Minimum Carbon Trusses: Constructible Multi-Component Designs with Mixed-Integer Linear Programming

Truss optimization is a rich research field receiving renewed interest in limiting the carbon emissions of construction. However, a persistent challenge has been to construct highly optimized and often complex designs. This contribution formulates and solves new mixed-integer linear programs that enable consideration of the interplay between environmental impact and constructability. Specifically, the design engineer is enabled to design with multiple materials and/or structural components, apply separate minimum and maximum cross-sectional area bounds, and constrain the complexity of the structural connections. This is done while explicitly considering compatibility and constitutive laws. The results demonstrate that the lowest embodied carbon designs change significantly when constructability constraints are applied, highlighting the need for an integrated optimization approach. In one example, introducing a lower-carbon material option has almost no effect on the environmental performance, whereas another sees an improvement of nearly 29%. The extensibility of the formulation to design with three component types and additional constraints is demonstrated for a prestressed tensegrity example.