Baidurya Bhattacharya

Professor of Civil Engineering

Indian Institute of Technology Kharagpur

Video lectures:

Structural Reliability - design assessment and safety targets

Youtube playlists

PART A (BASICS)

Week No.

Lecture No

Lecture Title

Topics

Concepts Covered

Lecture Duration

File Name and link

1

1

Introduction

Overview

Introduction and course overview

8:38

Content books and format

Contents of Course, Books Recommended, Format

6:50

Engineering - joys and challenges

Definition of Engineering , Reasons for Structural Failure

4:50

Ronan Point

Progressive Collapse in Buildings, Redundancy, Prevention by Design

3:39

Comet aircrafts

Fatigue and Stress Intensity Factor, Fatigue Reliability

8:30

Lithium ion batteries

Structural reliability of Separator of Li ion Batteries

4:29

Complexity

Managing uncertainties, Liability and Penalty of Structural Failures

2:24

Factors of safety

Design Load, Safety Factors, Design Codes

2:57

Conclusion

Decision Making under Uncertainties, Standardization of Decision Process

8:11

2

Review of Probability Theory

Set Theory

Definitions, set relations and operations on sets

7:28

Set algebra

Algebra of sets and measure

5:12

Definitions of Probability

Different Approaches to Probability, Definition of Probability

6:24

Examples

Examples on classical definition of probability

8:43

Probability of joint events

Conditional Probability, Bayes Theorem, independence, total probability

8:54

Examples

Example of Probability Problem involving Networks

5:08

Example of Probability Problem involving the Game of Bridges

3:54

Example of Probability Problem involving Environmental Hazards

2:56

Example of Probability Problem involving Diagnostic Test

6:17

3

Review of Random Variables

Random variables

Definition of Random Variables, probability laws governing random variables - CDF, PDF, PMF

6:55

Moments and Expectations

Moments and Expectations of Random Variables

3:04

Examples

Example on range of projectile

2:59

Example of Random Variables involving Weld Flaws

5:13

Example of Random Variables involving Computer Network

3:08

Example of Random Variables involving Bridge Flood

3:29

Example of Random Variables involving Expected Profit Safety Device

5:06

Example of Random Variables involving Jacket Problem Failure

5:56

Conditional Distribution and Mean

Conditional Distribution and Conditional expectation

5:27

Example

Conditional Distribution: rainfall example

4:22

More on expectations

Characteristic Function

2:13

Moment Generating Function, Markov, Bienyame, Chebyshev and Lyapunov Inequalities

2:07

2

4

Common Probability Distributions (discrete)

Common Discrete RVs

Table Common Discrete RVs including PMF, CDF and moments

0:56

Uniform and Bernoulli Trials

Uniform and Bernoulli Trials

5:17

Geometric

Geometric Distribution

2:09

Mean Return Period

Mean Return Period

5:15

Binomial and Negative Binomial

Binomial and Negative Binomial

5:45

Examples

Example of Geometric Binomial etc. distributions involving Rainfall

2:04

Example of Common Discrete RVs involving Oil Exploration

5:24

Example of Common Discrete RVs involving Binomial Dart

6:27

Hypergeometric Distribution

Hypergeometric Distribution

5:27

Poisson Distribution with Example

Poisson RV arising out of homogeneous and inhomogeneous Poisson processes, example on weld and defects

11:00

5

Common Probability Distributions (continuous)

Common Continuous RVs

Table of common continuous RVs, CDF, PDF and moments; Uniform RV, Poisson process

5:33

Exponential Distribution

Exponential RV

5:11

Return Period Revisited

Return Period

3:59

Erlang and Gamma Distribution

Erlang and Gamma Distribution

2:42

Central Limit Theorem

Central Limit Theorem

6:56

Normal distribution

Normal CDF

5:41

Lognormal Distribution and Example

Lognormal Distribution and Example

4:18

Extreme Value Distributions

Extreme Value Distributions

4:54

Weibull Distribution and Example

Weibull Distribution and Example

6:33

6

Joint Probability Distributions (part 1)

Joint Random Variables Introduction

Lecture plan

1:59

Joint probability laws

Joint CDF, PMF and PDF; marginal and conditional CDF PMF and PDF;

9:07

Example

Joint Probability Mass Function - visualization

4:25

Bivariate Density of Jointly Random Variables - visualization

4:17

Probability Integration

2:30

Joint Moments

Joint Moments of Random Variables; expectation of function of random variables; joint characteristic function; joint moment generating function; conditional moments - conditional mean and variance

