STUDY ON SEISMIC BEHAVIOR OF RC COMPOSITE CORE WALLS WITH CONCEALED STEEL TRUSS SUBJECTED TO COMBINED ACTION

Transcription

1 STUDY ON SEISMIC BEHAVIOR OF RC COMPOSITE CORE WALLS WITH CONCEALED STEEL TRUSS SUBJECTED TO COMBINED ACTION CAO Wanln 1, CHANG Wehua 2, ZHANG Janwe 1 1 College of archtecture and Cvl Engneerng, Bejng Unversty of Technology, Bejng, Chna 2 Chna Academy of Buldng Research, Bejng, Chna Emal:changwehua@cabrtech.com Abstract: In ths paper, renforced concrete composte core wall wth concealed steel truss were proposed. Ths new composte core wall ncludes two knds of composton. One s composton of two bearng systems, ncludng truss and core wall, the other s composton of two materals, ncludng steel and concrete. Two 1/6 scale core walls specmens were desgned,ncludng a normal renforced concrete core wall and a renforced concrete composte core wall wth concealed steel truss. The expermental study on the sesmc behavor of two core walls subjected to combned acton of compresson, bendng moment, shear and torque, was carred out. The load-carryng capacty, stffness, ductlty, hysteretc behavor, energy dsspaton and falure mechansm of the core walls were dscussed. The test results showed that the sesmc performance of core walls was mproved greatly by the concealed steel truss. Based on the rotatng-angle softened truss model theory, ths paper presents a three-dmensonal model for analyss of renforced concrete composte core walls wth concealed steel truss subjected to complex loadng. Through the results of calculaton concded wth the test well, ths model can predct the ultmate strength of the load-carryng capacty of renforced concrete composte core walls wth concealed steel truss, and provde a tool to obtan the entre load-deformaton hstory. Key words: steel truss, renforced concrete core walls, combned acton, sesmc performance,nonlnear analyss 1. INTRODUCTION Wth the progress of Chnese urbanzaton accelerated, more and more hgh-rse buldngs have been set up n the ctes. It s beleved that Chna s much more lkely to be strcken by earthquakes. How to mprove the sesmc behavor of the core wall wth restrcted thckness has become a key problem of sesmc desgn. Concealed steel truss s able to greatly mprove sesmc performance of normal shear wall and core wall (Cao et al, 23, 24, 25,27). The experment and research show SRC shear walls have good yeldng ablty (Anwar Hossan etal,24. Drver etal,1998. Hossan,24)In ths paper, the author tres to propose that concealed steel truss could be added n shear core to ncrease the sesmc performance of t. 2. EXPERIMENTAL DETAIL In order to nvestgate the sesmc performance of RC core wall wth concealed steel truss, two core walls are desgned. The test specmens are labeled as CWT-1 and CWT-2, respectvely. Where CWT-1 s the normal RC core wall wthout concealed steel truss; CWT-2 s the RC core wall wth concealed steel truss whle mantanng the man renforcement of CWT-1. The dmensons of specmen CWT-1 s the same as specmen CWT-2. Two specmens are both symmetrc constructon. The shear span rato of both specmens s 2.1. Specmens are three layers of the bottom of core wall. The heght for fst and second layer are 83 mm, and the heght for the thrd layers s 6 mm, and heght of based were 36 mm, and the thckness of the loaded plate at the top was 3 mm, and the dstance from the loadng pont to the surface of model based was 226 mm, and the heght of the specmen was 277 mm. The thckness of the couplng wall-column s desgned as 75mm.

