Comparisons of concrete-encased composite column strength provisions of ACI code and AISC specification

Transcription

1 Engineering Structures 24 (2002) Comprisons of concrete-encsed composite column strength provisions of ACI code nd AISC specifiction C.C. Weng *, S.I. Yen Deprtment of Civil Engineering, Ntionl Chio Tung University, Hsinchu, 30050, Tiwn, ROC Received 20 September 2000; received in revised form 9 My 2001; ccepted 26 June 2001 Abstrct In the ACI-318 code (1999) nd AISC-LRFD specifiction (1993), different pproches re used for the design of concreteencsed composite columns. The clculted member strengths bsed on these two design provisions my show significnt difference in some cses. The objective of this study is to investigte the difference between these two pproches nd to evlute the ccurcy of their strength predictions by compring to 78 physicl test results done by previous reserchers. This comprtive study indictes tht the ACI-318 pproch generlly gives closer predictions thn the AISC-LRFD does. The sttisticl results show tht the ACIto-experimentl cpcity rtio hs men vlue of 0.90 with coefficient of vrition (COV) of 15% nd the AISC-to-experimentl cpcity rtio hs men vlue of 0.73 with COV of 21%. Also investigted herein re the difference of design philosophy between the design provisions, the filure mode of the tested specimens, the column strength interction digrm, nd the effect of steel rtio on the ccurcy of the strength predictions Elsevier Science Ltd. All rights reserved. Keywords: Concrete-encsed composite column; Physicl test result; Design provision; Sttisticl result; Design philosophy; Filure mode; Steel rtio 1. Introduction The composite concrete nd steel structurl system combines the rigidity nd formbility of reinforced concrete with the strength of structurl steel to produce n economic structure. For concrete-encsed composite structurl members, n dditionl dvntge is tht the concrete used for encsing structurl steel not only increses its stiffness, but lso protects it from fire dmge nd locl buckling filure. In the United Sttes, specific regultions for the design of concrete-encsed composite columns re included in two different sets of structurl design specifictions. One is the building code for structurl concrete of the Americn Concrete Institute (ACI)[1], nd the other is the specifiction of Lod nd Resistnce Fctor Design (LRFD) published by Americn Institute of Steel Construction (AISC) [2]. The ACI-318 provisions (1999) for the design of the encsed composite columns follow the sme procedure s * Corresponding uthor. Tel.: ; fx: E-mil ddress: weng@cc.nctu.edu.tw (C.C. Weng). tht for the reinforced concrete columns. In contrst, the AISC-LRFD provisions (1993) re bsed on nlogous to the steel column design. Both ACI nd AISC design provisions re pplied to concrete-encsed structurl steel columns nd to concrete-filled pipes or tubing. The AISC-LRFD rules specificlly require t lest 4% steel rtio of the composite section comprised of structurl steel. However, the ACI rules hve no such limittion on steel rtio. In ddition, the former is recommended for symmetric composite section, but the ltter is recommended for both symmetric nd unsymmetricl sections [3,4]. It is noted tht the bove-mentioned specifictions often give significntly different vlues of clculted ultimte member strengths [5,6]. The objective of this study is to investigte the differences between the ACI nd the AISC pproches for the design of concrete-encsed composite columns nd to evlute how well they model the ctul column behvior through series of sttisticl comprisons. The studies re mde to compre the predicted strengths by using the ACI nd the AISC pproches with 78 physicl test results of encsed composite column done by previous reserchers such s Mirz, Ricles, Ymd, Nk, Wkbyshi, Yokoo nd Stevens [7 13] /02/$ - see front mtter 2001 Elsevier Science Ltd. All rights reserved. PII: S (01)

