Residual Strength of Concrete-encased Steel Angle Columns after Spalling of Cover Concrete

Transcription

1 Reidual Strength of Concrete-encaed Steel Angle Column after Spalling of Cover Concrete *Chang-Soo Kim 1) and Hyeon-Jong Hwang ) 1) School of Civil Engineering, Shandong Jianzhu Univ., Jinan 50101, China ) College of Civil Engineering, Hunan Univ., Changha 41008, China 1) mukan05@nu.ac.kr ABSTRACT In concrete-encaed teel angle column, in which teel angle are placed at four corner and the corner angle are connected by tranvere reinforcement, premature palling of cover concrete may occur due to the hrinkage of concrete and the weakne plane between cover concrete and core concrete that i created by mooth urface of teel angle and dene tranvere reinforcement. However, concreteencaed teel angle column how good load-carrying capacity even after coverpalling due to the high contribution of teel angle to trength and tiffne and the good confinement effect of teel angle and tranvere reinforcement on core concrete. To invetigate the reidual trength after cover-palling, a numerical tudy wa performed conidering the train compatibility, confinement effect, local buckling, and cover-palling. The numerical invetigation howed that when the teel contribution i high and the confinement efficiency i high, concrete-encaed teel angle column exhibit relatively large reidual trength even after palling of cover concrete at corner. 1. INTRODUCTION Compared to conventional concrete-encaed teel (CES) ection uing a wideflange teel core, concrete-encaed teel angle (CES-A) ection can maximize the contribution of teel to flexural trength and tiffne, particularly under biaxial bending: the train and moment-arm of teel are ignificantly increaed by placing teel angle at four corner, and the corner teel angle connected by tranvere reinforcement provide good confinement to core concrete (Kim et al. 014 and 017) (Fig. 1). Previou tet reult (Kim et al. 014 and 017) howed that even after palling of cover concrete at corner (1t peak), the axial load continuouly increaed up to the nd peak without ignificant degradation in tiffne, and the maximum load and effective flexural tiffne of CES-A column were 1.53 and.07 time thoe of a 1) Aociate Profeor ) Aitant Profeor

2 conventional CES column uing a wide-flange teel core of the ame area, due to the high contribution of teel angle. Fig. 1 Advantage of CES-A Section In the preent tudy, to invetigate the reidual trength of CES-A column after cover-palling, a numerical tudy wa performed by a propoed analyi model. The propoed model conidered the train compatibility, confinement effect, local buckling, and premature cover-palling. For verification, the prediction by the propoed model were compared with previou tet reult, and a numerical parametric tudy wa conducted for variou deign parameter.. NUMERICAL MODELING AND VERIFICATION.1 Concrete Since the ditribution of confining preure in CES-A ection i imilar to that of rectangular tied RC ection, exiting concrete confinement model can be ued regarding teel angle and tranvere reinforcement a longitudinal bar and tranvere bar, repectively (Montuori and Piluo 009; Nagapraad et al. 009). In the preent tudy, the compreive tre-train relationhip of concrete wa characterized by the confinement model of Saatcioglu and Razvi (199 and 1999) (Fig. (a) and (b)), which i applicable to a wide range of material (concrete of f' c = MPa and tranvere reinforcement of up to f yt = 1400 MPa) and wa verified againt extenive tet reult of column under concentric and eccentric loading. r c / co f c if r c co r 1 c / co fc (1) c co f c if c co c85 co

