A smooth shear strength function for steel flexural members

The strength of web plates in shear may be governed by one of three types of behavior: yielding, inelastic buckling, or elastic buckling. A separate function is needed to define the strength for each of these failure modes. Consequently, the shear strength of flexural members is defined by a piecewise continuous function that varies with the ratio of web height to thickness. The shear strength function is continuous, but its first derivative is not. Optimization of steel members with such nonsmooth constraint functions is limited because most algorithms assume the objective and constraint functions are smooth. In order to improve this situation, an alternative function is sought for the inelastic (transition) region such that the first derivative is continuous or nearly so. ical and finite element models as well as experimental data are used to predict the inelastic buckling behavior. This data is used to fit a polynomial of p -th order ( p > 1 ) for use in design. The value of p which results in a smooth curve may not agree well with the finite element results, so depending on how much nonsmoothness can be tolerated, a nearly smooth but conservative curve may be most suitable for optimization applications. Such a curve is appropriate for design using optimization methods since it models the inelastic buckling behavior of webs in shear and does not violate the assumptions of derivative-based optimization methods.