Numerical Analysis of Cyclic Loading Test of Shear Walls based on OpenSEES

Transcription

1 The 14 th World Conferene on Earthquake Engineering Otober 12-17, 28, Beijing, China Numerial Analysis of Cyli Loading Test of Shear Walls based on OpenSEES Han Xiaolei 1,2 Chen Xuewei 1 Jak CHEANG 1 Mao Guiniu 1 Wu Peifeng 1 1 Tall Building Struture Researh Institute, South China University of Tehnology, Guangzhou 5164, China 2 State Key Laboratory of Subtropial Arhiteture Siene, South China University of Tehnology, Guangzhou 5164, China ABSTRACT : Neither the original struture nor the altered struture of the Garden Hotel in Guangzhou aords with the dutile details of seismi design based on urrent Chinese odes. In order to explore the seismi performane of the original shear wall struture and the altered shear wall struture, the yli loading testes of the shear walls with different reinforement ratio and onstrutional details are arried out. This paper presents the numerial analysis of the yli loading testes of shear walls with SWNA (Shear Wall Nonlinear Analysis) program. SWNA program is seondary developed based on OpenSEES and MVLEM. Compare with the testes, the numerial results onfirmed the auray of this analysis proedure in representing the nonlinear behavior of the shear wall, suh as the shifting of natural axis, shear deformation, loal ollapse and ollapse mehanism. The analysis proedure based on MVLEM, whih saves the alulating ost due to fewer DOFs, an stimulate the nonlinear behavior of the shear wall, and fit for global inelasti analysis and performane based design of tall building struture. KEYWORDS: Shear wall, Cyli loading test, OpenSEES, MVLEM, Nonlinear analysis 1. FOREWORD Reinfored onrete shear wall struture is one of the most important forms in industrial and ivil strutures. Nonlinear analysis of shear wall struture is the fous and diffiulty point. There are mainly two models whih are usually used in nonlinear analysis: miroosmi and maroosmi model. The former simulate shear walls with solid and shell element whih have distint and aurate theory but is not appliable due to large amount of alulation and diffiulty in experiment analytial orretion. The latter simulate shear walls with multiple vertial springs whih has a better desription of nonlinear behavior for the whole struture. It is suitable for nonlinear analysis of the whole struture due to small amount of alulation and simple analytial orretion. A program for nonlinear analysis of shear walls (SWNA) based on further development of OpenSEES and MVLEM is put forward in this paper. Compared to the yli loading test results of shear walls from the Garden Hotel, the numerial analysis results validated that the nonlinear behavior of shear wall an be simulated well in maro-sale by MVLEM. 2. BACKGROUND Nonlinear model of shear wall inludes two models: miroosmi model and maroosmi model. There are mainly three models inluded in miroosmi model: integrated model, separate model and omposite model [1]. Maroosmi model is suitable for nonlinear analysis for the whole struture due to fewer DOFs. The main maroosmi models are as follows: A pseudo-dynami test of a 7-story full-sale moment frame was arried out by Kebeysasawa [2] and shear wall was simplified to three vertial line element model (TVLEM), as shown in Fig.1(a). Four vertial line element model was suggested by Linda [3] based on improvement of TVLEM, as shown in Fig.1(b). Two-dimension plate model was suggested by Milev [4] based modifiation of TVLEM, as shown in Fig.1(). In order

