Journal of Constructional Steel Research

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Journl of Constructionl Steel Reserch 66 (2010) 487 495 Contents lists ville t ScienceDirect Journl of Constructionl Steel Reserch journl homepge: www.elsevier.

de Cresce El Des,, Mounir Khlil El Des Deprtment of Structurl Engineering, University of São Pulo, Brzil Deprtment of Civil Engineering, Federl University of São Crlos, Brzil rticle info strct

1 Journl of Constructionl Steel Reserch 66 (2010) Contents lists ville t ScienceDirect Journl of Constructionl Steel Reserch journl homepge: Evlution of pssive confinement in CFT columns Wlter Luiz Andrde de Oliveir, Silvn De Nrdin, An Lúci H. de Cresce El Des,, Mounir Khlil El Des Deprtment of Structurl Engineering, University of São Pulo, Brzil Deprtment of Civil Engineering, Federl University of São Crlos, Brzil rticle info strct Article history: Received 16 Septemer 2009 Accepted 23 Novemer 2009 Keywords: Concrete-filled steel tuulr columns Confinement effect Anlyticl models of confinement Experimentl nlysis Circulr cross section This pper presents the experimentl results of 32 xilly loded concrete-filled steel tuulr columns (CFT). The lod ws introduced only on the concrete core y mens of two high strength steel cylinders plced t the column ends to evlute the pssive confinement provided y the steel tue. The columns were filled with structurl concretes with compressive strengths of 30, 60, 80 nd 100 MP. The outer dimeter (D) of the column ws mm, nd the length/dimeter (L/D) rtios considered were 3, 5, 7 nd 10. The wll thicknesses of the tues (t) were 3.35 mm nd 6.0 mm, resulting in dimeter/thickness (D/t) rtios of 34 nd 19, respectively. The force vs. xil strin curves otined from the tests showed, in generl, good post-pek ehvior of the CFT columns, even for those columns filled with high strength concrete. Three nlyticl models of confinement for short concrete-filled columns found in the literture were used to predict the xil cpcity of the columns tested. To pply these models to slender columns, correction fctor ws introduced to penlize the clculted results, giving good greement with the experimentl vlues. Additionl results of 63 CFT columns tested y other reserchers were lso compred to the predictions of the modified nlyticl models nd presented stisfctory results Elsevier Ltd. All rights reserved. 1. Introduction Concrete-filled steel tuulr (CFT) columns hve mny constructionl dvntges, such s high energy sorption, formwork economy nd high ductility ecuse the steel tue effectively confines the concrete core. Mny reserchers hve studied this type of column in recent decdes, e.g., [1 14]. There re vrious nlyticl models proposed y different codes nd reserchers for evluting the strength of CFT columns considering the confinement effect or not. However, to e relistic, the prediction of the xil lod cpcity of these columns must consider the confinement effect provided y the steel tue. In this wy, the xil lod cpcity of the CFT columns in most of the cses is higher thn the sum of the resistnce of their components, which re the steel tue (A f y ) nd the concrete core (A c f c ). Oserving two interntionl code provisions, the differences re cler. The Eurocode 4 [27] hs complex expression to predict the xil cpcity of CFT columns, in which the confinement is considered. On the other hnd, the ANSI/AISC [16] hs more simple eqution, nd the sic difference lies in the considertion of the confinement contriution for the CFT column xil cpcity. Corresponding ddress: Deprtmento de Engenhri de Estruturs, Av. Trlhdor Socrlense, 400, São Crlos - SP CEP: , Brzil. Tel.: ; fx: E-mil ddress: nluci@sc.usp.r (A.L.H.C. El Des). Beck et l. [17] conducted reliility nlysis on CFT columns y considering four different code provisions (CAN/CSA S16:2001 [18], Eurocode 4:2004 [27], ANSI/AISC:2005 [16] nd ABNT NBR 8800:2008 [19]). The errors of the resistnce models were determined y compring 93 experimentl results for ultimte lods with code-predicted column resistnces. Regression nlysis ws used to descrie the vrition of the model error with the column slenderness nd lso to descrie the model uncertinty. As result, it ws found tht the prediction given y ANSI/AISC is overly conservtive for very short columns, while the prediction y EC4 is not conservtive. This occurred ecuse the confinement effect is over-estimted y the EC4 formul, even for short columns. For lrge slenderness rtios, concrete confinement is miniml, column ehvior is minly elstic, nd resistnce models of the four design codes ecome slightly conservtive. 2. The pssive confinement in CFT columns The confinement effect hs een studied for mny yers. One of the first works on this suject ws conducted y Richrt et l. [20] nd Considère [28] (pud [20], where the ehvior of reinforced concrete columns using spirl reinforcement ws studied. Richrt et l. [20] concluded tht the internl pressure provided y the spirl reinforcement should e multiplied y 4.1 to llow for the confinement effect. In recent yers, mny uthors hve presented nlyticl models to predict the confinement effect in reinforced concrete columns nd lso in concrete-filled steel tuulr columns X/$ see front mtter 2009 Elsevier Ltd. All rights reserved. doi: /j.jcsr

