Optimization of timber trusses considering joint flexibility

This paper presents the optimization of metal-plate-connected plane timber trusses with special emphasis on joint flexibility. The optimization is performed by the non-linear programming approach. Since various truss design parameters such as type of truss configuration, span/depth ratio, number and type of diagonal and vertical members and type of joint connections simultaneously affect each other, all of these parameters are proposed to be considered simultaneously in a single mathematical model. The optimization model for cost optimization of timber trusses was thus developed. The economic objective function was defined to minimize the structure’s self-manufacturing costs, subjected to the design, stress and deflection (in)equality constraints. The finite element equations were as the equality constraints defined for the calculation of the internal forces and the deflections of the structure. The stiffness matrix of the structure was composed by considering the fictiously decreased cross-section areas of all the flexible connected elements. Constraints for the dimensioning of the timber members were determined in accordance with Eurocode 5 in order to satisfy the requirements of both the ultimate and the serviceability limit states. The cross-section dimensions and the number of fasteners were defined as independent optimization variables. A numerical example demonstrates the applicability of the presented approach.