A study on the stiffness effects of link beam on the behavior of coupling shear wall

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1 A study on the stiffness effects of link beam on the behavior of coupling shear wall Seyyed Mahmoud Sheikhaleslamzadeh 1* and Taner Yilmaz 2 1 Department of Civil Engineering, Shabestar Branch, Islamic Azad University, Shabestar, Iran. 2 Department of Research Areas, Ece University, Izmir, Turkey. *Corresponding author: Abstract Coupling shear wall has been highly considered in recent years. Due to architectural limitations, sometimes the architect is forced to use two spans separate from shear wall. The study results have shown that using coupling shear wall will have better results than single wall in structure behavior and the desired performance can be achieved by using thinner plates. Coupling steel shear wall has many positive properties like high ductility, sufficient resistance, high energy absorption capacity and easy implementation. This study examined the behavior of coupling shear wall and the stiffness effects of link beam on it. The results showed that energy absorption in structures increases and additional displacements are avoided by increasing the bending stiffness of link beam. On the other hand using corrugated plates instead of flat plate causes the increase of small displacements of system capacity but the increase of change of these plates causes the loss of resistance in this type of plates and they finally bear forces like flat plates by showing post-buckling behavior. The stiffness of link beam affects more on displacements and the values of drift and displacement. But this change of stiffness does not have any effect on the force absorbed by frame. Keywords: coupling steel shear wall, energy absorption, link beam, stiffness INTRODUCTION Coupling steel shear walls have been considered in recent years to take the lateral energies of earthquake and wind in tall buildings. This new phenomenon which is rapidly increasing in the world has been used in the construction of new buildings and the reinforcement of existing buildings in earthquake-prone countries like America and Japan. Using them has about 50% steel consumption saving in buildings compared to moment resisting frames. Coupling steel shear walls are a simple system in terms of implementation and have no special complexity. Thus, engineers, technicians, and technical workers can implement it by the existing technical knowledge and without need to acquire new skills. The accuracy of implementation is as the same as common accuracies in the implementation of steel structures by observing it, the confidence coefficient is higher than the other systems. According to its simplicity and production in plants and installation in place, the implementation speed of the system is high and implementation costs are reduced to a higher degree. The system is one of the stiffest X-shaped bracing systems in terms of shear stiffness and due to the creation of vent (opening) at any point, it has the efficiency of all bracing systems. Also the system behavior in elastic field and its energy absorption is better than bracing systems. In steel shear walls system due to the expansion of materials and connections, the tension adjustment is better than other resistant systems against lateral loads like frames and a variety of bracing in which materials are usually grouped and connections are focused and the system behavior is more suitable especially in plastic field. RESEARCH BACKGROUND Steel shear walls include a steel plate, two boundary columns and horizontal beams. This set behaves like the girders of vertical plate beam which are fixed joint to the ground. Columns act as the wings of this vertical girder and steel wall plate acts as girder. The performance of horizontal beams is like stiffeners in girders [1]. Steel shear walls are implemented very easily and can be easily constructed in construction workshops and do not need any new technology. The idea of steel shear walls is based n using diagonal tension field which is created after steel sheet buckling. This idea has been seriously considered in the last 15 years [2].The results of these tests show that this system can act as a fully ductile and resistant system against lateral loads. In Canada s national building code, steel shear walls were divided into three types of high flexibility, average flexibility, and normal flexibility [3]. Coupling shear wall system has been highly considered in recent years. Due to architectural limitations, sometimes the architect is forced to use two spans separate from shear wall. The study results have shown that using coupling shear wall will have better results than single wall in structure behavior and the desired performance can be achieved by using thinner plates [4]. It was also observed that link beam has a very important role in the capacity of this system and strengthening link beam increases the capacity of this system [5]. Now we want to study this system according to these facts. In this system, it is assumed that firstly all the used materials are isotropic. Secondly in intended analyses, the members enter the nonlinear stage. Thirdly the members still have cargo ability and brittle fracture does not occur in them. On the other hand, it is assumed in modeling that lateral loads enter the frame alongside the steel plate and the errors such as distortion, welding defects and so on are not considered. It is also assumed that border elements like beam and column have a very important role in determining the cargo capacity of plate while applying lateral load and strengthening these members increases the cargo capacity of steel plate. The other 7615

