Proceedings of the 3rd International Conference on Environmental and Geological Science and Engineering

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1 Modeling of Hysteretic Damper in Three-Story Steel Frame Subjected to Earthquake Load Mohammad Saeed Masoomi 1, Siti Aminah Osman 1, and Shahed Shojaeipour 2 Department Civil and Structural Engineering 1, Department Mechanical and Materials Engineering 2 Universiti Kebangssan Malaysia Bangi, Malaysia msaeed@vlsi.eng.ukm.my, saminah@eng.ukm.my, shojaei@vlsi.eng.ukm.my Abstract: - This paper presents the nonlinear time-history and response spectrum analysis for a three-story steel moment frame and a braced frame by hysteretic damper against earthquake load which analyzed by SAP2000 software. The mentioned frames were analyzed by Eigenvalue method for linear analysis and Ritz-vector method for nonlinear analysis. Simulation results were presented as a time-displacement graph based on dynamic analysis, the dynamic base shear force is also calculated. Key-Words: - Time-history Analysis, Hysteretic Damper, Steel Structure, Earthquake Load, Braced Frame. 1 Introduction Nowadays one of the most important problems in designing of structures is the exact analysis of structure against dynamic loads such as wind load, earthquake, walking people, moving vehicles, and vibrating of heavy machinery that have the potential to cause dynamical effect on structures [1]. Basically this kind of loads has a lateral effect on structures compared with live and dead loads that have gravity effect on structures. One of the best solutions to resist with these loads is using of lateral restrain devices. Since the last two decades a lot of ideas and researches have been carried out to decrease the structures weight and vibration control systems [2], this paper is based on using a hysteretic damper as a lateral resistance member in steel frame. 1.1 Earthquake Earthquake is one of the most devastating natural disasters. There have been numerous studies in earthquake engineering with intention to decrease and avoid losses caused by earthquake are essential and worthwhile [3]. In many countries, building structure has been designed such that it will not collapse during a strong earthquake, it will be repairable after a middle earthquake and there will not be any structural damage after a light one. However this approach cannot avoid secondary losses caused indirectly by earthquakes such as damages to initial fitting and expensive items in the building as well as fires that break out after earthquake [4]. 1.2 Effect of Earthquake on Structures Behavior of structures during an earthquake that applies horizontal load is vibrating. Lateral load always cause structure to collapse in earthquake. The motion of the ground cause the structure to vibrate, and the amplitude and distribution of dynamic deformations and their duration are of concern to the engineer. The most important objective of earthquake design is that the structure should not be hazard to life and limb in the event of strong shaking. The vibration maybe in the elastic range with no damaging amplitude, but during strong ground shaking, members may undergo plastic strain and may occur some cracking [5]. 1.3 Response of Structures The forces that the seismic waves impart to structure are depending on the weight of the structure and the acceleration of the supporting earth (Newton second Law, ). Each structure also has a natural frequency or speed of vibration. If the structures natural vibration frequency coincides with seismic waves of the same frequency, then more of the seismic kinetic energy can enter the structure, causing greater potential of damage. During seismic activity the structure and the soil will vibrate at the same rate, allowing increased amounts of kinetic energy to enter the structure. This energy must safely dissipate to prevent damage to the structure [6]. 1.4 How to Protect Structure from Earthquake In the last three decades some countries have studies the effect of those lateral forces such as earthquake and wind to structures, and suggest some guidelines for design codes against lateral loads [7], [8] and [9]. However in recent years building codes have required more conservative design criteria to account for the seismic forces that a structure must dissipate. These building code requirements are forcing building owners to use more conservative seismic-resistant designs. ISSN: ISBN:

2 1.5 Integrated Finite Element Analysis of Structures SAP2000 (Integrated Finite Element Analysis of Structures) is a software pack from Computers and Structures, Inc (University of Berkley) for structural analysis. SAP2000 is a fully integrated system for modeling, analyzing, designing, and optimizing structures of a particular type for general structures, including bridges, stadiums, towers, industrial plants, off shore structures, piping systems, buildings, dams, soils, machine parts and many others. Creation and modification of the model, execution of the analysis, and checking and optimization of the design are all done through this single interface. Graphical displays of the results, including real-time display of time-history displacements, are easily produced. This program offers a quantum leap forward in the way models are created and modified and in the way analysis and design are managed [10]. All of these programs feature sophisticated capabilities, such as fast equation solvers, force and displacement loading. Non-prismatic frame elements, highly accurate shell elements, Eigenvalue [11], Ritz dynamic analysis [12] and multiple coordinate systems for skewed geometry, many different constraint options, the ability to merge independently defined meshes, a fully-coupled 6-by-6 spring stiffness, and the option to combine or envelope multiple dynamic analyses in the same run. 2 Characteristics of the Model Model is designed in form of moment resistance frame. The dead loads of 700 kg /m² were assumed for all floors and roof and the live load of floors and roof is selected equal to 300 kg/m². This analysis is based on Uniform Building Code (UBC-97) for those parts that will analyzed by code s formulas as below. According to UBC-97 for soil type II, model is assumed as a simple building frame system with diagonal damper bracing in both X and Y directions. According to the code the effect of accidental torsion for structures with less than 18 m height can be ignored [13]. The connection between the columns and base is assumed as a fully fixed support. The double (DIN Steel Section) IPE 180 profile sections are assumed for all columns (Fig 1). All beams assumed to be made from double IPE 240 standard sections and finally hysteretic damper (Figures 6-B) with damping ratio of 5% is used for all bracing members. Mass centre of all floors are assumed in a same location and it is supposed to be in the centre of structure (Fig 3). Shear force on each storey is calculated according to the code and it is represented in Fig 2. Mass source: Fig. 1 Column Cross Section Fig. 2 Shear Forces Elasticity Modulus (E): Unit Weight (W): Poisson ratio ( ): 0.3 Minimum Yield Stress : 2400 = 1980 = = Strategy of Earthquake Load The overall analysis will be carried out based on the model simulation of the chosen three story steel frame. ISSN: ISBN:

3 The scope of this paper is presented to limit the following areas in order to achieve the aforementioned research objective. 1. Steel resisting moment frame and steel braced frame by damper will be considered for analysis (figure 6) 2. Effect of damper to dissipate the earthquake energy and maximum displacement through the timedisplacement graph will be considered. 3. Effect of bracing member on dynamic base shear will be considered. 3.1 Damping The damping device used in this study is a hysteretic damper with damping ratio of 5% ( ), thus the most important parameter is damping coefficient ( ) which is needed to define in the software as a nonlinear device. The natural frequency and mass of structure are as below: The simulation of the three story steel moment frame is carried out in three dimensional. The frame is resisted by diagonal damper as shown in Fig 6-B. as for a verification, the control frame model simulation without damper is also been carried out. The simulation result are the compared by hand calculation as shown in Table 1 and 2. The frames are analyzed in X direction and time-displacement of the third story and dynamical base shear is displayed in the tables and will be expound.whilst table 2 shows the base shear values from SAP2000 and hand calculation. These results show that the frame is stiff enough to resist against El Centro ground motion. The earthquake base shear is calculated according to UBC-97 formulas and the amount of base shear depends on total structural weight and earthquake coefficient (C). 4 Fig. 4 El Centro Ground Acceleration TABLE 1 PERIOD AND NATURAL FREQUENCY OF MOMENT FRAME Fig. 3 Steel 3.2 Damping Results and Discussion The mentioned frame will be analyzed by non-linear time history, linear response spectrum analysis that is required to obtain the seismic response. Total displacement of the top level that has the larger displacement in these frames, thus the first step is to extract the natural frequencies and in the second step is to extract the seismic response in time history analysis by ground motion applied (El Centro 1940). Figure 4 shows the time-acceleration graph of El Centro 1940 [14]. NUMBER OF MODES PERIOD (S) N. FREQUENCY ( ) SAP2000 H/C SAP2000 H/C TABLE 2 BASE SHEARS (MOMENT FRAME) TYPE OF ANALYSIS BASE SHEAR ( ) SAP2000 H/C STATIC BASE SHEAR DYNAMIC BASE SHEAR Figure 5 displays the time-displacement graph of third floor for the first 10 second of El- Centro As figure shows the maximum displacement of m occur in 2.5 (S) that is the maximum ground motion in El Centro, and also because of existing natural damping ISSN: ISBN:

4 in frame the displacement going to be zero in couple of seconds. As mentioned in UBC-97 and Chopra 1995 the damping ratio for steel structures should be consider 5%, if there is no damping in structure material the vibration will continue forever. It is already defined in the previous research [16] that the hysteretic damper with damping ratio of 5% ( ) will be added as a diagonal member to the moment frame. Again the simulation model with damper is carried out and the new results of base shear and time displacement are then compared with that of control frame model. The strategy describes the result of the time history analysis of building system subjected to horizontal ground motions (El Centro Earthquake 1940). The three dimensional analysis of the result is for three story steel moment frame and the frames resisted by diagonal damper. The frames are analyzed in X and Y direction and time-displacement of the third story and dynamical base shear are explained in Table 3 and 4 and compare with the result in Table 1 and 2 it will be find out the how dampers are effective in structures. Steel with Diagonal Hysteretic Damper TABLE 3 PERIOD AND NATURAL FREQUENCY (MOMENT FRAME WITH DAMPER) ER OF MODES OD (S) EQUENCY ( ) TABLE 4 BASE SHEARS (MOMENT FRAME WITH DAMPER) Type of analysis Base shear ( ) STATIC BASE SHEAR DYNAMIC BASE SHEAR Type of analysis Base shear ( ) STATIC BASE SHEAR 5326 DYNAMIC BASE SHEAR 2698 with Damper Fig 5, Time-Displacement Graph (Moment Frame) Fig 7 Time-Displacement Graph for with and without Damper 4.1 Discussion Figure 8 shows the difference between period and frequency of two types of moment frame and moment frame with added damper. The Figure also demonstrates how diagonal damper helps to decrease the period of frame and of course the frequency ( ) would be increased. A B Fig 6 (A) Three Story Steel (B) ISSN: ISBN:

5 Fig 8, Period and Frequency of Frames with Damper 4.2 Benefits and disadvantages of using damper Benefits of using damper are the following: 1. Decrease the displacement in the top level of structure. 2. Hysteretic dampers help the structure to be more flexible in vibration caused by earthquake or wind load. 3. Dampers are not very heavy comparing with shear wall or bracing members and do not increase the structural weight dramatically. Disadvantages of using damper are the following: 1. The disadvantage that could be considered is using of diagonal damper in frames may cause some architectural problems. 5 Conclusion and Further Work In this paper the behavior of three dimensional steel frames under seismic load has been studied through the FEM technique. The frame periods, natural frequency and dynamic base shear were obtained using the FEM by SAP2000 (v14 Advanced). In the other hand it is clear that dampers help to decrease the maximum displacement in structures, although shear wall and bracing member have the same performance but sometimes they increase the frequency dramatically and it cause danger in the structure base level. The designers should make sure that the column cross section area is adequately enough to support the maximum shear. In the further work we determine to make a new damper with special materials. [5]B.S. Taranath, Structural analysis and design of tall building. [6]R. W. Clough and J. Penzien Dynamics of Structures. California. Berkeley University. [7]Iranian code of practice for seismic resistant design of building, Building and housing research center publications, Standard No Third edition [8]Uniform Building Code Vol 2. Structural Engineering Design. [9]Federal Emergency Management Agency. Guideline for the seismic rehabilitation of building. FEMA [10]Nonlinear Analysis and Design of Building. SAP2000 User Manual, Computer and Structure, Inc. California, Berkeley. [11]A. Jeffrey, Advanced Engineering Mathematics. Harcourt/Academic Press. [12]M. Miri and S Maramaee, The Effect of Asymmetric Bracing on Steel Structures under Seismic Loads. World Academy of Science, Engineering and Technology [13]L. Meirovitch, Principles and Techniques of vibration [14] F. Naeim, The Seismic Design Hand Book. [15] A.K. Chopra, Dynamics of Structures: Theory and Applications of Earthquake. University of Berkley. [16]M.S. Masoomi, Dynamic Characteristic of Steel Frame against Earthquake Load. National University of Malaysia (UKM), References: [1]A. Ghobarah, Performance-based design in earthquake engineering: state of development, Engineering Structures 23 (2001) [2]H. Liu, Structural identification and finite element modeling of a 14-story office building using recorded data, Engineering Structures 27 (2005) [3]Z. Jian, Current Situation of Research on Earthquake, ISSN: X [4]K. Bargi, Structural Dynamic and Earthquake Engineering. Tehran. ISSN: ISBN: