,

EUROPEAN CONVC:NTlON FOR Cm~STRUCTWr'ML STEELWOR«

IrJTERi~AT'On!AL ASSOCIATIO;;! FOR BRIDGE AND STRUCTURAL ENGIl"zEERING

©rr ~u~~rL

PREL!MINARY REPORT

l'. ~l E' G,...,ole ? • f I ! . .Ie-

.40 .JI/i ~.-

i0 - l~~ - it)

APRIL 1977

t '

IN CO-OPERATION WITH

STRUCTURAL STABILITY RESEARCH COUNCIL COLUMN RESEARCH COMMITTEE OF JAPAN

, I

STASlllTY OF STEEL STRUCTURES - LIEGE 13-15 APRll19n - PRELIMINARY HEPORT

CENTRAllY COMPRESSED HIGH STREt-'GTH STEEL ROUND AND SQUARE TUf;ES ;

THEORETICAL AND EXPERIW,ENTAlINVESTIGATIONS

1 - 10L~0duc~ion

G. SAlliC. L. FINZI and C. URBANO Centro Stud; Cortruz ioni Metalliche (C.S.C.M.1

of the l,titulO di Scienza e Tecnica delle Costruzioni Politecnico di Milano - Italy

O·...:i::,S "LO the ii7:prover.lent of the steelr.i3.king ~echnology neri st~el C;Ui':: i:t i<os and new types of cross-sect ions are now available for the use in s:eel constructions. In particular the engi~eer r.~y ado?t ~eld­able steels with a very high yield stress and great duct ility c,r co1.d for;:-,ed sq,ua::-e and rectangular tubes for the design of the c08;:>ression Ti1~::-'::ers. 3ut, in principle, the carrying ca.pacity of these ty~(-S of cc ~ \.!",ns -:;,<=.'.1 not be evaluated with reference to the L.C.C.S. ~o"dirr,cn­s':'cr:al :occ)(ling curves III . In fac"t the european curves have been ca!'rieG ,")ut as the result of a wide experi:-nental and theoret iCol inves­tibation en rolled or welded colu:r.ns in steel with "the elastic 1init i:1 :!":e !"'c.:lge of 200-: 4fjJ N~-2151. Therefore ~he european cur'vi7S nay · no, i;;; .. ,ediately be adopted for COlU;:;;lS in steel "'l1:h a m"ch h':'s1-.er eles:ic liDit (in the range of [;lG~71G Nr;"i'7;-2 ) as here cor.si,.:'.'?red. fur::-.er;:-.ore the LC.C.S. curves );;ay !:>e not be apFlied to the cold for;:;ed sc.u2re "tubes because the structural ir.lperfectio:1s cue t·j the p2.~ ic"...!lcr rr.anufacturing procedure a!"e ent :irely different' fro;7l -::-t~0se

of -che relIed or helded shapes \-ihich have been considered in the t.C.C.S. studies. On "the o-::her side it is not worth es"tablishing new buckli..;g c~::-ves for a ,,<:"" ~~eel quality', beceuse the "theoretical and experimental ·,.,:01'1.;

needed is excessive for a material in continual progress. cr., the contrery it is possible to select among the european curves, "the O:1e which shows the best agreement with the experi~ntal and ~heoreti­cal results carried out on the columns in "the new steel. This ap~roach allows for important reduction of the experimental work needed to support "the selection of a particular buckling curve; it has been adop­tee in order to determine the buckling curves for rolled round t"bas and for tubes built-up by welded cold formed plates in Nic~age steel. This approach is based on "the remark that the differerlce of tr.e !'>'-1ckl­ing curves. one frOEl another, is mostly due to the S1:ruct~:!:'al ir.;perfec­t;;O:1S and the greatest difference occurs at the value 1 of th", r,O:1-dir:lensioZ1al slenderness. \orneD "the width to 'thickness T'a:tics a:-e jOri E:1cugh tr~t local buckling may be excluded, the $trength of c~e c01u",ns depe;)ds -.:pon the geometrical irnperfection~ and the Ill2.te:-ial b;"c7!·.oge­neirus, tr,erEfore . the experimental "ork ca.:;} be limi"ted to the r"easu­reDen"ts o~ these quantities (stub-cclumn tests, tensile tests, ::-eoidual stresses m-easurements etc.) and the load bearing ca?eci"ty cf i: he co­lu=s is carried out by a numerical simulation ?rocedu..'"'e 111\ "'h::ch takes into account the real geometrical imperfections and rr~terjal inho~oEe~ei~ies. This ap:;rocch cen be accepted because the results of "the :1u:"le.'ical sic..!laticn procedure have been checked against the buckling tes~ results a~G very good agreement has Deen found (the co~risc~ co~cerns

