EVALUATION OF SEISMIC BEHAVIOUR OF MASONRY INFILLS IN RC FRAME BY PUSHOVER ANALYSIS H. R. Khoshnoud 1 and A. K. Marsono 2 1 Faculty of Civil Engineering, University of Technology of Malaysia, Johor, [email protected]2 Faculty of Civil Engineering, University of Technology of Malaysia, Johor [email protected]ABSTRACT Reinforced concrete frame building with masonry infill walls is one of the popular structural systems in the world. In the most cases, the effects of masonry infill walls have been not considered in the structural model. Typically, masonry infill walls in RC frame buildings operate like diagonal compression struts which participate in lateral resisting system. In this paper the effects of masonry infill walls is considered on seismic response of whole building in RC frame with open ground story. For appraise these effects, two structural models with and without infill walls are considered by utilizing different static and dynamic nonlinear analysis. Firstly bare frame have been analyzed and designed according to code2800 for lateral drift and internal forces due to seismic response. Then, based on the designed frame two models with and without infill walls will be appraised with different nonlinear static and dynamic methods. The results of this study indicate that masonry infill walls have a significant effect of seismic behavior of building by increasing the lateral stiffness of structure, change the scenario of plastic hinge formation, ductility of system and behavior factor of building. After the collapse state of infill walls at the lower stories, the RC frame must resist the lateral load and the structure deteriorate its stiffness at the lower stories. Also there is a soft storey collapse scenario by SEE6 / 1 / IIEES Six th International Conference of Seismology and Earthquake
Transcript
EVALUATION OF SEISMIC BEHAVIOUR OF MASONRY INFILLS IN RC FRAME BY PUSHOVER ANALYSIS
H. R. Khoshnoud1 and A. K. Marsono2
1Faculty of Civil Engineering, University of Technology of Malaysia, Johor, [email protected] of Civil Engineering, University of Technology of Malaysia, Johor [email protected]
ABSTRACT
Reinforced concrete frame building with masonry infill walls is one of the popular structural systems in the world. In the most cases, the effects of masonry infill walls have been not considered in the structural model. Typically, masonry infill walls in RC frame buildings operate like diagonal compression struts which participate in lateral resisting system. In this paper the effects of masonry infill walls is considered on seismic response of whole building in RC frame with open ground story. For appraise these effects, two structural models with and without infill walls are considered by utilizing different static and dynamic nonlinear analysis. Firstly bare frame have been analyzed and designed according to code2800 for lateral drift and internal forces due to seismic response. Then, based on the designed frame two models with and without infill walls will be appraised with different nonlinear static and dynamic methods. The results of this study indicate that masonry infill walls have a significant effect of seismic behavior of building by increasing the lateral stiffness of structure, change the scenario of plastic hinge formation, ductility of system and behavior factor of building. After the collapse state of infill walls at the lower stories, the RC frame must resist the lateral load and the structure deteriorate its stiffness at the lower stories. Also there is a soft storey collapse scenario by formation of plastic hinges at to ends of first story columns. Thus consideration of masonry infill walls in structural model is a vital part of seismic appraise of RC frame of buildings. Keywords: masonry infill wall, pushover analysis, performance based design.
