Heat Transfer on a Disk: A Closed-Form Solution for Suspension Bridge’s Main Cables Exposed to Fire

Abstract

The heat transfer problem is often considered to be the kernel of a fire resistance analysis. In fact, one- or two-dimensional closed-form solutions have long laid the foundation for an engineer’s understanding of the temperature distribution within a structural element exposed to fire. Although many closed-form solutions of the thermal problems for structural members in buildings exist, the literature is surprisingly thin for bridge structures—and even more so for suspension bridge structures. This paper addresses that sparsity by presenting a generalized approach for the formulation and solution of the heat transfer problem for a suspension bridge main cable exposed—either partially or completely—to fire. The approach first normalizes and then nondimensionalizes the problem. It then divides the resulting generalized time-dependent heat equation with spatially dependent boundary conditions into a steady-state and transient problem and subsequently solves each piece with a classic separation of variables technique. The functionality of the solution is assessed by performing both an error analysis and a computational time comparison with numerical results for three verification problems.