Keywords: structural optimization, genetic algorithm, pitch-roof steel frame, haunched members.

Single storey frame buildings are extensively used for industrial, commercial and leisure buildings. The requirement in such buildings is to select structural system, which cover large areas without intermediate columns. Majority of these buildings is constructed in steel because it provides economical solution. Among the available steel structural systems, four commonly used forms are listed in the following.

1. Pitched roof portal frames with pinned-base stanchions
2. Pitched roof lattice girders with fixed-base stanchions
3. Pitched roof trusses with fixed-base stanchions
4. Space trusses with fixed-base stanchions

It is needless to note that pitched-roof portal frame with pinned-base stanchions is more economical compare to others. The cost of the concrete foundations for fixed bases offsets the saving in material costs that result from designing for fixed supports. Generally, the pinned-base portal frames provide economic solutions in practice unless fixed bases become necessary due to serviceability requirements. Further economy can also be attained in such frames if haunches are provided to the rafters at eaves to withstand the large moments develop at these regions.

Steel portal frame appears to be the simplest structural form used in single storey buildings. However, its design necessitates consideration of many different structural criteria that are required in the design of complex structures. Plastic or elastic theory can be used in the design of these frames. Since the mid 1950s portal frame construction has been widely based on the principles of plastic design. By taking advantage of the ductility of steel, plastic design produces lighter and more slender structural proportions than similar rigid frames designed by elastic theory. It is also common practice for reaching the most cost-effective form for these frames with relatively large spans (15 to 20 meters) is to provide haunches for the rafter members in the eaves. This allows a lighter section to be used for the rafter than the column.

In this study, genetic algorithm based optimum design method is developed for pitched roof portal frames with haunched rafters subjected to multiple loading cases such as dead, imposed and wind and with appropriate combinations of these loads. The algorithm developed obtains the frame with minimum weight by selecting appropriate sections for rafters and stanchions from the standard universal beams sections of British steel sections tables and specifies the optimum length and the depth of the haunch required for the frame. It is assumed that the haunch will be made from the same universal beam section, which is adopted for the rafters. The entire set of universal beam sections table which cover the sections from 914x419x388 to 254x102x28 is used for the genetic algorithm to select from. Two sets are prepared for the depth and the length of haunches. The set used for selecting the depth values varies from 10cm to 74cm with the increment of 2cm. The other set which contains the values for the length that varies from 50cm to 500cm with the increment of 25cm. The serviceability design constraints include limitations of span/360 for vertical displacements and overall height/300 for lateral displacements as imposed by BS5950. Combined strength constraints cover the local capacity and overall buckling checks for rafters and stanchions, which are subjected to axial and bending moment. Furthermore, the lateral torsional buckling of stanchions and rafters between the effective torsional restraints provided to both flanges is also considered within the design constraints according to BS5950.

It is apparent that response of each candidate frame under the loading considered is required to measure the suitability of the universal sections selected. This makes it necessary to carry out the analysis of frame that has members at eaves region with varying cross section. For this purpose, stiffness matrix of non-uniform member is obtained using numerical integration together with uniform members. Initially, the design algorithm is based on the elastic theory and a pitched-roof portal frame designed by using the algorithm developed. Further investigation can be carried out to determine the effect of purlin spacing and spacing between the frames to the final designs.

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