Civil PG Conference, MIT, Pune. April 24 th -25th 2015, Paper no.
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Different approaches in modeling of RC shear wall: wal l: A review A. L. Mulla1, Satish Rathod2, Y. R. Suryawanshi3 Dept. of Civil Engineering, JSPM’S Imperial College of Engineering and research, Wagholi, Pune.
Abstract — RC shear walls are used in new structures as well as in the rehabilitation of existing structures. Shear walls (SWs) are vital to limit deformation demands under earthquake excitations. So correct modeling of shear walls is most important issue in linear and nonlinear analyses of building for Predicting the behavior of RC shear walls under lateral loads such as winds and earthquake. This paper presents various modeling techniques that have been used by researchers in modeling of RC shear walls. These range from macro-models, micro-models such as finite element models and fibre models. For the purpose of finite elements modelling, different techniques utilizing either shell elements or combination of frame elements with mid pier frame can be used. The paper discusses the efficiency of each modelling approach in representing both the global and local behavior of RC shear walls. . The aim of this study is to investigate the suitability, simplicity, accuracy; effectiveness of different structural models
Index Terms —Shear wall, Macro modelling, modelling, Micro modelling, modelling, Frame element, Shell element.
I. INTRODUCTION
Shear walls are part of the lateral force resisting system that carry vertical loads, bending moments about the wall strong axis, and shear forces parallel to the wall length. Shear wall system is one of the most common and effective lateral load resisting systems that is widely used in medium- to high-rise buildings. It can provide the adequate strength and stiffness needed for the building to resist wind and earthquake loadings, provided that a proper design is considered, that cares for both the wall strength and ductility. During the recent years, an enormous effort has been done to provide analytical models that are able to simulate the actual behaviour of RC elements including shear walls. The rapid increase in the computational efficiency of computers helped the researchers to develop more sophisticated models that can account for several phenomena of RC shear walls that were used to be ignored in the analysis due to their complexity. For these models to be verified, experimental research is continuously conducted on RC shear walls tested under monotonic, cyclic, or dynamic loading. The numerical modeling of RC walls is not involved only in the applications for new construction, but it is also extended to the applications of retrofitting of existing structures. In that case, it is important to construct a representative model that is able Manuscript received April 13, 2015
to evaluate the expected response of an existing RC shear wall under certain lateral load hazard, and to predict its expected mode of failure in order to be able to choose the most suitable and effective retrofitting technique for that wall that would meet a target performance. The numerical modeling of RC elements started by Clough et al. (1965) when they proposed the first nonlinear macromodel, and by Ngo and Scordelis (1967) who proposed the first application of the finite element method of analysis in RC elements. Since then several advancements were done in the area of modeling of RC elements including shear walls. The objective of this paper is to present the different numerical models proposed by researchers for the analysis of RC shear walls II. LITERATURE REVIEW A. Analysis of Shear Wall with Openings Using Solid65 Element [7]
Previous researches on the behavior of shear walls with openings assumed elastic analysis utilizing shell and brick elements. The present work adopts nonlinear finite element analysis using solid65 element. The analysis comprises both material and geometric nonlinearities. Solid65 element models the nonlinear response of concrete material based on a constitutive model for the triaxial behavior of concrete after Williams and Warnke. Five shear wall models with different opening sizes are analyzed. A sixth model of a solid shear wall is also presented to compare the analysis results. The paper studies the effect of the size of the openings on the behavior of the reinforced concrete shear walls. Modeling of Shear Wall Using Solid65 Element The solid65 element models the nonlinear response of reinforced concrete. Solid65 models the concrete material based on a constitutive model for the triaxial behavior of concrete after Williams and Warnke. It is capable of plastic deformation, cracking in three orthogonal directions at each integration point. The cracking is modeled through an adjustment of the material properties that is carried out by changing the element sti ffness matrices. If the concrete at an integration point fails in uniaxial, biaxial or triaxial compression, the concrete is assumed crushed at that point. Crushing is defined as the complete deterioration of the structural integrity of the concrete.