INTRODUCTION
The Reinforcement concrete frame buildings with masonry infill walls are widely used all across the world. In the most cases the effects of masonry infill walls have been not considered in the structural models and treated as nonstructural members. The experience resulted from previous earthquake shows that infill walls have significant effect on seismic response of building and even may cause collapse of building. Typically, based on macro model approach, masonry infill walls in RC frame building operate like diagonal compression struts which they participate in lateral resisting system. Consequently they increase the strength and stiffness of structure. Generally they have brittle behavior and when they reach to their collapse state, often at lower floors, they loss their stiffness and only bare frame should carry all lateral loads on that stories. Therefore in the most cases a soft story collapse is typical for infill RC building which the infill walls are missing in bottom stories. One of the typical masonry infill RC frames,
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commonly for access to parking lot, is the open ground story buildings (Fig. 1). In this sort of infilled RC frame base level are opened and masonry infills are in upper stories. In most cases, especially for new buildings, the effects of infill walls are not considered in the model and seismic behavior of building is limited to a linear analysis of bare frame. The focus of this study is on seismic performance of masonry infill RC frame with open ground story. To achieving this objective, the seismic response of a bare frame and a partially infill frame is considered by utilizing static and dynamic nonlinear analysis. According to the design office approach, a bare frame, first has been analyzed and designed for lateral drift and then for internal forces due to seismic response. Then, the designed frame will be appraised with different nonlinear static and dynamic methods with and without infill walls.
Nonlinear Static and Dynamic Analysis
Nonlinear time history analysis (NLTH) is the most accurate solution, but its intrinsic complexity and the required additional efforts regarding to thousands run steps for several ground motions causes NLTH to be limited to research area rather than design offices. Thus there is a major trend toward using the nonlinear static procedures (NSP). The NSP as an essential part of performance based design is now widely used especially at practical propose because of its simplicity and ability to predict seismic demands on inelastic response of buildings.One of the most popular static nonlinear procedures is pushover analysis which included in several seismic codes like Eurocode8, ATC40, FEMA356 [1]. The Pushover analysis is a series of incremental linear analyzes that in each step, a portion of lateral load is applied to the structure [2]. For monitoring the material nonlinear behavior of elements especially for yielding and post-yielding behavior, plastic hinges or plastic zones can be defined in two ends of beams or columns or any other locations of elements in which a plastic area may be formed. In each series of linear analysis, the response of system will be determined regarding the assumption that the stiffness of the structure is constant. According to the results of the each iteration, the yielding of each element is checked based on predefined criteria. If yielding is occurred the stiffness of structure is modified, lateral load is proportionally increased and another static analysis is performed. This process will continue until lateral roof displacement of building reaches to a predefined target displacement or a mechanism is formed. The result generally is presented in the form of base shear verses top story displacement. The above procedure currently is used in most seismic codes. Two main ideas of this procedure are the seismic behavior of structure based on first mode of vibration and the constant dynamic specifications of structure during the analysis. These two ideas generally are not correct for all buildings [3] especially for those that higher modes effects are important. On the other hand with forming plastic zones in structure, it loses its stiffness. Therefore the periods and mode shapes of system will be changed during the analysis. In N2 method [4], the pushover analysis of MDOF system is combined with the response spectrum of equivalent SDOF system. In this method, the usage of inelastic spectra rather than elastic spectra is one of the main advantages of this method over conventional method like ATC40. In order to apply the N2 method to infilled RC frame two modifications need to be made to the initial N2 method [5]. Firstly, the pushover curve has to be idealized as a multi-linear force–displacement relation rather than a simple elasto-plastic one. Secondly, inelastic spectra have to be determined by using specific reduction factors (i.e. the R–μ–T relation) appropriate for infilled frames, e.g. those proposed in [6].In the modal pushover analysis (MPA) [7] the seismic demand is obtained by pushover analysis for whole model (MDOF) and nonlinear time history analysis for an equivalent SDOF unless an inelastic response (or design) spectrum is available. This procedure must be iterated for each number of desire first modes and combination of these “modal” demands due to the first modes (normally two or three) provides an evaluation of the total seismic demand on inelastic systems. In modified modal pushover analysis (MMPA) [8] it is assumed that the response of building for higher modes is linear. So in this procedure the elastic influence of higher modes combined with the inelastic response of first mode reduce the computational effort. Modal Pushover Analysis (MPA)
