Calculation of slab-column middle connection under combined shear and unbalanced moment

Transcription

1 Callation o slab-olmn middle onnetion nder ombined shear and nbalaned moment Ha Li 1, a, Nan Go 2,b, Yiing Lin 3, 1,2,3 College o Civil Engineering, Northeast Forestr Universit, Harbin 154 China a liha7515@163.om, b tmgonan@163.om, liniing199@ahoo.n Kewords: slab-olmn onnetions, vertial shear, nbalaned moment, shear reinorement Abstrat. The prpose: The method to allate slab-olmn middle onnetions nder ombined interation o vertial shear and nbalaned moment is given to peret the design method o slab-olmn strtre; ethod: The allation method is proposed based on the allation method o slab-olmn onnetion and the experimental data made b domesti and oreign sholars is sed to veri. Reslt: The reslts veriied b the ormla are shown to be in good agreement with atal reslts. Conlsion: The interation o shear and nbalaned moment are taken into aont in the ormla, inlding the transer mode o nbalaned moment and the beneiial eets o shear reinorement, to make the allation more reasonable. Introdtion Flat-slab sstem, in whih slab is diretl spported b olmn withot beams. And it is intensivel sed de to its a series o otstanding advantages, sh as dereasing loor-to-loor height, inreasing nmber o strtral stories and eetive area when maintain the overall height nhanged, eas to deoration and good lightning and ventilation eets. Bending pnhing ompond ailre is ased b the vertial shear and nbalaned moment borne b the slab-olmn onnetion at the same time in the proess o earthqake, whih makes the lat-slab onnetions beome the weak link in the whole lat-slab strtre, then leads to lat-slab strtre s serios damage or even ollapse. Bt, onl anti-shear heking method o slab-olmn onnetion is given in the Chinese onrete strtre design ode (GB51-21), while the slab-olmn onnetion s ailre harateristis nder ombined interation o vertial shear and nbalaned moment are not taken into aont, whih makes hard to design. Despite this, the lat-slab sstem is widel applied in pratial engineering, and the basi strtral orm ontains mltilaer slab-olmn strtre and middle-high slab-olmn and shear wall strtre, and also it is widel adopted in ramed-tbe strtre. Thereore, the transer mode o nbalaned moments, the interation o shear and nbalaned moment and the beneiial eets o shear reinorement are onsidered simltaneosl in the lat-slab onnetion ormla, whih promotes lat-slab sstem widel sed in seismi design. At present, the experimental std and theoretial analsis are mainl inlded based on the slab-olmn onnetion researh, while the experimental std inldes slab-olmn onnetions the pnhing resisting perormane and experiment [1], the lexral perormane and experiment [2~4], and the analsis and experiment o slab-olmn onnetions nder ombined shear and nbalaned moment [5~7]. The pnhing resisting element was sed in the speimen ondted b Sotheast Universit in the several experiments, in whih the vertial load and horizontal li load are onsidered simltaneosl. Bease o std shear reinorement was sed in onl one speimen [7], whih annot eetive response the atal stress o slab-olmn onnetion and the beneiial eets o std shear reinorement in earthqake. In the theoretial researh, the allation method o slab-olmn onnetions nder ombined shear and nbalaned moment mainl inldes ACI ode method and the method proposed b Ynhang a, however, the transer mode o nbalaned moments, the interation o shear and nbalaned moment and the beneiial eets o shear reinorement are not onsidered simltaneosl in both methods. 884

2 Thereore, the allation ormla proposed in this paper is based on the slab-olmn onnetion design method, ACI318-11ode and the ormla o slab-olmn onnetions nder ombined the vertial shear and nbalaned moment proposed in the Chinese onrete strtre design ode. Then, the ormla is veriied b the related experiments. The rrent ormla At present, there are onl two design methods that slab-olmn onnetion nder ombined shear and nbalaned moment are onsidered. One is ACI ode method, the other is proposed b Yhang a and Xilin Lv [5,8]. Slab-olmn strtre design method based on ACI ode. The ACI ode method s basi thoght is some nbalaned moment ( α )o slab-olmn onnetion is transerred b bending o the hidden beams arranged near the axis, the other ( α )is transerred b the eentriit 1 o onnetion shear. The oeiient α an be expressed asα = 1, and a t, a m 1+ 2/3 a t / a m the length o onnetion ailre setion along the diretion o moment and perpendilar to the moment, and the onentrated reation ased b the vertial load is replaed b the eqivalent onentrated reation design vales ased b the nbalaned moment. This method onl onsiders the transer mode o the nbalaned moment withot onsidering the interation o shear and nbalaned moment. The method proposed b Yhang a and XilinLv. This method is based on Johansen s sperposition theor and the expression o the ritial ombined load is + = 1, when nder two independent loads. slab-olmn onnetion s pnhing shear strength(onl onsidering the strength provided b onrete); onnetion s nbalaned moment design vales; slab-olmn onnetion s lexral apait, = 6.89 ( m ' + m ) ; onnetion s shear design vales; m, m ' slab s positive and negative ltimate resistant moment in nit width respetivel, m = Ash ( 1.5ρ / α1 ) m ' = ' As ' h (1.5ρ' '/ α1 ) Thogh the interation o shear and nbalaned moment is taken into aont in this method, the transer mode o the nbalaned moment is not onsidered. oreover, the beneiial eets o shear reinorement are not onsidered in the allation o slab-olmn onnetion s pnhing shear strength. The ormla proposed in the paper The expression o ormla.the design sggestion o slab-olmn middle onnetionnder ombined shear and nbalaned moment: ( 1 α ) Fle + = 1 (2-1) F le the eqivalent onentrated reation design vales nder onsideration o the nbalaned moment aording to the Chinese onrete strtre design ode; slab-olmn onnetion s pnhing shear strength; onnetion s nbalaned moment design vales; slab-olmn onnetion s lexral apait; onnetion s shear design vales; 885