2 488 W.L.A. de Oliveir et l. / Journl of Constructionl Steel Reserch 66 (2010) Nomenclture f ck f c f y D t L E cm compressive strength of concrete men compressive strength of concrete yield strength of steel externl dimeter of tue steel tue thickness length of column Young s modulus of the concrete given y Eurocode 2 Those models tke into ccount the conclusions given y Richrt et l. [20], where the compressive strength of the concrete in the column core is incresed y the confinement effect promoted y the ties in the cse of concrete columns, nd y the steel tue for CFT columns. Fig. 1 shows the pssive confinement for concrete columns nd CFT columns. The confining stress distriution is very complex in concrete columns confined y ties nd spirls since the lterl restrint of concrete expnsion is highly loclized, s seen in Fig. 1, nd c, for circulr, squre nd rectngulr concrete columns, respectively, where the rching ction in confined concrete column cn e seen [21]. The prolem with the loclized expnsion of concrete does not occur in CFT columns. According to [4,5,8], the circulr CFT columns present etter gin of lod cpcity due to the confinement effect, s shown in Fig. 1e. The squre or rectngulr cross sections present some loss of the confinement effect compred to circulr sections, ut they re still etter thn concrete columns, s shown in Fig. 1d (the seprtion of steel nd concrete is slightly exggerted in the cption). 3. Reserch significnce There re mny vriles tht ffect the confinement effect in CFT columns, such s the concrete compressive strength, lengthto-dimeter rtio (L/D), dimeter-to-thickness rtio (D/t), type of loding (in the concrete core or in oth mterils), shpe of cross section, eccentricity of loding, etc., nd there is no nlyticl model le to tke into ccount ll vriles. Thus, in this work, the ility of three nlyticl models to predict the xil lod cpcity of CFT columns ws tested. The models chosen were proposed y Susnth et l. [9], Johnsson [11] nd Htzigeorgiou [12], which re le to predict xil strength of CFT short columns with good ccurcy. However, for CFT usul columns, the models overestimte the lod cpcity. To correct the vlues of the xil lod cpcity for regulr CFT columns nd find tool to predict their xil cpcity, slenderness correction fctor ws introduced in the three models. The results of the nlyticl models were compred to the results for 116 CFT columns, where 32 were tested y the uthors nd 63 were from the literture: 15 from [22], 13 from [23], 18 from [24] nd 17 from [25]. 4. Experimentl progrm Thirty-two CFT columns with different vlues of concrete compressive strength (f c ), L/D nd D/t rtio were tested under concentric loding to nlyze the influence of those prmeters on the generl ehvior nd lod cpcity of CFT columns. These tests re prt of reserch progrm on the suject, in which 64 CFT columns were studied y the uthors, nd the results of 16 of them hve lredy een presented in [14]. The min geometric chrcteristics of the tested specimens re the externl dimeter