2 60 C.C. Weng, S.I. Yen / Engineering Structures 24 (2002) Nomenclture A c, A r re of concrete nd longitudinl reinforcement, respectively A s, A w re of steel shpe nd web of steel shpe, respectively B 1 moment mgnifier suggested in AISC-LRFD specifiction c 1, c 2, c 3 numericl coefficients, c 1 =0.7, c 2 =0.6 nd c 3 =0.2 for encsed composite columns c r thickness of concrete cover from center of longitudinl reinforcement to the edge of section in the plne of bending D overll dimension in the direction of buckling E c elstic modulus of concrete E m modified modulus of elsticity F cr criticl stress of column F my modified yield stress F y specified yield strength of steel shpe F yr specified yield strength of longitudinl reinforcement f c specified compressive strength of concrete h 1 width of composite cross section perpendiculr to the plne of bending h 2 width of composite cross section prllel to the plne of bending I g gross section moment of inerti KL effective length M n nominl moment cpcity without xil lod M u fctored moment M u1, M u2 the smller nd the lrger required moments pplied t both ends of the column, respectively P 0 composite column cpcity under unixil compression P c criticl lod of column P n nominl xil compressive cpcity P u fctored xil lod r rdius of gyrtion r m modified rdius of gyrtion Z plstic section modulus of steel shpe d moment mgnifier suggested in ACI-318 code f b resistnce fctor for bending, tken s 0.9 f c resistnce fctor for compression, tken s 0.85 l c slenderness prmeter 2. Review of design methods 2.1. ACI-318 pproch In the US, the ACI building code hs been the sole mjor reference for the design of composite columns until the publiction of the AISC-LRFD specifiction in The following sections briefly introduce the concerned strength provisions for the concrete-encsed composite columns s recommended in section of the ACI-318 building code (1999) Axil compressive strength Under unixil compression, the nominl compressive strength, P n, of concrete-encsed composite column cn be found by summing up the xil-lod cpcities of the mterils tht mke up the cross section. This leds to P n 0.8P 0 P f ca c F yr A r F y A s where P 0 f c A c F yr A r F y A s column cpcity under unixil compression compressive strength of concrete re of concrete yield strength of longitudinl reinforcement re of longitudinl reinforcement yield strength of steel shpe re of steel shpe (1) (1b) The nominl xil compressive strength P n for n encsed composite column is limited to 0.8P 0 owing to minimum eccentricity under xil lod for ll designed columns.

3 C.C. Weng, S.I. Yen / Engineering Structures 24 (2002) Second-order effect The ACI-318 pproch requires tht ll columns be designed s bem-columns trnsferring both sher nd bending moment t joints. The columns shll be designed ccording to the fctored forces nd moments from second-order nlysis. As n lterntive to the second-order nlysis, design cn be bsed on first-order elstic nlysis nd moment mgnifiction pproch. The moment mgnifier d is expressed s M u1 M u2 d 1 P 1 (2) u 0.75P c with M u1, M u2 =the smller nd the lrger required moments t the ends of the column, respectively; P u =fctored xil lod; nd P c =criticl lod of column, tken s P c p2 EI (2b) (KL) 2 where KL=effective length; EI=flexurl rigidity. To ccount for the vritions in stiffness due to crcking, creep nd nonlinerity of concrete, the EI vlue of bove eqution cn be conservtively tken s 0.25E c I g, in which E c is the concrete elstic modulus nd I g is the gross section moment of inerti. It is lso noted tht the second-order effect cn be neglected if the column slenderness rtio, KL/r, meets the following requirement: KL r M u1 M u2 (3) Flexurl nd xil lods The ACI-318 provisions for the strength interction between xil nd flexurl lods for concrete-encsed composite columns re essentilly the sme s those for ordinry reinforced concrete columns. They re bsed on strin comptibility nlysis t the limit stte to develop thrust moment (P M) interction reltion. The following ssumptions re mde in the nlysis: Plne section remins plne. The mximum concrete compressive strin is limited to The Whitney stress block, hving mgnitude of 0.85f c, is used for the concrete. Tensile strength of the concrete is neglected. Strin hrdening of steel shpe nd rebr is neglected AISC-LRFD pproch Although the AISC specifiction hs included design provisions for composite bems with sher connectors since 1961, the design requirements for composite columns were not recommended until the publiction of the first edition of the AISC-LRFD specifiction in The concept of extending the steel column design methodology to the composite columns using the modified properties ws first introduced by Furlong [14]. Modified yield stress F my, modulus of elsticity E m nd rdius of gyrtion r m were incorported into steel column design equtions for the design of composite columns. This procedure ws presented by the Tsk Group 20 of the Structurl Stbility Reserch Council (SSRC) in 1979 [15]. The following sections briefly introduce the concerned strength provisions for encsed composite columns s recommended in Chpter I of the AISC-LRFD specifiction (1993) Axil compressive strength The cpcity of n encsed column is determined from the sme equtions s tht for bre steel columns except the formuls being entered with modified properties F my, E m nd r m. The nominl xil compressive strength of n encsed composite column is P n A s F cr (4) where A s is the re of the steel shpe nd F cr is the criticl stress of the column given by the following equtions: F cr (0.658 l2 c )Fmy for l c 1.5 (5) nd F cr l F 2 my for l c 1.5 (6) c where l c =(KL/pr m ) F my /E m ; F my =modified yield stress; r m =modified rdius of gyrtion; E m =modified modulus of elsticity. The modified properties F my, E m nd r m ccount for the contribution of concrete nd rebrs in the composite section. The modified vlues F my nd E m cn be determined by the following equtions: A c A r F my F y c 1 F yr c A 2 f c (7) s A s nd A c E m E s c 3 E c (8) A s where c 1, c 2, c 3 =numericl coefficients, for encsed composite columns c 1 =0.7, c 2 =0.6 nd c 3 = Second-order effect For columns designed on the bsis of elstic nlysis, the fctored moment M u shll be determined by second-order nlysis or by the moment mgnifiction method. The moment mgnifier B 1 is expressed s

