Effects of Circular Opening Dimensions on the Behavior of Steel Plate Shear Walls (SPSWs)

Transcription

1 Effects of Circular Opening Dimensions on the Behavior of Steel Plate Shear Walls (SPSWs) H.Valizadeh¹, R.Shahinpar¹ and M.Sheidaii² 1- M.S. in Structural Engineering, Iran Marine Industrial Co. (SADRA) 2 -Assistant Professor, Civil Engineering Dept., Urmia University, Urmia, Iran St52eel@gmail.com Abstract In recent years there is a developing attention to steel plate shear walls (SPSWs) thanks to their proper function exposing to lateral wind and earthquake loads. Furthermore, their application in steel and concrete structures in order to strengthening them has raised a lot of focus upon. In some cases existence of opening is unavoidable due to architectural reasons or installed heating and cooling systems on the walls. That leads to a decrease in capacity and improper functioning of these systems that also results in an intense variation in inplane stress distribution. In this paper impact of circular opening dimensions on behavior of steel plate shear walls has been closely studied. On this purpose using ABAQUS finite element method a nonlinear analysis has been conducted considering geometrical and material nonlinearity in the models. Analyzed models indicate that the reduction factor and (1-D/H) respectively for resistance value and stiffness value predict lower error versus the increases in opening diameter. Keywords: Steel plate shear wall, Opening, Nonlinear analysis, Initial Stiffness, Ultimate capacity 1. INTRODUCTION Since early 197 s several types of steel plate shear walls are offered in order to use in lateral resistant system of structures. The first vast research program on steel shear panels is carried out by Takahashi and his colleagues in 1973 [1]. They have performed some tests with quasi static loading and unloading on stiffened and unstiffened steel shear panels in one or two stories. The initial method for analyzing and designing of steel shear walls is commenced with replacement of steel plate with some equivalent diagonal truss elements [2 and 3]. Now, the base of recommendations in Canadian steel structures design code about steel shear walls are comply with mentioned method. In the late 198s, Sabouri and Roberts [4] did their theoretical and laboratory investigations related to steel shear walls which are caused a new method for analyzing and designing of the walls called Plate and Frame Interaction method (PFI). Consequently, results of 16 tests on steel shear panels are given with a low yielding stress steel plates and aluminum plate with opening. The results are redounded to offering reduction coefficient for resistance and stiffness because of openings in the walls [5 and 6]. In the year of 25 a creditable test performed by Kharrazi [7] on one story shear panel to develop an innovated method called Modified Plate and Frame Interaction (M-PFI). In addition to shear force, overturning moment was also considered which results in attaining conservative outputs. According to improve the previously offered reduction coefficients, in this paper are suggested new reduction factors to be used in steel plate shear walls with openings at the center. It is also considered the effect of diameter increasing of openings on structural behavior of shear walls. 2. FINITE ELEMENT MODELING All the specimens are composed of frame and infill steel shear plate which are analyzed using ABAQUS program. Prediction of models behavior is based on nonlinear quasi-static analysis including geometric and material effects. The plate and boundary elements of frame are modeled using shell element of S4R. This is a four nodes and double curvature element with 6 degrees of freedom. The material is isotropic with the same strain hardening inelastic behavior in tension and compression. The yield stress and ultimate strain are respectively assumed 25 MPa and.625 for the infill plates and 35 MPa and.875 for the frame elements. E=2 GPa, E t =2 GPa and Poisson s ratio =.3 are assumed. The Von-Misses yielding criterion is adopted. All models are loaded by applying a lateral displacement control system at conjunction nodes of beams to columns.