2 Specmens are poured wth fne-stone concrete. Concrete strength grade s desgned as C35 and the average of the measured cube concrete compressve strength of CWT-1 and CWT-2 s 44.1 MPa, 42.4 MPa respectvely. Mechancal propertes of steel bars are tabulated n Table 1. Schematc vew of test set-up s llustrated n Fgure 1, and Schematc vew of dsplacement gauges s llustrated n Fgure2. The dmensons and renforcement detals for specmen CWT-1 s llustrated n Fgure3. The dmensons and renforcement detals for specmen CWT-1 s llustrated n Fgure4. Dsplacement meter Dsplacement meter Specmen 2t Jack 1t Jack Fxed bolt Reacton wall Dsplacement meter 1 3 Dsplacement meter 3 Dsplacement meter 5 eccentc dctance Dsplacement meter 2 Dsplacement meter 4 Dsplacement meter Fg.1 Schematc vew of test set-up Fg.2 Schematc vew of dsplacement gauges Fg.3 Geometry and renforcement detals of specmen CWT-1

3 Steel Bar and Profled Steel Fg.4 Geometry and renforcement detals of specmen CWT-2 Table1 Mechancal propertes of steel bar and profled steel Yeld Strength f y /MPa Ultmate Strength f b /MPa Elongaton Rate /% Elastcty Modulus /MPa 8# ron wre φb4 Steel Bar Profled Steel Steel Plate Durng experment, the vertcal axal load was mposed at the top of model through vertcal jack, and the vertcal beam connected wth the vertcal jack through the rollng bearngs. The vertcal pressure was 132kN, and regulator system used to mantan ts value remans unchanged, after vertcal axal load was mposed. A low-frequency cyclc loadng s horzontally appled at verge of loaded plate of specmen by a push and pull jack. The specmens were subjected to eccentrc horzontal loadng. The dstance from the dsplacement gauges to wall base s 226mm, 166mm, 83mm respectvely. Axal loads for specmen CWT-1 and specmen CWT-2 are 132kN. All the stans, dsplacements and loads are recorded and analyzed by IMP data gatherng system connected to the specmen. The crackng of the specmen s montored durng the experments. 3 EXPERIMENTAL RESULTS AND ANALYSIS 3.1 Load-Carryng Capacty The measured loads correspondng to concrete crackng, effectve yeldng of the secton and ultmate load-carryng capacty of the specmen are tabulated n Table 2, where F c s concrete crackng load whch s the measured load correspondng to the frst concrete crack; T c s concrete crackng torque whch s the measured load correspondng to F c ; F y s yeld load whch s defned as the average of postve load and negatve load, snce postve yeld load s close to negatve yeld load; T y s yeld torque whch s correspondng to F y ; F u s ultmate load whch s the maxmum horzontal load appled to the specmen; Snce the specmens are symmetrcal structure,f u s defned as the average of postve load and negatve load; T u s ultmate torque whch s correspondng to F u and μ yu =F y /F u = T y /T u, represents the rato of yeld strength to ultmate strength. Table 2 Expermental results of carryng-load capacty Specmen Concrete Crackng Load Yeld Load Ultmate Load F c /kn T c /kn m Relatve F y /kn T y /kn m Relatve F u /kn T u/kn m Relatve Rato of Yeld to Ultmate μ yu Relatve CWT CWT It s observed form Table 2 that: (1) Compared wth the normal core wall, the crackng load s slghtly ncreased by addng the concealed steel truss wthn the wall. (2) Compared wth the normal core wall, the yeld load and ultmate load are all sgnfcantly ncreased by addng the concealed steel truss wthn the wall. The measured yeld load and ultmate load for CWT-2

