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Modelling of tall shear walls for pushover analysis of reinforced concrete buildings
Abstract
Well designed and detailed reinforced concrete shear walls in a building can provide the required lateral stiffness and strength, as well as ductility, for resisting seismic loads. A pushover analysis is preferred to an equivalent static analysis to estimate the non-linear behaviour of a building under seismic loads. The present study investigated the different options for modelling a tall and solid shear wall in a pushover analysis of a regular multi-storeyed building. Two approaches were adopted for modelling the non-linear behaviour of a shear wall. The first one was based on lumped (point) plasticity, where the shear wall was modelled using column elements (Model 1). The second one was based on spread (distributed) plasticity, where the wall was modelled using fibre-based wall elements (Model 2). The analyses of Models 1 and 2 were compared based on the pushover curves, demand and capacity spectra plots, and formation of hinges. The observed non-linear behaviours of the two models were very similar. It is concluded that the modelling of a tall and solid shear wall using column elements is adequate for pushover analysis, provided the hinge properties are defined properly.
In a precast concrete wall type building, the joints between the precast wall panels are critical interfaces of force transfer. This paper investigates the influence of modelling the grouted vertical joints (considered to be emulative joints) between the wall panels on the behaviour of a building under lateral loads. To quantify the influence, three different types of models were investigated (i) monolithic model without considering the joints, (ii) walls with gaps for the joints and (iii) walls with shear link: elements for the joints. Next, two different modelling approaches were considered: (i) reference models using two-dimensional (2D) membrane elements and (ii) simplified models using one-dimensional (1D) equivalent column elements. Nonlinear static pushover analysis was carried out on standalone wall panel assemblages (with and without openings) and on a typical mid-rise building. To capture the material non-linearity under increasing roof displacement (drift), multi-layered membrane elements and point plasticity in the column elements were used for the two types of models, respectively. From the observed results, it was found that a model with gaps for the joints gives an overestimation of drift and conservative estimation of lateral strength compared to the model with link elements. Also, it was observed that the behaviour of a wall panel assemblage modelled using column elements was comparable to that of a model using membrane elements till the peak strength, with acceptable variation in the post-peak behaviour. Hence, it can be inferred that a model using column elements for the panels and link elements for the joints as demonstrated in this paper, is suitable for the pushover analysis of large buildings made of precast wall panels. the structural systems of precast concrete buildings are commonly classified into four categories (i) skeletal frame system, (ii) large panel or wall system, (iii) cell system, and (iv) hollow block system 1. this paper is related to precast concrete building with the wall system. the behaviour of a wall type building mainly depends on the behaviour of joints between the wall panels. Based on the location, these joints are classified as (i) horizontal joints, and (ii) vertical joints. The horizontal joints with through-dowel bars between the panels are stiffened by the gravity loads. However, for convenience of construction, the vertical joints do not contain through reinforcing bars. rather these joints are achieved by using overlapping dowel bars. Hence, the drift of a wall under lateral loads mainly depends upon the deformability of the vertical joints. in a nonlinear analysis of a wall or a wall type building, it is necessary to characterize the behaviour of the vertical joints under in-plane shear. also, it is necessary to incorporate an appropriate model for the joint in the computational model of the structure. to achieve a vertical joint, there are different methods available (for instance, usage of overlapping U-bars, looped wire ropes, or steel plate inserts, etc.). in India, presently vertical joints are achieved using commercially available looped wire ropes in steel boxes, commonly referred to as loop boxes. figure 1 shows a building and view of a vertical joint constructed
The shear walls constitute the primary lateral load resisting system in a reinforced concrete building with such walls. Hence, a wall needs to be modelled adequately in an analysis of the building for seismic loads. In this paper, a typical reinforced concrete multi-storeyed building with a centrally located tall shear wall was investigated for three approaches of modelling the nonlinear flexural behaviour of the wall. First, the wall was modelled using column elements with lumped plasticity at the ends (Model 1). Model 2 was developed using layered shell elements for the wall. Finally, fibre-based wall elements based on spread plasticity, was adopted to model the wall (Model 3). Cyclic pushover analysis, non-linear time-history analysis and incremental dynamic analysis were performed using the models. It was observed that for the cyclic pushover analysis, the fibre-based approach of modelling the wall gave better estimate of the hysteresis behaviour, as compared to the model based on column elements. For the non-linear time-history analysis, the higher frequency components in the variations of the moment and rotation at the base of the wall were captured only in the fibre-based approach. However, the results from the incremental dynamic analysis were comparable for the three models.
