Keywords: interaction diagrams, rapid design, composite cross-sections, ultimate strength analysis, arc-length method, fully yield surfaces, biaxial bending.

The main objective of this paper is to present a new formulation by which the biaxial interaction diagrams and moment capacity contours of a composite steel-concrete cross-section can be determined, which make use of an incremental-iterative procedure based on arc-length constraint equations. Furthermore, a new procedure based on a Newton iterative method is proposed to design the required reinforcement for sections subjected to axial force and biaxial bending moments.

The proposed method adopts a tangent stiffness strategy for the solution of the non-linear equilibrium equations thus resulting in a high rate of convergence. Considering the solution of non-linear equilibrium equations, involved in the evaluation of the interaction diagrams, the proposed incremental-iterative method is advantageous with respect to the existing ones [1,2,3]. The advantage is that the solution is obtained by solving just two coupled nonlinear equations and the convergence stability is not sensitive to the initial or starting values of the basic variables, involved in the iterative process, or to how the origin of the reference loading axes is chosen or to the strain softening effect for concrete in compression.

The method proposed in the paper, for design of cross-sections, consists of computing the required reinforcement area supposing that all structural parameters are specified and, under given external loads, the cross section reaches its failure either in tension or compression. The problem is formulated by means of three equilibrium equations for the section. The condition of ultimate limit state is enforced by a compatibility equation imposing the maximum strain on the section to be equal to the limit strain of the corresponding material. These nonlinear equations are manipulated so that one of them is uncoupled and the Newton iterative strategy is applied only to the remaining coupled equilibrium equations. The proposed approach is advantageous with respect to the existing ones [1,3], in that the solution is obtained by solving just three coupled nonlinear equations and the convergence stability is not sensitive to the initial or starting values of the basic variables involved in the iterative process. This method, as compared to other iterative methods used in the solution of nonlinear equations for the design of cross-sections, is very stable, converging rapidly if the initial value of the required reinforcement area is properly selected.

1

C. Dundar, B. Sahin, "Arbitrarily shaped reinforced concrete members subject to biaxial bending and axial load", Computers and Structures, 49, 643-662, 1993. doi:10.1016/0045-7949(93)90069-P

2

J.A. Rodrigues, J.D. Aristizabal-Ochoa, "Biaxial interaction diagrams for short RC columns of any cross section", Journal of Structural Engineering, ASCE, 125, 672-683, 1999. doi:10.1061/(ASCE)0733-9445(1999)125:6(672)

3

S.F. Chen, J.G. Teng, S.L. Chan, "Design of biaxially loaded short composite columns of arbitrary section", Journal of Structural Engineering, ASCE, 127, 678-685, 2001. doi:10.1061/(ASCE)0733-9445(2001)127:6(678)

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