4 are ncreased respectvely by 11.2% and 27.3% n comparson wth the specmen CWT-1. (3) Compared wth the normal core wall, the rato of yeld strength to ultmate strength s sgnfcantly ncreased by 14.6%. 3.2 Stffness The measured stffness and stffness degradaton coeffcents for the test specmens are tabulated n table 3. Where K s the ntal tangent stffness; K c s the secant stffness correspondng to the crackng state of the wall; K y s the secant stffness correspondng to the yeld state of the wall; β c = K c / K represents the stffness degradaton coeffcent from the ntal elastc state to the crackng state; β yc = K y / K c,representng the stffness degradaton coeffcent from the crackng state to the yeldng state; β y = K y / K represents the stffness degradaton coeffcent from the ntal elastc state to the yeldng state. The followng observatons can be made from Table 3: (1) Specmen CWT-1 and Specmen CWT-2 have almost the same ntal elastc stffness K. (2) Specmen CWT-1 and Specmen CWT-2 have almost the same crackng stffness K c. The data ndcate that n ntal state stffness s determned by concrete strength and specmen dmenson and concealed steel truss does not have much effect on stffness K and K c. (3) The yeld stffness K y for the core wall wth concealed steel truss shows a sgnfcant ncrease over that for the core wall wthout concealed steel truss. Ths can be explaned by the concealed steel truss embedded n the core wall restrctng the expandng of concrete cracks and resultng n the stffness slower degradng. It s seen from all state of experment that the stffness n fnal stage s more stable for the core wall wth concealed steel truss, whch s more favorable for sesmc resstance. (4) Compared wth the normal core wall, the value of β yc are all sgnfcantly ncreased by by addng the concealed steel truss wthn the wall. (5) Compared wth the normal core wall, the value of β y s sgnfcantly ncreased by 13.4%. Table 3 Measured stffness and stffness degradaton coeffcents Specmen K /kn mm -1 K c /kn mm -1 K y /kn mm -1 β co β yc β yo β yo Relatve CWT CWT Ductlty The measured dsplacement and ductlty ratos for the test specmens are lsted n table 4, where all the dsplacements are measured at the top plate of the core wall. u c s the dsplacement at the crackng state; u y s the dsplacement at the yeldng state; u d s the postve ultmate dsplacement of the specmen; andμ=u d /u y s defned as the ductlty rato of the shear wall (u d s calculated wth postve value n ths paper). It s observed form Table 4 that: (1) The yeldng dsplacements for specmens wth concealed steel truss show a lttle ncrease over that for the specmens wthout concealed steel truss. (2) The ultmate dsplacements are sgnfcantly ncreased for the core walls wth concealed steel truss. (3) The ductlty rato for specmen CWT-2 s ncreased by 2.4% n comparson wth specmen CWT-1. Therefore, the ductle behavor of the core wall can be sgnfcantly mproved by settng concealed steel

5 Specmen truss wthn the core wall. Table 4 Expermental results of dsplacement and ductlty coeffcent u y /mm u d /mm postve negatve average postve negatve average μ μ Relatve θ p θ p Relatve CWT /58 1. CWT / Hysteretc Behavor and Energy Dsspaton Capacty The measured load-dsplacement hysteress loops for the specmens are shown n Fgure 5. And comparatve skeleton curve of postve loadng are shown n Fgure 6. It s seen that the hysterss loops for the specmen CWT-2 s wder than that of CWT-1. The core walls wth concealed steel truss present larger nner hysterss loop areas than the normal core walls wthout concealed steel truss. The core walls wth concealed steel truss, therefore, provde better energy absorbng capacty. It s also notced that the core walls wth concealed steel truss exhbt better plastc deformaton capacty and ductlty and ther load-carryng capacty s also ncreased. 8 6 F/kN 8 6 F/kN 8 6 F /kn u/mm u/mm (a) CWT-1 Fgure 5. Measured hysteress loop (b) CWT-2 2 u /mm CWT-1 CWT-2 Fgure 6. Skeleton curve of postve loadng The elastc-plastc energy dsspaton capacty of the specmens can be evaluated usng the nner area of the hysteress loop. The greater the nner area s the better the energy dsspaton capacty wll be. In analyss descrbed n ths paper, the area n the frst and thrd quadrant of the hysteress loop s approxmately computed and used as an ndex of energy dsspaton capacty, whch s a part of the total energy dsspaton. The measured energy dsspaton for specmens are lsted n Table 5 accordng to the ndex. It s observed from Table 5 that the energy dsspaton capacty of the core wall s sgnfcantly mproved by addng concealed steel truss wthn the core wall. Compared wth specmen CWT-1, energy dsspaton for the specmen CWT-2 ncreased 34.38%. Specmen Table 5. Measured results of energy dsspaton n frst quadrant of hysteress loop Total Mass of Renforcement /kg Mass of Concealed Steel truss Energy Dsspaton /kn-mm /kg postve negatve average Relatve Increase of Energy Dsspaton /% CWT CWT

