Analysis and Design of Reinforced Concrete Shear Walls Using Mathematical Programming and Optimization

Analyzing and reinforcing concrete members (such as beams, columns, and shear walls) are fundamental to civil and structural engineering. Classical design methods based on hand calculations or interaction diagrams are available for various reinforced concrete sections. The goal of this study is to develop a new alternative design method of reinforced concrete shear walls using mathematical programming and numerical optimization. The design of reinforced concrete shear walls is based on the latest American Concrete Institute ACI 318-19 Code. The design method relies on an optimization formulation to determine the minimum required steel area subject to given factored loads (such as a combined bending moment and axial force on a concrete section). This study intends to present the design of concrete shear wall sections in a rigorously derived framework using different formulations. To make it more practical for civil and structural engineers to use, a widely available numerical solver in a Microsoft Excel spreadsheet is adopted as the optimization engine. Concrete shear wall examples are analyzed and designed using the proposed method, and the results are compared with those obtained using classical design methods. The new method using numerical optimization works well and is easy to implement in an Excel spreadsheet. The proposed design method provides a useful alternative for practical engineering applications.