- 77 -

j"ollo\.ling thi:: l'hi1050k'hy th~ influen..: .. i:; l'.)illt~'c! ,'U~ '-'f th~ V.'ll·.lc'US

I·r);:~:ihl'-! imp.' .t~\.~t L.,tl::' on th .. ~ bt:~kling :~t~~l'll~:th "-'f tht.~ I' .. 'l! .. -'J l"'t.'UllJ

,,,1>"': in Ni'·II . ll~'· :'.,.· .. 1: it m.:ly ~ls,' b,' :'llf.g .. "",-",l ,.:> .IJ.c~I't rh.' 1.:. '(:4\.'S. rlJrv .. ' If,: 't r",,'r rh~ dt."~igi17 ("ll tht.' :~...tic.:II ;-;.iJ .. " ,-",f th~ luhul...!t' ':<.Jlur.ln~ in tlinl.i,!;r sT<,,~L As fdr '[h~ tu!:>.'>' l'ui.it-up by .: ... 1<1",d c01J for';.;ed p]att':~ .n'I:' .. ';."'n:'ideread, i~ ":('If."!t..~ '-'11t rh .. lt th .... ~u\. ... klinb ("-Ur'Vc"'

"ht,l:r.f·rj f1°0m tIlt, :.dmulation . 15 lr..litt:" "iiff .. ,t' .. 'nt rl''i. .. ''Ii:'\ lh .... L.C.L.S .. \.'lh!:.;' ..

:;(;m.., c()mpJl'i::<'Il~' r.u\"", .:-l.!ar th~ 1''''3:::C\l, ,~f tll.' p.'u·r ic·uldl' ::'hodp" ,'f tho:' I.t.:r;k 1 i ng f.~\Jt·V"; it::.:: shown th.d.t th~ bu~i...l i ng ~Ul"V\." ... 'Ot ..iinl,'Ld fr\,..110 th~ ::ir.:ulation {l1..1Y b .. l' .. duced 1:0 E.C.C.S. ncn-dimt'l1:"ional ew'v<- ".2" by introducillg ..J r.1"...!ifi.?c slenderness as it .. b ,:ugge::'tt'd. for t!1.:- J~"i6n of .!r:r:rutric.:llly l<'.1d~d anjl;les. in Chapt.:'l' 9.~ of th~ [.C.C.S. ~lilnu.ll

I hi "fld in tht' A.S.C. L Guide 15> I TIl', rrohlC'm is qui:-e different in the ,'",",,' of thL' ..:old form",d !>quare till· ... ,; alld tr..:: :lu::-Rrical simulation can \lot bo:' appli.:'d ' in ,,)I"J~r to c· .. ·du·:C' thl'! experi::;ental work need~ for determining thE' bu;:kling curve: th0. manufacturing procedure produces th~ residual stresses to b~ biaxial while the nUr.1erical si~ulation takes into ' account the uniaxial r.,,,idual stress~s only. In addition ther.? are not easy exp<"riw,:,nral m~thod~ fordeter~ining these distributions of biaxial stresses. for dll these reasons the buckling strength of cold formed square tubes can only be obtained by test5. The C.l.D.E.C.T. has sponsored d wide experimental program on square tuhf'S \.lith thicknesses from 0 to 1,) rml .:hich has been carried out through a joint venture of the Insritut du G'nie Civil of Li~8e eni~~r­sity and of the C.S.C.H. of Milan Polytechnic. Six groups of 12 buckling tests have ceen performed in the renge of the non-di~ensional slenderness from 0.82to 1.26:namely in tr.e rane~?f sl~ild€rnes::iC~ ~here the ir.i~i:rfect ions mas'!: 1] affect the b~a!'ing c3pacity 0= the colu~ns. The ex?eri~ental non-dimensional buckling curve {mean value of the test results less twice the standard devia­tion} is ::.ig~~I="" -~an :.":.C .. S .. C'..lrV~ 11 c";=or :;ar:e ("f ;o'!..!'1pli::i:cj" ,:~!'1d on the safe side, it could be suggested to adopt E.C.C.S. curv~ "e" for the design of centrally compressed cold formed square tubes with ,hicl"~ness up to 101m!.