8:38

Independence and Dependence

Statistical independence among Random Variables; independence among functions of RVs; measures of dependence; correlation coefficient and its properties

6:13

Example

Joint Density of H and T

8:50

Continuing with H and T; convolution - probability of failure

4:07

Correlation and Nonlinear transformation

4:46

3

7

Joint Probability Distributions (part 2)

Function of Random Variables

Function of one RV - one to one, many to one; example - Cauchy from tangent map of uniform; modifications of tangent map to produce finite moments; lognormal from normal; chi square from normal;

12:29

Examples

Distribution of the sum of 2 IID Geometric RVs

2:07

Distribution of the sum of 2 Uniform RVs - by convolution and by Jacobian of transformation

6:57

Transformation of Random Variables: H,T to V,A; marginal densities

4:36

Joint Normal

Bivariate normal distribution - conditional and marginal distributions; multivariate normal - conditional and marginal distributions;

14:32

Example

Correlation and nonlinear transformation of bivariate standard normals - squaring and exponentiating

9:02

Example of Cable Design: Linear Combination of Normals

5:09

Convergence of Sequence of Random Variables

Preliminaries - convergence of a sequence of real numbers, limit, examples of sequence of RVs; four types of convergence of RVs - almost sure, in probability, in mean square, in distribution - hierarchy

8:03

Law of Large Numbers

Strong law and weak law

3:57

8

Monte Carlo Simulations (part 1)

Introduction to Monte Carlo Simulations

Lecture plan; in which sort of scenarios we resort to simulations - computer simulations, simulation of probabilistic events - Monte Carlo simulations; Outcomes of MCS

7:48

Estimation of Pi

Estimation of Pi using random points in a plane - theoretical approach and through Monte Carlo Simulations; convergence of estimates

10:30

Random Number Generators

True RNGs - physical sources, pros and cons; pseudo RNGs - properties particularly period of generator, multiple recursive generators - Marsenne twister;

8:01

Lehmer Algorithm

Linear congruential generators - full periodicity, Fermat's little theorem, optimal values of multiplier and modulus in Lehmer algorithm.

4:18

Tests of Randomness

Limitations of test, monobit frequency test, block frequency test, moments test, turning points test, etc.

11:10

9

Monte Carlo Simulations (part 2)

Generating Continuous Deviates

The inversion method; drawbacks of inversion; generating exponential deviates

8:19

Demonstration of CLT with sum of exponentials

4:44

Generating Normal Deviates- the box Muller transform

7:30

Generating Discrete Random Deviates

The inversion method and direct methods for generating various discrete distributions - Bernoulli, geometric, binomial, Poisson

5:07

Example: picking shoes from a closet

3:07

Generating Dependent Samples

When complete joint distribution is known, example involving H and T;

6:25

Generating correlated normals and example on Cable Pf

6:40

Generating Correlated Non Normals

When only marginal distributions and covariance are known (for generating dependent non-normals), example two Lognormals

7:16

Variance Reduction techniques

Uncertainty in basic MCS, Importance Sampling

6:39

PART B (FUNDAMENTALS OF RELIABILITY)

Week No.

Lecture No

Lecture Title

Topics

Concepts Covered

Lecture Duration

File Name and link

4

10

Definition and Scope of Reliability

Introduction

Recap and course plan

1:47

Definition and Scope of Reliability

2:18

History and development of the subject

5:37

Growth of Structural Reliability

5:07

Measure of Reliability

Reliability and Related Measures

2:04

Repairability and Non-Repairability - availability

3:57

11

Problem Formulation in Reliability

Reliability Problem Formulation

How to approach reliability problem formulation based on available information and purpose at hand: physics-based vs. phenomenological, element vs. system, time-dependent or not; which variables are random

7:46

Setting Up Structural Reliability Problems

Structural reliability as a physics-based reliability problem: Having an appropriate mechanistic model of structural response; Defining limits of satisfactory performance, hence "failure" and hence "limit state"

5:06

Examples

Example: Fatigue Life of Metal Component

5:53

Example: Two Elements in Series and Parallel

6:42

Example: Cable Strength

8:01

Example: Frame

5:30

Example Cantilever Beam

9:59

Example: Traffic safety

2:01

12

Representation of Systems

System Representation Introduction

Different ways of representing a system: Series and parallel configuration of binary elements, role of mutual dependence, load sharing; multistate elements;

