ABSTRACT
Single-storey frame structures are extensively used in commercial, industrial, and leisure buildings. The nature of those buildings necessitates selecting a structural system which covers the area without intermediate columns. As steel provides an economical solution in those buildings, they are commonly constructed with steel frames (Saka 2003). Pitched roof steel portal frames are themost popular steelwork among the structures used in single-storey buildings. It is estimated that 50% of single-storey buildings are constructed with steel portal frames (Salter et al. 2004). Since the bending moment at the column-to-rafter joint is very high, the decision is made to haunch a part of the rafter adjacent to the joint. The haunch makes this part of the rafter linear non-prismatic. Because of non-uniform distribution of the bending moment in the non-prismatic member, material savings can be achieved, while the cross-section capacity is satisfied. Despite the additional cost of fabrication, the use of a tapered member in structural elements provides a more economical structure than the uniform member (Fraser 1983). When the direct stiffness method is adopted to fulfill the structure analysis, the stiffness matrix for each element of the structure should be necessarily constituted. The stiffness matrix for prismatic element is well documented in the text books. However, different developed stiffness matrices for non-prismatic members are not somehow practical to use. Saka (2003) implemented the stiffness matrix of non-prismatic member developed by Matheson et al. (1959; cited in Saka 2003) to carry out the optimization process on steel portal frames. Luo et al. (2007)
adopted the transfer matrix method to a deduced general expression for the components of the stiffness matrix of non-prismatic members. Both developed stiffnessmatrices require long computation time as the matrices components are in integration form. Hence, in this study, it is attempted to develop a practical and generalized stiffness matrix for both prismatic and non-prismatic members so that it could be brought into office daily use. A typical pitched roof steel portal frame with a haunched-rafter is depicted in Figure 1.
