Enhanced solution strategies for the ultimate strength analysis of composite steel–concrete sections subject to axial force and biaxial bending

We present a family of algorithms for evaluating the ultimate limit state of composite and reinforced concrete (RC) sections of arbitrary polygonal or circular shape, either simple or multicell, subject to axial force and biaxial bending. All algorithms are based upon a secant strategy for computing the stiffness matrix used in the equilibrium iterations while they differ in the scheme adopted to estimate the ultimate values of axial force and bending moments. In this respect they enhance in several ways two analogous algorithms presented in a previous paper [L. De Vivo, L. Rosati, Ultimate strength analysis of reinforced concrete sections subject to axial force and biaxial bending, Comput. Methods Appl. Mech. Engrg. 166 (1998) 261–287] for reinforced concrete sections. First, it is shown the specialization of some new formulas, proved elsewhere, for evaluating the entries of the secant stiffness matrix solely as function of the position vectors of the vertices of the section, assumed to be polygonal, and of the constitutive parameters of the nonlinear stress–strain laws for the materials. Second, the case of sections made of or containing either circles or segments of circular arc is exactly taken into account without the need of approximating such shapes by polygons. Third, the extensive numerical tests carried out for a wide range of RC sections and for a benchmark steel–concrete section have shown that the convergence rate and the stability of the new algorithms considerably increase with respect to the ones presented in De Vivo and Rosati (1998). As outcome of the numerical experiments, two solution strategies have been selected as the optimal ones since they combine both global convergence and a satisfactory convergence rate.