Question

Suppose you are working on a structural reliability problem in which the limit-state function is denoted by g(x) in the original random variable space, and G(u) in the standard normal space, respectively.

How can you compute the Hasofer-Lind reliability index? Describe the procedure concisely. No lengthy derivations needed

Answer 1

To calculate the Hasofer-Lind reliability index, define limit-state functions, transform variables into standard normal space, and then use optimization or numerical methods to find the shortest distance to the failure surface, which is the reliability index.

Step-by-step explanation:

To compute the Hasofer-Lind reliability index (also known as the reliability index β), follow these steps:

• First, define the limit-state function in the original variable space, g(x), and in the standard normal space, G(u).
• Next, identify and transform the random variables involved in the limit-state function into equivalent standard normal variables.
• After that, calculate the shortest distance from the origin to the failure surface in the standard normal space, which is the reliability index β.
• This involves solving an optimization problem to find the point on the failure surface that is closest to the origin in the standard normal space.
• Finally, use numerical methods such as the First-Order Reliability Method (FORM) or simulation techniques to estimate this distance if an analytical solution is not feasible.

The Hasofer-Lind reliability index represents the number of standard deviations that the mean of the basic variables is away from the limit state, providing a measure of the safety level.