Optimum Frame Design with Reused Stock Elements

This paper presents optimization methods for the synthesis of frame structures from a stock of reused elements. Reusing structural elements over multiple service lives has the potential to reduce the environmental impacts of building structures. This is because reuse avoids sourcing new material, reduces waste and requires little energy. Reusing elements implies that their cross-sections and lengths determine the design of a structure. Structural optimization methods, previously developed by the authors, can be applied to synthesize structures from reused elements [1]. By employing a mixed-integer linear programming (MILP) scheme, a globally optimal usage of the available stock elements can be obtained. These previous developments are limited to trusses with pin-jointed members subject to normal forces only. On the other hand, state-of-the-art discrete optimization methods for frames with beam elements subject to normal and shear forces as well as bending moments are provided in [2] and are equivalently based on MILP. This paper combines the methods of [1] and [2], in order to expand the range of structural typologies that can be designed from an element stock. Fundamental to this method is the optimal assignment of available elements to positions in the structure. The optimization approach is applied to two possible reuse scenarios: (A) the use of an individual stock element for each beam position, and (B) a bin-packing approach, where multiple beams can be cut from single stock elements. Taking into account stress and displacement constraints along beams with distributed loads, makes the method applicable to typical limit states [2]. Case studies highlight the applicability of the proposed method to realistic scenarios. Hereby the minimum-weight solutions of different frame structures provided in [2] are used as benchmarks. Optimizing the equivalent systems subject to different stock compositions (cross-sections and lengths) illustrates the influence of the stock on the weight and capacity utilization of a structure. It is concluded that reusing structural elements may result in oversized structures if not enough suitable stock elements are available. However, comparing the environmental impacts of the benchmark structures made of new material against those of the corresponding reuse cases shows that the latter have a significantly lower environmental impact.