Optimization of selected 2-Dimensional steel truss shapes using a new mathematical formulation

ABSTRACT: The purpose of this study is to carry out an investigation on the existing truss systems in order to introduce a mathematical formulation relating to the geometrical shape of the truss so that the mid-span deflection of the truss can be optimized. Every time there is a need to use a truss structure it is difficult to decide which truss type, bay width and height would produce the optimum truss shape with minimum mid-span deflections and its corresponding minimum bottom chord stress for a specific span length. The results of this study is expected to produce a set of guidelines to help researchers, designers and practicing engineers to determine the most appropriate and efficient truss system for their specific usages. In order to achieve this aim, a total of two sets of two-dimensional trusses with eleven different shapes of common symmetry, made of steel with pinned and roller supports were studied to identify which truss shapes and sizes are efficient for the purpose of this study. The design loads are applied to the joints so that there is no moment to be resisted by the members. Initially, the virtual work method was applied on selected truss shapes in order to obtain the amount of deflection at mid-span of the trusses. Afterwards, hand calculation was carried out followed by computer analysis using MAPLE 12 and then the use of TABLE CURVE 2D v5.01 for mathematical approach to derive the deflection formula. Finally, STAAD Pro was used to analyze and design the truss structures. The analysis of all sets of trusses enabled the comparison among the various spans, height and bay width of trusses. Thus, the changes in mathematical deflection formula, due to the number of bays and shapes of trusses were lead to obtain the specific optimum height and minimum deflection for each truss system. In other words, the occurrence of minimum deflection along the truss span and optimum height presents the optimum truss. Besides the above mentioned outcomes a significant advantage was achieved due to mathematical formulation. The formula derived demonstrates an easy, fast and accurate way of calculating the deflection value at mid-span of trusses. Currently, virtual work method is the most efficient and accurate way of determining the deflection. Although this method is the most common one it is dependent on long and complicated procedure. The formula derived in this study has introduced a new approach to determine the mid-span deflection of trusses in an extremely short and easy way. …………………………………………………………………………………………………………………………