2 The 14 th World Conferene on Earthquake Engineering Otober 12-17, 28, Beijing, China to solve the oordination problem of flex springs and two side-bars, Vulano and Bertero [5] proposed a modified model in whih multiple vertial springs are used to replae rotation springs representing ompression bending stiffness and a horizontal spring is used to represent shear stiffness, as shown in Fig.1(d). KV K1 KH K2 K1 K2 K1 K2 K1 K3 K4 K2 KV KR KH L KH (a) TVLEM (b) FVLEM () 2-D plate model (d) MVLEM Fig.1 Maro model of shear wall 3. THEORY OF MVELM The oordinative relation of flex springs and two side-bars is ambiguous in TVLEM, whih is avoided in MVLEM. By given hystereti relation of tension-ompression and shear behavior, the shift of the neutral axis during the seismi response ould be taken into aount. The entire shear wall is modeled as a stak of n MVLEM wall elements whih are plaed one upon eah other. The ross-setion of shear wall is divided to several parts whih are simulated by springs. The tension-ompression behavior of springs an be gained form material onstitutive model. The onstitutive model form the program DRAIN-2D [6] is taken as the restoring fore model of the springs, as shown in Fig.2. As to general shear walls, the parameters of restoring fore model an be taken as follows: α=1., β=1.5, γ =1.5, δ=.5 [7]. The solving equation of the fore and deformation of the key points in spring onstitutive model urve are list in Table 1. There is a shear spring whih has a distane of L from the bottom representing shear deformation of the 2-D MVLEM whih has 3 DOFs together. There are three horizontal springs inluding two-way shear springs and a rotation spring in 3-D MVLEM whih has 6 DOFs in general. The 3-D MVLEM is shown in Fig. 3. Table 1 Formulas of parameters of restoring fore modelof vertial spring parameter desription funtion k Initial elasti stiffness k1 = A E / L 1 F r Craked tensile fore of onrete Fr = ft A F y Yield fore of steel bar Fy = fyas Δ Yield deformation of steel bar Δ = A E / L y 3 y s s k Hardening stiffness of steel bar k3 = fhardks F Limit pressure fore of onrete F = fka Δ Limit deformation of onrete Δ = ε L F u Residual fore after onrete rushing Fu = fu A Δ Residual deformation after onrete rushing Δ = ε L u u u

3 The 14 th World Conferene on Earthquake Engineering Otober 12-17, 28, Beijing, China Either the linear elasti onstitutive model or the shear onstitutive model in DRAIN-2D ould be adopted as the restoring fore model of horizontal shear spring, as shown in Fig.4. The height oeffiient is determined by urvature distribution of the element. The trial alulation with different value of (=,.2,.3,.4) was arried out by Vulano and the best result was gained when =.4 whih was taken in this paper. Axial Fore Fy Fr u r k1 βfy Fu γ( max- y) k3 αfy k' k" y max Axial Deformation y k"=k'( ) max δ x u η2 τ φ2 khz Shear Fore Qy αqy ki khy kt y Shear Deformation z yi F Fig.2 Restoring fore model of vertial spring spring zi y Fig.3 Sketh of MVLEM3D element Fig.4 Restoring fore model of horizontal shear 4. INTRODUCTION TO OPENSEES OpenSEES stands for Open System For Earthquake Engineering Simulation [8]. It is an open-soure system of earthquake simulation and allows the ustomers add new material onstitutions and new types of elements to the system by programming. OpenSEES is mainly applied to analysis the seismi response of the struture. And it has a large library of materials and elements. The 2-D MVLEM based on unaxial onstitutive model was added to OpenSEES by Kutay Orakal [9] aording theories above. Shear walls an be well simulated by this element after analytial orretion of yli loading test. Based on the 2-D MVLEM, the 3-D MVLEM was added by Matej Fihinger [1] aording to onstitutive model of spring. The dynami harateristi of shear walls ould be refleted well by the 3-D MVELEM. Numerial analysis of yli loading test of shear walls from the Garden Hotel in this paper is based on the 3-D MVLEM. OpenSEES is an analysis program based on Tl/Tk sript language. Nonlinear solving is realized by adaptive transition program whih modify the step size automatially until a onvergent solution is gained. 5. LOW CYCLIC LOADING TEST OF SHEAR WALLS There are 12 shear wall speimens in the low yli loading test of the Garden Hotel [11]. And the first 4 speimens are numerial simulated in this paper. The height of the speimen is 1.9m, and the parameters suh as reinforement, onstrution measure and axial ompression ratio are listed in Table.2. The setional reinforement are shown in Fig.5~Fig.6. The strength of onrete taken as fu,m=34.43mpa is determined by blok samples test. The strength of steel bar taken in the model is determined by material test, as listed intable.3. The loading equipment is shown in Fig.8. NC tension-ompression atuating ylinder from MTS. US. and hydrauli jak (5T) is taken as horizontal and vertial loading devie respetively.