4 62 C.C. Weng, S.I. Yen / Engineering Structures 24 (2002) M u1 M u2 B 1 1 P 1 (9) ulc 2 A s F my Flexurl nd xil lods For n encsed composite column symmetricl bout the plne of bending, the interction of compressive nd flexurl lods should be limited by the following biliner reltionship: P u 8M u 1.0 for P f c P n 9f b M u 0.2f c P n (10) n nd P u M u 1.0 for P 2f c P n f b M u 0.2f c P n (11) n where P u M u P n M n f c 0.85 f b 0.9 fctored xil lod fctored moment nominl xil compressive cpcity nominl flexurl cpcity without xil force To determine the nominl flexurl cpcity M n, the commentry of AISC-LRFD specifiction provides n pproximte eqution for doubly symmetric composite sections s follows: M n ZF y 1 3 (h 2 2c r )A r F yr where Z h 1 h 2 c r A w h 2 2 A wf y 1.7f w F y (12) ch 1 A plstic section modulus of steel shpe width of composite cross section perpendiculr to the plne of bending width of composite cross section prllel to the plne of bending thickness of concrete cover from center of longitudinl reinforcement to the edge of section in the plne of bending web re of steel shpe 3. Survey of previous tested composite columns In 1996, Mirz et l. studied sixteen encsed composite columns subjected to strong xis bending in which second-order effects were significnt. The height of the columns ws 4 meters for ll specimens. As observed from the tests, concrete strin in extreme compression fiber reched round prior to filure of specimens. It ws noted tht the bonding t the interfce of steel flnge nd the surrounding concrete hd little effect on the ultimte cpcity of the composite column [7]. Ricles et l. (1994) presented experimentl results of eight concrete-encsed composite columns. The crosssectionl dimensions of the columns were mm, which were reltively lrge in scle s compred to the specimens of other reserchers. All columns were subjected to strong xis bending nd were tested under monotonic xil lod nd cyclic lterl lod. It ws observed tht the mximum cpcity of the specimens developed fter the yielding of longitudinl reinforcements nd steel flnge. The test results lso indicted tht the sher studs were not effective in enhncing the flexurl strength [8]. Experimentl results of five smll-scle encsed composite columns presented by Ymd et l. (1991) re collected in this study. All specimens were subjected to strong xis bending nd the pplied loding included combintions of xil nd trnsverse forces t both ends of the column. Test results showed tht most of the specimens reched the mximum cpcity when concrete splled nd rebrs yielded in the tension side [9]. Nk et l. (1977) presented experimentl results of four pinned-ended encsed composite columns subjected to strong xis bending. The pplied loding included combintions of xil nd bending forces. Nk et l. indicted tht the filure mode of specimens could be divided into two ctegories: (1) concrete crushing filure nd locl buckling of steel flnge in compressive side; nd (2) concrete crushing filure nd buckling of rebrs in compression side nd yielding of rebrs in tension side [10]. In 1971, Wkbyshi et l. crried out test results of four pinned-ended encsed composite columns. All specimens were subjected to strong xis bending nd the pplied loding included sttic xil lod nd trnsverse force. It ws observed tht s the lod ws incresed to the ultimte cpcity of the columns, buckling of longitudinl reinforcements in compression side nd yielding of rebrs in tension side were found for most of the tested specimens [11]. Yokoo et l. (1967) presented experimentl results of nineteen simply supported encsed composite short columns. It ws reported tht s the lod pproched to the filure condition, wide crcks ppered on the bottom fce for ll specimens, nd filure took plce due to crushing of the concrete [12]. In 1965, Stevens presented experimentl results of 22 pinned-ended encsed composite columns subjected to wek xis bending. The pplied loding included sttic

