Paper Title
Optimum Design of Steel Domes Subjected to Wind Load

Abstract
This study deals with the problem of optimum design of steel domes. The optimization problem is formulated to take the weight of the dome as the objective function and solved using genetic algorithm. The actual design variables are the joint coordinates and members size. Dealing with joint coordinates as a design variable make hundreds of design variables in the problem and dealing with such number of variables is extremely tedious. An automated procedure to generate the joint coordinate is followed in this study to overcome this problem. This procedure reduces the number of variables to five only which are the number of meridians in the dome, the total number of rings in the dome, the factor (B) that controls the distance between successive rings, the vertical spacing between the first and second ring and member sizes. The first four variables are treated as continuous design variables, but for member sizes this is followed by the selection of nearest available discrete values which provided from standard lists of AISC section tables. The side constraints for this problem were considered as the lower and upper bounds of number of meridians, number of rings, the factor B and the vertical spacing between the first and second rings. The behavior constraints are the restrictions on the maximum stress, displacements and buckling. The classical matrix stiffness method is used for the analysis of the dome. The design of steel dome members is done according to LRFD-AISC provisions. A program was coded in MATLAB programing language for generating the geometry of dome, calculation of external loads (dead, and wind loads) and analysis and design of the dome members. The procedure for solving this problem consists of two main levels; level 1 investigating the optimum dome geometry using genetic algorithm, while level 2 generating the geometry of dome, calculation of external loads analysis and fully stressed design of the dome members and calculating the weight of the dome using the developed program. The results showed that the optimum sections were not fully stressed and the displacement constraint controlled the problem. It is also concluded that the height of the domes increased with the increasing in dome diameter in an approximate linear manner with an optimum height to span ratio ranging from 0.48 to 0.49. The results also showed that the number of meridians and rings were increased with the increasing in dome diameter. For the case of fixed supports and varied spacing between rings the increasing in dome diameter (from 10 m to 20 m) it is found that the weight of the dome increased with a maximum percentage of 89.7%, the vertical spacing between the first and second ring is decreased with a maximum percentage of 42.5%, the factor B increased with a maximum percentage of 33.7%, and this case gave lighter domes with a maximum reduction percentage of 11.89% in compared with the case of hinge supports and a maximum reduction percentage of 23.46% in compared with the case of domes with fix supports and constant spacing between rings. For the case of hinge supports and varied spacing between rings, the increasing in dome diameter (from 10 m to 20 m) it is found that the weight of the domes increased with a maximum percentage of 89.9%,the vertical spacing between the first and second ring is decreased with a maximum percentage of 44.7%,the factor B with a maximum percentage of 32.3%. For the case of with fix support and constant spacing between rings, the weight of the domes increased with a maximum percentage of 88.3%,the vertical spacing between the first and second ring is decreased with a maximum percentage of 52.2%. Keywords - Optimum Design, Domes, Steel Design