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In the modal pushover analysis (MPA), which has been developed by Chopra and Goel [7], the seismic demand is determined by pushover analysis for whole model (MDOF) and nonlinear time history analysis for an equivalent single degree of freedom or the peak value can be estimated from the inelastic response (or design) spectrum for each modes. Combining these “modal” demands due to the first two or three modes provides an evaluation of the total seismic demand on inelastic systems. Details of the implementation are described in Chopra et. al.[7]. In the following, a brief explanation for MPA procedure is presented. The governing equation on the response of a multistory building with linear response is:
(1)Where u is the vector of N lateral floor displacements relative to ground, m, c and k are the mass, classical damping and lateral stiffness matrices of the systems u”
g(t) and is the horizontal earthquake ground motion and each element of influence vector is equal to unity. In a system with linear response, the lateral forces fs have a linear relation with displacement vector u and stiffness of k as ku. It means the stiffness of system during the analysis does not change. Therefore the response of the system has a constant slope as k. With the formation of plastic hinges in the structure, it losses its stiffness so the lateral forces fs has a nonlinear relation with displacement vector u. For the matter of simplicity, for each structural element, the nonlinear relation can be idealized as a bilinear curve. On the other hand, the unloading and reloading curves differ from the initial loading branch. Thus, for each displacement point like u1 is more than one lateral force fs. So for finding fs, it is necessary to know the path history of displacement because the amount of fs is depending on the path of loading or unloading. First differential of displacement u or u’ (speed vector) can give the path history of loading, therefore in inelastic system Equation (1) is as shown below:
(2)It can be shown that with assumption of u=DnϕnΓn , Equation (2) will be as follows:
(3)
(4)The Equation (3) can be solved if the relation of Fsn/Ln and Dn are available. If the curve of base shear and displacement Vbn-um is obtained from a pushover analysis for whole structure then it can be converted to Fsn/Ln-Dn as shown in Equation (5):
(5)Fsn/ Ln is acceleration because it is from dividing force of Fsn by mass of Ln. Thus we have:
(6)
The term of ω2nDny is acceleration too. Knowing Fsny/ Ln and Dny from Equation (5), the elastic
vibration period Tn of the nth mode inelastic SDOF system is computed from:
(7)
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Description of Models
For evaluation of aforementioned procedures, two 5-story concrete moment resisting frame with and without masonry infill walls, have been analyzed and designed with 3 spans of 4 meters and the height of 3.06 meters for each story, based on equivalent static analysis according to Iranian code of practice [9] and ACI 2005 for concrete design. The detail design of bare frame is presented in another paper [2]. The member sections of stories are presented in figur. 1. The dead and live load is 1.4t/m, 0.4t/m for stories and 1.2t/m, 0.4t/m for roof respectively. it is assumed that buildings are located in high level seismic zone with a design base acceleration 0.3g and soil profile type IV (soft deposits and high moisture in north of Iran). All buildings have intermediate R.C. MRF system with behavior factor, R=7 and importance factor I=1.0. The cracked moment of inertia has been considered 0.35Ig1 and 0.7Ig for beams and columns respectively to calculate the design drift. The self weight, weight due to loads and total weight of structure for both frames are 51.6, 86.4 and 138 ton respectively. The yield stress of main bars is assumed fy=4000kg/cm2. The fundamental period of vibration of all buildings is calculated based on dynamic analysis instead of using empirical formula (T=0.07H0.75).
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Figure 1. Bare frame and partially infilled frame and their sections specifications
In this study, a concentrated uncoupled moment hinges (M3) and a concentrated coupled P-M3 hinges are used for modeling of plastic zone of beams and columns respectively. In the analyses, the masonry infill walls are modeled by two compression diagonal struts, thus a concentrated axial force hinges (P) is used for modeling of plastic zone of infill walls. To perform nonlinear static and dynamic analysis for MDOF buildings, the SAP2000 NL version [10] was employed and for nonlinear time history analysis for equivalent SDOF system a program was developed by the authors.