D = mm; the thickness of the steel tue t = 3.35 mm nd 6.0 mm; L/D = 3, 5, 7 nd 10; nd f c = 32.7 MP, 58.7 MP, 88.8 MP nd MP. The Young s modulus of the concrete ws clculted ccording to the expression of EC2 [15] (Eq. (1)). ( ) fck MP E cm = (1) 10 The smll dimeter ws chosen sed on the lod cpcity of the test mchine. All specimens were tested with concentric loding pplied on the concrete core. The columns were identified with nmes such s: C1 (t = 3.35 mm lck tues) or C2 (t = 6.0 mm pinted white tues) + concrete compressive strength + L/D rtio + C (lod pplied in concrete core). For exmple: C1-60-5D-C, C1 mens column with wll thickness of the tue of t = 3.35 mm, 60 refers to the concrete strength clss (in MP), 5D is the length of column (5 dimeter), nd C indictes tht the lod ws introduced in the concrete core. The yielding stress of the steel tue ws otined y tension tests, ccording to ASTM A [26] with I specimens. The verge vlue dopted for the yielding stress (f y ) ws MP for C1 nd MP for C2 tues, nd the corresponding strin ws 1.4 for C1 nd 2.0 for C2 tues. The elstic modulus for the steel ws tken s E s = MP. Concrete of four different compressive strengths (C30, C60, C80 nd C100) were used s column filling mteril. The mixes were produced using the ville mterils, nd the detils re presented in [14]. The xil compressive strength ws determined y tests on cm cylindricl specimens t 28 dys, the sme dy of the columns tests. The tests were performed using n Instron 8506 servo hydrulic ctutor. The detils of the test mchine, the loding rtios nd the instruments used re lso presented in [14]. 5. Tests results The filure mode of the specimens ws function of the L/D nd D/t rtios nd lso of the concrete strength. The short columns (L/D = 3) filed due to the crushing of the concrete core, ggrvted y the locl uckling of the steel tue fter hving reched the yielding stress of the steel. In Fig. 2 nd, for C1 nd C2 columns, respectively, it cn e oserved tht the C2 columns cn etter restrin the expnsion of the concrete core for the sme concrete compressive strength (30 MP). The increse in the lterl strin in columns with t = 6.0 mm is uniform long the height compred to columns with t = 3.35 mm, where the lterl strin is more loclized t the middle height. The specimens filled with norml strength concrete (C30 nd C60) showed significnt increse in the cross section dimensions without ny sudden loss of lod cpcity, s seen in digrms of Fig. 6. For C1 columns, filled with high strength concretes (C80 nd C100), the confinement effect provided y the steel tue ws not enough to give ductility to the columns, ut for C2 columns the steel tue ws le to confine the concrete core even for high strength concrete. C1 columns with L/D = 5 presented sher filure of the concrete core for ll concrete compressive strengths considered (Fig. 3). For C2 columns, the thickness of the steel tue ws cple of restrining sher in the concrete core. This columns filed y uckling, s seen in Fig. 3. Both C1 nd C2 columns presented