3 Fig. Numerical Modeling for CES-A Section The definition and calculation of thee material propertie for concrete modeling are available in the literature. To take into account the ditinctive local failure mechanim of CES-A column in the analyi, the concrete model wa modified a follow. 1) Premature cover-palling may occur due to the hrinkage of concrete and the weakne plane between cover concrete and core concrete that i created by longitudinal and tranvere reinforcement, and thi phenomenon i more obviou when higher trength concrete and dener reinforcement are ued (Collin et al. 1993; Cuon and Paultre 1994). Epecially in CES-A column, the premature cover-palling i more pronounced at corner due to the mooth urface of teel angle (Kim et al. 014 and 017). Thu, for the tre f c,u of cover concrete at corner, the propoed model aumed Eq. () (cae 1 in Fig. 3). In the abence of experimental data, the ultimate train of ε cu,u = i recommended baed on tet reult. fcu, 0 if c cu, u for cover concrete at corner () ) Steel angle provide good confinement to core concrete, but the effect of local buckling on the confinement hould be alo conidered. Thu, unlike the exiting model (Montuori and Piluo 009; Nagapraad et al. 009), in which the full leg b of teel angle i aumed to exert the confining preure in whole analyi tep, the propoed model aumed that only the effective leg b,eff exert the confining preure after local buckling of teel angle (Fig. 4).

4 Thu, in the calculation of the confining preure, Eq. (3) wa ued for the ineffective width w i. w b b (3) i c,eff The calculation of the effective leg b,eff (or effective width) conidering local buckling of teel angle i given in the next ubection. Fig. 3 Spalling of Concrete Cover at Corner of CES-A Section Fig. 4 Confinement of Steel Angle and Tranvere Reinforcement. Steel Angle The tre-train relationhip of teel angle wa characterized by a rounded curve (Fig. (c), Eq. (4)) (Ramberg and Ogood 1943; Ramuen 003) or typical trilinear curve (Fig. (d)). The definition and calculation of thee material propertie for teel angle modeling are available in the literature. n f f 0.00 if f fy E f y (4) m f f y f f y u y if f y f fu E 0. fu f y Generally, in the deign of conventional CES column, local buckling of the teel core i not conidered, becaue the concrete encaement prevent the local buckling.

5 However, in the cae of CES-A column, the tructural behavior after palling of cover concrete at corner i trongly affected by local buckling of teel angle. In the preent tudy, the critical buckling tre f b wa determined by Eq. (5) (Gerard 1946), and the pot-local buckling behavior wa decribed by the effective width approach (von Karman et al. 193; Bambach and Ramuen 004(1) and (); Mazzolani et al. 011). In the effective width approach, the tre reditribution within a buckled teel plate i implified by auming that only a certain width of the plate remain effective. f b kb E t 1 1 b E,ec E,tan (6) E E,ec where η = platicity reduction factor in Eq. (6) (Stowell 1948); k b = local buckling coefficient; ν = Poion ratio (0.3 in elatic or 0.5 in platic); t and b = thickne and width of teel; E, E,ec, E,tan = elatic, ecant, and tangent moduli, repectively. Leg of teel angle can be modeled a plate imply upported along three edge with one longitudinal edge free, and Bambach and Ramuen (004(1) and ()) propoed two method for thoe plate element to conider the tre gradient and initial imperfection: elatic and platic effective width method. Of the two method, in the preent tudy, the elatic effective width method wa implemented with a modification to take into account the effect of tranvere reinforcement. The modified equation for the buckling coefficient conidering the pacing of tranvere reinforcement are given in Table 1 (the newly introduced econd term of k b i the modification). Table 1 Effective Width for Leg of Steel Angle (Bambach and Ramuen (004(1) and ()) and Modification) Stre Local Buckling Coefficient**, Elatic Effective Stiffne***, Ditribution* k (Modified) b b ( 1) SS Free Free SS b kb Ck 0.34 t C k b kb Ck 0 t C k b b kb Ck t Ck ,eff 1 1 = 1 1 =1 1 1 = 1 1 =1 (5)

6 * SS = imply upported edge, Free = free edge, f, 1 f = edge tree of a plate element ( f 1 f ), and f / f1 = ratio of edge tree ( 1 ). ** To take into account the effect of tranvere reinforcement, the econd term / C b i newly introduced baed on the reult of finite trip analyi and k t regreion analyi. *** f / f, and = 0. = imperfection enitivity coefficient to conider initial imperfection. y b It i noted that, in the preent tudy, the critical buckling train ε b of teel angle wa aumed to be greater than the peak train ε co,u of cover concrete (i.e., ε b ε co,u ince cover concrete retrain local buckling of teel angle), and the local bucking of teel angle wa aumed to incorporate palling of cover concrete at corner (i.e., f c,u = 0 if ε ε co,u ) (cae in Fig. 3)..3 Column Analyi In the preent tudy, the effect of bond-lip between concrete and teel wa not conidered, becaue it i le pronounced in CES-A column where large axial compreion i expected to be applied and external force are tranferred to concrete and teel angle directly. To take into account the econd-order effect, the deflection hape of the column wa approximated a a coine curve (Wetergaard and Ogood 198). Fig. 5 Verification of Numerical Analyi

