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Reliability Analysis of Dynamic Systems by Bin Wu

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Appendix II

Analytical Solution of HL Safety Index

β should be easily obtained through an iteration process satisfying the conditions given in equation (2.18), so too the design point.

By using the technique of Lagrange multipliers, Shinozuka [108] found that the minimum distance represented by the HL safety index is

image (AII.1)

where the gradient is defined as

image

An excellent first-order interpretation of this expression (AII.1) was given by Ang and Tang [109], which is demonstrated as follows.

In general, for a nonlinear limit state function G(x) involving ...

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