Numerical analysis of heat-curved I-girders

•The paper presents a simplified computational method for heat curving steel.•Equations for non-linear stress distribution are cast in a parametric form and solved numerically using Wolfram Mathematica V.9.0 computer algebra package.•Solutions are presented as polynomials and graphical plots to directly calculate the curvature.•Legitimacy is confirmed based on comparisons with available experimental and theoretical values.

Heat curving is a practical and economical process used by steel fabricators for curving structural steel. In this method, the flange edges of a fabricated straight girder are asymmetrically heated to induce residual curvature on cooling. Available analytical methods for predicting the resulting residual stress, strain and curvature are complex and iterative because of the need to account for material and geometric non-linearity. This paper presents a single-step, non-iterative, numerical procedure for determining the effects of heat-curving on residual stress and strain based on a previously developed simplified analysis. Thermal equilibrium equations for idealized heating profiles are first recast in a general parametric form and then solved numerically for standard heating width and temperature using modern technical computing. The resulting solutions are expressed as polynomial functions to allow the solution space for the residual curvature to be graphically represented. Curvature predictions using this simplified approach are shown to be within 11% of measured values and within 5% of values obtained using more rigorous numerical methods.

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