Based on equilibrium and compatability conditions, as well as a new stress-strain relationship for softened concrete, a truss-model theory was presented in a previous paper to predict the shear strength and behavior of low-rise reinforced concrete structural walls. The iterative procedure used to trace the load-deflection history is not suitable for design purposes. In this second paper of a series, a direct solution of the load-deflection history is obtained. Furthermore, it is shown that three different failure modes (under-reinforced, balanced and over-reinforced) can be clearly identified, depending on the relative contribution of longitudinal steel to that of the concrete. For each failure mode, an explicit formula is derived for the prediction of shear strength. A simple procedure is recommended for the shear design of low-rise structural walls.
For the push-over analysis of a building with a shear wall, modelling of the shear force versus drift behaviour of the shear wall is necessary. This paper presents a method for predicting the behaviour of a low-rise framed shear wall. The method is based on the softened truss model. The in-plane normal stress and strain generated in the wall in presence of boundary elements, were evaluated based on finite element analyses of walls. The method of solution by the softened truss model was modified to incorporate the effect of boundary elements. The predicted non-linear shear force versus drift curve was simplified to generate the shear hinge property of a wall.
Results from two large-scale flanged shear walls tested under static cyclic displacements are presented. The objectives of the tests were to provide insight into the behavior of shear walls under cyclic displacements, and more importantly, to provide data to help corroborate constitutive models for concrete exposed to arbitrary loading conditions. The results indicated that the presence of an axial load, although relatively small, and the stiffness of flange walls have a significant effect on the strength, ductility, and failure mechanisms of the shear walls. Finite element analyses using provisional constitutive models are also provided to show that the procedures employed are stable, compliant, and provide reasonably accurate simulations of behavior. The analyses presented also indicated that two-dimensional analyses capture main features of behavior, but three-dimensional analyses are required to capture some important second-order mechanisms.
SUMMARYA full‐scale shake table test on a six‐story reinforced concrete wall frame structure was carried out at E‐Defense, the world's largest three‐dimensional earthquake simulation facility, in January 2006. Story collapse induced from shear failure of shear critical members (e.g., short columns and shear walls) was successfully produced in the test. Insights gained into the seismic behavior of a full‐scale specimen subjected to severe earthquake loads are presented in this paper. To reproduce the collapse process of the specimen and evaluate the ability of analytical tools to predict post‐peak behavior, numerical simulation was also conducted, modeling the seismic behavior of each member with different kinds of models, which differ primarily in their ability to simulate strength decay. Simulated results showed good agreement with the strength‐degrading features observed in post‐peak regions where shear failure of members and concentrated deformation occurred in the first story. The simulated results tended to underestimate observed values such as maximum base shear and maximum displacement. The effects of member model characteristics, torsional response, and earthquake load dimensions (i.e., three‐dimensional effects) on the collapse process of the specimen were also investigated through comprehensive dynamic analyses, which highlighted the following seismic characteristics of the full‐scale specimen: (i) a model that is incapable of simulating a specimen's strength deterioration is inadequate to simulate the post‐peak behavior of the specimen; (ii) the torsional response generated from uniaxial eccentricity in the longitudinal direction was more significant in the elastic range than in the inelastic range; and (iii) three‐dimensional earthquake loads (X–Y–Z axes) generated larger maximum displacement than any other loading cases such as two‐dimensional (X–Y or Y–Z axes) or one‐dimensional (Y axis only) excitation. Copyright © 2011 John Wiley & Sons, Ltd.