Electromechanical Finite Element Modeling of Unstiffened Smart Steel Shear Walls (SSSWs)

Transcription

1 Electromechanical Finite Element Modeling of Unstiffened Smart Steel Shear Walls (SSSWs) Y. Shahbazi 1, M. Eghbalian 2, M.R. Chenaghlou 3, K.Abedi 4 1- PhD Student of structural Engineering, Sahand University of Technology, Tabriz, Iran 2- M.S of structural Engineering, Sahand University of Technology, Tabriz, Iran 3- Associate Professor of structural Engineering, Sahand University of Technology 4- Professor of structural Engineering, Sahand University of Technology y_shahbazi@sut.ac.ir me_eghbalian@yahoo.com mrchenaghlou@sut.ac.ir k_abedi@sut.ac.ir Abstract In this research, electromechanical finite element modeling of unstiffened smart steel shear walls (SSSWs) is investigated using ANSYS. The SSSWs are made of an elastic host plate and piezoelectric active layers. In this approach, the piezoelectric pieces are used parallel to the diagonal direction of steel plate. In other words, the piezoelectric segments will be placed parallel to the tension field of plate which happens after buckling. This new combination can be imaged as combination of SSWs with diagonal piezoelectric braces. Load bearing capacity of plate will be increased after post-buckling when an electric field intensity vector is applied. Keywords: Finite Element modeling, Steel Shear Walls, Actuator, Smart structure, ANSYS 1. INTRODUCTION Steel shear walls (SSWs) are one of the options of lateral force resisting systems. Using SSWs has increased due to the fact that this system is more cost-effective compared to the moment frame system. The SSWs can be used in both new and retrofitted structures in seismically high risk zones. In this system, buckling of the plate which is completely connected to the main frames will not be considered as a structural failure. In other words, the post buckling strength of the plate is several times that of the elastic. Steel shear walls (SSWs) are constructed in two forms of unstiffened and stiffened forms. The unstiffened form is the best passive choice for designers, because of its simple constructional details and lower cost. Three design approaches has been proposed up to now. The first is the Canada code method [1]. The second is the truss equivalent element which was proposed by Elgaaly who modeled SSWs as some strip elements which are just affected by tension forces. The main problem of this method is that the interaction between columns and SSWs has been neglected [2]. In real conditions, the interaction exists. Although the columns are designed for 100% of bending moment, a portion of the moment is carried by the SSWs. If SSWs are thin, they will exhibit out of plate buckling, even for such a little moment. In these conditions, the behavior of shear wall panels is erratic. The third method was suggested by Saboori and Roberts [3]. The method is based on plate frame interaction (PFI). In PFI method, the interaction was taken into account, but they neglected the moment bending effect for SSWs. Also, some experimental studies for evaluating SSWs behaviors have been executed. Takanashi and Takemoto et al. [4], Mimura and Akiyama et al. [5] implemented cyclic vibration experiments on twelve 1 and 2 storey buildings. Caccese and Elgaaly et al. [6] set up lateral cyclic vibration experiments on eight 3 storey and seven 2 storey specimens. Timler et al. announced that SSWs are more economic than concrete shear walls. They also recognized that the design cost ratio of steel structures to the concrete ones is 0.66 and for the total cost of construction the ratio is Berman and Bruneau did cyclic vibration experiments on six 1 storey specimens [7]. Piezoelectric stack actuators have been widely used to control large structures which require high control forces. Some reported cases of usage of piezoelectric stack actuators in large structures include that of Aizawa et al. [8] for response control of a four story structural frame by inserting the actuators into the

