Approximate optimal design of fire-resisting beams and columns

Abstract

It is well known that a steel flexural beam or a compressed column designed for ordinary load conditions is rarely optimal in relation to the fire design condition. Moreover, if the addition of a protection layer is the only viable possibility in order to obtain the required fire resistance, the total cost will be probably higher than the cost of a thicker section which verifies both ordinary and fire situations. For these reasons, the beam and column shape selection problem is posed in this paper as a multicriteria optimisation task. By using an approximate solution for the stress and temperature field on a wide flange profile, and by inverting the usual stress evaluation formulas for ordinary loads, the optimal combination of geometric parameters of the steel section are obtained. If the maximum design stress is set as a fraction of the steel yielding stress, the application of the proposed method gives rise to a list of different solutions for increasing slenderness and weight; all the optimal shapes satisfy the ultimate limit state conditions for both ordinary and fire situations, and reduce considerably the design effort expended in the selection phase of an optimal shape inside the stock list. The proposed examples illustrate the effectiveness of the optimisation procedure.