W.L.A. de Oliveir et l. / Journl of Constructionl Steel Reserch 66 (2010) 487 495 489 c d e Fig. 1. Effectively confined concrete for concrete columns nd CFT columns. Fig. 2.

good ductile ehvior when filled with norml strength concrete, ut tht ws not oserved for C1 columns, where high strength concrete ws used (Fig. 6).

For high strength concrete, there ws significnt loss of lod cpcity fter the pek lod ws reched (Fig. 6c nd d). For norml strength concrete the columns were still le to show ductility fter the pek lod.

3 W.L.A. de Oliveir et l. / Journl of Constructionl Steel Reserch 66 (2010) c d e Fig. 1. Effectively confined concrete for concrete columns nd CFT columns. Fig. 2. () C1-3D tested column; () C2-3D tested column. Fig. 3. () C1-5D tested column; () C2-5D tested column. good ductile ehvior when filled with norml strength concrete, ut tht ws not oserved for C1 columns, where high strength concrete ws used (Fig. 6). Columns with L/D = 7 nd L/D = 10 nd tue thickness of 3.35 mm (C1 columns) presented filure y sher t the middle height of the columns (Figs. 4 nd 5). For high strength concrete, there ws significnt loss of lod cpcity fter the pek lod ws reched (Fig. 6c nd d). For norml strength concrete the columns were still le to show ductility fter the pek lod. For C2 columns with L/D = 7 nd L/D = 10, the filure occurred y overll uckling. Fig. 4 shows column with L/D = 7 efore testing, nd in Fig. 5 the uckling of columns with L/D = 10 cn e seen. In generl, thick tues were le to prevent sher in columns, independent of the column slenderness, which ws not oserved when thin tues were used. The specimens filled with norml strength concretes showed elsto-plstic post-pek ehvior with strin-hrdening, while the

490 W.L.A. de Oliveir et l. / Journl of Constructionl Steel Reserch 66 (2010) 487 495 Fig. 4. () C1-7D tested column; () C2-7D columns efore testing. Fig. 5.

The specimens with L/D 7 exhiited insufficient rdil strin for moilizing the confinement effect. This ws confirmed y the redings of the two strin guges plced round the column.

4 490 W.L.A. de Oliveir et l. / Journl of Constructionl Steel Reserch 66 (2010) Fig. 4. () C1-7D tested column; () C2-7D columns efore testing. Fig. 5. () C1-10D tested column; () C2-10D tested column. ones with high strength concrete presented elsto-plstic ehvior with strin-softening, s oserved y Johnsson [11]. The specimens with L/D 7 exhiited insufficient rdil strin for moilizing the confinement effect. This ws confirmed y the redings of the two strin guges plced round the column. The mesured rdil strin t the pek lod ws out 1.5 for the columns with L/D = 10 nd more thn 10 for the short columns. 6. Anlyticl models nd comprisons Three nlyticl models were studied nd used to predict the xil cpcity of CFT tuulr columns: [9,11,12]. The models re sed in the sme theory of lterl pressure promoted y the steel tue, ut they show different procedures to predict the confined concrete strength (f cc ). The sequence of procedures to predict the xil strength of CFT columns using ech one of the nlyticl models is shown in Tle 1. Tle 2 shows the mesured concrete compressive strength (f c ) for specimens C1 nd C2, the confined concrete strength (f cc ) clculted y ech model nd the reltions etween experimentl results of the xil cpcity (F exp ) nd the predicted vlues using the nlyticl models. Tle 2 lso shows the results for the 32 tested columns. Despite the differences etween the three clculted vlues for the confined concrete strength, the predicted xil cpcities of the CFT columns re quite similr. The confined concrete strength nd the predicted xil cpcity re denoted s f cc,sus nd F Sus for the model proposed y Susnth et l. [9], respectively, f cc,joh nd F Joh for the model proposed y Johnsson [11] nd f cc,ht nd F Ht for the model proposed y Htzigeorgiou [12]. Tle 2 shows the comprisons etween the experimentl results nd predicted ones, for men vlues. They re close, ut on the unsfe side, since the predicted results re little higher thn the experimentl ones. This hppened ecuse the nlyticl models re dequte to predict the xil cpcity only for short columns, nd the results considered tke into ccount slender nd short columns. In n ttempt to correct the prediction for slender columns, correction fctor (λ Oliveir ) ws introduced. This fctor ws clirted y the 32 experimentl results. A logrithmic regression ws mde considering the reltion etween the experimentl results nd the resistnce of the cross section of CFT columns

