gi rder approaches t h a t ofthe Sunl of the component par t s as the r e s t r a i n t s to s l ipp ingare removed.

b. I e ~ ~Tests The shear and twis t of a longnarrow rec tangle are given by the formula

= Mbc 2

and e = Mbc G

and r cG6where i s the shear s t r e s s e i s the angle of twis t inradians per inch b i s th o width of the rec tang le and ci s the thickness of the rec tang le . Since an I-beam i s com-posed of a n l l i ~ b e rof rec tang les an approximate so lu t ionfor the to r s iona l s t resses and twis t can be made dividingthe I-beam in to a number of rec tangles an d summing up thesec t ions . However since the pla te thickness en te r s intothe formulae as square and cube terms i t becomes a ques t ionas to what th ickness to use when severa l rec tangles s re puttogether. Fig. 20a gives u diagramatic idea of the shear

s tr es s d is tr ib u ti on when s l ipping i s allowed to occur f r e e l y.F ig .2 0b g iv es a si lni lnr pic tu re fo r the so l i d gi rder in whichno s l ipping occurs . The increased s t reng th due to the grea ter effect ive m O ~ n tarm of the shear s t r e s s i s apparent . Fora r ive ted gi rde r whore some s l ipping takes place the r e s u l t -ant s t r e s s d i s t r ibu t ion f a l l s between the two dis t r ibu t ionsshown in Fig. 20 and 20b.

In Table are given the computed to r s iona l cons tan t s of the various girdors t e s ted . Two values are givenone i s c O ~ u t e dassuming f ree sl ippage and the other i s com-puted on the bas i s of no s l ippage. The measured to r s iona lconstant fo r the r ive ted gi rde r s average a l i t t l e more thanone- thi rd of tha t fo r the equivalent s o l i d sec t ion . Thewelded girders average 68 per cen t . The welded I-beam gi rders do not have a fac to r of 100 per cent since al thoughthe weld does prevent s l ipping a t the toe of the angler e l a t i ve s t r a i n can occur a t the corners of the angles .

OI design computations i f a value of the to r s ionconstant of one- thi rd the so l id sect ion i s used the computedangles of twis t should be f a i r l y close to the actual values .To compute the s t r e s s e s these values of e should be used inthe formulae. As s: 1own in Ta ble th e computed s t r e s s e sare c lose enough fo r d es ig n p ur po se s. There i s l i t t l e need


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9

to go in to an y refinements in the ca lcu la t ions s ince thebehavior of the gi rde r w i l l depend. so l a rge ly on the s l i pSince th i s s l i p depends on many fac to rs , and i s r e l a t i ve ly

unpredic table , the behavior of the gi rde r s m y be quitevar iab le .

The di rec t s t resses shown in Table are qui tel a rge . Since the di rec t s t resses increase with the squareof the twis t , and the twis t of the r ive ted gi rde r i s threetimes tha t of the so l id gi rder, these d i rec t s t res se s w il lbe nine times those in the so l i d g i rde r. The d ir ec t s tre ss esare secondary s t resses and therefore have l i t t l e e ff e c t onthe ul t imate load-carpying capaci ty of the g i rde r. Howevera permanent twis t w i l l r e su lt in the gi rder, i f these s t r e s s -es exceed the yie ld poin t .

c . Tests of Box i r e r ~- The t e s t s on the r ive tedgirdern showed t h a t they behaved about as predidted by Bred t sformula, except as th i s i s modified by s l i p Table showstha t the tors ion constant i s about oneth i rd tha t which i spredic ted by Bred t s theory. In computing th is tors ionconstant , one must remember t h a t the bui l t -up rec tangularsect ion i s not a box but a f igure more l ike an H-beam s incethe s t r e s s in the f lange must t r ave l outs ide the bo x sect ionto the r ive t and back again before i t i s t r ans fe r red to theweb. Fig. 21a shows the sect ion act ing in the s t r e s s t r ansf e r The dot ted l ine shows the edges of the sect ion used tocompute A in B red t s formula. Fig. 21 a also gives a dia

gramatic pic tu re of the shear s t r e s s t r ans fe r in a bo x sec t - .ion where s l ipping i s allowed to occur. Fig. 21b shows theshear s t r e s s t r ans fe r when no s l ipping occurs . The reasonfo r the effec t iveness of the box sect ion i s obvious when onenot ices the la rge effec t ive moment arm of the shear s t r e s s

The shear curves fo r Fig . 17 show tha t Bred t s theorygives a f a i r apprOXimation fo r the average shear s t r e s s , andth i s computation ca n be made more exact by adding the s t r e s sdue to the twis t of the s ides of the box. Bred t s theory assumes tha t the shear s t ress i s constant through the th icknessof the box, and when the thiclm ess of a wal l i s small in compar ison with the d is tance of the pla te to the center ofgravi ty of the box, th i s approxj_mation i s sm all . A ctually ,the s t r e s s increase from the ins ide of the box wall to theouts ide . The cQrrect ion added to th e av erage shear as givenby Bredt s formule. gives the m ximum s t r e s s on the outs ideof the box. Since the r ive ted box twis t s more than the so l idbo x the correc t ion i s l a rger in the former Case. In Fig . 19th i s correc t ion i s neg l ig ib le s ince the welded box did nots l i p resu l t ing in a smal ler angle of r o t a t i on .