5 C.C. Weng, S.I. Yen / Engineering Structures 24 (2002) Tble 1 Composite column test dt crried out by Mirz et l. (1996) Specimen Steel shpe d b f t w t f M TEST (kn- B D (mm) A r (mm 2 ) F ys (MP) F yr (MP) f c (MP) KL (mm) P TEST (kn) no. (mm) m) *: Test results of these specimens re plotted in Fig. 3 to compre with the P-M curves constructed bsed on ACI code nd AISC-LRFD specifiction. xil forces t both ends of the specimen with vrious eccentricities. Two filure modes were observed from the tests. They were (1) crushing of concrete on one fce ner the top of structurl steel shpe, nd (2) crushing of concrete on one fce nd yielding of steel in compression, being ccompnied by tensile crcks of concrete on the opposite fce [13]. 4. Comprisons between test results nd predicted cpcities Listed in Tbles 1 7 re the dimensions, mteril properties nd the test results of 78 encsed composite columns collected in this study. In Tbles 8 14, test results re compred with the predicted cpcities using ACI-318 nd AISC-LRFD pproches. In these tbles, P TEST represents the ultimte column cpcity obtined from the test results done by previous reserchers; P ACI nd P LRFD re the predicted nominl cpcities using ACI-318 nd AISC-LRFD pproches, respectively. All predicted vlues re crried out ccording to the given provisions except tht the strength reduction fctors re tken s 1.0. Also given in the tbles re the ACI-toexperimentl cpcity rtio nd the AISC-to-experimentl cpcity rtio. More detiled comprisons re presented s follows Comprisons Tble 8 shows the comprisons between the test results done by Mirz et l. (1996) nd the predicted cpcities using ACI-318 nd AISC-LRFD pproches. This tble revels tht ll the predicted cpcities bsed on the ACI-318 pproch re conservtive (up to 28%) s compred with the test results (except specimen No. Tble 2 Composite column test dt crried out by Ricles et l. (1994) Specimen M TEST (kn- B D (mm) Steel shpe A r (mm 2 ) F ys (MP) F yr (MP) f c (MP) KL (mm) P TEST (kn) no. m) W W W W W W W W Test results of these specimens re plotted in Fig. 4 to compre with the P-M curves constructed bsed on ACI code nd AISC-LRFD specifiction.

6 64 C.C. Weng, S.I. Yen / Engineering Structures 24 (2002) Tble 3 Composite column test dt crried out by Ymd et l. (1991) Specimen Steel shpe d b f t w t f M TEST (kn- B D (mm) A r (mm 2 ) F ys (MP) F yr (MP) f c (MP) KL (mm) P TEST (kn) no. (mm) m) Test results of these specimens re plotted in Fig. 5 to compre with the P-M curves constructed bsed on ACI code nd AISC-LRFD specifiction. Tble 4 Composite column test dt crried out by Nk et l. (1977) Specimen Steel shpe d b f t w t f M TEST (kn- B D (mm) A r (mm 2 ) F ys (MP) F yr (MP) f c (MP) KL (mm) P TEST (kn) no. (mm) m) Test results of these specimens re plotted in Fig. 6 to compre with the P-M curves constructed bsed on ACI code nd AISC-LRFD specifiction. Tble 5 Composite column test dt crried out by Wkbyshi et l. [11] Specimen B D (mm) Steel shpe A r (mm 2 ) F ys (MP) F yr (MP) f c (MP) KL (mm) M TEST (kn- P TEST (kn) no. d b f t w t f (mm) m) ). The predicted cpcities bsed on the AISC-LRFD pproch re found even more conservtive (up to 42%). Tble 9 displys the comprisons between the test results done by Ricles et l. (1994) nd the predicted cpcities using ACI-318 nd AISC-LRFD pproches. The predicted cpcities using these two pproches re conservtive (up to 22 nd 40%, respectively) s compred with the test results. Comprisons between the test results done by Ymd et l. (1991) nd the predicted cpcities using ACI-318 nd AISC-LRFD pproches re shown in Tble 10. It is observed tht the predicted cpcities bsed on the ACI-318 pproch re conservtive up to 44% nd those bsed on the AISC-LRFD pproch re conservtive up to 69%. Tble 11 lists the comprtive results of the predicted cpcities using ACI-318 nd AISC-LRFD pproches to the test results done by Nk et l. (1977). The tble shows tht the predicted cpcities (except specimen No. 3) bsed on the ACI-318 pproch re resonbly conservtive (up to 5%) s compred with the test results nd those bsed on the AISC-LRFD pproch re much more conservtive (up to 31%). The predicted results obtined from using ACI-318 nd AISC-LRFD pproches compred with test results done by Wkbyshi et l. (1971) re presented in Tble 12. It is found tht the predicted cpcities bsed on the ACI-318 pproch somewht overestimte the test strengths (up to 12%), with the exception of specimen No. 1. On the contrry, those bsed on the AISC- LRFD pproch re conservtive (up to 24%), except specimen No. 1. Tble 13 displys the comprisons between the test results done by Yokoo et l. (1967) nd the predicted cpcities using ACI-318 nd AISC-LRFD pproches. It is seen tht the predicted cpcities for some specimens bsed on the ACI-318 nd the AISC-LRFD pproches re slightly unconservtive (up to 21 nd 5%