10:48

System Representation By Enumeration

System Representation By Enumeration

6:41

System Representation by Structure Function

System Representation by Structure Function

8:02

Example two unit systems two state and three state elements

Example: two unit systems, two state and three state elements

9:07

Example two unit dependent parallel

Example: two unit dependent parallel

10:38

5

13

Representation of Systems (Continued)

Reliability block diagrams

Introduction: "success oriented", two-terminal network, a determinate truss example, a highway bridge example

5:07

RBD: system with three-state elements

3:06

RBD: Series Parallel Arrangement

3:22

RBD: Bridge Network Arrangement - with bidirectional and unidirectional key elements

7:09

RBD: Repeated Elements; 2 out of 3 redundant system; redundant truss example

8:04

Cut Sets

Introduction, "failure oriented", minimal cut sets, path sets, minimal path sets, examples

6:34

Structure function of Minimal Cut Sets; hence system structure function; examples

4:40

Example: Minimum Cut Sets from RBDs

8:08

Example Minimum Cut Sets of truss structures

4:19

14

Representation of Systems (Continued)

Fault Trees

Fault Trees - definition, symbols and construction

3:26

Example: Fault Tree of highway bridge

3:20

Example: RBD to FT

3:17

Example: FT of system with multistate elements (diodes)

3:41

FT with common cause elements

4:05

Fault Tree with Repeated Elements (using cut sets)

5:31

Fault Tree from system Description

5:40

Example: FT of a Fire Fighting System

5:54

Types of Redundancy

Types of Redundancy: active, standby (warm and cold)

12:51

15

Time Dependent Component Reliability

Introduction

How time appears in reliability formulation (in a physics based formulation); Lecture plan for Parts C and D

11:23

Random time to failure (TTF)

Recap of "failure" : physics-based vs. phenomenological approach to failure, First Passage Time; inability of directly observe TTF for structural components and systems; current focus (in Part B) on directly observed TTFs

3:46

Functions of TTF

Reliability as a function of time, its properties; PDF, CDF of TTF

4:05

Mean time to failure, its lack of relevance for structures; mean residual life

8:35

Examples: Reliability, MTTF, MRL from PDF or CDF of TTF

8:18

Example: Exponential TTFs making up a Binomial problem

2:53

Poisson arrival of Shocks

Interarrival times - IID exponentials, TTF to kth shock, Gamma distribution; sum of Gamma RVs

6:07

Example Poisson Shocks

3:18

Example: Gamma TTF

5:14

Generalizing TTF to number of cycles

Example Fatigue Reliability

5:53

6

16

Time Dependent Component Reliability (Continued)

Hazard (or, Failure Rate) Function

Definition; relation between hazard function and reliability function; properties of hazard function

8:25

Characteristic Life and Example

3:23

Hazard function for Exponential TTF: constant failure rate; Hazard function for Poisson occurrence of shocks - Gamma distributed TTFs - increasing, constant and decreasing failure rates

10:45

Hazard Function for Uniform, Normal, Lognormal TTFs

9:30

Power Law Hazard Functions and Weibull TTF

6:33

Bathtub Hazard Curve

5:26

Design Life from minimum acceptable Reliability and maximum acceptable Hazard

3:07

17

Time Dependent Component Reliability (Continued)

Estimation of TTF Statistics from test data

Recap of previous lectures; Description of test program and basic test data; estimation of PDF, Reliability and hazard functions from data

7:07

Example: estimation from completed tests on identical samples

Example: Observed failure times of 10 identical components from Shooman's Book - CDF PDF Rel and Hazard functions

14:35

Example: Observed failure time intervals of 172 identical components from Shooman's Book - CDF PDF Rel and Hazard functions

9:43

Example: Observed failure times of 25 identical components from Naikan's Book - PDF Rel and Hazard functions

4:16

Estimation from censored tests - censoring by time and censoring by number of failures

Types of censoring; Example: Censored by Time - Test on 50 samples stopped after 30 hours (only 6 failed), TTF distribution type is known - taken from Gnedenko et al

10:05

Example: Censored by number of failures - Test on 9 samples stopped after 3 failed, TTF distribution type is known - taken from Gnedenko et al (part 1)

12:01

Example (contd.): Censored by number of failures (part 2)

