Nonlinear elastic analysis of steel planar frames under fire loads

•The nonlinear elastic problem for a planar frame subjected to thermal loadings is resolved here.•The elastic law accounts for thermal deformations and for temperature-dependence of the elastic modulus.•The elastic problem is formulated in a mixed equilibrium-compatibility form.•After integration of the field equation an ‘exact’ finite element is derived.•The nonlinear algebraic problem is solved numerically by the Newton–Raphson procedure.

The nonlinear elastic problem for planar frames, made of rectilinear beams subjected to thermal loadings, is resolved here. The basic element is an Euler–Bernoulli beam, whose elongation is a nonlinear function of the displacements. The elastic law accounts for thermal deformations and for temperature-dependence of the elastic modulus. The elastic problem is formulated in a mixed equilibrium-compatibility form and an ‘exact’ finite element is derived. Assembling the element relations, the governing equations for the frame are recast in a discrete form. The nonlinear algebraic problem is solved numerically and results are compared with those provided by a FE software.