7 .4 Verification For verification, the nonlinear numerical analyi reult by the propoed model were compared with the previou tet reult (Kim et al. 014 and 017). Fig. 5 how the comparion. Although ome dicrepancie were oberved in the behavior, the prediction (thin dahed line) generally agreed with the tet reult (thick olid line). 3. RESIDUAL STRENGTH AFTER COVER-SPALLING To invetigate the effect of deign parameter on reidual trength after coverpalling, a parametric tudy wa performed for a typical CES-A column hown in Fig. 6 (quare cro-ection with equal-leg teel angle connected by batten, and 50 mmthick cover concrete). The default parameter and variable parameter are preented in the figure. Fig. 6 Parametric Study for Reidual Strength after Cover-palling Fig. 6 how the numerical interaction curve of the CES-A ection, which correpond to the 1t peak load at cover-palling (thin dahed line) and nd peak load

8 after cover-palling (thick olid line). A expected, the nd peak load (or reidual trength) wa affected by the deign parameter, and in ome cae, the nd peak load wa greater than the 1t peak load: 1) a the teel contribution increaed (in the cae of uing higher trength (Fig. 6(b)) and/or thicker (Fig. 6(c)) teel angle), the reidual trength in the tenion-controlled zone (below the balanced failure point) wa increaed; wherea ) a the confinement efficiency increaed (in the cae of uing more compact teel angle (Fig. 6(d)) and higher trength, thicker, and/or dener batten (Fig. 6(e), (f), (g))), the reidual trength in the compreion-controlled zone (above the balanced failure point) wa increaed. In the cae of uing higher trength concrete (Fig. 6(a)), the interaction curve in the compreion-controlled zone wa expanded, but the reidual trength wa decreaed due to the decreaed teel contribution. Epecially in the practical range of axial load (generally in actual deign, P 0.1A g f' c according to the definition of compreion member and e 0 /b 0.1 to account for accidental eccentricity (ACI )), the nd peak load greater than the 1t peak load wa more obviou. The nd peak load or reidual trength i a meaningful factor in eimic deign and progreive collape analyi. Thu, further reearch i required to predict the reidual trength after palling of cover concrete at corner. 4. CONCLUSIONS To invetigate the reidual trength of CES-A column, a numerical tudy wa performed uing a propoed analyi model, in which the train compatibility, confinement effect of teel angle and tranvere reinforcement, local buckling of teel angle and it effect on confinement, and premature palling of cover concrete at corner were conidered. For verification, the numerical analyi reult were compared with the previou experimental tudy reult, and to invetigate the effect of deign parameter, a parametric tudy wa alo conducted. The numerical invetigation howed that when the teel contribution i high and the confinement efficiency i high, CES-A column exhibit relatively large reidual trength even after palling of cover concrete at corner. REFERENCES American Concrete Intitute (014), Building Code Requirement for Structural Concrete and Commentary (ACI ), Farmington Hill, MI. Bambach, M.R. and Ramuen, K.J.R. (004(1)), Effective width of untiffened element with tre gradient, J. Struct. Eng., ASCE, 130(10), Bambach, M.R., and Ramuen, K.J.R. (004()), Deign proviion for ection containing untiffened element with tre gradient, J. Struct. Eng., ASCE, 130(10), Collin, M.P., Mitchell, D., and MacGregor, J.G. (1993), Structural deign conideration for high-trength concrete, Concrete International: Deign and Contruction, 15(5), 7-34.

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