5:24

Example (contd.): Censored by number of failures (part 3)

8:36

18

System reliability - time-defined

System Reliability Time Defined

Recap of Part A of the course and Part B so far; Recap of element vs system reliability and phenomenological vs. physics based reliability; Introduction to System Reliability - in terms of element TTFs; plan for this lecture

6:21

Active k out of n systems-series system - order statistics of element TTFs, system TTF in terms of element TTFs; series system, special cases - independent elements, exponential element TTFs; example

8:37

Active Parallel System - system TTF in terms of element TTFs, special cases - independent elements, exponential element TTFs - MTTF

5:51

Unit vs Component Redundancy - example with IID elements

3:22

k out of n active redundant system - no load sharing considered, special cases - IID exponential elements, MTTF; examples: telephone system, pump drainage system

8:44

Dependent Active Parallel system - 2 unit system with dependent exponential TTFs, MTTF

8:07

Effect of dependence among elements

Example of two element systems with and without dependence - arranged in series or parallel

5:18

Standby Parallel

k out of n standby redundancy, spares and sockets, example - 1 active n -1 standby elements, special case of n=2, switching failure; example - fire fighting system

12:00

PART C (RELIABILITY OF STRUCTURES)

Week No.

Lecture No

Lecture Title

Topics

Concepts Covered

Lecture Duration

File Name and link

7

19

Capacity Demand Component Reliability

Introduction

Recap of Parts A and B; plan for Part C; Recap of element vs. system reliability, recap of phenomenological vs. physics based reliability problem formulation, recap of unique features of structural reliability

10:37

Key steps

Recap: key steps in structural reliability problem formulation, time varying loads, examples; four cases (levels) of modelling

9:37

Limit States

Failure as first excursion from the safe set - one failure mode at one critical location; capacity demand formulation - limit state equation; probability of failure in terms of limit state

4:37

Case 1 Time Invariant C and D

Reliability as probability content of the safe set in basic variable space - special case of 2 dimensional integration, special case of independent C and D; graphical representation

6:47

When C and / or D are time varying

Cumulative vs Overload Type Failure; first passage time

2:38

Examples

Example Proof Load

5:06

Safe Stopping Distance Example

4:13

Cable Reliability Example and types of approximate methods

7:40

20

First Order Reliability Methods (Part 1)

Introduction to FORM (first order reliability method)

The need for approximate solutions, recap of component level limit state function and failure probability; graphical representation of failure in 2-variable problem; non-linear g, mapping failure region from basic variable space X to an arbitrary space Y

5:20

FORM Algorithm Overview

Map from X to Y space: limit state h(Y) and joint PDF change shape and location; choose Y to be the space of independent standard normal variables U; rotational symmetry of joint PDF in U space; point on limit state h(U) closest to origin in U space; linearization of h(U), direction cosines and reliability index - why FORM works

15:49

Types of FORM Maps

Second moment (Hasofer-Lind) transform, full distribution transform, Nataf transform, Rackwitz-Fiessler transform, Rosenblatt transform - pros and cons and amount of information required for each

15:07

Key Steps and Benefits of FORM

The approximate nature of FORM solution, map from X to U, evaluate h(U) repeatedly, find minimum distance from origin to h=0; h not required in closed form, gradients of h not essential; reverse map gives design point in X space

4:38

Finding the minimum distance to the limit state surface

Gradient Projection Method - flow chart, graphical representation, Armijo's rule, convergence

12:22

FORM Design Point Idea

Map the minimum distance point u* back to the design point x* ; characteristic values, idea of partial safety factors - role of bias, uncertainty, sensitivity and reliability index

6:41

21

First Order Reliability Methods (Part 2)

FORM Recap

Main steps of FORM algorithm, graphical representation, pros and cons of FORM

4:23

Examples

FORM Example B1: Cable reliability problem involving 2 RVs - yield strength and axial load (both normally distributed) - find area and design values for given target reliability

8:21

FORM Example B2: Cable reliability problem involving 2 RVs - yield strength and axial load (both lognormally distributed) - find area and design values for given target reliability

5:13

FORM Example B3: Cable reliability problem involving 2 RVs - yield strength and area (both lognormally distributed), load deterministic - find mean area and design values for given target reliability

3:45

FORM Example B4: Cable reliability problem involving 2 RVs - yield strength and area (both normally distributed), load deterministic - find reliability. FORM Example B5: Cable reliability problem involving 2 RVs - yield strength and area (both normally distributed), load deterministic - find mean area and design values for given target reliability

