Ultimate strength analysis of composite sections under biaxial bending and axial load A.E. Charalampakis, V.K. Koumousis * Institute of Structural Analysis & Aseismic Research, National Technical University of Athens, Zografou Campus, Athens GR-15773, Greece Received 4 April 2007; accepted 18 January 2008 Available online 18 March 2008 Abstract A new generic fiber model algorithm is presented that allows for the efficient analysis of arbitrary composite sections under biaxial bending and axial load. The geometry of the cross section is described by multi-nested curvilinear polygons i.e. closed polygons with edges that are straight lines or circular arcs. The polygons may be convex or concave and may contain openings. The stress–strain dia- grams of materials consist of any number and any combination of consecutive polynomials, which allows for consideration of various effects such as concrete confinement and tensile strength, strain hardening of the reinforcement etc. The integration of the stress field is performed analytically. The algorithm focuses on the construction of moment–curvature diagrams, interaction curves and failure sur- faces. It can also be used for calculating the deformed state of a cross section under given external loads. Several examples are presented to demonstrate the versatility and the advantages of the proposed algorithm in comparison to existing methods. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Biaxial bending; Fiber model; Failure surface; Composite structure 1. Introduction The analysis of arbitrary composite sections under biax- ial bending and axial load has received extensive attention in the literature, as many of the widely used types of cross sections do not fall into the regular/symmetric category. The most common examples include L-shaped columns, symmetric sections with asymmetrically placed openings, structural steel and/or reinforcement, repaired sections and various composite sections. With the advent of powerful desktop computer systems, the efficient analysis of such cross sections has been made possible using the ‘‘fiber” approach. The results of such analyses agree closely with experimental data for flexural type of failure and monotonic loading and are widely used in design. Moment–curvature diagrams and failure surfaces can also be obtained. The former can be used as back-bone curves in non-linear analyses under cyclic loading. Further- more, they can be extended to include stiffness degradation, strength deterioration and pinching effects in various phe- nomenological hysteretic models, such as the Bouc–Wen model [1]. The failure surface is widely used in damage analysis, where a damage index can be derived from the distance of the current load state to the failure surface. It is also used in ‘‘bounding surface” plasticity theory, devel- oped by Dafalias and Popov [2] for metals and later extended for soils [3] and reinforced concrete (R/C) sec- tions [4]. However, the formulation employed in this study does not address phenomena that are related to stress– crack opening displacement behavior, which is based on fracture mechanics concepts [5,6]. Although the notion of the fiber model is simple, as it requires the equilibrium of internal and external forces, the computational task becomes tedious mainly due to the geometrical irregularities and the non-linear stress–strain laws. Therefore, the algorithmic implementation becomes important and there is a need for an efficient and stable algorithm. 0965-9978/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.advengsoft.2008.01.007 * Corresponding author. E-mail address: vkoum@central.ntua.gr (V.K. Koumousis). www.elsevier.com/locate/advengsoft Available online at www.sciencedirect.com Advances in Engineering Software 39 (2008) 923–936