Civil PG Conference, MIT, Pune. April 24 th -25th 2015, Paper no. ANSYS allows entering three reinforcement bar materials in the concrete, each material corresponding to the x, y and z directions of the smeared element (ANSYS, release 5.5).
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sections are located at the control points of the numerical integration
Figure 18. MVLEM model Figure 20: Solid65 element (ANSYS, release 5.5) B. Numerical tools for modeling of RC shear walls [6]
Three different modeling techniques of RC shear walls into the OpenSEES software were discussed. These models include fiber section model, flexure-shear interaction model and cyclic softened membrane model (CSMM). Numerical simulation of cyclic loading test of a slender shear wall based on OpenSEES in this paper shows that CSMM and fiber section model are able to simulate characteristics of the cyclic wall responses. Strength deterioration, stiffness degradation, hysteretic shape and pinching behavior are clearly captured in the analysis results, however because of fewer DOFs and less computing time, the fiber section model is applicable to tall shear walls too. Comparison between analytical model responses and test results show that the flexure-shear interaction model provides a reasonably accurate response prediction for a slender shear wall. a. Flexure- shear interaction model In order to capture the experimentally observed shearflexure interaction in RC walls, Orakcal proposed an analytical model that incorporates RC panel behavior described by a rotation- angle approach into the multiple-vertical-lineelement-model (MVLEM, Figure 18). The analytical model was based on the methodology developed by Petrangeli to the MVLEM element. Flexure-shear interaction model involves modifying the MVLEM by assigning a shear spring for each uniaxial element. Each uniaxial element is then treated as an RC panel element, with membrane actions, with uniform normal and shear stresses applied in the in-plane direction (Figure 19). The interaction between flexure and shear was incorporated at the uniaxial element level. This methodology involves the implementation of the finite element method together with a constitutive RC membrane model.
Application of the finite element method for the analysis of building structures with shear walls requires an understanding of the approximations involved i n the modeling assumptions to build these elements. The two modeling procedure and assumptions are explained below:
b. Fiber section model In this model, there are a number of control cross-sections along the element. Each cross-section is subdivided into concrete and steel fibers where uniaxial stress-strain laws are used to describe the response of the material in the longitudinal direction (parallel to the element axis). These
Frame Elements Based Model The shear walls are modeled using a set of frame elements. The most common modeling technique is to use a composition of mid-pier frame to represent the shear wall stiffness and a horizontal frame (rigid arm) to allow proper connections with intersecting beams and slab components. The most critical
Figure 19. Flexure-shear interaction model [9]. C. Nonlinear Analysis Methods for Reinforced Concrete Buildings with Shear walls [5]
Reinforced concrete (RC) shear walls are modeled utilizing different techniques either using shell elements or combination of frame elements. In the nonlinear analyses, the nonlinear material model of mid-pier frame is generally based on plastic hinge concept located on the plastic zones at the end of the structural elements or distributed along the member span length. The nonlinear behavior of the shell elements is generally modeled using multi-layer shell element with layered material model. In this approach, the concrete and the reinforcement inside the structural elements are modeled respectively with different layers. a. Linear Models for Shearwalls
Civil PG Conference, MIT, Pune. April 24 th -25th 2015, Paper no. point for this model is the proper selection of rigidity and stiffness property for the horizontal frame. Infinite rigidity of the upper frame can highly overestimate the bending moments especially at the connecting beams. This model is used widely in practice to model planar shear walls in building structures for linear and nonlinear analyses. This model might have no reliable results for very long, interacting or complex shear walls with openings. Shell Elements Based Model The shell element considered in most of the design software has six degrees of freedom at each node and an in-plane rotational degree of freedom, which makes it compatible with three-dimensional beam type finite element models. It is worth to know that a bilinear shape functions are used to define the displacement field of the quadrilateral elements, Wilson (2002). Therefore, shear wall modeling requires a mesh discretization in order to get realistic behavior. The advantage of using shell elements is the ability to model very long, interacting and complex shear walls within the three dimensional model. b. Nonlinear Material Models Shear Walls The nonlinear element models of shear walls are ranged from three dimensional nonlinear solid elements, two dimensional nonlinear shell elements to simplified models using frame elements. Continuum Finite Element Models
