**Structural Reliability**

The aim of these studies is to establish a relationship with the uncertainties that exist in the loads and in the structure properties with the probability of structure failure in a vibrating system. The uncertainties in the loading and response are quantified using principles of probability theory. This in turn facilitates prediction of the risk associated with the structure. The methods developed have been applied to predict the failure probability of structures subjected to seismic, wind and ocean wave loadings.

**Schematic of structural reliability problem formulation**

**Extreme Value Distributions & First passage times**

Failures due to overloading in vibrating structures are related to the extreme values and the first passage times of the response. For structural systems with multiple failure modes, analytical expressions are developed for approximating the joint probability density functions for the extreme values and the first passage times of response processes which are non-Gaussian and correlated.

**Schematic of first passage time and 2-D extreme value distribution function**

**Computational Structural Relaibility**

Computational methods are developed for predicting the occurrence of very rare events, such as, failures of nuclear power plants. These methods include Monte Carlo simulations, importance sampling based strategies, response surface methods etc.

Schematic of first passage time and 2-D extreme value distribution function

**Random Fatigue**

The random nature of structure response contributes to fatigue damage which ultimately leads to structural failure. Analytical methods are developed to characterize the rain-flow fatigue damage in vibrating structures due to non-Gaussian loadings.

Joint density of rain-flow maxima-minima and Contours for interval crossing