4 The 14 th World Conferene on Earthquake Engineering Otober 12-17, 28, Beijing, China Fig.5 Dimension and details of Spe.1 and Spe.2 Fig.6 Dimension and details of Spe.3 and Spe.4 Table 2 Parameters of speimens Speimen number No.1 No.2 No.3 No.4 Design ode Current ode Current ode Former ode Former ode Axial ompression ratio Vertial reinforement Ø6@11 Ø6@11 Ø6.5@5 Ø6.5@5 Horizontal reinforement Ø6@12 Ø6@12 Ø4@8 Ø6@12 Tie bar (end) Ø8@11 8 Ø8@11 8 Ø4@16 5 Ø4@16 5 Tie bar (middle) Ø8@11 12 Ø8@11 12 Ø4@16 1 Table 3 Parameters of reinforement The type of steel bar Yield sress Limit stress (MPa) (MPa) Yield strain (με) Limit strain (με) Elasti modules (N/mm 2 ) Ø Ø Ø Complete loading to axial ompression ratio required in vertial diretion is adopted and keep the same during the test. Horizontal low yli load is applied with atuating ylinder. Fore ontrol mode whih keeps the load inrement of eah step in 1% of strutural bearing apaity is adopted until the speimen yield. When the speimen yield, displaement ontrol mode is taken as the load mode. Yield displaement of the speimen is taken as the yli displaement inrement for three times of eah step. It is suggested that the test should be ended when the bearing apaity of the speimen drop to 6%~7% of the limit apaity or the speimen is obviously failed. Start Material properties, shear wall setion and reinforement input Vertial spring division Shear wall geometri modeling and element division Stati or dynami load input Vertial spring onstitutive parameter alulation Shear and torsion parameter alulation OpenSEES Tk/Lk sript language auto-generation Calling program and alulation Data reading Displaement, deformation and plastiity developing diagram auto-generation End Fig.7 Figure of experiment devie Fig.8 Flow hart of SWMA program

5 The 14 th World Conferene on Earthquake Engineering Otober 12-17, 28, Beijing, China 6. NUMERICAL ANALYSIS OpenSEES is a nonlinear finite element analytial program with high performane. But there is no visual operation interfae urrently. And the loation and onstitutive model of eah spring should be text input, whih ause pre-proess with a large amount of work. In order to solve the problem above, a nonlinear analysis program of shear walls (SWNA) is programmed by further development of OpenSEES based on objet-oriented language. The alulation flow is shown in Fig.8. The modified Kent-Sott-Park onstitutive mode [12],[13] is adopted as the onstitution of the onrete in the paper, as shown in Fig.9. The strength and dutility of onrete in restraint area an be taken into aount in this model. Aording to the setional reinforement, the stress-strain relation an be alulated by the program based on Eqn.1~Eqn.4. The bilinear model is adopted for steel bar, taking hardening oeffiient as 1/1. Elasti modules and yield stress are listed in Table 3. Aording to funtions listed in Table.2, restoring fore model of vertial spring is generalized by onstitutive model parameters whih ould be gained from the program. In order to study the effets of different divisions, shear walls simulated with different amount of springs, horizontal and vertial divisions are arried out in this paper. There are generally 16 examples whose properties are listed in Table.4. The onnetion of 3D MVLEM in horizontal divisions is realized by hinges of rigid arm. Then the plane setion assumption of overall setion ould not be obeyed and loal deformation of shear walls an be taken into aount, as shown in Fig.1. Vertial divisions of TestB are arried out in 1/4 parts at the bottom. The skeleton urve gained by the results of OpenSEES is shown in Fig.11. Only the positive values of skeleton urve are proposed due to its symmetri shape. (ε,kf') (ε2,.2kf') Strain ε Fig.9 Kent Park modified onrete model(1982) 2 ε ε Kf 2 ε ε ε ε (1) σ = Kf [ 1 Z( ε ε) ] ε ε ε2.2 Kf ε > ε 2 ε =.2K (2) ρs f yh K = 1+ (3) f.5 (4) Z = 3+.29f h +.75ρs.2K 145 f 1 sh Fig.1 Finite element model of speimen