3 A sggestion on vale. The ormla o slab that withot resisting shear element in the rrent Chinese onrete strtre design ode: =.7β h t η m h (2-2) The oeiient η,an be allated b the ollowing ormlas, and take the smaller vale: 1.2 α sh η 1 =.4 +,η 2 =.5 + ; β s 4m η 1 the shape inlene oeiient nder loal loads or onentrated reation; η 2 the ratio o allation setion perimeter and plate setion eetive height inlene oeiient; β s the ratio o long side and short side o retangle nder loal loads or onentrated reation, and β s shold not exeed 4, β s takes 2 when it less than 2; to irlar pnhing srae, β s takes 2; β h setion height inlene oeiient, β h takes 1 when h is not more than 8mm; β h takes.9, when h is not less than 2mm; meantime the vales are taken b interpolation; h setion eetive height,takes the average vale o the two setion eetive heights; m the allation setion perimeter,takes the distane between loal loads or onentrated reation s ation area peripheral h /2 perpendilar to the setion s most navorable perimeter. The Chinese 22 edition ode thinks the saet degree is too high o the resisting pnhing loads ormla in the 89 edition, and the oeiient is adjsted rom.6 to.7 and has introded plate setion height inlene oeiient β h. The ormla o 22 edition ode is preserved in the 21 edition, and the ormla is simple and the allation is onvenient. Bt ompared to the oreign odes, the ormla is more onservative in most sitation. The plate resisting pnhing shear takes the minimm in the ollowing three ormlas in ACI ode: 2 = β α sd = b =.33 b d b d b d (2-4) β the ratio o long side and short side o ation area o olmn setion nder onentrated loads or the reations; α s inner olmn, side olmn, orner olmn take 4, 3, 2 respetivel; b the ritial perimeter;d is the plate eetive height. The experimental vale and the design vale o resisting pnhing ormla in the Chinese ode ratio s average is ater XiaobinX [9] o HeBei United Universit onlded 67 slab-olmn pnhing experiments, while the experimental vale and the design vale o the Amerian ACI ode ratio s average is 2.285, and the ratio o them is 1.8. Thogh the expressions are dierent in the Chinese ode and the Amerian ode, the dierene o allation reslt is onl 8%. And ompared to experimental vale, the design vales given in both odes are mh more onservative, meanwhile, the Chinese ode is more onservative than the Amerian ode [1]. The reslt o slab-olmn onnetion plasti limit analsis nder vertial shear in paper[2,3]: 1 m m + 1, m = ; =(K+1)μ t t m h (2-3)K= [ ( )] 4 t t, t onrete ltimate ompressive strength and tensile strength; μ,μ t onrete ompressive strength and tensile strength redtion oeiient when materials inhomogeneit and omplex stress, an approximatel take.35. The range o K vale is between 1.12 and 1.75, and the range o (K+1)μ t is between.74 and.96 throgh the allation o onrete C2~C5. Compared to the Chinese ode, the oeiient is larger in the ormla. And ompared to ACI ode and the Chinese ode onservative design vale, the vale is more reasonable allated in ormla (2-3). The allation o resisting pnhing element plate. The ormla is given b JieTian, Kebin X [11], Zeeng Pan [12] o Nanjing Universit o Aeronatis and Astronatis and the Chinese 886 μ μ