14:22

8

22

First Order Reliability Methods (Part 3) and SORM

Recap of FORM Key steps and pros and cons

Lecture plan, Recap of FORM - Key steps and pros and cons

4:35

Examples

FORM Example C1: cable reliability problem involving 3 RVs - yield strength (Weibull), area (normal) and load (Gumbel) - find checking point and cable reliability. Use full distribution transformation

11:28

FORM Example C1 (contd.) Matlab Code and explanation

7:54

FORM Example D1: Cable reliability problem involving 4 RVs - yield strength (Weibull), area (normal), load Q (Gumbel) and load D (normal) - Q and D are dependent, find checking point and cable reliability. Use Nataf transformation.

9:29

FROM Example D1 (contd.): computation of gradients required for optimization; FORM Example D2 and D3: repeat D1 with Hasofer-Lind and Full distribution transformations, verification with Monte Carlo simulations

10:15

Second order reliability methods (SORM)

Introduction to SORM - an improvement over FORM, how to reduce errors in FORM and obtain better approximation of failure probability

5:27

SORM Steps - start with FORM, find minimum distance point and direction cosines, fit a paraboloid at the minimum distance point, update failure probability with curvature of the paraboloid

6:37

Examples

Example: Redo B4 2 RV Problem with SORM

5:55

Example: Redo C1 3RV Problem with SORM

4:03

Example: Redo D1 4RV Problem with SORM

5:11

23

Monte Carlo Simulations for Estimating Structural Reliability

Introduction

Introduction, need to estimate rare probabilities, recap of Lectures 8 & 9 - estimation of pi, cantileverd beam reliability, limit state, multidimensional integral

7:57

How and why it works

Expressing Pf as expectation of a suitably defined indicator function (true if failure occurs), moments of the indicator function, if the samples are IID then the Strong Law of Large Numbers holds for estimating Pf and estimated value converges to the true value of Pf

6:52

How many samples are enough

Estimated Pf is a random variable (since sample size is finite) - its mean is the true Pf, and if samples are IID then its variance is inversely proportional to sample size; Central limit theorem - recap, estimated Pf approaches the normal random variable, confidence intervals on the estimated Pf; COV of estimated Pf vs sample size

9:01

Generating random samples

Random Number Generation Algorithms, good properties of a generator, Matlab commands, setting the seed, Inversion of CDF for generating non-uniform deviates; examples - generating exponential deviates, Gumbel deviates, independent normal deviates, correlated normal deviates; generating Bernoulli, Binomal and Poisson deviates

16:59

Algorithm

Flowchart for estimating limit state probabilities; Example - Safe Stopping Distance in traffic engineering and probability of collision, Matlab code

9:52

Examples

Redo Example D1: 4RV Cable Reliability Problem involving 4 RVs - yield strength (Weibull), area (normal), load Q (Gumbel) and load D (normal) - Q and D are dependent, find checking point and cable reliability. Use Nataf transformation - Matlab code, estimated value vs. sample size

8:45

24

Importance Sampling Simulations for Estimating Structural Reliability

Introduction

Motivation: Recap - estimating Pf with basic MCS, variance of estimate vs. sample size for IID samples, graphical example of estimating limit state probability by conducting MCS on a plane, moving sampling distribution closer to the limit state

7:12

Methodology

Original sampling density fX and biased sampling density fV; estimated Pf seen as an expectation of a function of V that includes a correction factor fX/fV; variance of the new estimate; ideal case of zero variance

11:51

Algorithm and example

Flowchart; Redo Example D1 with importanc sampling - choice of sampling density, estimated value vs. sample size - comparison with basic MCS

18:04

Example

Example E1: Cantilevered Beam in deflection limit state, 3 RVs, solved by basic MCS and by Importance Sampling - comparison of results

6:57

9

25

(Physics Based) Capacity Demand Time Component Reliability(Part 1)

Introduction to Capacity Demand Time Component Reliability

Introduction, Capacity Demand, Time Component Reliability

13:03

Case 2 capacity demand time reliability with non-random variations

Case 2, capacity demand , time reliability with non-random variations

11:07

Example F1 cable reliability with corrosion

Example F1, cable reliability, corrosion

9:22

Example F2 cable reliability with corrosion and Periodic Loads

Example F2, cable reliability , corrosion ,Periodic Loads

11:35

26

(Physics Based) Capacity Demand Time Component Reliability(Part 2)