6 The 14 th World Conferene on Earthquake Engineering Otober 12-17, 28, Beijing, China Base Shear Fore(kN) Top Displaement(mm) TestA-1 TestA-2 TestA-3 TestA-4 Base Shear Fore(kN) Top Displaement(mm) TestB-1 TestB-2 TestB-3 TestB-4 Base Shear Fore(kN) Top Displaement(mm) TestC-1 TestC-2 TestC-3 TestC-4 Fig.11 Comparison of fore-deformation skeleton urve between the results of different divisions It an be known from Fig.11(a), spring divisions have a diret influene on the auray of alulation. The results beome stable when the amount of springs reahes about 6. It is seen from Fig.11(b), the more divisions along vertial diretion, the bigger deviation from the experiment results. So the length of vertial division should be longer than the length of plasti region. It an be seen from Fig.11(), horizontal division ould help to gain a reasonable result. When there are more than 3 divisions along horizontal diretion, a smooth urve of desend segment ould be gained without abrupt hange. Numerial simulation of shear wall model is divided into 4 parts along model height, and the setion is divided into 48 springs. There are 5 nodes, 4 elements and 3 DOFs. If analysis method antiipating do not satisfy the plane setion assumption, element ould be divided along horizontal diretion. Parameters of springs restoring fore model are input as defaulted without adjustment. A onvergent solution is gained by adaptive adjustment of step size and iterative method. Calulation desription: Take speimen 1 as a sample. The number of analysis step is 541. The PC used for alulation is desribed as following: CPU: AMD Athlon (tm)64 Proessor 32+(2.1GHz); Ram: 1GB. It osts 34 seonds to finish the alulation. The analysis results from numerial simulation of 4 shear walls are ompared to the results gained from the low yli loading test. The omparisons of hystereti loops are shown in Fig.12. Aording to the omparison, hystereti loops and skeleton urve ould generally math well, espeially the hystereti loops of speimen 1 and 2 designed aording with urrent ode. And the result of speimen 3 and 4 gained by numerial simulation is a little preipitate during the desend part, but still math well in strength and dutility. The results math well in inelasti beause that plane setion assumption is satisfied in the individual EVLEM. So it an not be simulated when strongly nonlinear ourred. This ould be improved by horizontal division. Life safety and ollapse avoiding are required for shear wall in performane based seismi design and no strongly nonlinear behavior should our [14]. So MVLEM is suitable for performane based analysis and design. Base Shear Fore(kN) Top Displaement(mm) Base Shear Fore(kN) Top Displaement(mm) Test OpenSEES Test OpenSEES (a)speimen 1 (b)speimen 2

7 The 14 th World Conferene on Earthquake Engineering Otober 12-17, 28, Beijing, China Base Shear Fore(kN) Top Displaement(mm) Base Shear Fore(kN) Top Displaement(mm) Test OpenSEES Test ()speimen 3 (d)speimen 4 OpenSEES Fig.12 Comparison of fore-deformation urve between experiment results and OpenSEES The animation of deformation of shear wall struture of the whole proess an be gained by the program SWNA, as well as the deformation and nonlinear states of springs. Take speimen 1 as an example, as shown in Fig.13~14. Nature axis shifts ontinuously under yli loading, whih an be seen from Fig.13. Fig.13 Deformation of vertial springs of shear-wall elements Fig.14 Collapse proess of shear-wall elements shown in SWNA The yield mehanism of shear wall desribed by MVLEM is shown in Fig.14. Plasti deformation is mainly ourred at the bottom. Steel bar yield firstly, then the onrete of two sides are rushed and out of work. The part rushed extend from edge to middle. The whole shear wall is failed at last due to desend of the resistane apaity of lateral load after most onretes are rushed and steel bars are yield. The failure mode omparison of speimen 1 is shown in Fig.15~16. (a)opensees Result (b)test Result Fig.15 Comparison of ollapse status of speimen 1 Fig.16 Loal ollapse of speimen 1 between FEA and experiment

