Optimal Performance-Based Rehabilitation of Steel Frames Using Braces

Abstract

This paper presents a mathematical programming–based approach for optimal retrofitting of steel structures with braces, subject to some given system performance criteria. The aim is to ensure the safety of the post-retrofitted structures under applied forces and limited displacement conditions. The proposed scheme uses a simple form of the classical ground structure–type concept to accommodate possible brace locations. Three rehabilitation cases are studied, each of which is formulated as an instance of a nonconvex and nonsmooth optimization problem generally referred to as a mathematical program with equilibrium constraints or MPEC. In spite of the fact that this type of problem is known to be challenging to solve in the mathematical programming literature, a simple, efficient, and robust approach to process is proposed. The system performance of all retrofitted structures is validated using exact nonholonomic evolutive analyses.