OPTIMUM COST DESIGN OF A STEEL-FRAMED BUILDING

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Abstract
The paper describes an investigation into the minimum cost design of a steel portal framed building. Computer programmes have been developed which permit:1)The simple “plastic” design of this type of structure in accordance with the relevant B.S. Codes and common industrial practice. 2)The costing of any “feasible” design in accordance with a cost model devised in conjunction with several members of the steelwork fabrication industry.3)The economical determination of the “least cost” design from the hyperspace of “feasible” designs.It has been assumed that the optimum shape of a structure (i.e. the specific combination of problem variables which produces the design of least cost) is a function of material and fabrication costs only. Accordingly, for any feasible design, the cost is defined as the sum of the individual material and fabrication costs for the structural steelwork, purlins and cladding. A model has been devised in which the problem has been formulated as a constrained non-linear optimization problem. The independent variables included in the model are: number of bays, frame spacing, eaves height, roof pitch, purlin spacing, building length and overall building width. Constraints are introduced by a consideration of site limitations, floor area and/or building volume requirements. Individual member selection is treated as a sub-optimization problem using simple “plastic” design. Using appropriate combinations of the independent variables any number of “feasible” designs may be generated. The “search” through the feasible design space for the least cost structure is accomplished using the non-linear variable metric simplex method. Methods by which the initial simplex is generated and subsequent “improved” designs are found, is discussed. Results illustrating the behaviour of the significant problem variables are presented in the form of cost response surfaces.

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