2 assumption is that the strip element can show the behavior of steel plate accurately and using this element will have better outputs than membrane elements. In significant buildings, it is needed to use dual systems in order to decrease displacements and optimize failure mechanism. The review of structural forms shows that generally in buildings, lateral loads are borne by stiff bending sets like shear walls, coupling shear walls, rigid frames and so on. Studies have shown that a variety of bending sets that are resistant to lateral loads can be considered as the members of cantilever structure which have displacements in different bending and shear mode while applying lateral load to them. Bending response includes the total bending combination of the set due to the axial deformations of vertical members and their single-curve bending. Shear response is the cantilever behavior of frame due to the deformation of members. Cantilever behavior in braced frames is due to the axial deformations of beams and bracings and in coupling shear wall it is due to two-curve bending of columns and beams. Theoretically, due to relative stiffness of walls and beams coupling shear wall will be able to respond the structure s need in bending and shear modes [6]. Coupling shear wall has been highly considered in recent decades and shown an appropriate behavior at the time of earthquake. Technology of design and construction of steel shear wall has been developed in recent years and the principles of its design and implementation entered to different codes like: 1. AISC seismic code [7]. 2. FEMA 450 regulations [8]. Various studies have been conducted on this system like a study on a variety of steel shear wall [9].A study on the effect of type and properties of the plate under cyclic loading [10]. The angle of creating tension field [11], plate thickness [12], connection of beam to column [13-14] and the presence of opening in plate [15-16]. According to the mentioned introductions, it is needed to introduce some criteria for optimizing the performance through the study and analysis of this system in buildings. It was also observed that link beam has a very important role in the capacity of this system and strengthening link beam increases the capacity of this system [6]. For common Ferro concrete coupling shear wall, desired plastic mechanism includes the flow of bending in coupling beams and plastic joints at wall base. But when a plastic mechanism of coupling steel shear walls develop under lateral forces, as shown n figure 1, tension field is shaped in all floors and plastic joints on coupling beams, boundary beams and column base. The difference of plastic mechanism between coupling steel shear walls system and coupling concrete shear walls prevents the development of study results for concrete systems to steel systems. Figure 1: Failure mechanism of coupling shear wall [7] STEEL SHEAR WALL SYSTEM Steel shear wall system is an effective method for the resistance of lateral forces and has been widely used in high earthquake-prone areas throughout the North America and Japan. A steel shear wall consists of a steel frame that can have both flexible and rigid connections and steel plates connected to beams and columns as shown in figure 1. The beams and columns of steel frame are respectively called vertical boundary elements and horizontal boundary elements. In most cases, the plates are thin and un-stiffened and provide lateral force resistance of pre-buckling insignificant and significant lateral force resistance of post-buckling in shear [5]. Figure 2: The elements of coupling steel shear wall The design of steel shear walls is provided in seismic rehabilitation guidelines for the existing buildings in Iran. It is a steel shear wall. In the above method, the composite columns of a box or tubular steel section filled with concrete and steel columns to which steel shear wall is connected to form the above system. Gravity loads are usually transferred by composite columns to horizontal members (up and down beams) and link beam which has high energy dissipation ability. Steel shear wall with or without hole should have boundary elements (beams and columns) on its four sides and should be welded to them. Steel shear walls should be designed in such a way to bear seismic loads alone or with 7616