6 3.5 Falure Mode Crack patterns at Falure for two specmens are llustrated n Fgure 7. In the core wall, the wall whch subject to the add stress of shear and torque call shear wall 1, the wall whch subject to the subtractve stress of shear and torque call shear wall 3, the wall whch subject to tenson as horzontal load s pull called shear wall 2, the wall whch subject to tenson as horzontal load s pull called shear wall 2, the wall whch subject to compressve stresses as horzontal load s push called shear wall 4. From observatons of the falure mode of each specmen, t s seen that the mechancal model for calculatng ts load-carryng capacty could be consder as shear and torque members. Compared wth the normal core wall, the concrete cracks n the core wall wth concealed steel truss are tner, closer, more n number and dstrbute over a larger area. CWT-1 shear wall 3 shear wall 2 shear wall 1 shear wall 4 (a) CWT-1 CWT-2 shear wall 3 shear wall 2 shear wall 1 shear wall 4 (b) CWT-2 Fg.7 Mode of falure for core walls specmens 4. THEORETICAL MODEL Based on the rotatng-angle softened truss model theory, ths paper presents a three-dmensonal model for analyss of renforced concrete composte core walls wth concealed steel truss subjected to complex loadng. Under combned acton of compresson, bendng moment, shear and torque, each element of the secton of core walls s subjected to two systems of stresses separately, ncludng a one-dmensonal stress system and a two-dmensonal stress system. The one-dmensonal stress system called system 1 ressted the longtudnal stresses due to compresson, bendng moment, shear and torque, and the two-dmensonal stress system ressts the shear stress due to shear and torque. The two-dmensonal stress system called system 2 ressts the shear

7 stress due to torson and shear. The two stress systems are combned through the compatblty equatons and the equlbrum of stresses n the longtudnal drecton. 4.1 two-dmensonal stresses (system2) The four walls are ted together by the requrements of equlbrum of shearng stresses. The shear flow q 1 wthn T V the secton of shear wall 1 s gven by q = 1 2A + 2h (1) cor cor WhereT s the torson the secton ressted; V s the shear the secton ressted; Acor s the area enclosed by the shear flow and Acor = bcor hcor ; and bcor = b 2a dl, hcor = h 2a dl ;b and h are respectvely, the wde and depth of the secton of core wall ; dl s dameter of strrups ; a s the concrete cover depth. T The shear flow q 2 wthn the secton of shear wall 2 s gven by q 2 = (2) A T V The shear flow q 3 wthn the secton of shear wall 2 s gven by q = 3 2A 2h (3) T The shear flow q 4 wthn the secton of shear wall 4 s gven by q 4 = (4) A Consderng the equlbrum of the shear element, the followng equatons can be obtaned by transformng the concrete prncpal stresses and bracng of truss stress nto horzontal and vertcal coordnate system and supermposng them wth the tensle stresses of the steel renforcement and steel, whch are shown n Fgure8. 2 cor cor 2 cor cor (a) shear element (b) concrete (c) steel renforcement (d) steel (e) steel bracng Fg.8 Stresses n element of shear wall wth concealed truss = cos θ + sn θ + ρ + ρ + ρ cos α+ ρ cos α' (5) l d r sl st xl xt xb xb xb ' xb ' = sn θ + cos θ + ρ sn α + ρ sn α' (6) t d r xb xb xb' xb' τ = ( + )snθ cosθ ρ snαcos α ρ sn α'cos α' (7) lt d r xb xb xb ' xb ' q = τ t (8) lt d