The shear wall is modeled with continuum elements using nonlinear solid elements existed in many advanced finite element analyses’ software as ANSYS, ABAQUS, etc. The continuum elements offer superiority in accurately modeling the concrete and reinforcement details (Nicolae and Reynouard, 2000). Reinforcement can be defined in three different directions. The plasticity model for concrete is based on the flow theory of plasticity, Von Mises yield criterion, isotropic hardening and associated flow rule. The continuum elements also capture important behavioral responses such as axial-flexure interaction, inelastic shear deformation, steel confining effect on concrete behavior, concrete compression softening, and concrete tension stiffening (Spacone and ElTawil, 2004). Multi-Layer Shell Element The shear wall is modeled using a fine mesh of smeared multi-layer shell elements. The multi-layer shell element is based on the principles of composite material mechanics and it can simulate the coupled in-plane/out-plane bending and the coupled in-plane bending-shear nonlinear behaviors of RC shear walls (Miao et al, 2006). The shell element is made up of many layers with different thickness. And different material properties are assigned to various layers (Figure 17)
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Rebar 2
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Concrete la e
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Rebar 1
Figure 17. Multi-layer shell elements D. Comparison of Practical Approaches for Modelling Shear walls in Structural Analyses of Buildings [4]
Shell elements formulations generally consist of out-of plane (plate) and in-plane (membrane) degrees of freedom. The membrane element with drilling degrees of freedom was a challenge for the engineering community for many decades. The membrane elements generally combined with plate elements to form a “shell element” that has six degrees of freedom at each node and an in-plane rotational degree of freedom, which makes it compatible with three-dimensional beam-type finite element. This approach was successful and many analysis software have adopted various formulations for the shell elements. In practical engineering, although the shell element appears to have full compatibility with threedimensional beam element, some limitations in the formulation were identified. Although drilling rotations allow introducing external loads in the form of drilling moments, analytical results show inconsistency and sensitivity to mesh sizes and loading conditions. a. Shell Elements Based Model The shell element can be used efficiently for the analysis of building structures with shear walls. The shell element considered in most of the design software has six degrees of freedom at each node and an in-plane rotational degree of freedom, which makes it compatible with three-dimensional beam-type finite element models. It is worth to know that a bilinear shape functions are used to define the displacement field of the quadrilateral elements, Wilson (2002). Therefore, shearwall modeling requires a mesh discretization in order to get realistic behavior. The advantage of using shell elements is the ability to model very long, interacting and complex shearwalls within the three dimensional model. The optimal size of the mesh and the effects of mesh size on the results are shown in the numerical examples below. Although the shell element formulations include the drilling degree of freedom, analytical results show inconsistency and sensitivity of the drilling moment to mesh sizes and loading conditions. This shortcoming has significant effects on the bending moment of the in-plane beams connected to the shearwall. To resolve this problem, in engineering practice, the beam connecting to shear wall are generally modeled to some extend inside the shearwall shell elements.
Civil PG Conference, MIT, Pune. April 24 th -25th 2015, Paper no.
“Ri id” Element
Beam framin into wall
Figure 14: Rigid element defined along the top chord of the wall
“Ri id” Element
Beam framing
a. Frame Elements Based Model The shearwalls are modeled using a set of frame elements. The most common modeling technique is to use a composition of mid-pier frame to represent the shearwall stiffness and a horizontal frame (rigid arm) to allow proper connections with intersecting beams and slab components. The most critical point for this model is the proper selection of rigidity and stiffness property for the horizontal frame. Infinite rigidity of the upper frame can highly overestimate the bending moments especially at the connecting beams. This model is used widely in practice to model planar shearwalls in building structures for linear and nonlinear analyses. This model might have no reliable results for very long, interacting or complex shearwalls with openings.