2 bottom of a column to produce a bending moment force. Kamada et al. [9] tested a model of a 4 storey building, 3.7m in height and 2,000 kg in total weight, in which thirty two stack-type piezoelectric actuators integrated into the columns were used for bending moment control. Fujita et al. [13] tested a smart structure using piezoelectric stack actuators for active micro vibration control of a 2 story 2,500 kg steel frame building model. 2. FINITE ELEMENT MODELING OF SSSWS AND VERIFICATION An adequate mathematic model for evaluating of the SSWs behavior is necessary. In this paper, According to abilities of finite element method in complicate problem, the ANSYS software which is executed due to FEM is used. There are some assumptions for SSSWs modeling as below: The BEAM189 element is used for beams and peripheral columns modeling. The SHELL181 element is used for SSWs modeling. The SOLID5 element is used for the piezoelectric actuators modeling. Element meshes was fined so that the answer for two consecutive steps has not tangible difference. The Arc length method with ability of solving the nonlinear equations has been used. All columns have fixed supports and in each storey, the out of plate displacements of columns have been so closed leading to restriction in their out of plate buckling. The mechanical and electrical field variables are so small that the linearized elasticity, linearized piezoelectricity, and linearized dielectricity theories are applicable. The elastic materials (the core layer) are isotropic but the piezoelectric materials (the outer layers) are anisotropic (either orthotropic or transversely isotropic, or hexagonal system), all being homogeneous. Each piezoelectric outer layer is completely covered by one integrated electrode, so there is only one applied control voltage to the actuator layer (control input or force) and one measured voltage observed from sensor layer (measured output). The piezoelectric layers are electrically polarized in the thickness direction, parallel to the electric field intensity. The polarization and electric field intensity vectors are parallel and both of them normal to the neutral axis of the smart piezoelectric stack in order to establish the axial mode of actuator dynamics. The former finite element assumptions (without PZT stack) are considered in one passive specimen with similar experimental analysis. As shown in figure 1, the experimental specimen is a single bay 1 story called SPSW2 tested by Lubell et al. [10].The properties of specimen are listed in table 1. Figure 1. Single bay 1 story Specimen, SPSW2, tested by Lubell et al. Table 1- Properties of specimens for verification Story Length Height Beam Section Column Section Thickness of Plate S75 8 S

3 Comparison between FEA and experimental results for same passive specimen is shown in Figure2. Also, failure propagation circumstance in both FE and experimental analysis is compared in Figure3. Figure 2. The comparison between FE and experimental analysis Figure 3. The comparison of failure propagation circumstance in both FE and experimental analysis The model is yielded and buckled at the top-left connection between plate and column for both FE and experimental analysis. The comparisons show that the numerical difference is small and ignorable for the FE modeling and following analysis. 3. PROBLEM DESCRIPTION The behavior of thin steel plates, which are adequately supported along their boundaries and subjected to shear loading, is stable in the post- buckling domain. The Load bearing capacity of plate could be increased after post-buckling when piezoelectric segments will be placed parallel to the tension field of plate. It must be considered that the piezoelectric materials accomplish both extension and shear actuation mechanisms. The extension actuator consists of an elastic core, sandwiched between two piezoelectric active outer covering layers. The piezoelectric layers are polarized transversely, i.e., the polarization vector is 3

4 parallel to the applied electric field intensity vector. On the other hand, the shear actuator consists of two elastic layers, sandwiched one piezoelectric active layer. The piezoelectric layer is polarized transversely, i.e., the polarization vector is perpendicular to the applied electric field intensity vector. Here, the piezoelectric stacks, 53mm wide and 1mm thickness, are used as an extension mechanism in SSSWs (see Figure 4). The objective is making additional piezoelectric braces which have extension or contraction. The extension or contraction behavior is depended on applied electric field intensity vector. If this field is similar on both faces of each piezoelectric layer, the extension will be occurred. In contrast, dissimilar electric field caused to contraction. The material and geometric parameters of the piezoelectric stacks are agreed with IEEE standard for PZT5H. Figure 4. Smart Steel Shear Walls (SSSWs) model in ANSYS 4. STATIC ANALYSIS Three sets of loadings and analyses are applied to the model of the SSSWs: 1) Static mechanical load: mechanical incremental shear loading at the top- left connection of the model in the absence of the electric field 2) Static electrical load: electric field applied to piezoelectric layers in thickness direction in the absence of the mechanical load 3) Static combined electrical/ mechanical load: mechanical incremental loading at the top- left connection of the model in the presence of the electric field. This analysis is executed in two states. In one state, the mechanical and electrical incremental loads are applied simultaneously. In other ones, the mechanical loading is applied completely. Then, the potential difference is applied. The results show that two mentioned states have the same outputs. Because of appearance of the dielectric strength threshold and dielectric breakdown phenomena, one is not able to apply any arbitrary electric field intensity to the piezoelectric outer layers. These phenomena depend directly on the size and geometry of the piezoelectric layers [7]. The results of ANSYS analysis for three sets of static loads, as inputs and mechanical displacements, as outputs are represented (Figure 5). (a) 4