Case 3 Capacity Demand Time Component Reliability

Case 3, Capacity Demand ,Time Component Reliability

5:57

Example Bridge with known number of Random Pulses

Example, Bridge ,Random Pulses

9:25

Case 3b capacity demand time reliability with Poisson Loads

Case 3b ,capacity demand, time reliability , Poisson Loads

7:08

Example G2 bridge with Poisson loads

Example G2, bridge ,Poisson loads

9:42

Case 3c capacity demand time reliability with Poisson Loads and aging

Case 3c , capacity demand, time reliability ,with Poisson Loads ,and aging

11:14

Example G2 bridge with Poisson loads and aging

Example G2, bridge ,Poisson loads ,aging

10:37

27

(Physics Based) Capacity Demand Time Component Reliability(Part 3)

Introduction to Random aging problems in Component Reliability

Introduction , Random aging problems, Component Reliability

3:06

Example G4 Random Corrosion Loss and IID Poisson Loads on a bridge

Example G4, Random Corrosion Loss ,IID Poisson Loads ,bridge

3:06

Introduction to Case 4-first passage-stochastic process definition

Introduction ,Case 4, first passage, stochastic process, definition

10:20

First Passage Probability for stationary Gaussian process and reliability

First Passage Probability, stationary Gaussian process, reliability

10:20

Example first passage reliability

Example, first passage reliability

8:45

Introduction to Reliability Based Maintenance

Introduction, Reliability Based Maintenance

8:44

Example Preventive Maintenance no repair vs perfect repair

Example, Preventive Maintenance, no repair ,perfect repair

7:34

Example Preventive Maintenance options benefit cost ratio

Example, Preventive Maintenance, options, benefit cost ratio

4:55

10

28

Capacity Demand System Reliability Formulation - Time Invariant Case (Part 1)

Recap of Course so far

Course Recap

3:41

Introduction to Structural System Reliability

Introduction, Structural System Reliability

10:20

Two-unit series system series part 1

Two-unit series system series, Part 1

10:28

Two-unit series system series part 2

Two-unit series system series, Part 2

10:59

Two-unit series system series part 3

Two-unit series system series, Part 3

9:44

29

Capacity Demand System Reliability Formulation - Time Invariant Case (Part 2)

Series system reliability - structural member with 3 failure modes - FORM

Series system reliability, Structural member with 3 failure modes , FORM

22:53

Series system reliability - structural member with 3 failure modes - MCS

Series system reliability , Structural member with 3 failure modes , MCS

16:14

Series system - determinate truss

Series system, Determinate truss

14:28

Series system - multiple performance requirements and multiple load combinations

Series system , Multiple performance requirements , Multiple load combinations

12:37

30

Capacity Demand System Reliability Formulation - Time Invariant Case (Part 3)

Introduction to Reliability of Active Parallel and Other Redundant Systems

Introduction to Reliability ,Active Parallel , Redundant Systems

8:15

2 Unit Systems - Brittle vs Ductile Part 1

2 Unit Systems, Brittle vs Ductile , Part 1

4:13

2 Unit Systems - Brittle vs Ductile Part 2

2 Unit Systems ,Brittle vs Ductile ,Part 2

10:24

2 Unit Systems - Brittle vs Ductile Part 3

2 Unit Systems , Brittle vs Ductile ,Part 3

8:10

Indeterminate Truss Reliability- Brittle and Ductile Cases

Indeterminate Truss Reliability, Brittle and Ductile Cases

23:05

Reliability Bounds and Concluding remarks

Reliability Bounds ,Concluding remarks

4:21

PART D (RELIABILITY BASED DESIGN)

Week No.

