This paper presents the optimal reliability-based design of the skeletal structures under the both probabilistic constraints of stress at service load level and plastic collapse at ultimate load level. The upper and lower bounds of the effective region satisfying the both constraints were determined by the proposed method. Then, a new probabilistic displacement constraint at the service load level was added to the above constraints. Herein, a minimum structural weight is regarded as an optimal criterion, and it was assumed that the strength of members and the static external loads were normally distributed. Finally, two design examples are presented to demonstrate the availability of the proposed method.
The results show that the proposed method can be used to optimize the structure under the both probabilistic constraints of stress at service load level and plastic collapse at ultimate load level, and the upper and lower bounds of effective region obtained by the proposed method agree with the results of numerical experiments.