3 other members of lateral resistant system. Boundary elements should be evaluated like beams and columns. In this code, a guideline was presented to calculate stiffness by linear and static dynamic method, non-linear static method and nonlinear dynamic method, and also a guideline was presented to calculate the resistance of linear static and dynamic method, linear static and dynamic method, and non-linear dynamic method. An acceptance criterion in this code is linear static and dynamic method. One of the disadvantages of steel shear walls with stiffener on steel plate is large proposed and significant workshop costs. Some ideas were proposed to improve the behavior of steel shear walls without stiffener and create tension field after yield for energy dissipation. One of the most important methods is to increase axial forces in columns around steel plate in a wall system without decreasingly ductility in steel plate. They transfer the created strains to the foundation. There are different methods for the approximate analysis of coupling shear walls and one of their most important ones is continuous medium method. In continuous medium method, joint beams are considered as a joint continuous medium and the structure is simplified. Then, by considering compatibility conditions alongside the vertical line of bending milestones in link beam, Differential equations governing the behavior of coupling shear walls are obtained in terms of walls axial force or lateral displacements. By solving the above differential equations and applying boundary conditions, internal forces in walls and link beams can be calculated [3]. The distribution functions of parametric tension for the cores of shear wall were presented in reference [4]. The cores of coupling shear walls can be used in tall structures in a more desired way. used for all floors [5]. The required length of each part of beam for n tensile strips is equal to [18]: (2) XΔ is the length of each part of a directed beam, L is the width of panel, h is the height of panel, n is the number of tensile strips and the equivalent level of each strip is defined according to equation 3 [18]: (3) In which As is the representative for the surface of each strip. Another method by which the behavior of steel shear wall plate can be modeled in a desired way is using membrane element. For appropriate modeling and to show the resistance different shown by steel wall plate in tension and pressure, it is needed to use orthotropic elements. In modeling with membrane element, the reticulation of steel plate should be tiny enough. In this regard, it was recommended to use at least 4 tiny plate elements in each direction [9]. One of the biggest advantages of this type of modeling is the possibility to change the angle of internal axes in membrane element during the process of design. This feature can be used to define the angles of internal tensions of steel plate on different floors of a structure. It should be noted that using the standard models of membrane element in which elastic behavior and isotropic materials were used did not provide valuable information because this kind of models cannot properly diagnose the transferred forces from boundary element [9]. the schematic model of strip element is according to figure 2. TYPES OF MODELING One of the best and practical methods of modeling which its results are consistent with reality is strip modeling that was presented in 1983 [18].In this method, a series of tensile parallel elements with equal distances and both joint ends were used for modeling shear wall panel. (Figure 3) According to energy formulas in elastic tensions, equation 1 was introduced in 1983 to find the angle of tension fields: (1) In which a is the angle of tension field to the vertical axis, t is the metal plate thickness, h is the floor height, L is the span of shear wall, Ic is the moment of inertia of vertical boundary element in shear wall, Ac is the cross section of vertical boundary element in shear wall, Ab is the cross section of horizontal boundary element in shear wall. It should be noted that each strip will have a cross section equal to plate thickness in the assumed width. Studies have shown that about 10 strips in each panel can have appropriate results but less than that amount will cause damage to obtained results. On the other hand, according to the suggestions presented by researchers for a multi-floor structure if the angle difference a is not too much in different floors the average angle a can be Figure 3: Strip element model 7617

4 THE COMPARISON OF THEORETICAL AND LABORATORY BEHAVIOR OF STEEL SHEAR WALL To better understand the behavior of steel shear wall, several tests were performed as cyclic loading and monotonic loading on laboratory samples of this type of shear wall. The test results were shown in figures 3 and 4. THE DIFFERENCE BETWEEN USING FLAT AND CORRUGATED SHEAR WALL In some references, using corrugated steel shear walls for light building systems has been suggested. The presence of corrugation in plates makes a difference in their deformation than flat plates, thus these plates show a rather different behavior. Figure 5 shows the pushover chart of two samples of steel shear wall with 3 mm thickness in flat and corrugated modes. Figure 4: The chart of theoretical and laboratory results [17] Figure 6: Force-displacement curve of shear wall with flat plate and corrugate plate The review of charts indicates that in low displacements, corrugated plate has higher resistance but this resistance does not continue and in a low special displacement the resistance and cargo capacity of corrugated plate are immediately