Fracture around the connections between the roof and the columns in the supporting wall of a long-span structure was reported as a key issue in the recent earthquake disasters in Japan. A school gymnasium needs highest-level seismic resistance, because it is used as a shelter when in the event of earthquake disaster. Especially for a lightweight steel roof supported by stiff RC structure, deformation concentrates around the connections. Accordingly, slip occurs at the pin/roller supports, and the steel members near the support exhibit plastic buckling and fracture. This kind of damage may be due to vibration of cantilever columns in the gable wall as reported in previous studies. Therefore, it can be prevented by designing the roof and supporting structure simultaneously so that a global vibration mode dominates against seismic motions. However, most of studies focused on the characteristics of seismic response of school gymnasium or the method for seismic design, and few studies have focused on the design to reduce the seismic response of the connections of the steel roof. The second author proposed an optimization approach to design of the supporting columns of a long-span arch to reduce the responses of the arch. It has been shown that flexibility rather than stiffness of the columns reduces the response of upper arch especially in the normal direction of the arch.
In this study, we propose an optimization method for stiffness design of RC columns of a school gymnasium to reduce the interaction forces between the steel roof and supporting structure under seismic motions. The objective function is the maximum force at the connections, which is evaluated using the SRSS method for the seismic motions corresponding to the specified acceleration response spectrum. Constraints are given for the total weight and the interstory drift angles of columns. The sizes of columns are optimized using simulated annealing (SA).
It is shown in the numerical examples that the maximum interaction force is drastically reduced to about half of the reference model through optimization. The property of optimal solution to reduce the interaction force is investigated in detail from the mode shapes, natural periods, and effective mass ratios. It is shown that the depths of the RC columns of the frame in the longitudinal direction increases while the depth of the columns in the transverse direction decreases. As a result, the shear stiffness of the longitudinal frame is increased, the vibration mode of the top of the frame in the transverse direction is suppressed, and the maximum shear force of the bearing is reduced. Furthermore, 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 maximum interaction forces of optimal solutions using SRSS method is smaller than the average of the time-history analysis due to the difference of the damping factor between the dominant mode and the target value for generating the artificial ground motions. Besides, the results of the time-history analysis also show that the maximum shear force of the bearing is reduced due to the suppression of the dominant vibration mode.