MidPier Element
In modeling shearwalls with “shell elements”, the drilling moment of the shearwalls and the bending moment of the in plane connected beams are changed dramatically with mesh density. For finer meshes 10 times reduction of the drilling moment can be estimated. Introduction of top chord frame stabilise the results considerably. Good estimation of the properties of the top chord frame is very important not to affect the overall stiffness of the structural system. Best results are obtained using a top chord frame element to enhance the fixity of the beams framing into the shearwall. Using one penetrating rigid element along the top mesh give good results for coarse meshes. For finer mesh (20x20) 15% differences are exist in drilling moments for shearwalls and bending moments of the beams along major direction. E. Advancement in modeling of RC shear walls [3]
This paper presents different modeling techniques that have been used by researchers in modeling of RC shear walls. These range from macro-models such as lumped plasticity, multiaxial spring models, combined models, up to micro-models such as finite element models and fibre models. The paper discusses the efficiency of each model in representing both the global and local behaviour of RC shear walls.
Figure 15: Rigid element penetrating along one mesh length
“Ri id” Arm
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Beam framin into wall
Wall
Fi ure 16: MidPier Model Based on numerical results for different buildings models and shearwalls configurations and the different analyses set results of the example building, the following conclusions can be made
a.Micro-Modeling versus Macro-Modeling The two main approaches for modeling of RC members are micro-modeling and macro modeling. Micro-modeling such as the finite element analysis or fiber analysis is based on representing the behaviour of different materials that compose the RC element and the int eraction between them. The member is discretized into small elements and principles of equilibrium are applied. This approach is complex and needs high numerical processing efforts, and hence it might not be practical for large structures and it is limited to model individual structural components such as a column, a beam or a wall. On the other hand, macro-modeling is based on representing the overall behaviour of the RC element, such as the wall deformations, strength, and energy dissipation capacity. The global behaviour of the RC element using a macro-model should be calibrated using an experimental verification to adjust the parameters needed for the model. This approach is simple and does not require high numerical efforts, which makes it suitable to simulate the response of large structures. b. Hysteretic Models The cyclic behaviour of RC shear walls should be defined using a hysteretic model that is able to simulate different inelastic phenomena of reinforced concrete materials. The modeling of the hysteretic behaviour of the RC element can affect the element response significantly (Anderson and Townsend 1977). These models can be used to represent the axial, flexure and shear behaviour of the element. The hysteretic model consists of a primary curve (backbone curve) that control the monotonic loading and some hysteresis rules that control the loading and unloading element behaviour under cyclic loading. The control parameters of the hysteresis rules are adjusted to simulate the actual cyclic behaviour of the tested wall.
Civil PG Conference, MIT, Pune. April 24 th -25th 2015, Paper no. c. Micro-Modeling of RC Shear Walls Finite element method of analysis The number of the finite elements is chosen according to the level of accuracy required and the available analysis tool. The FEM of analysis is capable of tracking the member’s global behaviour (e.g. member forces and displacements) in addition to its local behaviour (e.g. crack pattern, material stresses and strains). The first FE model used for RC element was proposed by Ngo and Scordelis (1967). The proposed two-dimensional linear model used constant strain triangular (CST) finite elements to model the concrete and steel elements, linkage elements were used to represent the bond between steel and concrete elements, and the effect of cracking was included in the model. Fibre (layer) model In this model, the member is divided longitudinally into several segments, and each segment consists of parallel layers. Some layers would represent the concrete material and other layers would represent the steel material. In other type of models, each single layer was divided into a finite number of fibres as shown in Figure 5 (a). The constitutive laws for concrete and steel materials are defined, and hence the moment-curvature relationship of the member can be calculated at each load level. This model accounts for the distribution of flexibility along the member length and the axial-flexure interaction.
Figure 5 (a) Fibre beam element proposed
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behaviour). The nonlinearity of this model was represented uniformly along the entire member length. The main problem of this model was its inability to represent the element stiffness or strength degradation with cyclic loading.
