Theoretically optimal bracing for pre-existing building frames

Abstract

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.

Layout optimization of building frames subject to gravity and lateral load cases

“…Secondly, it is clear that as r VH increases, the optimized layouts tend to include highly inclined members to transmit the applied vertical loading more directly towards the supports. This is at variance with the finding by Lu et al (2018), who suggest that there should be a 45 • intersection angle between columns and bracing member pairs; however, this observation only applies if the columns are assumed to have infinite reserves of strength, which is not the case here.…”

“…The optimal layouts obtained using the 'holistic' strategy adopted differ from those obtained when seeking to brace a frame comprising pre-existing members (e.g. as considered by Lu et al 2018). 2.…”

“…As stated by Lu et al (2018), for the design of steel framed buildings, British Standard 5950-1:2000 suggests the following load combinations:…”

“…As a result, in many bracing optimization studies, it is first assumed that the sizes of the main columns and beams in a structural frame are determined by consideration of gravity load cases (only), and that these members will have sufficient strength to play their required roles in resisting lateral loads without needing to be resized; this scenario has been considered by various workers (e.g. Kim et al 1998;Liang et al 2000; Terán-Gilmore and Coeto 2011; Stromberg et al 2012), and was recently considered in more detail by Lu et al (2018). There are in contrast relatively few examples of what may be termed 'holistic' optimization of the structural frame, in which all load cases are considered when identifying the locations and sizes of members forming the frame of a building.…”

Topology Optimisation in Structural Steel Design for Additive Manufacturing

“…However, one of the most impressive developments can be found by Larsen et al [398], a near-optimal truss design based on the homogenisation-based continuum TO. Practical applications of truss optimisation to bracing the systems design have some interesting contemporary examples in [399][400][401][402][403].…”