Theoretically optimal bracing for pre-existing building frames

Bracing is commonly used to provide resistance to lateral forces in building structures. However, traditional bracing design approaches appear not to be underpinned by clear fundamental principles. Here, theoretically optimal arrangements of bracing members are sought for pre-existing building frames, already designed to carry gravity loads. For sake of simplicity existing frame elements are assumed to be capable of carrying additional loads and three types of bracing are considered: tension only bracing, bracing intersecting only at the corners of the existing frame, and unconstrained optimal bracing, where bracing elements can intersect at any location. Layout optimization techniques are used to identify initial design solutions; these are then related to Michell trusses to obtain exact reference volumes, against which the efficiency of other bracing layouts can be judged. It is shown that from a theoretical standpoint tension only bracing is inefficient and that the optimal angle of intersection between a pre-existing frame member and intersecting tension/compression bracing member pairs is 45^°, something that can potentially be adopted as a basic principle when designing bracing for a pre-existing frame.