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 performance-based 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 |
19-23 |
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, tL
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.