5 W.L.A. de Oliveir et l. / Journl of Constructionl Steel Reserch 66 (2010) Tle 1 Sequence to clculte the predicted xil cpcity y using the three nlyticl models studied. Model Expressions Oservtions Susnth et l. [9] Johnsson [11] Htzigeorgiou [12] ν = c ( ) D ( ) D ( ) D 10 6 t 10 4 t 10 2 t Empiricl fctor ( ) ν c = ν c fc ν fy c Poisson rtio of steel tue filled with concrete ( ) ( ) 2 fc fc fy fy β = ν c ν s ν s is the Poisson rtio of steel tue, tken equl to t f rp = β f D 2 t y Lterl pressure t the pek lod f cc = f c + 4 f rp Confined compressive strength of the concrete F Sus = A c f cc + A f y Axil cpcity of CFT column ν = 0.3 ν c = 0.2 ε v = (2 ) Initil considered vlues here εv (ν νc ) ε hr = ] Restrined steel strin [ 1+ 2 t E (D 2 t) Ec ε h = ν ε v + ε hr Finl lterl strin of steel σ h = E (ε 1 ν 2 h + ν ε l ) nd σ l = E (ε 1 ν 2 v + ν ε h ) Steel s lterl nd longitudinl stresses 2 t σ lt = σ h Compressive confining pressure ((D 2 t) ) k = σlt f 0.21 fc c f c in MP Prmeter tht reflects the effectiveness of confinement ( k f cc = f c σlt + 1) Confined compressive strength of the concrete. fct For f ct ws used here the expression of Eurocode 2. F Joh = A c f cc + A σ l Axil cpcity of CFT column σ h = f y [ ( ) ( ) ] D exp ln t + ln fy 11 fy in MP Hoop stress of the steel f rp = 2 σ h t Men confining stress D 2 t f cc = f c f ( rp f yc = 0.5 σ h F Ht = A c f cc + A f yc 4 f 2 y 3 σ 2 h ) Confined compressive strength of the concrete Compressive yield stress Axil cpcity of CFT column Tle 2 Vlues of compressive strength of concrete (f c ), confined compressive strength of concrete (f cc ) nd the rtios etween experimentl results of CFT tested columns nd xil cpcity of columns predicted for ech nlyticl model. Specimen f c (MP) f cc,sus f cc,joh f cc,ht F exp (kn) F exp /F Sus F exp /F Joh F exp /F Ht C1-30-3D-C C1-30-5D-C C1-30-7D-C C D-C C1-60-3D-C C1-60-5D-C C1-60-7D-C C D-C C1-80-3D-C C1-80-5D-C C1-80-7D-C C D-C C D-C C D-C C D-C C D-C C2-30-3D-C C2-30-5D-C C2-30-7D-C C D-C C2-60-3D-C C2-60-5D-C C2-60-7D-C C D-C C2-80-3D-C C2-80-5D-C C2-80-7D-C C D-C C D-C C D-C C D-C C D-C Men Stndrd dev C.O.V. 13.6% 10.6% 10.3%