2 - Rolled Rou~d Tubes Rolled round tubes p 108 X 6 are considered. in Nicuage steel ~ith

elastic limit of 670 !I ~-2 • O\.ling to the hea~ treat~ent a~d to the roller straightening, neither structural ncn geometrical imperfections are present at the end of the nanufacturing prccedure on the ste~l plant; but afterwords som~ i..,;;erfections IT.af be introduced during toe fabrication and t-!'1e erec­tion. Therefore the question arises how to take these imperfections into account in a lcgical way before perfonling 1:he buckling tests. It h3S been accepted to bend the coluJ:l!1s. in tre buckling plane. in order to ~btain at midspan a residual deflection of about 1/1000 of the leng~h (corresponding :0 the european standard). The residual deflections are connected ... i 1:~ the residual stresses • .:hich have c pat tel';'\ like that due to the cold straigtl:eninr:. T~elve buckling tests have been perfo~~d on the bent tubes at tha no;)-dimensiona: slenderness }. / A = 1.1. ,he comp::'ementcr tests ~ere: s~ub-col~~ tests, tensile~ests en coupons. N~asure~~nts of 1:r.e cross-se~tional di",ensions. In »articular the st\.!b-colu:nn tesc!';

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S'h:::'\·;EQ c:!.e2!"·2.~l t~at no res:.cual s'tresses are pre:::ent in the L":J~:':S !tc:s cel : ver<;c·'. T2~le 1 shows the results of the buc~ling H,S"ts in c:'::-.e;-;­s5.0;-,21 25 "Eell 25 in non-diDensio:1al form. The nu~e~~c~l si~ulation of the buckling tests has been c2rri~d C~~ tak i~g i~~c ~cco~~~ the following data. Tlle residual curvature of ~~e C € :ltEr" l:':-:e cf tr.e columns due to bending is deduced fro::1 tr.e r;;~cs\..::-,e­

Jjje~ts o~ -::-.'2 re~i':::v21 displacei7:ents .. The different resicii..!ul s~ress disLrib'..l~:'c:-~~, Et: the varicus cross-sections of the coluii.ns, are c~~ai­ned fr'c;:-, -::-.e c.nalysis of t:;e inelastic loading process 1.:;'ich lee.ds LO the Deas!.::'eG resic.ual displacements end curvatures. The el'lst ic li::-,it of the ~2-:erial is deduced froQ the stub-column tests. The resu2.;:s cf the m':IT,erical sirr.ulation are compared wi1::h the expe::-inen­tal OTIEeS in cable land very good agreement is found: therefore i~ ~ay be co~cl~d~d that the nu~e::-ical siDulation procedure is suitable for the study of the behaviour of the tubes.

.c-J o

(",m)

1~ 73 2~03 1~ gO 1,91 1~ 95 1 "" <I , 0" 1,85 1,93 1 .. 85 2,07 1 04 , v_

1 .. 80

::t:ecyty

0,5733 O,EW7 0,5[69 O~SE64

O,05f3 0,6677 0,6:367 O~6eE.3

0, 66e7 0,6596 0 .. 6648 0 .. 67CS

o/a l'

tests

0,6914 0,6289 0,6709 0,5717 0,6899 0,6554 0,6467 0,6461 0,6734 0,0514 0,6560 0,5412

0,6594 0,0204

Table 1

A a )"

2 (em)

-2 (kg=r )

