A Second-Order Second-Moment Approximate Probabilistic Design Method for Structural Components Considering the Curvature of Limit State Surfaces

The current engineering structural design code employs a direct probability design method based on the Taylor series expansion of the performance function at verification points, retaining only linear terms. This approach ignores the curvature and other nonlinear properties of the performance function, leading to insufficient accuracy. To address the deficiencies of the current design method, this paper develops an approximate probability design method that considers the curvature of the limit state surface, integrating it with the second-order moment theory based on the direct probability design method. Using a simply supported plate as a representative example, this paper systematically compares the performance of the proposed design method with the direct probability design method, the partial coefficient method, and the design value method in reinforcement design. The reinforcement areas calculated by the four methods are similar, confirming the correctness and practicality of the proposed method for engineering applications. The accuracy of the design outcomes from the various methods is validated through Monte Carlo simulation. The results indicate that the method proposed in this paper exhibits a high accuracy, with the relative errors of the reliability indices in the two examples being 0.346% and 0.228%, respectively—significantly lower than those of the direct probability design method (2.919% and 0.769%, respectively). This underscores the effectiveness and substantial benefits of the proposed method in structural reliability design, offering a dependable, highly accurate, and economically viable design tool for engineering applications.