Ground motion ensemble
Three ground motions were intended to be far 9 to 12 km, for a set of fault rupture with strike-slip mechanism at magnitude of 6.9. The specifications of the used records are given in Table 1. Each ground motion was scaled so that the five-percent-damped spectral ordinate at the period of the spectrum of ground motion matched that of the CODE2800 design response spectrum (soil profile type IV, 180 m/s, T0=0.15,Ts=1sec, S=1.75) at the same period (Fig 2).
1 - Although according to the table 6-5, FEMA 356, Effective stiffness value for nonprestressed beam is 0.5EcIg but for
similarities with code2800 it is assumed 0.35EcIg.
a Data Source: PEER (http://peer.berkeley.edu.smcat) b Closest distance to fault
Figure 2. Standard response spectrum and 5%-damped response spectra of scaled motions – the fundamental period of bare frame and partially infilled frame are 0.8 and 0.4 second respectively
Analyzing of Frames by MPA procedure
According to the previous section, first a linear dynamic analysis performed for both frames to find dynamic characteristics like periods and modal mass participation (Table2). In table 2 αn=LnΓn /M or αn= M*/M and Mn= ΣMiφ2
i or Mn=Ln/Γn. .In the next step, a nonlinear static analysis conducted for all frames with different base acceleration in order to develop the base shear-roof displacement, Vbn-um pushover curve and convert it to Fsn/Ln-Dn curve. Then for each case a nonlinear time history analysis performed to realize peak deformation of Dn of the 1th-mode inelastic SDOF system by the authors program (Figure 3).
Figure 4. Response of inelastic SDOF and MDOF of bare and partially infilled frame
Figure 3 shows the response of inelastic equivalent SDOF system of bare frame and partially infilled frame to ground excitation under nonlinear time history analysis. For both cases the response of system in first mode is inelastic, but the inelastic response of bare frame is significantly more than partially infilled frame due to less strength and stiffness. It is worth noticing that the axis of oscillation will be moved and the system will oscillate around the new position after yielding. Figure 4 shows the comparison of first mode response of SDOF which is multiplied by Γn with nonlinear time history roof displacement response of MDOF. It shows acceptable estimation especially for bare frame, of first mode response of SDOF for actual response of MDOF system by NLTH. It is interesting that the time of performing a SDOF nonlinear time history analysis in comparison of whole system is very short
Evaluation of seismic response of models
Both bare frame and partially infilled frame have been analyzed by different static and dynamic procedures. According to the results of analysis, the linear equivalent static analysis and nonlinear static analysis of the FEMA356 and MPA nonlinear procedures are assessed by comparing maximum story displacements, inter story drift to nonlinear time history dynamic analysis (NLTH). It is assumed that the results of NLTH are the exact solution and are our benchmarks.
Figure 5. comparison of displacement and drift ratio for bare frame and partially infilled frame and PIF (left), different procedure for bare frame (middle) and for partially infilled frame (right)
The target displacement is about 20.54, 20.89 and 20.82cm by FEMA356, MPA and NLTH respectively. According to code2800, inelastic lateral displacement can be calculated from
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elastic response multiple by 0.7R, which R is building behavior factor. Therefore actual lateral roof displacement is 22.54Cm based on elastic analysis. Figure 5 shows maximum displacement to height ratio and inter story drift ratio evaluated by elastic analysis, FEMA356, MPA and NLTH. The results show two different patterns for lateral displacement and drift for bare frame and partially infilled frame. For bare frame almost all procedures show an incremental increase in lateral displacements of stories and inter story drift ratio which predictable for moment resistant frame. For model with infill walls, lateral displacement and inter story drift ratio for lower stories is more than the others which it means a soft story collapse will be formed on the ground level. Lateral displacement and inter story drift ratio for upper story levels are close together because of the bracing action of infill walls which give more stiffness to upper stories and make these levels more rigid. More rigidity in upper stories means less ductility in these stories and it cases reduction of energy dissipation of system. The elastic procedure has always most amount of error in both models. The figure shows that FEMA356 and MPA procedure are more accurate estimation than others for bare frame and infilled frame respectively. As in both models the participation of higher modes are