Optimizing Structures with Semi‑Rigid Connections Using the Principle of Virtual Work

Abstract

In this paper, the virtual work optimization method (VWOM) has been generalised to consider structures with semi-rigid connections. The VWOM is an automated method that minimizes the mass of a structure with a given geometry, multiple deflection criteria, and load cases while adhering to design code requirements. In the optimization process, members are selected from a discrete database to meet all strength and stiffness criteria. Connections are modelled using rotational springs, allowing some moment transfer. The rotational stiffness of each connection can be varied from rigid to pinned. The example of a pitched roof frame is used to explain the method. Two case studies are considered: (i) (i) a three-storey two-bay and (ii) a four-storey three-bay office building. The VWOM produced results up to 26.7% lighter than results in the literature. Furthermore, the structures were optimized for a range of rotational stifness, where all connections in the structure were assumed to have the same rotational stiffness. Characteristic jumps in the optimized mass versus rotational stiffness were observed.