Figure 6 Two-component element model. One-component beam-column element This element which was developed by Giberson (1967) consisted of one linear elastic member with two nonlinear rotational springs at the two member ends as shown in Figure 7. The member’s nonlinear deformations were assumed to be lumped at the zero-length end springs (lumped plasticity). For this model, the deformed shape was assumed to have a double curvature with a fixed point of contraflexure at the middle of the member, and the plain sections were assumed to remain plain. The one-component model and the general twocomponent model need an appropriate hysteretic loaddeformation (or moment-curvature) models to be defined. This requires definition of different properties of the member’s plastic hinges such as stiffness, strength, ductility, cyclic behaviour, etc., which may be difficult to be defined unless some assumptions were made. Multiple spring model Multiple spring model This model was proposed by Takayanagi and Schnobrich (1976). The multiple spring model consisted of a number of inelastic springs that are connected in series using rigid members as shown in Figure 7. The inelastic properti es of each spring were varied according to the segment properties and the level of axial load on that segment, however the segment properties were assumed to be constant along the segment length. The model was used to represent the behaviour of coupled shear walls, while the coupling beams were modeled using one-component elements. This model was used by Emori and Schnobrich (1981) to model the shears wall of a 10-storey frame-wall building. Linear shear deformations were assumed in the analysis. The models were found to satisfactorily represent the nonlinear behaviour of the studied str ucture.
(b) Multi-layer finite element model
d. Macro-Modeling of RC Shear Walls Two-component beam-column element The model developed by Clough et al. (1965) consisted mainly of two parallel components; one was fully elastic and the other was perf ectly elasto-plastic as shown in Figure 6. The two components were able to represent the material yielding (elasto-plastic behaviour) and the strain hardening (elastic
Figure 7 Multiple spring model Multi-axial spring model (MS model) This model was proposed by Lai et al. (1984) to simulate the axial-flexure interaction of RC columns. The proposed model consisted of an elastic linear member with two multiaxial spring elements (MS elements) of zero dimensions
Civil PG Conference, MIT, Pune. April 24 th -25th 2015, Paper no.
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located at the two member ends as shown in Figure 8. The MS element consisted of 5 concrete and 4 steel springs, each spring was assumed to be uniaxially stressed and its behaviour was governed by the hysteretic stress-strain characteristics of the simulated material (concrete or steel). The main input for this model was the material (concrete/steel) constitutive laws rather than the load-deformation relationship of the whole member. Multi-linear curves were used to represent the stressstrain or (force-deformation) relationship for concrete and steel springs. The spring deformations were conformed to the plane section assumption.
Figure 9 (a) Truss model used by Oesterle et al. (1984),
Figure 8 Multi-axial spring model by Lai et al. (1984): a) Member model, b) Inelastic element,
c) Effective concrete and steel spr ings. Truss models This model assumed that the wall will act as a statically determinate truss. The model consists of diagonal concrete compression struts, horizontal tension ties (representing the shear reinforcement), and two boundary elements at the wall ends to carry the moment acting. Figure 9(a) shows the truss model used by Oesterle at al. (1984) for analysis of shear response of RC shear walls. Other models based on the same analogy were used to calculate the capacity of RC walls, such as the Softened-Strut-and-Tie model shown in Figure 8(b). The model was used by Yu and Hwang (2005) to predict the shear capacity of RC squat walls. It is worth noting that, although such models are able to pr edict the capacity of RC elements, they cannot capture the cyclic or the hysteretic behaviour of these elements.
(b) Softened-Strut-and-Tie model Combined models Three Vertical Line Element (TVLE) model The model consisted of three vertical line elements connected to each other by rigid bars at the top and the bottom wall ends, two edge links with axial springs representing the boundary elements, and the central one-component element with three springs to control the vertical, horizontal, and rotational deformations of the wall as shown in Figure 10. The main problems about this model were the lack of deformation compatibility between the wall and t he boundary elements, and the difficulty in defining the properties of the springs.
