Application of Simulated Annealing Algorithm for Finding Optimal Shape and Optimal Span-to-Depth Ratio for Steel Roof Trusses Design by using SSTAAD Program

Abstract

This paper presents an application of SSTAAD program by using a proposed simulated annealing algorithm for finding optimal truss shape and optimal span-to-depth ratio of roof steel trusses. The objective function was the lowest weight per unit length of roof steel trusses. The structure items taken into account were grouped as: i) upper and lower chords, ii) diagonal web, iii) vertical web, and iv) support web, and nine design variables were formulated. The finite element method was employed to calculate nodal displacement and internal force of all the structure members. The numerical algorithm then searched for optimal design parameters with thirteen non-linear design constraints based on the Allowable Stress Design (ASD) method, following the American Institute of Steel Construction (AISC) standard. One hundred
and ninety roof truss samples were tested with the span-to-depth ratios ranged from 10 to 40, span space ranged from 10 to 40 metres, and roof slopes ranged from 5 to 40 degrees. The results showed that the top three best roof truss shapes were scissor, girder, and trapezoid shape, with the sample percentage of 67.9, 13.2 and 11.6, respectively. The best diagonal type was pratt, followed with warren and howe, with the sample percentage of 74.2, 24.2, and 1.6, respectively. The optimal span-to-depth ratios returning lightest roof structures ranged from 17 to 25.