19,36 66~11 19,29 66~11

19,42 66,01 ]9,23 67,66 18,98 67 .. 66 -19,04 66,89 19,29 67 .. 33 ]9,17 67 .. 33 19,42 65,91 19 .. 17 65~91

19,10 66,64 18,98 66 .. 64

mean value stcndard deviation

P/-JAX (t)

theory tests

86,17 88,S 85,25 80,2 85,49 86,0 86,41 87,4 85,30 88 .. 6 85,03 82,2 86 .. 85 84,0 85,87 83~4 85,59 86,2 83,34 82 .. 3 84 .. 61 83,S 84,81 81 .. 1

The influence of the shape of the initial out-of-SLrai~~ness i~~osed to the col~7~s on the load~bearing capacity may also be investigated by the s~~lation: the s~ne curve. the parabola, the real curve have been cons~dered. It has been found that this influence on the load bearing cepccity of the colur:~s is negligeable and therefore it Qay be concluded Lhat the method adopted to obtain the possible i~?erfectio~s is 2.cceptable. rurthernc~ the buckling curves were calculated taking in~o accou~c the poss~le i~perfections. The results are sumrr.a::-ized in fig.l. Curve 0 is calculated for tubes without :r-esidual stresses and .. ,ich ~he stand2rd e~ropean geornetriccl ipperfection. Curves 1, 2,3 and ~ pcir.~ out the effect of cold-straigthning by gagging and they refEr cO different a~?litudes of the ccrrectedout-of-s"trai~h~ess. Curve 5 is calcu12"ted for bent tubes with " initial out-cf-strcib~cness of 1/1000 of t:he length. The mean velue of the test results, plus or less twice the St2nc2rd