decreased and reach below the resistance level of flat plate. Corrugated plates first show a decrease in resistance and then move toward the ideal curve. It happens due to the deformation of corrugations in plates and formation of new corrugations on corrugated plates. With the increase of displacement, the resistance of corrugated plate increases and becomes equal to flat plate at a displacement about 60 cm which is a type of snap-through buckling in these plates. Corrugated plate reaches to the final values of its load sooner than flat plate and its value is more than flat plate. Figure 5: The theoretical and laboratory charts of cyclic loading [17] THE EFFECTS OF PLATE THICKNESS The amount of absorbed force increases with the increase of plate thickness. It means that the amount of this force is directly related to plate thickness. In figure 7, forcedisplacement curve was shown for different models with the plate thickness of 3,4 and 5 mm. As figures 3 and 4 show theoretical relations have a good match with the behavior of these plates and the behavior of this type of shear wall in each one of the static or cyclic bandings can be predicted by strip model and an acceptable approximation. In cyclic behavior, the material goes away from the theoretical imaginary line after passing several loops and this issue indicates the nature of steel plate. 7618

5 Computer models were made and analyzed by SAP2000 software. Figure 3 shows these, models. Thus the behavior of coupling steel shear wall was studied. Since the behavior of frame as two-dimensional is largely similar to its behavior in three-dimensional structures, it can be said that by examining a two-dimensional frame, its behavior can be largely predicted in a complete structure. Thus, by saving time and using computer models, favorable and desired results can be achieved in a much shorter time. Figure 7: Force-displacement curve for plates with different thicknesses As expected, the amount of buckling load increases with the increase of plate thickness. As the figure shows, this relation is linear and the amount of buckling load, final load and energy absorption increase with the increase of thickness in both types of plate. MODELING In this study to examine an optimal level of behavior in actual structures, some samples of shear wall with 3,5 and 7 floors were modeled. The height of panels in all cases was considered 3/5 m and the dimensions of panels span were considered 5m. The load applied to beams was considered 2500 kg/m by assuming that the span of their bending is 5 m. Table 1 shows the details of used models. In these models the connection of beam to column in all models was considered as rigid and the connection of plate to beam and column was modeled as joint. Model name M3-a M3-b M3-c M5-a M5-b M5-c M7-a M7-b M7-c Table 1: The details of used models Number of floors Thickness of floors shear wall plate (mm) 2, 1 2, 1 2, 1 3, 2, 2, 1, 1 3, 2, 2, 1, 1 3, 2, 2, 1, 1 3, 3, 2, 2, 2, 1, 1 3, 3, 2, 2, 2, 1, 1 3, 3, 2, 2, 2, 1, 1 Link beam IPE24 IPE27 IPE30 IPE24 IPE27 IPE30 IPE24 IPE27 IPE30 Paramet er of link beam stiffness (EI / L3) Figure 8: The samples of created computer models FLOORS DRIFT A large number of drifts can lead to the failure and damage of roofs, windows and structural and non-structural members. The relative lateral displacement of each floor is the difference of displacement in the center of gravity above and below that floor. This displacement is usually calculated for earthquake plan or earthquake utilization level and is referred to with the same names. The relative lateral displacement in each floor is made under the effect of lateral load by assuming the linear behavior of structure. The actual relative lateral displacement or inelastic relative lateral displacement in each floor is a displacement which is obtained by considering the actual and non-linear behavior of structure. This behavior can be considered only in earthquake plan. Figure 9 shows the floors drift calculated for analyzed models. Figure 9: The chart of floors drift As the charts show, the increase of bending stiffness in link beam decreases the values of drift and its most obvious one is for 5 floors. The maximum value of drift decreases about 1/5 times by the increase of stiffness in link beam to 1/5 times. 7619

6 PUSHOVER CURVE Pushover curve (capacity curve) is one of the most important results from pushover analysis. It shows to what extent the structure acted linearly and in which stage, it entered the nonlinear stage? The following figures shows pushover curves for modeled frames. Here, displacements are in terms of cm and basic cut is in terms of ton. Figure 10: The pushover curve of 3-floor frames The comparison of charts shows that the increase of bending stiffness in link beam does not cause much change in the results of analysis. The comparison of stiffness in link beam shows that the stiffness of link beam in models c is twice the models a. But the charts show that the shear capacity of frames has changed about a few percent. DISPLACEMENT In an earthquake, if the displacement of roof or floors goes beyond a certain limit, the structure will be considered as collapsed because in most cases, large displacement is