2 According to FEMA Code [8], the limiting lateral displacement is 2% of the wall height, which in this research it is taken more than 2% to be able to fully investigate wall behavior. Connections between plate and boundary elements and beams to columns are rigidly modeled. In order to model a rigid connection between columns and base plates, all degree of freedoms of lower nodes of columns are restrained. Out-of-plane deformation of the web post of beams is prevented due to the effect of floor constructions. Two analysis methods are available in ABAQUS program. In ABAQUS/Standard and ABAQUS/Explicit [9 and 1], the implicit and nonlinear dynamic explicit methods are respectively applied. Out of plane sudden deformation of steel shear plates causes a convergence problem in SPSW system analysis due to developing tension field action. Therefore the dynamic explicit method is used for analysis. Quasi static evaluation criterion would also be checked by considering kinetic energy that should have less value during the analysis. 3. MODELS SPECIFICATION The panels are initially designed by M-PFI method [7], in which, plate yielding occurs before its buckling. In other words, plastic hinges are formed in the columns. The dimension of panel is measured from beam and column axes. The panels with same height mm and three bay 227, and mm were considered. Slenderness ratio (b/t) for three series SPSW is. According to the panel bay, infill plate thickness for three series 1.25, 1.65 and was chosen. All the models (CRxx) have the circular geometry which are located at the center (Figure 1). The ratio of D/d varies from.1 to.5, in which, D=opening diameter, d=panel height, b=panel bay and t=plate thickness. Table 1 shows panel geometry for of SPSW3 and in Table 2 is shown specifications of boundary elements. Table 1- Geometry of SPSW3 models (mm) MODEL DIMENSION HEIGHT BAY PLATE THICKNESS SLENDERNESS RATIO RADIUS OF OPENING OPENING RATIO CR31 CR CR CR CR CR Table 2- Sections of boundary members (American standard profiles) BEAM SECTION SPECIMEN TOP BEAM BOTTOM BEAM COLUMN SECTION SPSW1 W14 34 W14 34 W14 48 SPSW2 W14 74 W14 74 W14 82 SPSW3 W14 99 W14 82 W DISCUSSION OF OUTPUTS In all specimens Expansion of the tension field and buckling waves began with one wave on the main diagonal and then, by increasing the lateral displacement of the specimen, second waves along the same direction as the main wave were formed. Figures 2 to 7 show diagram of base shear variation versus displacement and stiffness of specimen types of SPSW1, SPSW2 and SPSW3. It is clear that bay reduction causes decreasing in resistance and stiffness of steel plate shear wall. This phenomenon goes in a similar process with increasing in opening diameter. The displacement and expansion of the tension field in selected specimens is given in Figure 8. 2

3 (a) (b) (c) Figure 1. SPSW modelling a- Type CR16 b - Type CR26 c - Type SCR CR11 CR12 CR13 CR14 CR15 CR Displacement (mm) Figure 2. Base shear-displacement diagram (SPSW1) Stiffness (kn.mm) CR11 CR12 CR13 CR14 CR15 CR16 Figure 3. Stiffness-base shear diagram (SPSW1) 3

4 CR21 CR22 CR23 CR24 CR25 CR Displacement (mm) Figure 4. Base shear-displacement diagram (SPSW2) Stiffness (kn/mm) CR21 CR22 CR23 CR24 CR25 CR Figure 5. Stiffness-base shear diagram (SPSW2) CR31 CR32 CR33 CR34 CR35 CR Displacement (mm) Figure 6. Base shear-displacement diagram (SPSW3) Stiffness (kn/mm) CR31 CR32 CR33 CR34 CR35 CR Figure 7. Stiffness-base shear diagram (SPSW3) 5. NEW REDUCTION FACTORS FOR RESISTANT AND STIFFNESS Roberts and Sabouri [5] give a reduction factor of () for resistance and stiffness base on some theoretical and laboratory results when the opening is located on the center of shear plate. In a further research, Sabouri [6] suggested a modification on reduction coefficient as (1-A/A ) to improve the previous factor, where A equals to opening area and A shows plate area. Then, A.Mossavi [11] performed a program of theoretical investigation on panels with central circular opening and submitted separate modified reduction factors of (1-D/b) and (1-D/Z) to be applied respectively to resistance and stiffness. In which, b is panel width, Z equals to 4A/P, A is panel area and p is panel perimeter. According to our results, the panel geometry is one of the effective parameters in the reduction of resistance and stiffness, which is ignored in the previously offered reduction factors. Therefore, the reduction factors of and (1-D/H) are obtained respectively for resistance and stiffness, upon the results of this paper. In which, S equals to b/h, b and H are panel width and panel diameter respectively [12]. In Table 3 and 4 is evaluated the accuracy of presented coefficients for the reduction effect of resistance on shear wall behavior in comparison with Roberts and Sabouri [5]. Table 3- Difference percentage in resistance coefficient (panel dimension 3x3mm) D/d=.2 D/d=.35 D/d=.5 () Table 4- Difference percentage in resistance coefficient (panel dimension 45x3mm) D/d=.2 D/d=.35 D/d=.5 ()