- 79 -

~~~~a:~~~. ~~ Jl~0 shewn i~ fig.l. it '::;'t"'~--l:'~ t h .. it b..:>th the expt=!'ri:nental t"'~sults d~d the! tl"'~0 !.~ei:i~..ll ~\;.c'>S

":'11"C:- !1:'.:;;::o::>:.' th~n [.C .. C.S. curve 11 a": in par-ticu1.3!" r~~ ... ~:::fc:",::-:':..:~ 0= c~r\-c :- f!· ...... ::l drv~ " a" is about 10% at the sl€'~dc!:",l\~sS \ = \1'

(J' 1 ,;tar

.8

.6

.4

_____ f./L=1!10000

-_. __ tIL =1/1000

.Q ~4 ~6

FIGURE 1

3 - !~~es b~ilt-up with ~elded plates

·1.2

?ec~~~gular tubes 210 X 110 X 10 are studied, built-up by ~elcec cold for::1ed channels in Nicuage steel with elastic linit of 580 :"1 r,-m-2. The eX;:;E;T'i::1e .. -::al investigation has been linited to the stl.lb-col~:7ln tests~ to ~te residual stresses measu~ernents and to the tensil~ tests 0;) ce~?o~s. fig.2 shows t he distributions or the residual stresses a~d of ~~e el~s~ic lini-ts. The stress-strain diagra~s obtained fro~ the s~u~-col~~~ tes~s are com?c~~d in fig .. 3 with the d j agra~ calcu!~t~c taking i~~o account the distribution of the residual st~esses a~d o~ the E;l2.5-'::C linits sho:.J:} in fig.2; very good ag~eeC1ent is foune.

- 30 -

FIGURE 2

21.0 rEsiciual str€-S1!ES

i I

---1- ._ I I

{fic:siic limits

.54 __________ / _________ ~--:::~: ~ ~ _ flumE:rice.1 8-imulation

. ~5 1. '1.5 2.

FiGURE 3

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I',; buchi : ; ,', ,',,:":,,:: ,.tlld;!!,'.! h'l ·:!~'uldti_", ,1: ' " o:h<'wl1 .til fig.4: if ~"""l;" /1:,1 : ' ~) ~l\" i ~l\~~. i : ~ \'Pt! : ~id":'('d, th0 bt:c.:hl ~n ~~ ... ~l!:'''\."c.' "'::;'0SSt"S all th~

i:.C.C.S, ,' :::";,,:: !e'l' X ' I.:·: X ••. This l-"::,ulr mdY b~ c';o;plain~d if ;:h", flexural ,~ti ff"~':;s "f the t'.1t.h'S is :::ornpar~d with the flexu::oal stiff­ness of t~~ t :ii'i"::Jl \.it!ld~d b0X-5t!cttOn: for high axial force (~ = 0,9 I) th~ :;tiffn~s~ of the box-s~ction in the inelastic !'Jng<> i" !,7.t"l'.lt,·" rhJII that of t rw l'c'ctJllgul-ll' tube; O!) the cC:1tl-ary

FIGURE 4 . for lower cxial force (!/ = 0.7 71) the rectangular tube is stiffer than the ~eldec box-section. Th~ nondi:ce:1sic7:al E.C.C.S. CL:l" ,re "a" may be adopted safely for strong axis bu~kling design; but considering weak-axis buckling the

.8"1-_-+ __ +---=::'::

.4

A '1. '1.2 '1.4 '1.6

FIGURE 5

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::.( ........... $. "':t;:"\·~!.; l:UY r~0t l"e ~d0~'"\t~~J fur' t'll(~ dt,:,d,;l1 it d cons!st"(: I:t ~~'t"' f:.~ " (.' t" C'f :'.':;!\'" \" ~: : !'t'Lll.1j''',S1. ~~t'Vt):rt ht="]~ss it .i:~ i ~ ("~:~.ib1<." t ....... ~dc'~'~ a dc:.'l[.n cri~el'i .. ):~ ] ~k~ "that sugges-;:e-d (both in the Ch2?ter , .. ~ ef l:.~

LC.C .S. !~ar.u:;l end in tl:,: :\.S.C.r:. Guide) for The design of t11<" cc.:e:)~:-ically 10a~1l .. J angle's. j'b~ liriliting ~tress for weak. a:<is tn..:c::"l­ing is Ct"..:! ::':t?d ej)r~"'l"inb the 110n-diwcnsional cu!'ve II a l

' wi:-!) a T:'! .... -<;\ii:-i~d

,.:l<"nj"r:~ess rat io '';'X = (""g + J, ~(5 A/)' fol' ). < ], ~ ~ • fig. S S'h0 .... S g0C'd cgr",3c?~tent bet\.!ee!l the mod1{fied n a" curve1tar.d t!"-I~ J:>ucJ.;lir.g curve obtilined by th<" ;,u~c'rical sir.1ulaticn.

4 - Cold for~cd ~suar" tu~cs Cold fOrNed square tubes are considered ~ith thickness fro~ ~ to

