MATHEMATICAL MODEL FOR ESTIMATION OF SELF WEIGHT OF FLEXURAL STEEL MEMBERS

The first step in the design of plate girder is to estimate the self-weight of it. Although empirical formulae for the same are available, the level of their accuracy (underestimate or overestimate) with respect to actual self-weight is not known. In this paper, optimized sections are obtained for different spans subjected to different live load carrying capacities and self-weights are estimated. EXCEL solver, which adopts Reduced Gradient Method (RGM) was applied for optimization. The objective function was chosen as Cross-sectional area with twelve constraints based on LRFD (IS ۸۰۰: ۲۰۰۷) design specification for safety and serviceability. Simply supported (laterally restrained) plastic symmetric cross section without stiffeners is adopted for study. A mathematical model was developed based on best-fit curves between self-weight, span and live load carrying capacity and their trend line equations are obtained. The study revealed that, the ratio of self-weight to load carrying capacity was parabolic for a given span. The results from this equation are compared with the conventional formula and the standard deviation of the proposed model with respect to actual self-weight is in the range of -۰.۰۳ to ۲.۲۹ while that from the conventional model is in the range of -۰.۰۴ to ۹.۱۸.

Keywords:

symmetrical , plate girder , optimization , simply supported , excel solver , self-weight , load carrying capacity , constraints , plastic section , laterally restrained.