Optimisation of steel trusses with a choice of multi-stage prestressing conditions
This paper presents a methodology for optimisation of flat steel trusses with a system of high-strength tie bars, for each of which the possibility of multiple pre-stresses is provided. Pre-stress is one of the most effective ways to increase the carrying capacity of steel trusses with minimum material costs. Besides, a significant effect, according to the literature data, can be achieved by alternating stages of pre-stresses and payloads. At the same time, algorithms for designing such objects while choosing a sequence of force actions still need to be worked out. The problem of minimising the truss cost is considered taking into account strength, stiffness, and stability constraints. A search has been specified for the sequence of alternating the stages of pre-stress and the application of portions of useful loads, pre-stress forces, bar profiles, and cable cross-section area values. Multiple allowable scenarios of force impacts on a redundant template are used. It is acceptable to indicate the load absence condition in such template in some positions. A possibility has been implemented for the cable system to set a redundant topology which is controlled by including the ability to select negligible cross-section areas. As a result, the mathematical statement of the problem is reduced to discrete parametrical optimisation. A scheme of genetic algorithm is implemented with a mixed approach to the mutation operator in order to find efficient solutions. A methodology has been developed to calculate the stress-strain state of steel frameworks pre-stressed using high-strength cables in a single computational process to efficiently check for compliance with the problem constraints. The performance of the suggested procedure of the optimum search has been illustrated by the example of a steel arch truss. A possibility to use bars made of round pipes together with high-strength tie bars was provided. The efficient parameters of the framework and force impact modes have been determined. The expediency of alternating impacts caused by pre-stresses of cables and application of useful load parts is confirmed. The approach proposed will significantly increase the possibility of obtaining cost-effective design solutions for steel trusses.