The d i r ec t secondary s t r e s s in the box as shm n byFig . 17 can be sa fe ly neglec ted in the working range .


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- 10

The s t r e s s in the diaphragms was l a rge r than expected. I t may have been affec ted by loca l bending andreadjustments. The d i r ec t s t resses fo r the welded girderwere much l e s s than those fo r the r iv e te d g ir de r.

The measured s l i p in the jo in t s as given in the r epor ts i s the t o t a l of the s l i p in a l l the seams. The ac tua ls l i p in anyone corner of the box i s the plo t ted s l i p divided by four. I t can be shown* fo r a box with f ree s l ipp ingseams (no r ive t s or welds t h a t the long i tud ina l motion orwarping of an y point in the box sect ion i s the prod uct ofthe x an d y coordinates of the point mUlt ip l ied by the angleof twis t e when s l ipp ing occurs in a l l the seams. Since inthe same corner, the web and the f lenge warp in opposite d ir e c t i o n s t h e r e l a t i ve s l i p i s equal to twice t h i s product .Thus the r l ~ t v s l i p in the corner of ~ bo x of height hand width w would be whe/2. When the bo x i s r ive ted , theac tua l s l i p i s l ess than the computed va.lue above, an d t h i sac tua l s l i p i s a measure of the tors ional constant . For thegauge l i n e s on which s l i p was measured in the t e s t the r e l at ive s l i p fo r loose sewns i s 426. For gi rder T-6 the measured s l i p fo r the s tr aig ht l in e p or t io ns of the s l i p curvei s 10.5 Mt 10 -8 fo r one seam.

Then the twis t angle i s given by:

6 = M e due to s l ipGJ no s l ip

6 = M 10.5 M(10) \8 Go r ., GJ 42 G

= ...1...- + ...1...- M (21 1.2G 57.8 33.3 G

The value of 21.2 i s the effec t ive to r s ion constant , and provides a check on the value computed di rec t ly from th e curve.This check i s n ot a bs ol ut ely independent , since the value of s inherent in the second term.

5 - CONCLUSIONS

The to r s ion t e s t s herein repor ted indicate t ha t the.fol lowing r e su l t s may be concluded.

1 . Fabricated I-beam and box sect ions do not behavethe same as the equivalent s o l i d sec t ions .

2 . The s l i p which occurs in the seams of bui l t -upsect ions i s apprec iable undor tors ional loading and increasesthe twis t an d s t resses of such sect ions markedly.

~ - - - - - - - - - - - - - - - - - - * N.A.C.A. Roport No. 502, T ~ R YFOR R I ~ f f i YFAILURE OF

\ . STPJLIGE I 1 CENTR LLY LO DED COJIuUMNS


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3 . The to r s iona l constant of the r ive ted bui l t -upI and box sec t ions tes ted in th i s progra 1l was a.bout oneth i rd t h a t of the equivalent so l i d sec t ion .

4. f the twis t angle i s computed using the r e

duced value of the tors ional constant , shear s t resses computed from th i s value wi l l agree f a i r l y wel l with theac tuul values .

5 . Direct secondary s t resses a.re quite la rg e inthe bui l t -up I - sec t ion an d may be impor tant .

6 . D irec t secondary s t resses are small in aboxsec t ion when s t ressed i n the working range .

~ The d i r ec t s t r e s s e s vary with the square of thea.ngle of ti.vist . .

8 . Bl edt s theory gives good e.pproximate valuesfo r the shear s t r e s s in bo x sec t ions .

9 . In applying Bred t s theory to a fabr ica ted boxsect ion, one must be care fu l to use the sec t ion bounded bythe s t r e s s path . This wi l l not be n rec tangu la r soct ionwhen the corners are formed by r ive ted ang les .

10. Build-up welded I b e l l i ~ sfabr ica ted with f langeangles had a to r s ion constt mt two-thirds th2,t of the equival en t so l id sec t ion .

11 . Buil t -up welded box girders had a to r s iona lconstant close to t h a t predic ted Bred t s theory.

12. The outs tanding legs an d par t s of 8. fabr icatedbox s ec tio n n ot included in the bo x have l i t t l e e f f e c t onthe to r s iona l proper t i e s of the sect ion.

