2021 Volume 86 Issue 790 Pages 1655-1663
Since there is a close relationship between the form and force in the large span spatial structures, it needs to design a suitable structural form corresponding to the stress transmission. Furthermore, it is desired to construct efficiently with saving resources for reducing environmental loading. Structural engineers need to judge totally by considering various requirements (e.g. structural safety, aesthetics, constructability, and economics) for a short time.
A structural rational form can be found easily using the optimization method. There are various studies of computational form-finding methods for large-span spatial structures. Recently, it has been applied for the realization of practical design. Generally, optimal shape tends to be a complex shape. According to the construction reports of its application, it can be confirmed that issues about constructability of complex shapes and reducing scaffolding material have been solved in the construction phase. It is significant to solve the construction problems during the early design phase by using optimization methods.
Removing supports is one of the important construction processes for spatial structures. Generally, it is mentioned that depending on the support conditions during the removal process, the internal stress may be higher than those in the completed state in the RC large-span structures. From a point of view of safety, it is necessary to plan to remove supports carefully. Furthermore, planning for the construction process depends largely on the experience of the contractors/designers. In the case of complex shapes, it can be imagined that it involves a lot of trial and error and is extremely difficult. If the construction plan can be reasonably designed at the stage of the form-finding process, it will be possible to realize further resource-saving and efficiency of construction materials. There are a lot of studies about optimization for removing supports in the construction process of the truss or tensile structures. However, to the author's knowledge, there are a few studies for RC spatial structures.
This paper presents a simultaneous optimization method for the large span spatial structures obtaining the process of removing supports in the construction and the shape of the completed state. An optimization problem is formulated to minimize the summation of the strain energy during removing supports. The optimization algorithm consists of two methods. The coordinates of B-spline control points are optimized using Sequential Quadratic Programming (SQP). Furthermore, Local Search (LS) is used for obtaining the order of removing supports.
It is shown in the numerical examples that not only obtaining strain energy minimized shape, react force and stress are suppressed during the process of removing through optimization. In the case of a 2D arch, the optimal order is to start from the end with removing the center at last. In the removal phase, it is effective to leave the center support during the removal to reduce bending deformation. By using this method, it can realize the construction plan for the supports considering both structural safety and constructive efficiency. Moreover, the proposed methods require less computational cost than the heuristic method shown in the numerical example. In the optimization using NP2, it is possible to obtain the solution with less computational cost than using NP1. However, the order of removal of supports becomes complicated. From a point of view of practical design, this result needs caution to avoid mistakes in construction.