7 C.C. Weng, S.I. Yen / Engineering Structures 24 (2002) Tble 6 Composite column test dt crried out by Yokoo et l. [12] Specimen Steel shpe M TEST (kn- B D (mm) A r (mm 2 ) F ys (MP) F yr (MP) f c (MP) KL (mm) P TEST (kn) no. d b f t w t f (mm) m) Specimen nos 17 to 19 were bent bout minor xis. Tble 7 Composite column test dt crried out by Stevens [13] Specimen M TEST (kn- B D (mm) Steel stnchion A r (mm 2 ) F ys (MP) F yr (MP) f c (MP) KL (mm) P TEST (kn) no. m) (20 lb) (20 lb) (20 lb) (20 lb) (20 lb) (20 lb) (20 lb) (20 lb) (20 lb) (20 lb) (20 lb) (20 lb) (20 lb) (65 lb) (65 lb) (65 lb) (65 lb) (65 lb) (65 lb) (65 lb) (65 lb) (65 lb) respectively) to the test strengths. But the predicted cpcities for other specimens re conservtive (up to 13 nd 43% for ACI-318 nd AISC-LRFD, respectively). As shown in Tble 14, the predicted cpcities using ACI-318 nd AISC-LRFD pproches re compred with test results done by Stevens (1965). This tble shows tht the predicted cpcities bsed on the ACI- 318 pproch re somewht unconservtive (up to 9%) to the test results for four specimens but re conservtive (up to 29%) for the others. For those bsed on the AISC- LRFD pproch, ll predictions re found to be quite conservtive (up to 50%).

8 66 C.C. Weng, S.I. Yen / Engineering Structures 24 (2002) Tble 8 Comprison between test results (Mirz et l. [7]) nd predicted vlues using ACI code nd AISC-LRFD specifiction Specimen no. Eccentricity (mm) P TEST (kn) P ACI (kn) P LRFD (kn) P ACI /P TEST P LRFD /P TEST Men vlue: Stndrd devition Coefficient of vrition 9.2% 9.6% Tble 9 Comprison between test results (Ricles nd Pboojin [8]) nd predicted vlues using ACI code nd AISC-LRFD specifiction Specimen no. Eccentricity (mm) P TEST (kn) P ACI (kn) P LRFD (kn) P ACI /P TEST P LRFD /P TEST Men vlue: Stndrd devition: Coefficient of vrition: 5.2% 5.4% Tble 10 Comprison between test results (Ymd et l. [9]) nd predicted vlues using ACI code nd AISC-LRFD specifiction Specimen no. Eccentricity (mm) P TEST (kn) P ACI (kn) P LRFD (kn) P ACI /P TEST P LFRD /P TEST Men vlue: Stndrd devition: Coefficient of vrition: 6.2% 9.2% 4.2. Observtions Bsed on the comprtive results presented in the bove section, the following observtions re obtined: 1. An exmintion of the men vlues of the predictedto-tested cpcity rtios listed in Tbles 8 14 indictes tht the predicted cpcities bsed on the ACI- 318 pproch re bout 8 25% closer to the test

9 C.C. Weng, S.I. Yen / Engineering Structures 24 (2002) Tble 11 Comprison between test results (Nk et l. [10]) nd predicted vlues using ACI code nd AISC-LRFD specifiction Specimen no. Eccentricity (mm) P TEST (kn) P ACI (kn) P LRFD (kn) P ACI /P TEST P LRFD /P TEST Infinite Men vlue: Stndrd devition: Coefficient of vrition: 3.4% 12.1% Specimen no. 4 ws tested under pure bending (unit: kn-m). Tble 12 Comprison between test results (Wkbyshi et l. [11]) nd predicted vlues using ACI code nd AISC-LRFD specifiction Specimen no. Eccentricity (mm) P TEST (kn) P ACI (kn) P LRFD (kn) P ACI /P TEST P LRFD /P TEST 1 Infinite Men vlue: Stndrd devition: Coefficient of vrition: 7.9% 12.7% Specimen No. 1 ws tested under pure bending (unit: kn-m). Tble 13 Comprison between test results (Yooko et l. [12]) nd predicted vlues using ACI code nd AISC-LRFD specifiction Specimen no. Eccentricity (mm) P TEST (kn) P ACI (kn) P LRFD (kn) P ACI /P TEST P LRFD /P TEST Men vlue: Stndrd devition: Coefficient of vrition: 9.3% 14.2% results thn those bsed on the AISC-LRFD pproch. For instnce, Tble 9 shows tht the men vlue of the cpcity rtio of the ACI-318 pproch is while tht of the AISC-LRFD pproch is This observtion revels tht the ACI-318 pproch generlly gives better ccurcy thn tht of the AISC- LRFD pproch in predicting the cpcities of the encsed composite columns. 2. Comprisons of the vlues of coefficient of vrition (COV) listed in Tbles 8 14 show tht ll of the COV

