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The civil engineering community, and structural engineers in particular, have long recognized the important role played by variability and incomplete information in their profession: (i) random system properties, (ii) unpredictable future loads and strength deterioration, (iii) human errors, and (iv) imperfect mathematical models. Ensuring adequate safety and reliability for all stakeholders in the presence of these uncertainties is therefore a central objective of design analysis and assessment of structural systems. This course aims to give the students the ability to model uncertainties and manage risks in civil engineering activities in a way that best serves the interests of society.INTENDED AUDIENCE : 4th year advanced UG students, 1st year MTech, 1st year PhD studentsPRE REQUISITE : Must have completed at least 2nd year UG curriculum in engineering with course(s) in Engineering Mechanics Must have taken courses in probability & statistics, linear algebra and basic calculusSUPPORTED INDUSTRIES : All companies with R&D facilities, all national labs including DAE, ISRO, DRDO labs
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Part A: Basics
Week 1:Pre-requisites. Introduction and overview.
Review of basic probability. Random variables, probability laws, common probability distributions – origins and interrelations.
Simple one variable example problems.
Week 2: Random variables
Functions of random variables.
Joint probability distributions, conditional distributions. Joint Normal distribution. Concepts of point process. Simple one- and multi- variable example problems
Week 3: Monte Carlo simulations
Introduction to Monte Carlo simulations. Generation of samples from various discrete and continuous distributions, generation of dependent samples
Variance reduction techniques. Examples: simple coding problems
Part B: Fundamentals of Reliability
Week 4: Basic definitions
Reliability – historical development, applications, different measures of reliability. Component vs. system reliability.
Probabilistic formulation of civil engineering problems. Concepts of performance requirements and definitions of failure.
Week 5: Systems reliability
General formulation of system reliability problems - representation of failure, series and parallel systems, redundancy, fault trees, cut sets.
How structural systems are different.
Week 6: Time to failure
Time to failure based formulation of reliability problems – components and systems. Reliability and hazard functions. Poisson processes.
Part C: Reliability of Structures
Week 7: Capacity-demand-time
Capacity-demand-time (“physics based”) formulation for structural components: limit states. Closed form solutions of simple limit state probabilities. Concept of first passage problem.
Week 8: Approximate solutions
Approximate solutions to component reliability problems: FORM, SORM, MCS Examples: Solution of benchmark problems
Week 9: Structural systems reliability
Formulation of and approximate solutions to structural system reliability problems.
System reliability bounds
Week 10:Maintenance
Reliability-based maintenance. Perfect and imperfect repair – effect on reliability and hazard functions.
Part D: Reliability based Design
Week 11: Design codes
Probability-based design and design codes – partial factors of safety. Examples.
Week 12: Reliability & society
Determination of target reliabilities. Concepts of robustness and resilience.