13. The l imi t ing values fo r the tors ion c on stcnt o fa fabrice. ted beam w i l l be the value fo r the so l i d sect ionsmd the sum of the values of the component pa r t s . Tho actualvalue of th0 constant wi l l be between th o boundary values andwi l l depend on the degree of s l i p

6 - ACKNffiVLEDGlmNTS

These t e s t s are a pa r t of a program sponsored andf inanced by the Associa t ion of Iron ~ Stee l Engineers a tthe Fr i t z Enginee ring Labora to ry of Lehigh Univers i ty. Thework i s boing car r i ed out in d i r ec t c oo pe ra ti on w it h theCrane Specif ica t ions Committee of the A.I . S.E. under thechairmanship of Fre.nk W Cramer. Spocio.l a clmovllodr.,mcnt i sdue to Bront Wiley, Managing Director 9f the Associa t ion .The genera l progr lu i s undor the direct ion of Bruce Johnston,Associate Director of the Laboratory. Many thanks c.re alsodue Hale Sutherland, Director, and H.J . Godfrey, Enginoer ofTes t s of the laboratory, fo r t .heir cooporn t ion in tho invost igs . t ion .


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T LE I

WELDED GIRDER

MeasUl ed Values of in 4 Remarks on Test2.17 3- in . Diaphra.gm Spacing

2.25 3 - in . i o p h r a ~ nSpacing Flange angles added

2.03 3 - in . Diaphragm Spacing Flange angles cut off

2.09 o diaphragms

2.09 Theoret ica l value byJredt1s Theory

OLTED GIRDER

Measured Values of n 4

Slipping B u i l t Up Fr ic t ion

Remarks on Test

0.0391 0.242 3 - in . Diaphragm SpacingDiaphragms bol ted on 1 s ide

.0393 .445 3- in . Diaphragm Spacing

Diclphragms 001 ted on 2 s ides.1090

.0647

.0639

.0222

.0250

.0204

.0146

.180

.229

.282

.131

.264

1.35

1.32

3 - in . Diaphragm SpacingDiaphragms bol ted on 3 s ides

6- in . Diaphragm SpacingDiaphragms bol ted on 3 s ides

12- in . Diaphragm SpacingDiaphragms bol ted on 3 s ides

24- in . Diaphragm Spacing. Dic.phragms bol ted on 3 s ides

48- in . Diaphragnl SpacingDiaphragms bol ted on 3 s ides

No Diaphragms

Theoret ica l value fo r f ree lys l ipp ing bo l t s


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T BLE I I

Direc t s t r e s s i n Di rec t s t r e s sShear in Web Shear i n l e ~Web, 4 i n . from t Edge of F l ange

Twis t , e i nGirderRad ians / i n .

Computed ComputedAngle

Cover ComMeasured 1 = t G e Measured 1- = tG8 Measured Computed Pla t e puted*

Measured

T -l 0.0057 16,800 17 ,100 26,600 34 ,200 -12 ,6 00 -10 ,300 + 11 ,5 00 + 16 ,4 00 +12,500

T- 2 .0040 12,800 12 ,000 16 ,000 24,000 3,600 4,900 + 9,500 + 6,000 + 6 ,000T- 3 .0024 13,400 10,800 16 ,000 21,600 - 1 ,800 1,800 + 3 ,200 + 3 ,700 + 2 ,100T- 4 .0014 6 ,200 6 ,300 7,600 0 12 ,600 1,2 00 600 + 80 0 + 70 0 + 600

~

A ll v alu es g iven f o r to rque load of 40,000 i n l b .

Formula fo r d i r e c t

f = E e ~

L

s t r e s s a t e ~ ~ o f f lange:

t h 3 + 6h 2 + 2 t t w324

(h t + 2 t w +

+ 2 t h 3 16 t a h t - 4at )

0

JFormula fo r d i r e c tf = e ~

s t r e s s i n web:

th 3 + 6h 2 + 2 t r W31,24 (h t + 2 t t w ~

h = he igh t o f webt = web th ickness

y = d is t i l l l ee = angle of

t = f lange p l a t e th icknessw = width o f f lange

to p o in t in web where s t r e s s i stv l i s t i n rad ians

ti l = th ickness o f f lange anglea = dis tance to bottom o f f lange angle

computed


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TABLE

C9mputed J Ratio Meusured Rat io Rat io-Girdor Sum of

o l ~ J Col.4 Col.4Sol id

ndividuul Col.2 n 4 C o l . l Col.2

Par ts Beam in 4

- - - _ 11 2 3 4 5 6

T l 0.26 1.20 0.22 0.49 I 1.89 0.41I

T 2 I .26 1.20 .22 .83 I 3.20 .69I

I IT 3 .88 3.64 .24 1.10 1.25 .30

T 4 .88 3.64 .24 2.43 2.76 .67I

rr_5 .38 .57.80 .011

20

40 53.70 .35I I

T Q .38 57.80 ~ O l 21.30 56.Q9 .37

T 7 .38 57.80 01 20.30 .1

53

50 .35

L WT 7 I C: 8O 154.0038 .01 1142.00 .94 Girder T 7 with in te rmi t t en t welds on s e ~ ~ s

to prevGnt s l ipping


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ig o l t e d Box i n Tors i on achine


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Fig Torsion Tes t on Girder T 2


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ig Torsion Test on Girder T


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torsional properties of fabricated i-beam and box sections 1941

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