From least-weight to least-environmental-impacting truss structures

Abstract

Climate change is changing the world. Where previously efficient use of materials was mainly applied to realize cost savings, this can also help to reduce the footprint of a construction. There is a rather direct and obvious relationship between the amount of material required in a construction and its environmental impact. Of course, the environmental impact is not solely dependent on this metric, but minimizing the weight of the structure is a great starting point. This thesis focusses on minimizing the environmental impact of a welded truss bridge. In addition to the required volume of construction material, the environmental costs for the welding and conservation are also taken into account. A case study is performed on a bicycle bridge crossing a highway that is built in the Netherlands.

The thesis starts with a review of multiple methods that minimize the weight of a structure. Within the field of structural optimization, The Ground Structure Method (GSM) appears to be the most suitable method for large structures that consist of slender structural elements. Making utterly high refinements in the GSM-model will result in a structure with definitely the lowest volume possible. However, this structure will have lots of smaller and shorter elements that will require in total more welding and conservation. This will not lead to a least-environmental-impacting structure. Thus the main question arises:

Will, within the ground structure method, minimizing on the environmental impact result in a significantly different structure than a minimization on weight?

The objective function for the environmental impact consists of the three considered contributing factors: the construction material, welding and the conservation. The environmental impact for the three factors is determined with a Life Cycle Assessment (LCA). Finally, every contributing factor is unified into a single indicator value through the Environmental Cost Indicator (ECI) method.
The objective function also consists of three variables which represent: the volume of construction material, the welding volume and the surface of the structure. The volume is already known, since it is the regular GSM minimization. The welding volume can be determined through the joint-cost method, which is adding an artificial length to each member. The surface area of the structure is harder to determine. The relation of the volume of a construction element and its surface area is generally speaking non-linear. Multiple implementations were investigated. The aim is to perform the optimization on a fully connected ground structure, and so the assumption is made to make the relation between the volume and surface area linear. A circular hollow cross section with a variable radius and a constant wall thickness is implemented into the optimization method. The final objective function to minimize the ECI costs is a mixed-integer linear programming problem (MILP).

This method is tested on the established benchmark for a cantilever structure and on a case study for a bicycle bridge. The shape of the optimal structure is dependent on the amount of nodes within the design domain. The results for the cantilever structure does clearly reflect this. Depending on the amount of nodes in the design domain, the minimization of the environmental impact is decreased between 0 and 37%, while the weight is at most 2.5% higher. The difference of the environmental impact between the least-weight and least-environmental-impacting structure keeps increasing as the node density increases.
The bicycle bridge is optimized in a 2D and 3D design domain. The design domain of the bicycle bridge appeared to be too big to be solved by the MILP formulation optimization, thus the domain is reduced to a single span of the bridge. Furthermore, the amount of nodes in the design domain is limited to improve the computability of the problem. In both the 2D and 3D variant the regular minimization on weight requires only a fraction of the time to solve the problem successfully. For the 2D case there is a difference between the minimization of the weight and ECI. The number of members in the least-environmental-impacting structure is reduced by 40%, which results in a 1% lower environmental impact. The MILP could not converge properly in 4 hours in the 3D design domain. This is mainly because the model size did increase a lot compared to the 2D design domain. Going from 2D to 3D adds a third axis, which increases the amount of constraints by 50%. Likewise, the number of nodes in a 3D domain increase more rapidly than in a 2D domain.

All in all, the method is implemented successfully and validated with the cantilever structure. The proposed method will result in a structure with an equal or lower environmental impact compared to the regular least-weight minimization. However the minimization of the environmental cost with the proposed optimization method is able to solve problems with around 5,000 variables. To solve larger models successfully it is advised to either reduce the connectivity of the ground structure or to apply the joint-cost method with an LP.