8 N + = h t (9) ( v t) t d Where l, t are normal stresses n the l and t drectons, respectvely; τ lt s shear stress n the l -t coordnate;, are prncpal stresses n the d and r drecton, respectvely; α s the angle of nclnaton d r of the d-axs wth respect to l -axs; θ s the angle of nclnaton of the bracng of truss wth respect to l-axs; ρ sl, ρ st are renforcement ratos n the l and t drectons, respectvely; st, sl are steel renforcement stress n the l and t drectons, respectvely; ρ xl, ρxt are steel ratos n the l and t drectons, respectvely; xt, xl are steel stress n the l and t drectons, respectvely; ρxb, xb are bracng steel ratos and bracng steel stress n α drecton, respectvely, and ρ xb Axb = b h snα ρ, are bracng steel ; xb' xb' ratos and bracng steel stress n the α ' drecton, ρ xb' Axb ' =. t s effectve thckness of shear flow of b h sn α ' core wall secton. The two-dmensonal compatblty condton can now be derved for the renforced-concrete membrane elements subjected to shear and normal stress as shown n Fg.8. Usng the prncple of transformaton of stran, the compatblty equatons can be obtaned as follows: = cos θ + sn θ (1) 2 2 l d r = sn θ + cos θ (11) 2 2 t d r γ = 2( + )snθ cosθ (12) lt d r Where l, t are average normal strans n l and t drectons, respectvely; γ lt s average shear strans n the l t coordnate ; d (postve for tenson). xb, xb', r are average prncpal strans n the d and r drectons, respectvely, are the bracng stans n the n the drecton α and n the α ' drecton, respectvely, gven by = cos α+ sn α+ γ sn 2α (13) xb ' = l cos α' + t sn α' + γlt sn 2 α' (14) xb l t lt

9 Accordng to Bredt s theory, the angle of twst φ s gven by φ γds /2A cor γ lt h (15) = = the curvature of the concrete strutψ and the angle of twst φ of member are related 4 1 ψ = ϕ θ + φ θ (16) 2 cos sn 2 As shown n Fg.9, the thckness of the wall s desgnated as t e, however, due to the bendng of the concrete struts, a certan porton of the area near the bottom edge may be n tenson. Ths tensle area wll be neglected. The porton of the area that s n compresson wll be consdered as effectve. The depth of ths effectve area s desgnated t d. If the stran dstrbuton wthn the effectve depth t d s assumed to be lnear, then the maxmum compressve stran ds at the surface can be wrtten as ds ψtd = (17) Unt wdth of concrete strut stran dagram actual stress block Fg. 9 Bendng of concrete struts The average of compressve stress of dagonal concrete strut s gvng by ds d f c ( d, r) d d ds = (18) 4.2 one-dmensonal stresses (system1) The longtudnal stresses n the secton must be n equlbrum wth the appled axal force and baxal moment. Snce torson and shearng force cause addtonal longtudnal stresses n the secton, ther contrbuton must also be taken nto account. The concrete, renforce and steel stresses obtaned from stran dstrbuton over the secton, and usng the materal consttutve laws, when ntegrated over the secton, should add up to the sectonal force. Hence ' ' snθ t e A c c s s xc xc xz xz c As (19) N + t b = da + da + A + A 4 4 (2) M + tbx = yda+ yda + y snθda + A y t e c A c c c A s s s s A x x x xz xz xz x nteracton between systems 1 and 2 Lnks between the two dealzed systems are the longtudnal strans shear and torson. Hence, each wall s subjected to a shear force and a longtudnal stran t and longtudnal forces due to t.equatons of the modfed compressons feld theory can then be used to solve for complete state of stress and stran n each wall. The stran can be computed as follow: cen = t + ϕy (21) t