5 Tables 5 to 7 show comparatively the differences of suggested reduction resistant coefficient with the others. As it is seen the average difference of this paper with individual FE results is only 2.9%. Table 5- Difference percentage comparison in determining of resistance for SPSW1 series D/d= D/d= D/d= D/d= D/d= A/A D/b Table 6- Difference percentage comparison in determining of resistance for SPSW2 series D/d= D/d= D/d= D/d= D/d= A/A % D/b Table 7- Difference percentage comparison in determining of resistant for SPSW3 series D/d= D/d= D/d= D/d= D/d= A/A D/b The difference for suggested stiffness coefficient is 3.4% due to Tables 8 to 1. Negative averages in the Tables show being of non conservative in coefficient. Table 8- Difference percentage comparison in determining of stiffness for SPSW1 series D/d= D/d= D/d= D/d= D/d= A/A D/Z D/H Table 9- Difference percentage comparison in determining of stiffness for SPSW2 series D/d=.1 D/d=.2 D/d=.3 D/d=.4 D/d= A/A D/Z % D/H

6 Table 1- Difference percentage comparison in determining of stiffness for SPSW3 series D/d=.1 D/d=.2 D/d=.3 D/d=.4 D/d= A/A D/Z D/H CR21 specimen CR36 specimen Figure 8. Deformation and von mises stress distribution in ultimate capacity 6. CONCLUSIONS In this paper three groups of steel shear wall models are investigated using nonlinear finite element method considering geometric and material nonlinearities. The height and width of the portal frames are x227 mm and x mm. In the range of studied models in this research following upshots are apt to be presented. 1. Increasing in steel plate shear wall dimensions cause reduction in resistant as well as in initial stiffness of steel shear walls. 2. Resistance reduction in steel plate shear wall with increasing of circular diameter of opening in the center of the panel could be computed applying the following reduction factor: 3. Initial stiffness reduction in steel plate shear wall with increasing of circular diameter of opening in the center of the panel could be computed applying the following reduction factor: (1-D/H) 4. The average differences of suggested reduction coefficients are 1.86% and 2.7% in resistance and stiffness respectively. 5. The accuracy of the presented reduction factors is higher than others. 7. REFERENCES 1. Takahashi, Y., Takeda, T., Takemoto, Y. and Takagi, M., (1973), Experimental Study on Thin Steel Shear Walls and Particular steel bracing under Alternative Horizontal Load. 2. Thorburn, L.J., KulaK, G.L.and Montgomery, C.J.,(1983), Analysis and Design of Steel Shear Wall Systems. Struct. Eng, rept.17, Dep. Civil Eng, Univ. Alberta. 3. Timler, P.A. and Kulak, G.L.,(1983), Experimental Study of Steel Shear Walls. Struct. Eng.Rept. 114, Dept. Civil Eng. Univ.Alberta. 6

7 4. Sabouri-ghomi, S. and Roberts, T.M.,(1991), Hysteretic Characteristics of Unstiffened Steel Plate Shear panels. Thin-walled Structures, 14, Sabouri-ghomi, S. and Roberts, T.M.,(1992), Hysteretic Characteristics of Unstiffened Perforated Steel Plate Shear panels. Thin-walled Structures Lateral Load Resisting Systems: An Introduction to Steel Shear Walls (SSW).Saeed Sabouri, 21.(In Persian) 7. Kharrazi, M. H., (25), Analytical Method for Analysis and Design of Steel Plate Walls. Report to Steel Structures Education Foundation (CISC), Department of Civil Engineering, The University of British Columbia, Vancouver, BC, Canada. 8. FEMA 356, Federal Emergency Management Agency, (2), Prestandard and Commentary for the Seismic Rehabilitation of Buildings. American Society of Civil Engineering. 9. Hibbit, Karlsson, & Sorenson, Inc., (HKS), 23a. ABAQUS/Standard Theory Manual. Version 6.4, Hibbitt, Karlsson, & Sorenson Inc., Pawtucket, Rhode Island. 1. Hibbit, Karlsson, & Sorenson, Inc., (HKS), 23b. ABAQUS/Explicit User s Manual. Version 6.4, Hibbitt, Karlsson, & Sorenson Inc., Pawtucket, Rhode Island. 11. Abbasi Mosavi, Seyed Mehdi.Studying destruction behavior of steel shear walls with opening, M.Sc. Thesis, Civil Engineering Faculty, Sahand University of Technology, Tabriz, Iran, 26. (In Persian) 12. Valizadeh H. Experimental investigation of seismic behavior of steel shear walls with opening and diagonal stiffeners. MEng thesis, Faculty of Civil Engineering, Urmia University, Urmia, Iran; june 29. (In Persian) 7