Figure 10 Three Vertical Line Element model
Civil PG Conference, MIT, Pune. April 24 th -25th 2015, Paper no.
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F. An analytical model to predict the inelasti c seismic behavior of shear-wall, reinforced concrete structures [2] 2001
Figure 11 Axial-element-in-series model Multiple Vertical Line Element (MVLE) model The wall element was represented by a number of uniaxial elements connected in parallel using infinitely rigid bars located at the top and bottom wall ends; two external elements simulates the wall boundary elements, while the other elements simulates the combined axial-flexure behaviour of the central panel. A horizontal spring was used to represent the inelastic shear behaviour of the wall. The authors modified the axialelement-in-series model (AESM) by having two-component model for element 1, representing the cracked concrete and steel reinforcement behaviour, instead of the one-component element in the original model as shown in Figure 12. The constitutive laws for concrete (cracked and uncracked) and steel elements were defined to describe the hysteretic response of the materials.
A shear failure mode model based on experimental results has been added to the computer program larz. And studied most relevant problems and solutions devised during the development of this model. Validation of the model was carried out by comparing its results with the actual response of two b. Model for flexural failure mode The SINA hysteresis model implemented in the larz computer program (Fig. 3) was adopted in this study to model the non-linear flexural behavior and the moment curvature hysteretic relations for wall elements. As shown in Fig. 3, pinching effects and stiffness and strength reductions due to repeated cycles at the same deformation level were not implemented in the model for flexural behaviorreal buildings. In spite of the fact that the model is two-dimensional and, hence, it ignores the torsional response, the results obtained are satisfactory
Fig. 3. Hysteretic model for flexural mode of failure (beams, columns, shear walls).
Figure 12
Multiple vertical line element model
Figure 13 Modified axial-element-in-series
Model for shear failure mode Shear dominated behavior was also modeled using the SINA hysteresis model as shown in Fig. 4. Pinching effects and strength reduction due to repeated cycles at the same deformation level were now implemented in the hysteresis model. The model for the shear failure mode assumes independent of the shear strength of walls on both the bending moment and the axial force present in the wall.
Civil PG Conference, MIT, Pune. April 24 th -25th 2015, Paper no. Fig. 4. Hysteretic model for shear mode of failure (shear walls). This study has proposed and implemented a model to include the shear failure mode for walls in available computer programs. The model developed in this study is a macro-model validated with the experimental results of cyclic tests of shear walls G. Modeling of reinforced concrete shear wall for nonlinear analysis combining FEM panel model and boundary elements. [1]
A member model of reinforced concrete shear wall with boundary columns and beams was proposed for nonlinear and dynamic frame analysis. The reinforced concrete shear wall was idealized as axial springs for columns and a panel under plane stress states with rigid beams at top and bottom floor levels. Two methods were compared, in which isoparametric element and incompatible rectangular element with four nodes for the panel element were used. The model was verified through the analysis of T-shaped wall tests. The analytical results obtained by the proposed model showed generally good correlation with the experimental results. Shear deformation was overestimated by isoparametric panel element, whereas incompatible rectangular element, which incorporated flexural deformation by using internal displacements, gave better correlation with the experimental results of flexural yielding walls. For the walls in shear failure, the analytical results were basically same either by isoparametric element or incompatible element. a. Composition of RC Wall Member Model Three-Vertical-Line-Element-Model (TVLEM) It was formulated [Kabeyasawa, 1983] to idealize a generic wall member as three vertical line elements with infinitely rigid beams at top and bottom floor levels. Outside truss elements were represented by the axial stiffness of boundary columns, while the central element was a uniaxial model with vertical (axial), horizontal (shear) and rotational springs. This model has been verified by many test data resulting in a satisfactory correlation between calculated and measured response of structures that use shear walls. However, it was reported [Colotti, 1993] that the response was not adequately described for high shear stresses.
