Obtaining interaction diagram of concrete section exposed to fire by mathematical optimization

This paper proposes a novel method for obtaining the axial load-moment (P-M) interaction diagrams of reinforced concrete sections exposed to fire. The problem of obtaining the strength of a reinforced concrete section subjected to an eccentric load was converted into determining an optimum solution of a constrained nonlinear optimization problem. The proposed method does not limit the strains of both concrete and reinforcing bars. A sequential quadratic programming algorithm was used to solve the constrained nonlinear optimization. Discontinuity in the arctangent function was avoided by rotating the atan2 function. A bending moment offset from the tilted axis was introduced to solve the asymmetric section and uneven heating condition. The results of the examples confirm that the proposed method can produce the entire P-M interaction surface of an arbitrarily shaped reinforced composite section exposed to fire. The proposed method is much faster and more versatile than the incremental-iterative procedure. The proposed method can calculate equally spaced points on the Mx-My interaction curve which the incremental-iterative procedure cannot obtain. The proposed method can be applied to any combination of cross-sectional shape, material, and temperature history.