10 l.r.; t~e '!"'atio of the I:cninal -..;idt!l tothe "thickness is in 'tht? l"c.;lge J.' ~3(l • The iTlean value of the elC:s"tic lin}'!: in cO::lpressio;1 is ~50 II r.::-n -2 . As ,he dis,ribution of the r~sic~al stresses in the cold forrr.eo tu~es is biaxial, the nu~erical simulation cannot be applied and the b~c~l­ing cu~ve ~ust be obtained by tests. 'he experimental research has been spcnso:-ed by the'C.I.D.E.C.T. , the buckling tests have bern rerfCr7ted at the LieGe Universi'(y~ wi1ile the complementar "tests c:-:d the statis-.:ical e valuation of the r,osults have bee;) car:-ied out at the Milan Po!ytechllic. Six grc..:;:;s of t..,elve tube s I-:ere :es,ed with ncndimenslonal slenderr.ess in the range O>82~1,25 (the di~ensional slenderness were in the range 57~e7 ), namely in the range where the georr~trical anc str~ctu­ral it ... pe rfect io •• s are r.1ost 1)' effEct i ve and I-:here the pract ical a;:pli­catic,)s are ",or", frequent. There::ore .the statistical analysis of the test results give s r ·isc to the most interesting part of the ex;:;eri::-.en­tal buckling curve \.:hich can be cor.-,pored with the eu...."Opean ones. The detail!: of 'the experimental i;,ves'tigation and of the analysis of the results can be. found in another ccntri!:-ution presented for tf,e sa~e Cclloquiun. In a condensed forn the ~ain results are shown in fig.5.

0/0; 1. r

.8

.6

A __ .. 220. ;::220.;:: 8 A 220. x22! x: 7.1 lit 175 x:i75 X 5..6

2 0 175 ;::175 x: 7.1 ~ 150 x:15D x: 1 D. o 20.0. x: 20.0. xl o..

I I, !2 '.4 .6

FIGURE 6

- ;;3 -

1

'12

"fh(~ ~'''.1:1 , .. • .. ~':.:l\'=' It\~:-:; t\·h.' sf .. "lnt..i..:lrJ JeVidti ... 111S for th~ ~ix gl~0l!t'S '-."i buc;.~t!::~ t:1 '~ i:- t ·l':'\.:lt~ .jr~ c •. )mp.Jl~",,"'d with the non-Jim~n$10:1 .. ~1 1.: .......... 1.. .... :; ..

bt!c~l5r.5 t.::urVt'='. nh~ C'Or.lp.J.!" i$()ns of fig .. 6 conc~rn the nun-di~~rl$i':>:).:il r:~ ~ ~o:; of thL" ~~ .. :l-..lins, :-.iCr(,,·$:.,t. ... $ 0f tht! tt:bcs to th~ co!"'rcspo::ding "~.t:,:.::

p!",Quf 5~trf':';s !" c~~lr'~~s:;i('n fl':;n :h~ stub co:ui7In t~sts. . . . It" i:; ::;nc:r.-;n ti1~~ tl~t.'" \''''h3.r .. 1ctt:.rl~~t Ie value or 'the €)\;:h~rl:n-:,nt..3.1 ~\: ... "'''11.:'!~: !,:,!.:-(~ ~ ;=:,,~ i~; !~l.!: ~.\ .... ,,:.3.s~ hi5h~r th..3n E.C.C.S. L'.urvc U c" .. T:'-c-rer","\!"'c;l ::-:~~':!

r .. ::;u .lr!'J iir'e .:} \·.:!lict 5upport f;.)l" ext~nding to the range or thi~;":n::a-$5 6,101fJ71 --.:h" d"si:o;n ,~ritt>rid for cold forr:;ed tubes of the S.C.C.S.'

?':':f·(: f."!::il~ndd t. ten::; f~'!"- ~tt.."t"' 1 COr'.::3t !'UC-:: ion~"; ..

!'~ferences

f..C.C.S. - LU1'0pean Reco;:m:enclations for Steel Construction, ';=1:er­

dar.l,l'375. 121 G. Sallio. L. :lnzi. C. Urbano. R. Zandonini - F!ambement ~e5

t~bes en acier 2 haute limite elastique - Construction }let.311ique, No.2, 1975, pp.5-14.

/31 G. B.311io, L. fin~i, P. Setti, C. Urbano - Capacita ~ortente di di este tubolari ~o",presse in acciaio ad elevato limi­te elastico - Costru~ioni Metalliche, No.3, 1977.

! I~ I G. <>311io, V. Fetrini, C. Urbano - Sit:;ulazione m~i:1erica del cor::por­t:ar.1ento di eler.1enti strutturali compressi per incrt>::oen::' finiti del ca~ico assiale - Costruzioni Metalliche, No~

\51 .A..S.C .:::. 15j LC.C.S.

SU!!1;:-... "lry

1973. pp. 27-37. - Guice for Design of S--.:eel Transmission To~ers, 1971. - ~:anual on the Stabili::y of Steel Structures) Amst",:,c2.S,

1975.

The buckE:1g strength of various types of ' tubes in 'high ::;tr.:ng'::l: steal is $cudied D0th experi::oentally and theoretically: hot rolled round tl.!~es) tu~es built-up by welded cold formed plates and cold for~e1 square tubes are considered. Ir. this pe;:·er the philosophy is discuss<:d fo:, choosing the europ",en b;.:ckli':g C'.lc.;e '~hich fits best with the exp<:rimental and th",oretical re5'llts.

- J4 -