A Computer Method for Moment-Curvature Analysis of Composite Steel-Concrete Cross-Sections of Arbitrary Shape

Abstract

This paper presents a new computer method for moment-curvature analysis of arbitrary-shaped composite steel-concrete cross-sections that are subjected to biaxial bending and axial force. The complete moment-curvature diagrams are determined such that axial force and bending moment ratio is kept constant. A strain-driven algorithm has been developed, the solution of the nonlinear equilibrium equations is controlled by the assumed strain values in the most compressed point and by solving just two coupled nonlinear equations. Such an approach may be used to assess accurately the main features of the elasto-plastic behaviour of composite cross-sections: multiple yielding points associated to different materials, flexural and axial rigidity, moment-curvature relationship in pre and post-critical domain and curvature ductility detecting also unloaded regions of the cross-sections that may occur even under monotonically increasing of the total bending moment. Since the Jacobian’s of the resulted nonlinear system of equations is always positive definite the convergence stability is not sensitive to the initial/starting values of the iterative process and to the strain softening exhibited by the concrete in compression. By using a path integral technique on boundary of cross-section area, gradual spread of plasticity and residual stress distribution assumed for encased steel elements are accurately considered reducing also the computational time significantly. In order to illustrate the proposed method and its accuracy and efficiency, a computer program has been developed and used to study several representative examples. The numerical studies presented and comparisons made prove the effectiveness and time saving of the proposed method of analysis.

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

“…where kij represents the tangent stiffness coefficients of the crosssection [10]. Solving the above incremental system of equations imposing the condition of ΔN=0, since the axial force is kept constant (N=const), as the bending moments increase the incremental values for curvatures (z and y) may be expressed as: ) or in condensed form: (13) where explicitly the tangent stiffness coefficients of the cross-section are expressed considering the tangent Young modulus for each fibre, concrete and structural steel, as function of the fibre strains and the assumed nonlinear stress-strain constitutive equations at a specified temperature T [13].…”

“…Step 4 an adaptive-descent algorithm is applied [10]. In this way, by continuously varying the strain in most compressed point according with the adopted bracketing approach (bisection method used in this paper) the nonlinear system of equations (20) may be solved and global convergence is achieved.…”

“…The reinforcement bars contribution is added to Eqs. (10) above and its temperature is assumed to be equal to the temperature in the corresponding position of the concrete mesh. The incremental relation of the above nonlinear equilibrium equations relates small changes in the deformations to small changes in the actions sustained.…”

“…In the thermal analysis reinforcement is neglected, with the temperatures of the bars considered equal with the surrounding concrete temperature and also it is assumed continuity in terms of temperature at the interface between structural steel and concrete matrix. Residual stresses for encased steel profile may be incorporated in the analysis as described in [10]. The standard fire curve is used in this paper to obtain the gases temperature:…”

“…Thus, before to start the proposed approach the cross-section is analysed considering the section subjected to axial force N0 and small values for the bending moments about each principal axes (Mz0, My0) with a given bending moment ratio (tg=My/Mz). Since at this stage of analysis, only approximate values are needed both for the curvatures and the reference strain, the nonlinear equilibrium equations (10), associated to axial force and bending moments, are solved by applying the simple incremental approach as described in Eq. (12).…”