Lecture No

Lecture Title

Topics

Concepts Covered

Lecture Duration

File Name and link

11

31

Reliability Based Design

Introduction

Summary of parts A (lectures 1 - 9), B (lectures 10 - 18)and C (lectures 19 - 30) of the course above; plan for lectures 31 - 36

6:46

Reliability Based Structural Design Codes

Motivation - why standardize reliability based design

5:13

Recasting a reliability analysis forward problem to a design equation derivation problem - FORM based, tying factor of safety explicitly with a target reliability level; history of factor of safety in engineering

9:57

Emergence of Reliability Based Structural Design Standards - a short history (1947 - 2002)

10:28

The Structure and the Philosophy Behind Reliability Based Design Codes

Partial Safety Factors - examples in various codes; format of design equations in Structural Eurocodes

9:25

The high level requirements and philosophy behind the provision of the Structural Eurocodes

13:00

32

Reliability based partial safety factors (Part 1)

Partial Safety Factors

Derivation - 2 random variable (Capacity & Demand) limit state - FORM; the "forward" problem in reliability; introduce the "inverse" problem - locate appropriate distribution of capacity (find mean capacity) given target beta; present the design equation in terms of nominal quantities - bias, sensitivity - expression of factor of safety containing target beta

20:20

Generalization to n-dimensional case - locate checking point in U space, hence the design point in X space, hence derive partial safety factors in terms of bias, target beta, COV and sensitivity - derive design equation (for limit states separable into capacity and demand quantities)

11:38

Example: PSFs for a four-variable reliability-based cable design problem

8:29

33

Reliability based partial safety factors (Part 2)

Partial safety factors optimized for use in design equation

Recap of 4-variable cable design problem - a different look; normalize limit state equation by design equation; use of normalized random variables and nominal load ratio;

14:52

Are there many design equations that yield the same target beta? - Demonstration on 4-variable cable reliability example. For the same set of PSFs, how beta changes with changing nominal load ratios. The need to have a single set of PSFs in a class of design equation - selecting best set of PSFs to achieve minimum variation around target reliability for entire range of nominal load ratios

14:30

General Scheme of Optimizing Partial Safety Factors - deciding on scope of design, choosing the design equation format, defining loads and load combinations; identifying relevant design situation and their relative importance; optimization statement - objective function and constraints

10:24

Example: Optimized PSFs for ship hull girder bending design equation

14:15

12

34

Target Reliability Levels (Part 1)

Recap of Course so far

Summary of parts A (lectures 1 - 9), B (lectures 10 - 18)and C (lectures 19 - 30) of the course above; review of and plan for ongoing part D (lectures 31 - 36)

6:34

Objectives and constraints in design

Presence of randomness in decision variables and constraints; safety as a constraint; how rarely can safety and functionality be violated? - The need to set target reliabilities

13:48

Questions to be asked before setting target reliabilities

Consequences of limit state violation; how much loss of use or risk to life is acceptable; if unsafe, how much to spend to improve reliability; risk communication; the essential problem statements

11:29

Different methods of setting target reliabilities

Early attempts by structural reliability researchers; Introduction to calibration based, loss based and cost optimization based approaches

4:58

Target Reliability by Calibration

Selecting representative structures, method of evaluation, uncertainty quantification; pros and cons; reliability levels in existing (non-reliability based) codes of the day; different methods of computing of failure probability; deriving design equations to achieve a target beta; variation of beta with load ratios

15:25

35

Target Reliability Levels (Part 2)

Target reliabilities based on consequence and nature of failure

Lack of uniform reliability in traditional design codes for a given limit state; Early efforts by CSA and DNV; the primacy of life safety; the role of warning before failure

13:29

Novel structures (calibration not possible) - the ABS Mobile Offshore Base design guide

3:59

Target Reliabilities based on cost considerations

Target Reliabilities comparison-explicit cost consideration vs life and environmental safety- JCSS vs ISO 2394 vs Eurocodes

10:41

Target Reliabilities comparison - life saving cost vs monetary optimization and old vs new structures - ISO 13822 vs. ISO 2394:1998 vs ISO 2394:2015

7:28

Target Reliabilities for various consequences

Target Reliabilities comparison - Eurocodes vs ASCE 7

8:56

36

Target Reliability Levels (Part 3)

Introduction to Risk

Need for a common framework for considering a wide range of consequences; structural failure due to multiple hazards, which load combinations to consider; expected consequence of failure - risk; tolerable risk

10:43

Risk of Individual Fatalities

What risk to life is acceptable; society's reaction to life risk; acceptable individual risks by various agencies; fatal accident rate;

16:43

Fatality Risks from Structural Collapse

Observed rates of building collapse; acceptable annual rate of individual death from building failure; individual vs. multiple fatalities; voluntary nature of risk; role of warning before failure;

12:50

Target Reliability from Monetary Considerations

monetary value of human life; cost to save a statistical life

6:43

Conclusions and Acknowledgements

Course summary; Thanking teaching assistants, students, colleagues and mentors, and funding agencies

4:33