The solution of minimum reliability index for modified weak point of arbitrary curved beam under pure bending

This paper is based on the fundamental loading model of pure bending and the analytical model of a circular beam element with arbitrary initial deflection. The L. W. Guo solution is modified and generalized according to the elastic theory, and the analytical solution for the stress of the beam element with arbitrary initial deflection under pure bending is derived. Using yield theory of edge strength, an expression for the safety margin of one point in The arbitrary curved beam under pure bending (ACPB) is built. This paper modifies the model for weak points of service structures and establishes a foundation for safe design and inspection of imperfect structures. Also, according to the theory of the method of advanced first-order second-moment (AFOSM), this paper derives an expression for the reliability index of one point in ACPB. Lastly, it modifies the solution for weak points by solving the minimal reliability index.