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

摘要

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.