Optimization of shear wall allocation in 3D frames by branch-and-bound method

摘要

It is required that distribution of shear resistant elements such as walls or braces is appropriately accomplished in order to decrease torsional moment about a vertical axis due to lateral forces such as seismic or wind loads, which lead to local large displacements. An allocation design of shear walls in a multi-storied 3D building system, which is reduced to a design problem of appropriate selections of walls from a large number of discrete candidates, is a combinatorial optimality problem. Such a structural design is subjected to not only structural but also architectural and constructional constraints. In addition, when the scale of the design problem becomes larger, an effective scenario of computer support is indispensable to obtain rational design solutions. The present study deals with a combinatorial searching problem stemmed from the optimal allocation of shear walls in 3D multi-story frames subject to torsional moment about a vertical axis by application of the branch-and-bound method. The present problem is formulated as two problems; the searching problem for feasible wall allocations at each story and the minimization of the total amount of wall along the story. It is illustrated with some practical design examples that optimal solutions can efficiently be obtained by the present optimization method.