## Structural Reliability Theory

### Module aims

• To introduce students to the fundamental concepts and principles of structural safety. The approach to assessing the safety of both new and existing structures is considered, with techniques relevant for the latter being emphasised.
• To introduce the students to the most common quantitative approaches of structural reliability theory as well as to enable students to understand how such quantitative probabilistic approaches manifest in codes of practice.
• While the principle aim of the course is to promote understanding of the methods of structural reliability theory, a secondary aim is for students to appreciate the power of probabilistic methods in structural engineering.

### Learning outcomes

On successfully completing this course, students will be able to:

•  Understand the framework under which structural codes are developed, with particular reference to EN1990.
• Quantitatively describe loadings, in a probabilistic manner, for a variety of circumstances.
• Evaluate the nominal probability of failure of a structure using a time-independent reliability formulation.
• Employ a Bayesian framework to incorporate information from structural testing and inspection in order to modify models for structural capacity.
• Undertake First Order and Second Order reliability analyses for structural components.
• Apply simulation techniques, including crude Monte Carlo and Importance sampling, to evaluate the reliability of structural components or systems.
• Describe the capacity of structural systems using combinations of series, parallel and k-out-of-n subsystems.
• Understand the time-dependent nature of structural reliability and develop quantitative models for the time-dependent capacity of structures.
• Understand the key concepts of life-cycle cost analysis and to make considered judgements regarding optimal maintenance and/or repair strategies.
• Appreciate the power of probabilistic methods in structural engineering.
• Identify optimal values for partial factors and load factors in order to achieve a pre-determined level of reliability.

### Module syllabus

• Principles of Structural Safety.
• Fundamentals of Probability Theory: Univariate and multivariate probability distributions; Correlation; Bayesian inference; Probabilistic transformations; Combinations of random variables.
• Reliability Theory: Specification of limit-state functions; Cornell reliability index; Hasofer & Lind reliability index; Rosenblatt & Nataf transformations; Design points, FORM, SORM, linear and nonlinear limit state functions.
• Simulation techniques: Crude Monte Carlo, Latin Hypercube sampling, Importance sampling.
• System Reliability: Series systems, parallel systems, and k-out-of-n systems; Structure functions, cut sets and path sets; Correlated modes of failure; Failure domains for systems.
• Background to EN1990: Probabilistic formulations in codes, partial factors, safety factors, combination factors, loading levels.
• Life-cycle Analysis: Time-value of money; Cost-benefit analysis; Decision theory; Reliability profiles; Time-controlled and reliability-controlled maintenance strategies; Time-dependent capacity and loading, time-dependent reliability formulation.
 No. Topic Staff 01 Introduction to Structural Safety PS 02 Fundamentals of Probability Theory PS 03 Structural Reliability Theory PS 04 Structural Reliability Theory PS 05 Simulation Methods PS 06 System Reliability PS 07 Life-cycle Cost Analysis PS 08 Tutorials PS 09 Reliability basis of the Eurocodes PS

### Teaching methods

A combination of lectures and tutorials.

### Assessments

Assessment information will be provided separately.