Keywords: soil structure interaction, inelastic behaviour, finite element method,.

This paper covers the analysis of 2D framed buildings along with the foundation system and soil media underneath. The finite element method integrated with stiffness matrix method was used to analyse the frame-foundation-soil system under combined vertical and lateral loading. A computer code was developed to trace the inelastic response of the frame-foundation-soil system. The developed code predicts the sequential formation of plastic hinges in the frame member and the continuous deterioration of the stiffness of the frame. The failure criteria used was based on actual nonlinear analysis of reinforced concrete section. The soil media was assumed to have nonlinear stress-strain relationship. The paper focuses on the effect of interactive analysis on the inelastic structural response of the frame and its failure mechanism. The developed code is capable of simulating the behaviour of soil-structure interaction. The results show that the interaction has significant effects on the failure mechanism of structure.

Beam elements (2D) were used to model the frame members and the combined footing. The beam was assumed to retain the elastic property and the inelastic property was assumed to be lumped at the ends of the beam in the form of a plastic hinge. The inelastic property was evaluated considering the actual behaviour of the reinforced concrete section, the stiffness deterioration of the frame members with the loading history and the behaviour of the yielded section. The actual non-linear behaviour of reinforced concrete sections was carried out from which the 2D yield surface has been evolved. The formation of 2D plastic hinges in a member is based on the interaction of actual moment-axial forces in the section [1,2]. Plain strain 4-noded elements were implemented to model the underlying soil. The stiffness of the soil was formulated using the usual finite element method. The degradation of soil stiffness with the increase of stress level was carried out using a tangent modulus of elasticity derived from hyperbolic stress-strain model.

Upon application of the load, the structure initially behaves in a linear elastic fashion. On further application of load some of reinforced concrete sections will reach their ultimate capacity. A plastic hinge is formed at a section when the force state at a section either lies outside or on the yield surface. An iterative procedure has been employed to bring back the force state on the yield surface and redistribute the excess resultant forces. The theory of plasticity has been used to calculate the unbalanced forces, the inelastic deformations and the inelastic stiffness of the members [3,4]. The stiffness matrix of the frame has been modified after each new occurrence of a plastic hinge(s) and it is assumed to remain unchanged until a new hinge(s) is formed.

In soil media, in the first load increment, elastic properties of soil were used to generate the stiffness matrix using the standard finite element procedure. On further loading, the stiffness was modified based on the stress level in the soil by calculating the tangent modulus using a hyperbolic stress-strain model.

The results indicate that the non-interactive elastic analysis underestimate the moment at different beams and columns (up to 119%) compared to the interactive elastic analysis. Extending the analysis to the inelastic range will further significantly alter the bending moment diagrams and the percentage increase or decrease in bending moments compared to the inelastic non interactive analysis. Furthermore, the inelastic interactive analysis does not only alter the sequential formation of plastic hinges in the frame but it will also alter the load factors at which these hinges occur, the number of plastic hinges and their locations compared to the non-interactive analysis.

1

W.A. Thanoon, D.K. Paul, M.S. Jaafar, D.N. Trikha (2004), "Influence of Torsion on the Inelastic Response of 3-Dimensional RC Frames", Finite Elements in Analysis and Design Journal, Vol. 40, 2004 pp 611-628. doi:10.1016/S0168-874X(03)00099-4

2

W.A. Thanoon, M.S. Jaafar, A.A.A. Samad and D.N. Trikha (2000), "Inelastic Response of RC Framed Building", Journal of Institute of Engineers Malaysia, Vol.61 No.1 2000, pp33-48.

3

D.R.J. Owen and E. Hinton, "Finite Element in Plasticity", Prineridge Press Limited, Swansea, U.K., 1980.

4

G.A. Faris Al-Bermani and S. Ktipornchai (1990), "Elasto-Plastic Large Deformation Analysis of the Thin Walled Structures", Engg. Struct., Vol. 12, PP 28-36, 1990. doi:10.1016/0141-0296(90)90035-Q

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