6 492 W.L.A. de Oliveir et l. / Journl of Constructionl Steel Reserch 66 (2010) Tle 3 Results of tested columns nd rtios with predicted vlues from nlyticl models using the slenderness correction fctor. Specimen L/D D(mm) t (mm) f c (MP) f y (MP) F exp (kn) F exp /F Sus F exp /F Joh F exp /F Ht C1-30-3D-C C1-30-5D-C C1-30-7D-C C D-C C1-60-3D-C C1-60-5D-C C1-60-7D-C C D-C C1-80-3D-C C1-80-5D-C C1-80-7D-C C D-C C D-C C D-C C D-C C D-C C2-30-3D-C C2-30-5D-C C2-30-7D-C C D-C C2-60-3D-C C2-60-5D-C C2-60-7D-C C D-C C2-80-3D-C C2-80-5D-C C2-80-7D-C C D-C C D-C C D-C C D-C C D-C Men Stndrd dev C.O.V. 11.9% 7.9% 7.6% Tle 4 Results of columns tested y O She nd Bridge [22] nd rtios with predicted vlues from nlyticl models using the correction fctor if pplicle. Specimen L/D D (mm) t (mm) f c (MP) f y (MP) F exp (kn) F exp /F Sus F exp /F Joh F exp /F Ht S30CS50B S20CS50A S16CS50B S12CS50A S10CS50A S30CS80A S20CS80B S16CS80A S12CS80A S10CS80B S30CS10A S20CS10A S16CS10A S12CS10A S10CS10A Men Stndrd dev C.O.V. 10.1% 3.9% 5.8% (A c f c +A f y ). Eq. (2) shows the correction fctor, recommended for use only if the reltion L/D is lrger thn 3; otherwise λ Oliveir = 1. ( ) L λ Oliveir = 0.18 ln (2) D The comprisons etween the nlyticl models nd the results from the literture re presented in Tles 3 7. Tle 3 shows results for the 32 tested columns using the correction fctor to penlize the nlyticl model results. Tles 4 7 show the results from [22 25], respectively. The correction fctor ws used for L/D rtios greter thn or equl to 3. Oserving the results in Tles 2 nd 3, the men results for reltions etween the experimentl xil lod nd predicted ones re close to 1 for oth the Susnth nd Johnsson models. The xil cpcities of the CFT columns given y the three models enefited y the correction fctor. Only Johnsson s model still presented men less thn 1, 1.6% on the unsfe side. The Htzigeorgiou model presented the est pproch, in terms of the men, efore using the correction fctor: 2.6% under the experimentl vlues. After using the correction fctor, those vlues ecme 10.1% higher thn the experimentl ones nd therefore on the sfe side. Anlyzing the men vlues presented in Tle 4, only the ones predicted y Susnth s model were higher thn the experimentl ones, with difference of 2.9%. However, the stndrd devition of the vlues presented the higher vlue, 10.1%, showing lrge

7 W.L.A. de Oliveir et l. / Journl of Constructionl Steel Reserch 66 (2010) Tle 5 Results of columns tested y Gikoumelis nd Lm [23] nd rtios with predicted vlues from nlyticl models using the correction fctor if pplicle. Specimen L/D D (mm) t (mm) f c (MP) f y (MP) F exp (kn) F exp /F Sus F exp /F Joh F exp /F Ht C C C C C C C C C C C C C Men Stndrd dev C.O.V. 12.2% 11.0% 9.6% Tle 6 Results of columns tested y Gupt et l. [24] nd rtios with predicted vlues from nlyticl models using the correction fctor if pplicle. Specimen L/D D (mm) t (mm) f c (MP) f y (MP) F exp (kn) F exp /F Sus F exp /F Joh F exp /F Ht D2M3C D2M3C D2M3C D3M3C D3M3C D3M3C D4M3C D4M3C D4M3C D2M4C D2M4C D2M4C D3M4C D3M4C D3M4C D4M4C D4M4C D4M4C Men Stndrd dev C.O.V. 20.2% 18.8% 21.5% Tle 7 Results of columns tested y Yu et l. [25] nd rtios with predicted vlues from nlyticl models using the correction fctor if pplicle. Specimen L/D D(mm) t (mm) f c (MP) f y (MP) F exp (kn) F exp /F Sus F exp /F Joh F exp /F Ht Men Stndrd dev C.O.V. 7.4% 7.1% 7.3% sctter in predictions. Despite eing on the unsfe side, with mens of 4.8% nd 5.2%, the vlues predicted y the Johnsson nd Htzigeorgiou models presented the smllest stndrd devition of the vlues:, 3.7% nd 5.5%, respectively. In generl the three models were le to predict the results of the columns tested y O She nd Bridge [22]. The columns tested y Gikoumelis nd Lm [23] were compred with the predictions in Tle 5. The clculted vlues for

