Performance-Based Design and Optimization of Buckling Restrained Knee Braced Truss Moment Frame

A buckling restrained knee braced truss moment frame (BRKBTMF) is a novel steel structural system that combines steel trusses with buckling-restrained braces (BRBs) to form an alternative seismic force-resisting system. The combination of the steel trusses and the BRBs allows the BRKBTMF to have a large interior opening without the need to provide ductile detailing for the steel trusses. This makes the design very efficient and economical. More importantly, through the use of BRBs as the designated energy-dissipation devices, the damage is controlled within the BRBs, which can be replaced easily after the earthquake. This will drastically reduce the structural damage, repair cost, and repair time, which makes this structure more efficient and resilient toward future earthquakes. In this study, a modification of the performance-based plastic design (PBPD) procedure was derived to design the member sizes of the BRKBTMF. A parameter study was conducted by varying the inclination of BRBs to optimize the initial construction cost and expected financial loss during the maximum credible earthquake shaking. A prototype four-story office building located in Berkeley, California, was selected for this study. State-of-the-art site-specific hazard analysis, finite element models, and damaged fragility models were used to evaluate the seismic performance of the BRKBTMF with different BRB inclinations. The result shows excellent seismic performance in the proposed BRKBTMF, where the structure is able to satisfy both the drift and force limits. The parameter study shows that the design forces in the steel trusses are not affected by the inclination of the BRB. Instead, the design forces in the BRBs and columns increase as the inclination of the BRB becomes more horizontal. This results in larger column sizes and thus higher initial construction costs. The cost of the BRB is not significantly affected by the inclination of the BRB. This is because as the BRB inclination becomes more horizontal, the cross-sectional area of the BRB increases, but the length of the BRB decreases. The results of the nonlinear dynamic analysis show that the peak dynamic responses (peak interstory drift and floor acceleration) of the BRKBTMF are very similar among the different BRB inclinations. This shows that the proposed PBPD design methodology is very effective in designing the BRKBTMF. The detailed parameter study also shows that the BRB strain is the lowest when the BRB inclination is around 30 degrees or 90 degrees. As the BRB inclination gets closer to 60 degrees (using the geometry presented in this study), at the same interstory drift demand, the axial strain demand in the BRB is the highest. This results in a high degree of damage to the BRBs, which translates to the highest degree of structural damages and financial losses during the maximum credible earthquake shaking. Hence, it is recommended that optimal choices of BRB inclination are either horizontal or connecting directly to the end of the columns.