10 68 C.C. Weng, S.I. Yen / Engineering Structures 24 (2002) Tble 14 Comprison between test results (Stevens [13]) nd predicted vlues using ACI code nd AISC-LRFD specifiction Specimen no. Eccentricity (mm) P TEST (kn) P ACI (kn) P LRFD (kn) P ACI /P TEST P LRFD /P TEST Men vlue: Stndrd devition: Coefficient of vrition: 14% 14% vlues of the ACI-318 pproch re smller thn those of the AISC-LRFD pproch. This observtion indictes tht the column cpcities clculted using the ACI-318 pproch re less spred thn those obtined using the AISC-LRFD pproch. 3. For ll of the 78 column test results, Tble 15 indictes tht the ACI-to-experimentl cpcity rtio hs men vlue of 0.90 with stndrd devition of 0.14 nd COV of 15%. On the other hnd, the AISC-toexperimentl cpcity rtio hs men vlue of 0.73 with stndrd devition of 0.15 nd COV of 21%. 4. Fig. 1 shows the comprison of the sttisticl distribution of the predicted-to-tested cpcity rtio between the ACI-318 nd the AISC-LRFD pproches. It is observed tht the ACI-318 pproch (shown s solid brs in the figure) gives nerly bellshped norml distribution for the collected test results. Its pek is locted t the cpcity rtio between 0.9 nd 1.0. On the other hnd, the AISC- LRFD pproch shows wider spred distribution nd its pek is locted t the rtio between 0.6 nd 0.7. This sttisticl observtion provides vluble infor- Tble 15 Sttisticl results for the 78 tested specimens listed in Tbles 8 14 Reference Numbers of tested specimen Men cpcity rtio P ACI /P TEST P LFRD /P TEST Mirz et l. [7] Ricles nd Pboojin [8] Ymd et l. [9] Nk et l. [10] Wkbyshi et l. [11] Yokoo et l. [12] Stevens [13] Men vlue : Stndrd devition: Coefficient of vrition: 15.2% 20.7% Men vlue= {(numbers of tested specimen) (men cpcity rtio)}/ (numbers of tested specimen)

11 C.C. Weng, S.I. Yen / Engineering Structures 24 (2002) Regrding the difference of design philosophy dopted in the ACI code nd the AISC specifiction, it is noted tht the ACI-318 trets the design of concreteencsed composite columns through the extension of the design provisions for ordinry reinforced concrete columns. The ACI-318 pproch considers the steel shpe s n equivlent mount of reinforcement nd clcultes the cpcity of n encsed composite column bsed on strin comptibility nlysis procedure. On the other hnd, the AISC-LRFD pproch trets the design of concrete-encsed composite columns through the extension of the provisions recommended for bre steel columns. Tht is, the design of n encsed composite column is proceeded by trnsforming the reinforced concrete portion into n equivlent contribution of steel shpe. Then, the composite column is designed using the formuls developed for steel columns s given in Eqs. (4) (11). It is essentil to observe tht these equtions were originlly developed for bre steel columns in which the column strength is significntly influenced by residul stress nd initil out-ofstrightness of the steel column [16,17]. However, for concrete-encsed composite column, these two prmeters ply minor role becuse the reinforced concrete portion of the composite column is much less sensitive to the influences of residul stress nd initil out-ofstrightness. These observtions my provide prt of the resons why the AISC-LRFD pproch gives less ccurte nd wider spred predictions s compred with the 78 column test results Filure mode Fig. 1. Sttisticl distribution of predicted-to-tested cpcity rtios, P n /P TEST, using ACI-318 nd AISC-LRFD pproches for 78 specimens. mtion on the ccurcy nd relibility of the ACI-318 pproch in the prediction of the strength of concreteencsed composite columns. 5. Discussions 5.1. Design philosophy As observed from the test results [9 13], the filure modes of encsed composite columns cn be divided into two ctegories. They re: () bending tension filure, resulting from rebrs nd steel flnge yielding in tension side prior to concrete crushing in compression side; (b) bending compression filure, resulting from concrete crushing nd rebr buckling in compression side without yielding of rebrs nd steel flnge in tension side. According to the filure modes observed from the column tests, it ws found tht the concrete strin in extreme compression fiber ws ner prior to filure [7]. This observtion is consistent with the ssumption mde in the ACI-318 code in which the mximum concrete compressive strin is tken s In ddition, the experimentl results lso reveled tht the sher connectors between steel flnges nd concrete hd little contribution to the ultimte strength of encsed composite columns [7,8]. In generl, the existence of sher connectors ws found to be conducive to the ACI ssumption of plne section remining plne Effect of steel rtio Fig. 2 shows the distribution of the predicted-to-tested cpcity rtios of the ACI nd the AISC pproches corresponding to the steel rtios of the 78 tested specimens. Fig. 2. Comprison of the sctter of predicted-to-tested cpcity rtios, P n /P TEST, using ACI-318 nd AISC-LRFD pproches for corresponding steel rtio of 78 tested specimens.

