A Global Convergent Method for Strength Capacity Evaluation of Composite Sections Subjected to Fire

Abstract

The paper presents a new advanced computational method for ultimate and nominal strength analysis of composite steel‐concrete cross‐sections with arbitrary shape subjected to elevated temperatures. The capacity diagrams are evaluated for a given bending‐moments ratio, generating plane and smooth distribution points on interaction diagrams. The ultimate (maximum) strength capacity is formulated as a problem of constrained mathematical optimization of the total bending moment, whereas the proposed approach evaluates the nominal strength capacity by means of enforcing the nonlinear equilibrium equations in conjunction with a total strain field tangent at the ultimate strain surface. Both methods are unified within the same strain‐driven algorithm used to solve the resulted nonlinear coupled equations. This algorithm coupled with a bracketing approach by means of combining Bisection and Newton method represents the main computational framework to ensure global convergence of the developed methods. An adaptive effective plastic centroid has been introduced ensuring that the origin of the reference axes is within the iso‐load contour circumventing in this way any potential convergence issues. The computational examples prove the effectiveness and the reliability of the proposed method.