An updating Arc-Length approach based on Adiabatic Surface Temperature for instability analysis of thin-walled tanks due to fire loads

Thermal buckling of thin-walled steel storage tanks exposed to adjacent pool fires results from coupled fire dynamics, heat transfer, and nonlinear structural response. This study presents an integrated CFD–FEM framework for evaluating fire-induced buckling under varying wind speeds, directions, and filling levels. The fire environment is simulated using CFD, and the resulting Adiabatic Surface Temperature (AST) is applied as a physically consistent thermal boundary condition. A novel Updating Arc-Length Method (UALM) iteratively updates the temperature field during nonlinear analysis to capture the actual thermal state at buckling and predict the associated buckling mode, critical load, and time to instability. Compared with the conventional arc-length method (CALM), which uses a fixed temperature field, discrepancies of up to 74% are observed for empty tanks, demonstrating the importance of transient thermal evolution. Wind-driven flame deflection strongly influences both thermal exposure and structural response. Peak thermal exposure is concentrated at wind speeds of approximately 8–12 m/s and directions above 75°, whereas the most critical thermo-structural response of empty tanks spans a broader region of approximately 4–11 m/s and directions above 45°. Across the investigated cases, Buckling Proximity Index ( B PI ) values range from approximately 30–85%, depending on tank geometry, and represent a deterministic normalized measure of proximity to instability. Liquid-filled tanks exhibit substantially greater stability and rarely buckle when half-filled. Additionally, imperfection effects are particularly pronounced at a wind speed of 12 m/s and a wind-incidence angle of 30°. Overall, the proposed AST-based UALM framework provides an efficient and physically consistent tool for assessing critical thermal demand, deterministic proximity to instability, and the timing of fire-induced buckling.