10 Where cen s the longtudnal stran at secton centrc, taken postve f tensle. 4.4 solutons and result A tral-and-error method can be used as follow:1.select φ and assume cen,ϕ, t, θ ; 2.Calculate from Eq.(16); 3. Calculate from Eq.(1)~(14); 6. Calculate concrete calculate ds from Eq.(17); 4. Calculate t from Eq.(21); 5. Calculate r, l, xb, ' d from Eq.(18); 7. Usng the Veccho-collns stress-stran relatonshp of r ; 8. Usng the consttutve of steel calculate l, f t, f xl, f xt, f xb, xb' ψ xb f ; 9. Check θ by (5); 1. Calculate t from Eq.(6); 11. Calculate τ lt from Eq.(7); 12. Calculate q 1 from Eq.(1); 13. Check t by Eq. (2) ~(4); 14. Calculate Check cen by Eq. (19); 18. get T,φ. γ lt from Eq.(12); 15. Check 1 t by Eq. (16); 16. Check ϕ by Eq. (19); 17. The torque-twst curves for two specmens are plotted n Fg.1. Through the results of calculaton concded wth the test well, ths model can predct the ultmate strength of the load-carryng capacty of renforced concrete composte core walls wth concealed steel truss, and provde a tool to obtan the entre load-deformaton hstory T (kn m) 4 T (kn m) 试验 Φ (mrad m -1 ) 计算 试验 计算 Φ (mrad m -1 ) (a)cwt-1 (b)cwt-2 Fg. 1 Torque twst curve of subjected to core wall 5. CONCLUSIONS A new type of core wall wth concealed steel truss has been proposed and nvestgated. Two core wall specmens are desgned and a detaled expermental nvestgaton s carred out. The expermental results show that concealed steel truss affects not only the load-carryng capacty, stffness and ductlty, but also the mode of falure. From the experments, t s concluded that: (1) Core wall wth concealed steel truss can dsplay a sgnfcant ncrease n load-carryng capacty, stffness n later stages of loadng, ductlty, and energy dsspaton capacty compared wth a normal core wall wthout concealed steel truss. (2) Compared wth the concrete cracks n normal core wall, the concrete cracks n core wall wth concealed steel truss are closer and more n number, wdth of whch s tner. (3) Through the results of calculaton concded wth the test well, a three-dmensonal model ths paper presented can predct the ultmate strength of the load-carryng capacty of renforced concrete composte core walls wth concealed steel truss subjected to complex loadng, and provde a tool to obtan the entre load-deformaton hstory.

11 REFERENCES CAO Wan-ln, XUE Su-duo, ZHANG Jan-we. (23).Sesmc Performance of RC Shear Wall wth Concealed Bracng. Advances n Structural Engneerng, 6 : 1,1-13. CAO Wan-ln, DONG Hong-yng, HU Guo-zhen. (24). Sesmc behavor of RC coupled shear wall wth concealed bracngs and ts control effect for falure mechansm.journal of Buldng Structure, 25:3, CAO Wan-ln, HUANG Xue-mng, LU Zh-cheng. (25). Expermental study on sesmc behavor of renforced concrete core walls wth concealed bracngs. Earth Quake Engneerng and Engneerng Vbraton, 25:3, CAO Wan-ln, ZHANG Jan-we, TAO Jun-png, et al. (27). Sesmc Performance Comparson Between Shear Wall wth Concealed Steel Truss and Steel Truss, Journal of BeJng Unversty of Technology, 33:1,31-36 Anwar Hossan,K.M,Wrght,H.D. (24). Expermental and theoretcal behavor of composte wallng under n-plane shear. Journal of Constructonal Steel Research. 6:1, Drver,Robert G.,Kulak,Geoffrey L. et al. (1998). FE and smplfed models of steel Plate shear wall. Journal of Structure Engneerngs,124:2, Hossan,Khandaker M. Anwar. (24). Desgn Aspects of Double Skn Profled Composte Framed Shear Walls n Constructon and Servce Stages. ACI Structural Journal. 11:1,94-12.