Direct differentiation method for response sensitivity analysis of structures in fire

• Direct differentiation method applied to the analysis of structures in fire.
• Formulation accounts for coupling between fire, thermal, and structural domains.
• Validated against the converged finite difference solution.
• Application involving a protected steel beam subjected to natural fire.

Response sensitivity is an important quantity in structural reliability calculations, parameter importance studies, and design optimization. In the response sensitivity analysis of structures at ambient temperature, prior research has shown that the direct differentiation method provides improved accuracy and efficiency in comparison to the finite difference method. The direct differentiation method is extended here to the analysis of structures in fire, in which parameters exist in the fire, thermal and structural domains. Analytical expressions for the response sensitivities are derived for nonlinear heat transfer and structural finite elements, with specific consideration for the interdependencies between the physical domains. Numerical analyses were conducted for a steel beam exposed to natural fire conditions. Comparisons between the finite difference and direct differentiation methods demonstrate that the proposed formulations offer much promise for assessing response gradients of fire-exposed structures in a robust and computationally efficient manner.