equal to large damage in the floors of structure. Thus, building displacement is a good criterion for the design of structures especially in tall buildings. The main parameter of buildings design or control is resistance while the reaction of building in big earthquakes is alongside the yield and bearing big strains. According to force-displacement chart of structure, in this area, slight and controlling resistance changes of the behavior of building include deformation or displacement. The evaluation of non-linear increasing static analysis result usually occurs in the displacement of the roof that the structure experiences in earthquake plan. According to the emphases of different codes especially Standard 2800 about the displacement of roof, the importance of this variable is very much in the analysis of buildings. Thus, the present study examined this variable. This section mentioned the maximum changes of displacement in the last floor under pushover analysis and examined it in different modes. For the direct study of stiffness effects in link beam, maximum displacement to the stiffness of link beam were shown in figure 13. Figure 11: The pushover curve of 5-floor frames Figure 13: Maximum changes of displacement to the stiffness of link beam Figure 12: The pushover curve of 5-floor frames As the figure shows, the increase of stiffness in link beam reduces maximum displacement. It occurs because the rotation of beam under lateral force decreases with the increase of beam stiffness and thus displacements reduce. This change is linear. 7620

7 CONCLUSION 1. The comparison of theoretical relations and laboratory results in static and cyclic loads shows a good conformity and match. 2. In low displacements, corrugated plate bears more load than flat plate but this behavior is not usual and the resistance of corrugated plate immediately decreases with a slight increase in displacement. 3. The increase of plate thickness significantly increases the final load that can be borne by plate. 4. The increase of stiffness in link beam reduces the amount of floors drift. This procedure is more obvious in 5-floor frame than the other frames. So that the amount of maximum drift decreases 1/5 times with the change of beam stiffness to 1/5 times. 5. The changes of stiffness in link beam do not significantly affect the structure capacity curve (pushover). It is obvious that the doubled stiffness of link beam changes the capacity curve only a few percent. 6. The increase of stiffness in link beam reduces the maximum displacement. It occurs because the rotation of beam decreases with the increase of its stiffness and thus displacements reduce. REFERENCES [1] Astaneh-Asl A. Seismic Behavior and Design of Steel Shear Walls. Steel TIP~Report. Structural Steel Educational Council, Moraga. California July [2] Berman JW, Celik OC, Bruneau M. Comparing hysteretic behavior of light-gauge steel plate shear walls and braced frames. JStruct Eng, 2005;27(3): [3] Smith S, Coull A. Tall Building Structures, McGraw- Hill Book Company [4] Kwan AK. Shear lag in shear/core walls. JStruct Eng, 1996; 122(9): [5] Sabelli R, Bruneau M. AISC design guide 20: Steel plate shearwalls, AISC, Chicago [6] Borello DJ, Fahnestock LA. Behavior and mechanisms of steel plate shear walls with coupling. J. Constr. Steel Res, 2012;74:8-16. [7] AISC. Steel Plate Shear Wall Design, Guide20, First Printing American Institute of Steel Construction Inc., Chicago [8] NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures (FEMA 450): Provisions/Prepared by the Building Seismic Safety Council. Building Seismic Safety Council, National Institute of Building Sciences, [9] Astaneh-Asl A. Seismic Behavior and Design of Steel Shear Walls. Steel TIP~Report. Structural Steel Educational Council, Moraga. California July [10] Caccese V, Elgaaly M, Chen R. Experimental study of thin steel-plate shear walls under cyclic load. Jstruct Eng, 1993; 119(2): [11] Driver RG, Kulak GL, Kennedy DL, Elwi AE. Cyclic test of four-story steel plate shear wall. J. of Struct. Eng, 1998;124(2): [12] Elgaaly M, Caccese V, Du C. Postbuckling behavior of steel-plate shear walls under cyclic loads. J Struct. Eng, 1993;119(2): [13] Driver RG, Kulak GL, Elwi AE, Kennedy DL. FE and simplified models of steel plate shear wall. JStruct Eng, 1998; 124(2): [14] Xue M, Lu LW. Interaction of infilled steel shear wall panels with surrounding frame members. Proceedings of 1994 Annual Task Group Technical Session, Structural Stability Research Council: reports on current research activities [15] Sabouri-Ghomi S, Mamazizi S. Experimental investigation on stiffened steel plate shear walls with two rectangular openings. Thin-Walled Structures, 2015; 86: [16] Bhowmick AK, Grondin GY, Driver RG. Nonlinear seismic analysis of perforated steel plate shear walls. J Construc Steel Res, 2014; 94: [17] Veladi H, SazgariA, DavaranA. Experimental study and computer modeling of cyclic behavior ofsteel shear walls. 5 th International Conference on Seismology and Earthquake Engineering-Tehran [18] Thorburn LJ, Kulak GL, Montgomery CJ. Analysis of Steel Plate Shear Walls. Structural Engineering Report No. 107, Department of Civil Engineering University of Alberta, Edmonton, Alberta, Canada