not too much because of regularity of frames, so FEMA356 and MPA procedures results have almost same accuracy. Figure 6 shows base shear/weight ratio to roof drift ratio for bare frame and partially infilled frame. The target displacements and base shear are 20.6Cm, 40.4ton for bare frame and 7.15Cm, 85.8ton for model without infill walls. The first plastic hinge is formed at 0.23 and 0.46 for bare frame and infilled frame. The yield point of bare frame and infilled frame are at 0.25 and 0.56 respectively and the elastic ratio of both frames is 0.825. The ductility reduction factor and overstrength factor are 3.26, 1.1 for bare frame and 1.47, 1.21 for infilled frame. If we assume a safety factor 1.7 for ratio of limit state design and allowable stress design then the behavior factor for bare frame and infilled frame are 6 and 3. It means the behavior factor of frame with infill is half of bare frame and this frame must be analysis and design for a base shear more than two times of base shear of code2800. On the other hand the deflection amplification factors are 5.26 and 1.26 for bare and infilled frame respectively. According to code2800 this factor is 4.9 for intermediate RC frame.
Figure 6. Base shear/weight ratio to roof displacement ratio for bare frame and partially infilled frame
Figure 7a shows plastic hinges for both frames at performance point after pushover analysis. All plastic hinges are in beam not in any column for bare frame. The plastic hinges for lower stories beams are at B state which means immediate after yielding and IO for upper stories beams which is between immediate occupancy and life safety state. But for partially infilled frame, it shows infill walls for lower stories are at C state which means after collapse state and formation of plastic hinges for ground story for both beams and columns. Failure of lower stories infill walls and formation of plastic hinges for ground stories in columns and beams reveals a soft story failure mechanism. Figure 7b shows plastic hinges for both frames at performance point after NLTH analysis. It shows same results with differences in locations and the state of plastic hinges.
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(a) (b)Figure 7. Plastic hinges formation at the performance point for bare frame and partially infilled frame (a)
by pushover analysis (b) by NLTH analysisIn figure 7b the most plastic hinges are formed in beams and some upper stories columns for bare frame. The state of plastic hinges is after IO and immediate after yielding for upper and lower stories beams respectively.
CONCLUSION
This paper has evaluated the effects of masonry infill walls in seismic response of RC frame with opening at ground level story. To achieve this goal two RC frame with and without infill walls are subjected to three ground motions with special characteristics to the site specifications. The maximum results served as benchmark responses in comparison to elastic analysis, FEMA356 and MPA procedures results. The consideration of results is the bases for the following conclusions: The results of nonlinear static and dynamic procedure show the state of designed frame
without infill walls is around life safety but for infilled frame is at soft story mechanism at ground level and collapse of infill walls at lower stories.
The infill walls in RC frame have a significant role in seismic response of building and can change the scenario of plastic hinge formation, ductility of system and behavior factor of building.
The infill walls operate like compression only members and increase lateral stiffness of building. The increase of stiffness cases decrease target point and increase design base share and changed entire seismic response of building. The models without infill walls are not able to capture these effects.
As in most cases masonry infill walls in RC frame do not constructed separate from frame at practice, so they have interaction with frame as primary structural members. Consequently it is essential to include the infill walls in structural model for new building especially with open ground story.
Although the pushover analysis procedures are not accurate as much as NLTH analysis but their simplicity, fast algorithm and reasonable results to predict seismic behavior of buildings, make them to be best choose for practical purpose especially at design offices.
REFERENCE
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4. Fajfar, P. “A nonlinear analysis method for performance based seismic design, J. of Earthquake Spectra 2000. 16: 573-592.
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5. Dolsek M., Fajfar P., 2008. The effect of masonry infills on the seismic response of a four storey reinforced concrete frame—a deterministic assessment, Engineering Structures 30, 1991–2001.
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