Various methods have been presented for optimization of braced frames under constraints on seismic response. However, in most of those methods, the properties of beams and columns are fixed, and only the locations and cross-sectional properties of braces are optimized. Even when the cross-sectional properties of beams and columns are also optimized, optimal solutions with regular pattern are often found if many constraints for practical application such as local stresses and interstory drifts are considered.
In this paper, we demonstrate that new types of load path of braced frames are naturally generated through optimization. For this purpose, the cross-sectional properties of beams and columns and the locations of braces are simultaneously optimized. Thickness of each member is chosen as independent design variable. Constraints are assigned for the maximum top (roof) displacement and the stresses of columns under vertical loads.
The seismic responses are evaluated using the SRSS method for the seismic motions corresponding to the specified acceleration response spectrum. Optimization is carried out using the sequential quadratic programming that is categorized as a gradient-based nonlinear programming method. locations of braces are optimized by assigning a small lower-bound thickness for braces. However, existence of too thin braces is prevented by penalizing by underestimating the stiffness of thin members.
It is shown in numerical examples that a kind of truss frame consisting of the external column and straightly connected braces is generated through optimization. Although only top displacement is constrained, smoothly distributed lateral stiffness is observed in the optimal solution of a 10-story frame. By contrast, for a 20-story frame, some stories without braces appear as the result of optimization to generate a kind of mid-story isolation, which leads to reduction of acceleration in upper stories. The accuracy of SRSS estimation is confirmed by the time-history analysis against 10 artificial ground motions compatible to the design response spectrum. It is shown that the responses of the optimal 20-story frame can be further reduced by assigning viscous dampers in the stories without braces.