Structural Reliability

Textbook

No required textbook, selected readings will be provided in the class. See below for recommended text.

Optional Texts

• Primer: Ang, A. H-S. and Tang, W. H. (2006). Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering, 2nd Edition, Wiley (ISBN 978-0471720645).
• Ditlevsen, O. and Madsen, H. O. (1996). Structural Reliability Methods, Wiley (ISBN 978-0471960867), will be provided in PDF upon request.
• Melchers, R. E. (1999). Structural Reliability: Analysis and Prediction, 2nd Edition, Wiley (ISBN 978-0471987710).
• Lemaire, M. (2009). Structural Reliability, Wiley (ISBN 978-1-84821-082-0).
• P. E. Pinto, R. Giannini and P. Franchin (2004). Seismic Reliability Analysis of Structures, 1st Edition, IUSS Press (ISBN 88-7358-017-3).

Course Objectives and Emphasis

This graduate course offers a comprehensive review of most commonly used structural reliability assessment methods and their applications to engineering problems. Covered topics include formulation of the structural reliability problem, different reliability indices, first-order and second-order reliability methods (FORM and SORM), component and system reliability, structural reliability analysis under model and statistical uncertainties, and simulation and uncertainty quantification methods. The main objective of the course is to expose the students to fundamental concepts in structural reliability analysis and reinforce their understanding through applications to real life problems. Through a final project, each student will apply reliability methods to solve a selected engineering problem.

Computer Programs

Some homework assignments require the use of the reliability code, FERUM, which is a Matlab toolbox for general structural reliability analysis and finite element reliability analysis that was developed by Terje Haukaas. Matlab might also be needed for assignments and project. Matlab is available on the computers at the Engineering Computing Center (ECC) and FERUM can be downloaded from http://www.ce.berkeley.edu/FERUM/. Students are also encouraged to use other computer programs such as MS Excel, Mathematica and Mathcad.

Final Term Project

Each student is required to undertake a final term project. The project paper should be word-processed and contain sufficient details. The students, depending on their selection, either will be assigned a comprehensive project on seismic risk assessment of a real building or asked to select a suitable topic of their interest. In the latter case, an abstract (500 words maximum) of the project should be submitted to the instructor at least four weeks before the last day of classes. The instructor will assess the suitability of the project and make necessary changes to the scope (if needed). Two students will be allowed to work on the same project; however, the amount of work will be commensurate with the number of contributors. If two students choose to work together, the entire work should be performed together (not in two parts). Each student (group) will make a 15 min oral presentation on the final day, which will be graded as a part of the project.

Course Outline

Topics	Reading
I. Introduction Uncertainty and risk; structural and system reliability problems	Lemaire Ch1**
II. Basic Theory of Probability and Statistics Events and probability – set theory Mathematics of probability: axioms, theorems and rules Random variables Probability functions and partial descriptors Normal and lognormal distributions Distributions related to Bernoulli sequence and Poisson process Multiple random variables, joint probability functions, correlations Math. expectations of functions of random variables (linear & nonlinear) Distribution of functions and random variables	A&T*
III. Structural Reliability – Component Joint probability distribution models Elementary reliability analysis and indices Reliab. index by Mean-Value First-Order Second-Moment Method (MVFOSM) Hasofer-Lind reliability index (HL/FOSM) Generalized reliability index; Reliability “methods” First-Order Reliability Method (FORM) FORM examples and issues Second-Order Reliability Method (SORM) FORM importance vectors FORM sensitivity measures	CRC14**
IV. Structural Reliability – System Definition of “system” “Structural” system reliability analysis Inclusion-exclusion; Simulations; Theoretical bounding formulas; LP bounds	ADK1**, CRC15**
V. Structural Reliability under Model and Statistical Uncertainties Bayesian parameter estimation Reliability under epistemic uncertainties	ADK2**
VI. Simulation Methods Monte Carlo simulations; Importance sampling, directional sampling, etc. Simulations for system reliability analysis	REM Ch3**
VII. Uncertainty Quantification Response surface method (design of experiment; reliability computation) Dimension reduction method	CRC19*
VIII. Applications of Select Structural Reliability Methods (if time permits) Matrix-based system reliability method Probabilistic seismic hazard assessment (PSHA) Systematic treatment of uncertainty in earthquake engineering research Probabilistic codes and structural reliability (LRFD) Probabilistic models based on experimental observations Introduction to random vibrations	Journal papers are assigned

* Ang, A. H-S. and Tang, W. H. (2006). Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering, 2nd Edition, John Wiley and Sons (ISBN 978-0471720645).
** Electronic or paper copies will be provided by the instructor.