Shape optimisation of singly-symmetric cold-formed steel purlins

Abstract

This paper presents the results of a study aiming at shape optimising singly-symmetric cold-formed steel purlins. The “self-shape” optimisation algorithm previously developed, proven to be robust and to converge to known solutions is used for this purpose. Eight optimisation cases are considered, consisting of 1.5 mm and 1.9 mm thick purlins, spanning either 3000 mm or 8000 mm and drawn with either 4, 6 or 8 elements per half cross-section. The aim of the algorithm is to minimise the cross-sectional area subjected to the following constraints: (i) the sections must at least match the second moment of area, and the inward and outward bending capacities of commercial purlins used as reference profiles, (ii) be readily manufacturable using existing roll-forming process, (iii) can be connected similarly to existing purlins by offering vertical and horizontal flat elements long enough and strategically positioned to bolt the purlins to gusset plates and screw the roof to them, respectively, and (iv) have an opening wide enough to run services. The restraints provided by the roof sheeting is considered in the algorithm when calculating the bending capacities. Results show that the algorithm converges to consistent solutions and satisfactory satisfies all constraints, resulting in manufacturable and useable purlins. When compared to the reference purlins, the optimised solutions result in saving up to 6.6% of steel. This cost saving in material is quite significant for a mass-produced product such as purlins. The efficiency of the optimised purlins relative to the reference sections were further validated with FE analysis. The FE analyses confirm that the optimised 1.5 mm thick purlins are superior to the reference section. The optimised purlins may therefore benefit the cold-formed steel industry as they represent more economical solutions without compromising on the usability and performance of the products. However, the FE model shows that the 1.9 mm thick purlins may not have the expected performance and experimental testing is fully validate the optimised sections.