8 494 W.L.A. de Oliveir et l. / Journl of Constructionl Steel Reserch 66 (2010) c d Fig. 6. Lod vs. xil strin of 32 CFT tested columns: () L/D = 3, () L/D = 5, (c) L/D = 7 nd (d) L/D = 10. these columns were the est predictions mong ll. The predictions of the models of Susnth, Johnsson nd Htzigeorgiou presented differences of 0%, 2.5% nd 5.3% compred to the experimentl ones, on the sfe side. However, they presented lrge vriility in individul predictions. Despite eing on the sfe side, the mens of rtios etween the experimentl results nd the predicted ones for the columns of Gupt et l. [24] (Tle 6) presented the lrgest difference nd stndrd devition. This cn e ttriuted to the fct tht the columns tested presented higher vriility of the studied vriles, such s L/D, dimeter, thickness nd concrete compressive strength. Only the yielding strength of steel remins constnt. In ddition, the correction fctor mde the results more conservtive. If the correction fctor ws not pplied to these columns, the men vlues would e 1.060, nd for the models of Susnth, Johnsson nd Htzigeorgiou, respectively. Tle 7 presents the comprisons of the results for the columns tested y Yu et l. [25] nd the predictions. The comprisons indicte very close vlues nd the smllest stndrd devitions mong ll comprisons. In terms of the mens, only Johnsson s model gve predictions on the sfe side, of only 0.8%. 7. Conclusions This pper presented experimentl results of 32 CFT columns tested under concentric loding. In generl, ll columns filled with norml strength concrete (C30 nd C60) presented good ductile ehvior, without loss of cpcity fter reching the pek lod, s seen in Fig. 6. For columns filled with high strength concrete, the C2 columns seem to hve more ductility thn C1 ones due to the difference etween the tue thickness, where the thicker tue is le to etter promote the confinement of the concrete core. Three nlyticl models for the xil cpcity of CFT short columns were studied so tht the vlues of the xil cpcity of the 32 tested CFT columns nd nother 63 from the literture could e evluted. A fctor ws introduced to correct the vlues of predictions for slender columns when the L/D rtio is higher thn 3, presenting good results. In generl, the three nlyticl models showed good predictions for the xil lod cpcity of CFT columns. In most cses, the men vlues of the reltion etween the experimentl results nd predicted ones were higher thn 1, therefore on the sfe side. Even when the vlues were lower thn 1, they were close to 1, with difference of 5.2% for the columns tested y O She nd Bridge [22] predicted y the Htzigeorgiou model. References [1] Kloppel VK, Goder W. An investigtion of the lod crrying cpcity of concrete-filled steel tues nd development of design formul. Der Sthlu 1957;26(1):1 10 [in Germn]. [2] Grdner J, Jcoson R. Structurl ehvior of concrete filled steel tues. ACI, Journl 1967;64(7): [3] Attrd MM, Setunge S. Stress strin reltionship of confined nd unconfined concrete. ACI Mterils Journl 1996;93(5): [4] Shms M, Sdeghvziri MA. Stte of the rt of concrete-filled steel tuulr columns. ACI Structurl Journl, ACI 1997;94(5): [5] Schneider SP. Axilly loded concrete-filled steel tues. Journl of Structurl Engineering, ASCE 1998;124(10):

