Local buckling and slenderness limits for steel webs under combined bending, compression and shear at elevated temperatures

At elevated temperatures induced by fire loading, the I-section beam and column elements in a steel framed building experience combinations of axial, bending and shearing actions that may precipitate local buckling of the steel element. Under this loading regime, the Young's modulus, shear modulus and uniaxial yield strength may vary through the section depth because of the temperature gradient, and as a result predicting the local buckling capacity and the critical geometrical slenderness for coincident elastic local buckling and yielding are not straightforward. This paper presents an analysis of the elastic local buckling of the web of an I-section beam, by modifying a spline finite strip method of local buckling analysis to include the variation of material properties through the web. Necessarily, the method must also include the variation of mechanical strains through the web depth, in order that the limiting depth to thickness ratio that delineates yielding and elastic buckling (and hence the cross-section classification) can be prescribed. Under the combined loading, it is shown how the elastic local buckling coefficient and the web slenderness limit that classifies a non-compact section are dependent on the thermal gradient, the depth of the compression zone in the representation of the mechanical strain, and on the values of the shear strain. Graphical results are presented for the elastic local buckling coefficients as a function of the temperature and of the temperature gradient in a web with idealised edge restraint conditions. Since the local buckling response is crucial in establishing the formation hinges in flexural elements in the initial stages of thermal loading prior to the subsequent development of catenary action, the results are valuable for undertaking a rational fire engineering design of the steel elements exposed to a compartment fire, and they lend themselves to a codified approach for the structural behaviour.