12 70 C.C. Weng, S.I. Yen / Engineering Structures 24 (2002) The steel rtios shown in this figure rnge from 2% to 12%. For the specimens with steel rtio under 4%, it is observed tht the verge predicted-to-tested cpcity rtios of the ACI nd the AISC pproches re bout 0.62 nd 0.37, respectively. Both predicted-to-tested cpcity rtios re found quite conservtive. However, the verge rtio of the ACI-318 is still bout 25% closer to the test results thn tht of the AISC-LRFD. These observtions indicted tht the limittion of minimum 4% of steel rtio in n encsed composite section is essentil for the AISC-LRFD strength provisions. On the other hnd, for the specimens with steel rtio ner or bove 4%, it is observed tht the men vlue of predicted-to-tested cpcity rtios of the ACI-318 is 0.92, which is still more ccurte thn the vlue of 0.75 of the AISC-LRFD. In ddition, the COV of the ACI- 318 is found to be smller thn tht of the AISC-LRFD. This mens tht the ACI pproch lso gives better predictions thn the AISC pproch does when steel rtio is lrger thn 4% P M interction digrm Fig. 4. Comprisons between test results [8] nd nominl strengths preducted using ACI code nd AISC-LRFD specifiction. As shown in Figs. 3 6, the thrust-to-moment (P M) interction digrms of the ACI nd the AISC pproches re constructed to compre with the test results. The curves with the blck dots nd the white spots denote the nominl P M strength curves of the ACI nd the AISC provisions, respectively. Eq. (12) is used to determine the nominl flexurl cpcity of the AISC curve. Fig. 5. Comprisons between test results [9] nd nominl strengths predicted using ACI code nd AISC-LRFD specifiction. Fig. 3. Comprisons between test results [7] nd nominl strengths predicted using ACI code nd AISC-LRFD specifiction. As compred to the column test dt (denoted s strs) shown in these figures, it is observed tht both the ACI nd the AISC pproches give conservtive estimtes of the column strengths. However, the ACI curves show much closer predictions thn tht of the AISC curves. The comprisons indicte tht the simplified biliner P M interction equtions suggested in the AISC-LRFD specifiction give very conservtive predictions of the strength of the encsed composite columns.

