Simple empirical equations to predict temperature rise and deformation history in structural members under standard fires

Current methods, such as those adopted in building codes or requiring finite element (FE) analysis, are either overly conservative or computationally expensive with regard to tracing the thermal and mechanical responses of fire-exposed structural members. To bridge this knowledge gap, this paper presents a machine learning approach via symbolic regression to derive simple, uncoupled, and empirically-based expressions that can be used to predict the complete thermal and deformational history of structural members under fire conditions. The proposed approach and accompanying expressions are examined on four datasets that were collected from real fire tests covering concrete-filled steel tubes, reinforced concrete (RC) columns and beams, and timber floor assemblies. Then, two sets of expressions, accuracy-focused and dimensionless parameter-focused, using the Buckingham Pi Theorem, were derived and examined. Overall, the derived expressions are seen to agree well with the observations seen in standard fire tests. Finally, this study concludes by identifying future research needs, such as incorporating more nuanced physical constraints, to improve the accuracy and applicability of these predictive models for structural fire engineering.