8 The 14 th World Conferene on Earthquake Engineering Otober 12-17, 28, Beijing, China 7. CONCULSION AND PROSPECT Low yli loading test and shaking table test are the most visual and reliable measure to value seismi performane of shear wall struture. But there are several limitations due to lots of human and material resoures. Numerial simulation of yli loading test of shear walls based on OpenSEES in this paper show that the nonlinear behavior of shear walls inluding shifts of nature axis, influene of shear deformation, loal plasti status and failure mehanism ould be well refleted by the maroosmi element of adjusted MVLEM in some extent. And beause of fewer DOFs and less omputing time, this numerial model and OpenSEES are appliable to tall building strutures with shear wall. Aording to the analysis of shear wall, further development based on OpenSEES aiming at reduing the work of modeling and providing visible analysis results is programmed. The program SWNA an be applied to shear walls with different reinforement. The stati and dynami nonlinear analysis an be realized. And the quantitative seismi performane index of shear wall whih has a great signifiane for performane based seismi design an be gained regress analysis. REFERENCES [1] Shao Jianhua, Gu Qiang, Shen Yongkang. (28). Finite Element Analysis of Seismi Performane of Steel Plate Shear Walls[J]. Journal of South China University of Tehnology(Natural Siene Edition). 36:128~133. [2] Kabeyaawa Tetal.(1984). US-Japan ooperative researh on R/C full - sale building test[c], Part 5: Disussion of dynami response system. Pro. 8th of WCEE. [3] Linda P. Bahmann H. (1994). Dynami modeling and design of earthquake - resistant walls[j]. EESD, l23, P1331~135. [4] Milev J I. (1996). Two dimensional analytial model of reinfored onrete shear walls [C]. Pro. 11th of WCEE. [5] Vulano A. Bertero V V. (1987). Analytial model for prediating the lateral response of RC shear wall: evaluation of their reliability[r]. EERC [6] Kanaan, A.E. and Powell, G.H.(1973) DRAIN-2D A general purpose omputer program for dynami analysis of planar strutures[r], Report No. UBC/EERC-73/6, University of California, Berkeley. [7] Fishinger, M. and Isaković, T. (2). Benhmark analysis of strutural wall[c], Pro. 12th of WCEE. [8] MKenna, F. and Fenves, G. L. (2).The OpenSees Command Language Primer [Z], PEER, Univ. of California, [9] Kutay Orakal, Leonardo M.Massone, John W.Wallene, (26). Analytial Modeling of Reinfored Conrete Walls for Prediting Flexural and Coupled-Shear-Flexural Responses [R]. PEER, University of California. [1] Matej Fishinger, Tatjana Isakovi, Peter Kante. (24). Implementation of a maro model to predit seismi response of RC stureture walls [J]. Computers and Conrete, 1:2. [11] Han Xiaolei, Ji Jing. (26). The researh report of struture reformation seismi test for west tower of the Garden Hotel ( platina five-star hotel ) Guangzhou [R]. College of Arhiteture and Civil Engineering, South China University of Tehnology.. [12] Kent D C,Park R. Flexural Members with Confined-Conrete[R]. ASCE,Vol.97:1969~199. [13] B. D. Sott, R. Park, M. J. N. Priestley. (1982). Stress-strain behavior of onrete onfined by overlapping hoops at low and high strain rates[r]. 99:2,P13~27. [14] Los Angeles Tall Buildings Strutural Desgin Counil. (25). An alternative proedure for seismi analysis and design of tall buildings loated in the Los Angeles region[s].2.3.2,: P18~21. [15] Pan Donghui, Cai Jian, Zhang Xingfu. (26). Response Modifiation Fators of Shear Walls in Different Performane Levels[J], Journal of South China University of Tehnology(Natural Siene Edition). 34:P81~86.