Second-order P-Δ-δ analysis and design of angle trusses allowing for imperfections and semi-rigid connections

Single angle members have a broad range of applications, such as web members in roof trusses and bracing members in latticed towers. The structural behaviour of a single angle compression member in a truss is complicated. It is not uncommon to connect one angle member to another through their legs. Therefore, in practice, the member is under an eccentric force which introduces a pair of end moments. However, in most design codes such as BS5950 (2000) and Eurocode 3 (2003), these end moments are often ignored. To compensate for this load eccentricity, the Robertson constant in the Perry-Robertson formula is amplified so that the compressive strength is reduced for the negligence of end eccentricities. In this method of analysis, all connections are assumed to be pin-jointed; while in the design, the effective length is assumed on the basis of connection types (e.g. single-bolted, double-bolted or welding) which violates the assumption in the analysis. This paper proposes a design method for angle trusses using nonlinear analysis which eliminates the inconsistency between the analysis and the design. Laboratory tests of angles as web members of a truss were carried out. The test results are compared with the proposed theoretical and code design loads. In the proposed design method, there is no need to consider any effective length. The second-order P-Δ and P-δ effects are considered automatically by geometry update. The proposed method is readily applicable to design of practical steel trusses made of angle sections.