13 C.C. Weng, S.I. Yen / Engineering Structures 24 (2002) Fig. 6. Comprisons between test results [10] nd nominl strengths predicted using ACI code nd AISC-LRFD specifiction. From these figures, it is lso noted tht the pure xil compressive strengths clculted by using the ACI-318 pproch, (P n0 ) ACI, re ll lrger thn those of the AISC- LRFD pproch, (P n0 ) LRFD. The comprison between Eqs. (1, 1b) nd (4) revels tht the slenderness effect plys n importnt role in cusing this difference. In the ACI code, the slenderness effect is ccounted for only when the column slenderness rtio, KL/r, is lrger thn the vlue clculted from Eq. (3). However, in the AISC specifiction, ll columns re subjected to the influence of slenderness effect. As shown in Eqs. (5) nd (6), slenderness prmeter, l c, is lwys included in the clcultion of the AISC column strength. In ddition, it is found tht the difference in xil strengths predicted by the ACI nd the AISC pproches becomes smller s the column slenderness rtio decreses. This is minly becuse the vlue of the criticl stress, F cr, of the AISC- LRFD specifiction clculted from Eqs. (5) nd (6) becomes lrger s the vlue of l c decreses. 6. Summry nd conclusions Test results of 78 concrete-encsed composite columns done by previous reserchers re collected to evlute the ccurcy of the strength provisions of the ACI-318 code nd the AISC-LRFD specifiction. The following conclusions re obtined: 1. In generl, s compred with the test results, the ACI- 318 pproch is found to be more ccurte thn the AISC-LRFD pproch in predicting the cpcities of encsed composite columns. Also observed from the comprisons is tht the column cpcities predicted using the ACI-318 pproch re less wide spred (smller vlue of coefficient of vrition) thn those clculted bsed on the AISC-LRFD pproch. 2. For the 78 tested specimens, the sttisticl nlysis on the distribution of the predicted-to-tested cpcity rtios indictes tht the ACI-318 pproch gives bell-shped norml distribution curve with its pek locted t the rtio between 0.9 nd By observing the filure modes of the tested composite columns, the strin comptibility pproch used in the ACI-318 code is found to be ble to model the behvior of the concrete-encsed composite columns more relisticlly thn the section trnsformtion pproch recommended in the AISC-LRFD specifiction. 4. For concrete-encsed composite columns with steel rtio rnging from 2 to 12%, this comprtive study revels tht the ACI-318 pproch shows better strength predictions thn tht of the AISC-LRFD. It is lso observed tht significnt error my occur if the AISC-LRFD pproch is used to clculte the cpcity of n encsed composite column with steel rtio under 4%. Acknowledgements The finncil support of the Ntionl Science Council of Tiwn through contrct number NSC E is grtefully cknowledged. References [1] Buildings code requirements for structurl concrete (ACI ). Detroit (MI): Americn Concrete Institute (ACI), [2] Lod nd resistnce fctor design specifiction for structurl steel buildings. 2nd ed. Chicgo (IL): Americn Institute of Steel Construction (AISC), [3] NEHRP recommended provisions for seismic regultions for new buildings nd other structures. Wshington (DC): Building Seismic Sfety Council, [4] Viest IM, Colco JP, Furlong RW, Griffis LG, Leon RT, Wyllie LA. Composite construction design for buildings. New York: McGrw-Hill, [5] Furlong RW. Column rules of ACI, SSLC nd LRFD compred. Journl of Structurl Engineering, ASCE 1983;109: [6] El-Twil S, Snz-Picòn CF, Deierlein GG. Evlution of ACI 318 nd AISC (LRFD) strength provisions for composite bemcolumns. Journl of Constructionl Steel Reserch 1995;34: [7] Mirz SA, Hyttinen V, Hyttinen E. Physicl tests nd nlyses of composite steel concrete bem-columns. Journl of Structurl Engineering, ASCE 1996;122(11): [8] Ricles JM, Pboojin SD. Seismic performnce of steel-encsed composite columns. Journl of Structurl Engineering, ASCE 1994;120(8):

14 72 C.C. Weng, S.I. Yen / Engineering Structures 24 (2002) [9] Ymd M, Kwmur H, Zhng F. Reserch on the elsto-plstic deformtion nd frcture behviors of wide flnge steel encsed reinforced concrete columns subjected to bending nd sher (in Jpnese). Journl of Structurl Construction Engineering, AIJ (Architecturl Institute of Jpn) 1991;420: [10] Nk T, Morit K, Tchibn M. Strength nd hysteretic chrcteristics of steel-reinforced concrete columns (in Jpnese). Trnsction of AIJ 1977;250: [11] Wkbyshi M, Minmi K, Komur K. An experimentl study on elsto-plstic chrcteristics of concrete members using n encsed H-section subjected to combined bending nd xil force (in Jpnese). Bulletin of Disster Prevention Reserch Institute, Kyoto University 1971;14A: [12] Yokoo Y, Wkbyshi M, Sueng Y. Experimentl studies on steel concrete members with H-shpe steel (in Jpnese). Trnsction of AIJ 1967;136:1 7. [13] Stevens RF. Encsed stnchions. The Structurl Engineer 1965;43(2): [14] Furlong RW. AISC column logic mkes sense for composite columns, too. Engineering Journl, AISC 1976;1:1 7. [15] SSRC, Tsk Group 20. A specifiction for the design of steel concrete composite columns. Structurl Stbility Reserch Council (SSRC) Engineering Journl, AISC 1979;4: [16] Bjohovde R, Tll L. Mximum column strength nd multiple column curve concept. Fritz Lb. Report No , Lehigh University, Bethlehem, PA, [17] SSRC. Guide to stbility design criteri for metl structures. 4th ed. New York: John Wiley nd Sons, 1988.