Development Of Finite Element Codes For Shear Wall Analysis - Paknahad, Masoud (2008)

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Shear wall is commonly employed as a principal element to resist lateral loads due to wind or earthquake forces. An accurate mathematical model for shear wall structure needs to consider the effect of all components in the system i.e. shear wall, foundation, and subsoil. In addition to the necessity for accurate modelling of shear wall-foundation-soil system, the model must be proficient to capture the structural response of the shear wall building-foundation-soil and it should also be computationally efficient. Furthermore, since shear wall is a key structural element which plays a major role to ensure stability of the shear building system under lateral loads, it is essential to consider the inelastic response of the shear wall buildings. With the tremendous advancement in computer technology several finite element software’s are commercially available to researchers and engineers. However, this would not serve the objectives of the research investigator. In this study, new elements have been developed, modified constitutive law has been proposed, new computational algorithm has been utilised. Furthermore, this investigation focuses on the development of effective and suitable modelling of reinforced concrete shear walls. The modelling includes physical and constitutive modelling. (a) Physical modelling Most suitable elements had been adopted and some new elements have been developed for physical modelling of shear wall structural systems. The elements used for the purpose of mathematical discretisation of the shear wall structural system are: • Modified optimal triangle (MOPT) element with drilling degree of freedom to represent the superstructure and foundation. This element was developed in this study. • Interface element to represent the interfacial characteristics between the foundation represented by MOPT element with three degree of freedom per node (top continuum) and bottom continuum i.e. soil media idealised as plane stress /plane strain problem with two degree of freedom per node. This element was developed to incorporate slip and separation at the interface. • Super elements are groups of elements which are used to represent different substructures domain. • Nine node shell element has been used to represent the superstructure-foundation. This element is multi-layer in nature to simulate the R/C structures. • Coupled finite and infinite elements were used to model the near and far field in the soil media. These elements were employed when the modelling of soil structure interaction is in mind.All the above elements have been formulated based on continuum mechanics principle. (b) Constitutive modelling The following constitutive law for different materials are used in the problem of shear wall building-foundation-soil system. • Concrete; nonlinearities arising due to crushing, cracking and plastic yielding of concrete in one or two directions have been considered. • Steel; the steel reinforcement is assumed to be in a uni-axial stress state and is modelled as a bilinear material with strain hardening • Soil; to account for the nonlinear behaviour of the soil media, the nonlinear elastic model has been used Based on the above physical and material modelling two finite element codes have been developed during the course of this study: (i) Two dimensional finite element analysis of shear wall (2DASW) The modified optimal triangle element, super element, interface element and the nonlinear elastic model with different numerical techniques are included in its elements technology library in this FE code. (ii) Three dimensional finite element analysis of shear wall (3DASW) The 3DASW finite element codes deals with constitutive nonlinearities due to concrete and steel. The multilayer shell and beam elements are available in the element library of this finite element program.Both above finite element codes are equipped with pre, post processing and animation graphic facilities. The codes have been written using FORTRAN language and they are working under FORTRAN-95 Power Station. Accuracy and efficiency of the finite element codes has been achieved by analysing several benchmark examples available in literature. The finite element discretisation of different numerical examples used for the verification purpose and also computational efficiency indicate that, the finite element mesh with coarse mesh and wide range of element aspect ratio using MOPT produced good results. The results show accuracy and fast rate-convergence of super element and MOPT. An attempt has been made to highlight the computational efficiency of the developed 2DASW finite element codes by analysing actual shear wall buildings i.e. with and without opening. Results in terms of displacements and stresses are compared with those of commercial packages such as SAP-2000 and STAAD-PRO. It was observed that the contour of stress distribution, calculated by STAAD-PRO, SAP 2000 and the present study show that FE code using the present MOPT element is comparable in predicting stress distribution in the shear wall, but the MOPT element display more precise stress at the connecting beams. Moreover, the stress distribution evaluated by the developed FE code based on MOPT element formulation with coarse FE mesh, agrees well with the stress distributions given by the commercial packages where fine mesh was used. This comparison further proves the computational efficiency of the proposed formulation of the MOPT element.The validation of the 3DASW finite element has been made by analyzing a series of reinforced concrete (RC) structures studied by earlier researchers experimentally or analytically. The response of the RC structures in terms load–deflection curve, cracking pattern and prediction of ultimate load have been compared. It was found that the results predicted by 3DASW compared reasonably well with those reported in the literature. An extensive study has been carried out with respect to two dimensional analysis of shear wall-foundation-soil system subjected to vertical and lateral loading. It was observed that the displacement predicted by both linear and nonlinear interactive analyses showed remarkable differences in the values of displacement and stress distribution in the shear wall. This can be attributed to stress dependant nature of the tangent modulus. The computed displacement and stresses in nonlinear interactive analysis are further increased when compared to the linear interactive analyses. The effect of the shear wall building –foundation –soil interaction cannot be overlooked. The application of the 3DASW has been further enhanced by carrying out the inelastic analysis of the shear wall building. It was observed that; (i) Cracking patterns were initiated at the tension side at base of the wall and then spread across width and height of the wall. (ii) The cracking of concrete has significant influence on redistribution of normal stress σy. That is narrowing the zone of compression stress and transfer higher stress to un-cracked zone and reinforcement bars. (iii) Predefined target displacement is very helpful in proper prediction of load deflection curves.