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The purpose of this paper is to address unsteady heat conduction in two subsets of ordinary bodies. One subset consists of a large plane wall, a long cylinder and a sphere in one dimension. The other subset consists of a short cylinder and a large rectangular bar in two dimensions. The prevalent assumptions in the two subsets are: constant initial temperature, uniform surface heat flux and thermo-physical properties invariant with temperature. The engineering applications of the unsteady heat conduction deal with the determination of temperature–time histories in the two subsets using electric resistance heating, radiative heating and fire pool heating.

To this end, a novel numerical procedure named the enhanced method of discretization in time (EMDT) transforms the linear one-dimensional unsteady, heat conduction equations with non-homogeneous boundary conditions into equivalent nonlinear “quasi–steady” heat conduction equations having the time variable embedded as a time parameter. The equivalent nonlinear “quasi–steady” heat conduction equations are solved with a finite difference method.

Based on the numerical computations, it is demonstrated that the approximate temperature–time histories in the simple subset of ordinary bodies (large plane wall, long cylinder and sphere) exhibit a perfect matching over the entire time domain 0 < t < ∞ when compared against the rigorous exact temperature–time histories expressed by classical infinite series. Furthermore, using the method of superposition of solutions in the convoluted subset (short cylinder and large rectangular crossbar), the same level of agreement in the approximate temperature–time histories in the simple subset of ordinary bodies is evident.

The performance of the proposed EMDT coupled with a finite difference method is exhaustively assessed in the solution of the unsteady, one-dimensional heat conduction equations with prescribed surface heat flux for: a subset of one-dimensional bodies (plane wall, long cylinder and spheres) and a subset of two-dimensional bodies (short cylinder and large rectangular bar).

In this study, the effects of strain rate on the bending strength of full-scale wide-flange steel beams have been examined at elevated temperatures. Both full-scale loaded heating tests under steady-state conditions and in-plane numerical analysis using a beam element have been employed.

The load–deformation relationships in 385 N/mm²-class steel beam specimens was examined using steady-state tests at two loading rate values (0.05 and 1.00 kN/s) and at two constant member temperatures (600 and 700 °C). Furthermore, the stress–strain relationships considering the strain rate effects were proposed based on tensile coupon test results under various strain rate values. The in-plane elastoplastic numerical analysis was conducted considering the strain rate effect.

The experimental test results of the full-scale steel beam specimens confirmed that the bending strength increased with increase in strain rate. In addition, the analytical results agreed relatively well with the test results, and both strain and strain rate behaviours of a heated steel member, which were difficult to evaluate from the test results, could be quantified numerically.

The novelty of this study is the quantification of the strain rate effect on the bending strength of steel beams at elevated temperatures. The results clarify that the load–deformation relationship of steel beams could be evaluated by using in-plane analysis using the tensile coupon test results. The numerical simulation method can increase the accuracy of evaluation of the actual behaviour of steel members in case of fire.