9 W.L.A. de Oliveir et l. / Journl of Constructionl Steel Reserch 66 (2010) [6] Roeder CW, Cmeron B, Brown CB. Composite ction in concrete filled tues. Journl of Structurl Engineering, ASCE 1999;125(5): [7] Johnsson M, Gylltoft K. Structurl ehvior of slender circulr steel-concrete composite columns under vrious mens of lod ppliction. Steel nd Composite Structures 2001;1(4): [8] Shnmugm NE, Lkshmi B. Stte of the rt report on steel-concrete composite columns. Journl of Constructionl Steel Reserch 2001;57(10): [9] Susnth KAS, Ge HB, Usmi T. A cpcity prediction procedure for concretefilled steel columns. Journl of Erthquke Engineering 2001;5(4): [10] Elremily A, Azizinmini A. Behvior nd strength of circulr concrete-filled tue columns. Journl of Constructionl Steel Reserch 2002;58(12): [11] Johnsson M. The efficiency of pssive confinement in CFT columns. Steel nd Composite Structures 2002;2(5): [12] Htzigeorgiou GD. Numericl model for the ehvior nd cpcity of circulr CFT columns, Prt I: Theory. Engineering Structures 2008;30(6): [13] Htzigeorgiou GD. Numericl model for the ehvior nd cpcity of circulr CFT columns, Prt II: Verifiction nd extension. Engineering Structures 2008; 30(6): [14] Oliveir WLA, De Nrdin S, El Des ALHC, El Des MK. Influence of concrete strength nd length/dimeter on the xil cpcity of CFT columns. Journl of Constructionl Steel Reserch 2009;65(12): [15] EN :2004. Design of concrete structures, Prt 1 1: Generl rules nd rules for uildings. EUROCODE 2. Europen Committee for Stndrdiztion; [16] Americn Institute of Steel Construction. ANSI/AISC 360. Specifiction for structurl steel uildings. Chicgo (IL); [17] Beck AT, Oliveir WLA, De Nrdin S, El Des ALHC. Reliility-sed evlution of design code provisions for circulr concrete-filled steel columns. Engineering Structures 2009;31(10): [18] CAN/CSA S16-01:2001. Limit sttes design of steel structures. Ontrio (Cnd): Cndin Stndrds Assocition; [19] Associção Brsileir de Norms Técnics. ABNT NBR 8800:2008. Projeto e execução de estruturs de ço e de estruturs mists ço-concreto de edifícios: Procedimento. Rio de Jneiro [in Portuguese]. [20] Richrt FE, Brndzeg A, Brown RL. A study of the filure of concrete under comined compressive stresses. University of Illinois Bulletin. Bulletin 185. Chmpign (IL, USA): University of Illinois Engineering Experimentl Sttion; p [21] Cusson D, Pultre P. Stress strin model for confined high-strength concrete. Journl of Structurl Engineering, ASCE 1995;121(3): [22] O She MD, Bridge RQ. Design of circulr thin-wlled concrete filled steel tues. Journl of Structurl Engineering, ASCE 2000;126(11): [23] Gikoumelis G, Lm D. Axil cpcity of circulr concrete-filled tue columns. Journl of Constructionl Steel Reserch 2004;60(7): [24] Gupt PK, Srd SM, Kumr MS. Experimentl nd computtionl study of concrete filled steel tuulr columns under xil lods. Journl of Constructionl Steel Reserch 2007;63(2): [25] Yu Z, Ding F, Ci CS. Experimentl ehvior of circulr concrete-filled steel tue stu columns. Journl of Constructionl Steel Reserch 2007;63(2): [26] ASTM A370-07:2007. Stndrd test methods nd definitions for mechnicl testing of steel products. West Conshohocken (PA). [27] EN :2004. Design of composite steel nd concrete structures, Prt 1 1: Generl rules nd rules for uildings. EUROCODE 4. Europen Committee for Stndrdiztion; [28] Considère A. Résistnce à lá compression du éton rme et du éton fretté. Génie Civil; 1903 [in French].

Theme 8 Stability and buckling of members

Theme 8 Stability and buckling of members Elsticity nd plsticity Theme 8 Stility nd uckling o memers Euler s solution o stility o n xilly compressed stright elstic memer Deprtment o Structurl Mechnics culty o Civil Engineering, VSB - Technicl