(a) TVLEM Model (b) RC Panel Model Figure 1: Macro-Element Model for RC Wall Member
FEM Panel Model
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In order to improve the prediction of the overall (shear and flexural) behavior of RC structural walls, this study proposes a 4-node panel under biaxial loading to represent the wall effect (Figure 1(b)). The boundary column uses the same axial spring proposed in TVLEM. Using just one panel to constitute the wall, shear strain will be overestimated by the isoparametric element (Figure 2(a)), satisfactory result cannot be obtained for the flexural problem. Flexural deformation must be considered in the element. In this study, incompatible rectangular element is used, in which flexural deformation can be introduced (Figure 2(b)). 2
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(a) Isoparametric Element (b) Incompatible Element Figure 2: Panel Element – Isoparametric Element and Incompatible Element A new model for reinforced concrete shear wall was proposed, which combined a FEM panel element and boundary line elements. Two methods using isoparametric element and incompatible element for a panel were compared with the test results. The model with isoparametric element slightly overestimates shear deformation for flexural yield shear walls. The model with incompatible rectangular element is better than the model isoparametric element for prediction of shear and flexural displacement components. The model gave a good correlation between analytical and experimental results. III. CONCLUSION AND SUMMARY
The study of all above researches, experiments, practical tests, and findings it is concluded that 1. For modelling of shearwall there are two main approaches namely Macro modelling and Micro modelling, each approach has its own advantage and disadvantages due to idealizations and assumptions and choice of approach is mainly depend on response parameters of interest either local or global behavior of shear wall. 2. Choice of modelling of shear wall also depends on types of shear wall its dimension, shape, material used for wall, loading on wall etc. 3. Although the finite element method appeals for its accuracy and for its ability to model different phenomena and their interaction, it requires the solution of a large system of equations, and the integration of stress in two or three space directions. This model is complex and needs high numerical processing effort, and hence it might not be practical for large structures
Civil PG Conference, MIT, Pune. April 24 th -25th 2015, Paper no. 4. There are mainly six models included in macro scale model: one-component model, two-component model, multi-axial spring model (MS model), truss model, multi spring model and multi component model. The macro scale model is based on representing the overall behavior of the RC shear wall, such as the wall deformations, strength, and energy dissipation capacity. R EFERENCES [1] Shaohua1, Toshimi2, (2000) “Modeling of reinforced concrete shear wall for nonlinear Analysis”, World Conference on Earthquake Engineering [2] P.A. Hidalgo1 , R.M. Jordan2, M.P. Martinez 3, (2002), “An analytical model to predict the inelastic seismic behavior of shearwall, reinforced concrete structures”, Engineering Structures 24 (2002).pp 85–98 [3] K. Galal1 and H. El-Sokkary2, “Advancement in modeling of RC shear walls”, (The 14thWorld Conference on Earthquake Engineering October 12-17, 2008, Beijing, China) [4] J. Kubin1, Y. M. Fahjan 2 and M. T. Tan 3, (2008), “Comparison of Practical Approaches For ModellingShearwalls in Structural Analysis of Buildings”, the 14 thWorld Conference on Earthquake Engineering October 12-17, 2008, Beijing, China [5] Y.M. J. Kubin1 M.T. Tan2, (2010), “Nonlinear Analysis Methods for Reinforced Concrete Buildings with Shear walls”, 14th European Conference on Earthquake Engineering [6] Ali Soltani1,.Farhad Behnamfar2,.Kiachehr Behfarnia3,.Farshad Berahman4, (2011)“Numerical tools for modeling of RC shear walls”,8th International Conference on Structural Dynamics [7] Mazen A. Musmar, (2013), “Analysis of Shear Wall with Openings Using Solid65 Element”, Jordan Journal of Civil Engineering, Volume 7, No. 2,
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College Name: - JSPM’S Imperial College of Engineering a nd Research, Wagholi, Pune
Asst. Prof. Y.R.Suryawanshi PG-coordinator Structural Engineering
Asst. Prof. Satish Rathod Guide
Prof. Dr. A. W. Dhawale Head of Department Civil Engineering -----------------------------------------------------------------------------------------------
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