Optimal retrofit of moment resisting frames using braces accounting for geometric nonlinearity and serviceability conditions

• Three optimal retrofit approaches of existing structures with braces are proposed.
• The approaches incorporate elastic buckling using 2nd-order geometric nonlinearity.
• The optimization takes the form as a mixed integer nonlinear programming problem.
• The binary constraints eliminate brace members with non-practical (too small) sizes.
• Two-step optimization algorithm proposed presents an efficient solution scheme.

The paper proposes three novel optimal retrofitting strategies for moment resisting frames using cross braces to satisfy given serviceability limitations. The influences of 2nd-order geometric effects are included. The well-known “ground structure” method is used to generate an initial network of possible brace layouts and automatically determine the best one using an optimization algorithm. Of special note is the use of a constraint to impose a realistic design criterion, in which a brace can be selected only if its area lies within specified bound limits. This in effect eliminates members with non-practical (too small) sizes. The formulation is cast as a challenging instance of a mixed integer nonlinear programming problem, which accommodates simultaneously continuous and binary variables. A two-step optimization algorithm is proposed as an efficient and robust solution approach. The safety and integrity of the retrofitted structures are assessed using step-by-step nonlinear elastic analyses.