5 (b) (c) Figure 5. The ANSYS results for three sets of analysis: (a) force-displacement relation, (b) Voltage -displacement relation, (c) force- voltage-displacement relation 7. CONCLUSIONS The finite element numerical models of smart steel shear walls (SSWs) are constructed in ANSYS. The poling and electric field intensity in the active materials is parallel to the plate thickness direction. When this electrical field on faces of piezoelectric layers is similar, the extension or contraction will be occurred based on voltage sign. An adequate electric filed is applied, because the piezoelectric segments should behave as a longitude braces to increase the load bearing of SSSWs. The analyses show that for static loading, the load bearing capacity of SSSWs will be increased. This increasing could be achieved in two states. In one state, the mechanical and electrical incremental loads are applied simultaneously. In other ones, the potential difference is applied completely after mechanical load. Furthermore, the increasing of load bearing capacity of SSSWs is as well as for two states. The next step forward is probably closing a feedback loop around the system for example using a robust or adaptive control strategy. 11. REFERENCES 1. Canadian Standards Association (CSA), Limit states design of steel structures, CAN/CSA S16-01, Canadian Standards Association, Willowdale, Ont., Canada, (2001). 2. Caccese, V. and Elgaaly, M., Experimental Study of Thin Steel-Plate Shear Walls under Cyclic Load, J. of Str. Engrg., ASCE, 119[2], (1993). 3. Sabouri-Ghomi, S.; Ventura, C. E.; Kharrazi, M. H. K., Shear Analysis and Design of Ductile Steel Plate Walls, Journal of Structural Engineering, 131 [6], (2005). 4. Takanashi, Y., Takemoto, T. and Tagaki, M, Experimental Study on Thin Steel Shear Walls and Particular Bracing under Alternative Horizontal Load Preliminary Report, IABSE, Symp. On Resistance and Ultimate Deformability of Tsructures Acted on by Welldefined Repeated Loads, Lisbon, Portugal,

6 5. Mimura, H. and Akiyama, H., Load-Deflection Relationship of Earthquake Resistant Steel Shear Walls with a Developed Diagonal Tension Field, Transactions of AIJ, 260, Caccese, V., Elgaaly, M., Experimental Study of Thin Steel-Plate Shear Walls under Cyclic Load, J. of Str. Engrg., ASCE, 119[2], (1993). 7. Timler, P.; Ventora, C. E.; Prion, H.; Anjam, R., Experimental and Analytical Studies of Steel Plate Shear Walls as Applied to the Design of Tall Buildigs, Struct. Design tall Build, 7, (1998). 8. Aizawa, S., Kakizawa, T and Higasino, M. (1998) Case Studies of Smart Materials for Civil Structures Smart Mater. Struct., 7(5): Kamada, T., Fujita, T., Hatayama, T., Arikabe, T., Murai, N., Aizawa, S. and Tohyama, K. (1997). Active Vibration Control of Frame Structures with Smart Structures using Piezoelectric Actuators (Vibration Control by Control of Bending Moments of Columns), Smart Mater. Struct., 6(4): Lubell, A. S.; Prion, H. G. L.; Ventura, C. E.; Rezai, M., Unstiffened Steel Plate Shear Wall Perfomance Under Cyclic Loading, Journal of Structural Engineering, 126 [4], (2000). 6