This
course describes how to determine the probability individual components (e.g.,
beams, columns or connections) will fail and the probability that a system of
these components (e.g., a structural frame) will fail. In a philosophical
sense, it helps one realize that engineers can't guarantee a given outcome,
rather we are providing reasonable odds that the outcome will be as desired. It
also helps an engineer view things from a systems perspective, e.g., whether or
not redundancy improves the reliability of the system  it doesn't always 
and how reliable each component must be to improve the reliability of the
system. These concepts form the basis of performancebased design.
All the current LRFD structural and geotechnical design codes are derived from reliability concepts. The course describes how these codes are derived.
Class 
Date 
Topic 
Assignment 
1 
Aug 20 
Introduction


2 
Aug 22 
Review
of Probability 

3 
Aug 24 
Probability
Distributions 
Homework
#1 
4 
Aug 27 
Extreme
Value Distributions; Mathcad Example 

5 
Aug 29 
Asympotitic Distributions; Gumbel's Classifications 
Homework
#2 
6 
Aug 31 
Order
Statistics; Order Stat Ex, Spreadsheet 


Sep 3 
Labor
Day 

7 
Sep 5 
Bayes'
Theorem, Bayes' Theorem Example 

8 
Sep 7 
Transformation
of Variables; Mathcad Example 

9 
Sep 10 
The
Reliability Problem 
Homework
#3 
10 
Sep 12 
Second
Moment Formulations 

11 
Sep 14 
Linear
Limit States, Example 

12 
Sep 17 
Invariant
Formulations 
3.6
and Homework #4 
13 
Sep 19 
Nonlinear
Limit States 

14 
Sep 21 
Transformation
Methods 

15 
Sep 24 
Example
1, Example 2 
5.1
and Homework #5 
16 
Sep 26 
Determination
of the Safety Index 

17 
Sep 28 
Monte
Carlo Simulation 

18 
Oct 1 
Examples:
Mathcad, FOSM comparison 
5.4
and Homework #6 
19 
Oct 3 
EXAM
#1 (Old
Exam) 

20 
Oct 5 
Importance
Sampling; Example 
Project
Assignment 
21 
Oct 8 
Latin
Hypercube Sampling, 
4.1,
12 
22 
Oct 10 
Latin
Hypercube Example 

23 
Oct 12 
Antithetic
Sampling; Antithetic Sampling Example. Comparison 

24 
Oct 15 
Correlated
Random Variables, Example 
Project
Proposal 
25 
Oct 17 
System
Reliability 
Homework
#9 
26 
Oct 19 
Series
System Probability Bounds 

27 
Oct 22 
Ditlevsen Bounds, Example 

28 
Oct 24 
Parallel
Systems 

29 
Oct 26 
Enumeration
Methods for System Reliability 
9.1 
30 
Oct 29 
Probabilistic
Enumeration Methods for System Reliability 
Project
Progress Report 
31 
Oct 31 
Element
Replacement Techniques 

32 
Nov 2 
Codes
and Structural Reliability, Example 
Homework
#11 
33 
Nov 5 
Exam
#2 
Old
Exam 
34 
Nov 7 
Code
Calibration, Mechanistic Empirical Pavement Design Guide 

35 
Nov 9 
Modeling
of Uncertainty 

36 
Nov 12 
Quantification
of Uncertainty 
8.2,
3 
37 
Nov 14 
Distributions 

38 
Nov 16 
Human
Error 
Project
Progress Report 
Nov 
1923 
Thanksgiving
Recess 

39 
Nov 26 
Time
Dependent Reliability 

40 
Nov 28 
Discrete
Processes 
Homework
#13 
41 
Nov 30 
EXAM
#3 
Old
Exam, Excel Sol'n 
42 
Dec 3 
Discrete
Process Examples, Mathcad Worksheets: 1 year, 50 years, t_{L}
years 

43 
Dec 5 
Fatigue,
Example 

44 
Dec 7 
Presentations 

47 
Dec 12 
12: 45 P.M. Presentations 
The reading assignments should be completed before each lecture.
Homework is due on the dates shown.