4 nbondedprestressed onrete design ode or prestressed onrete strtres JGJ92-24 and the Chinese onrete strtre design ode or the slab-olmn onnetion resisting pnhing allation o resisting pnhing element respetivel. Aording to the experimental researhes, onsidering the aggregate olsion ater onrete raking, the beneiial eet o reinorement shear rition, throgh analsis and omparison, the allated in the rrent ode is more sae and reasonable. =.5 t ημ m h +.8 v A s (2-5) v anhor blot tensile strength design vale; A s all the steel setion area that interseted with the 45 pnhing ailre pramidal obliqe setion. A vale sggestion on. The ield line theor is adopted in the analsis o middle olmn slab-olmn onnetion nder the nbalaned moment. And aording to the Priniple o irtal Work, the lexral apait minimal pper vale is given as ollow: = ( m ' + m ) ;(2-6) 7.92 m, m ' slab s positive and negative ltimate resistant moment in nit width respetivel, m = Ash ( 1.5ρ / α1 ) m ' = ' As ' h (1.5ρ' '/ α1 ). The veriiation o ormla The ormla (2-1) proposed in the paper is veriied b the arrangement o experiments o resisting pnhing anhor bolt and nresisting pnhing element slab-olmn onnetion nder ombined shear and nbalaned moment. The rrent Chinese ode is sed to allate F le, and o nresisting pnhing element slab-olmn onnetion is aording to (2-3) to allate, while o resisting pnhing element slab-olmn onnetion is aording to (2-5) and is aording to (2-6). The reslts is saw the ollowing Table1 and Table2: Table1 The allation o nresisting pnhing element slab-olmn onnetion Sore Slab h 1 2 t (pa) (pa) (KN m) (kn m) F le Reslts [6] IC IC , [13] S S [14] S S S Table 2 The allation o resisting pnhing element slab-olmn onnetion Sore Slab h 1 2 t (pa) (pa) A s (mm 2 /m) (KN m) (kn m) F le Reslts [13] [14] SC SC SC SC SC (555) (555) (555) (555) [7] SSR (364) 126(9) The relevant experiment data is sed to veri the ormla given in the paper, the average o nresisting pnhing element slab-olmn onnetion allation reslt is 1.154, while the average o resisting pnhing element slab-olmn onnetion is So the ormla is more sae and reasonable. 887

5 Smmar 1) The interation o shear and nbalaned moment, the transer mode o nbalaned moment and the beneiial eets o shear reinorement are taken into aont in the ormla, whih perets the allation. 2) The reslts veriied b the ormla are shown to be in good agreement with atal reslts, and have a high ara allation and saet.i o ollow the heklist or paper will onorm to the reqirements o the pblisher and ailitate a problem-ree pbliation proess. Reerenes [1] ZhaoaSh: Pnhing Capait o Slab-Colmn Edge Connetions[J]. Jornal o Hnan Universit(Natral Sienes), 34(1) (27) p [2] S.W.Han, S.H.Kee,Y..Park, L.H.Lee, T.H.K.Kang: Hstereti Behavior o Exterior Post-Tensioned Flat Plate Connetions, Engineering Strtres[J]. ol.28(14) (26) p [3] Yi S: Experimental std on slab-olmn strtre sbjeted to low-le reversed horizontal load, Jornal o Bilding Strtres[J], ol.26(5) (25) p.1-7. [4] Qing W, Wenrang Cheng:Experimental std on seismi perormane o interior onnetions o lat plate strtres[j], Earthqake Engineering and Engineering ibration,4 (26) p [5] Ynhang a, Xilin Lv: Strength o Joints o Slab-Colmn joints Under Shear and Unbalaned oment[j], Strtral Engineers 2(1998)p [6] Hongtao Dan:Experimental Researh o Seismi Behavior o Slab-olmn Connetions[D], Chongqing Universit(24). [7] Tao Shen: Experimental Researh o Seismi Behavior o Slab-olmn Connetions[D], Sotheast Universit(24). [8] Ynhang a, Xilin Lv: Seismi Behavior o Reinored Conrete Slab-olmn Sstem[J], Jornal o Bilding Strtres ol.22(4), (21)p [9] Xiaobin X: Experimental Stdies on Pnhing Shear Capabilit o Conrete Filled Steel s Slab-Colmn Connetion[D], Hebei Poltehni Universit(28). [1] Chaoxn Zho: Researh on Eetive Beam Width odel o Reinored Conrete Flat Plate Strtres nder Lateral Loads[D], Chongqing Universit(211). [11] Jietian Tian, Kebin X: Experimental Investigation on Conrete Slab Colmn Connetions with Std Shear Reinorement[J], Jornal o Northern Jiao Tong Universit,ol.23(6)(1999)p [12] Zheeng Pan: Std on Failre odes and Stor Drit Ratio o Interior Slab-Colmn Connetion[D], Nanjing Universit o Aeronatis and Astronatis(211). [13] J Zho, Xilin L: Analsis o Interior Slab-olmn Connetion in RC Flat Slab Strtres nder Shear and Unbalaned oment[j], Jornal o Bilding Strtres,ol.188(5)(1997)p [14] Lo Y H,Drrani A J:Eqivalent Beam odel or Flat Slab.Bilding Part1: InteriorConnetions,ACI Strral,Jornal,ol.92(1)(1995). [15] Jing Kang: Seismi Behavior o RC Slab-Colmn Connetions with Shear-Std Reinorement [D],Tongji Universit(28). [16] A.A.Elgabr, A.Ghali:Tests on Conrete Slab-Colmn Connetions With Std-Shear Reinorement Sbjeted to Shear-oment Transer [J].ACI Strtral Jornal, 84(5)(1987)