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
(AII.1)
where the gradient is defined as
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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