结构载荷设计.ppt

Chapter 3
Component Reliability Analysis
of Structures
Chapter 3: Element Reliability Analysis of Structures
AFOSM — Advanced First Order Second Moment
Method
JC Method — mended by the mittee
MVFOSM — Mean Value First Order Second Moment
Method
Contents
MCS — Monte Carlo Simulation Method
MVFOSM —
Mean Value First Order Second Moment Method
Chapter 3 Component Reliability Analysis of Structures
MVFOSM — Mean Value First Order Second Moment Method …1
MVFOSM — Mean Value
First Order Second Moment
First Order: The first-order terms in the Taylor series expansion
is used.
This method is also named Mean Value Method or Center Point Method.
Second Moment: Only means and variances of the basic variables
are needed.
Mean Value or Center Point: The Taylor series expansion is
on the means values.
Linear Limit State Functions
1. Assumptions
where, the terms
are constants;
The terms are uncorrelated random variables.
2. Formula
According to the linear functions of uncorrelated random variables introduced in Chapter 1, the mean and standard deviation of Z are:
Consider a linear limit state function of the form
MVFOSM — Mean Value First Order Second Moment Method …2
According to the central limit theorem, as n increases, the random variable
Z will approach a normal probability distribution.
Formula of Reliability Index
If the random variables are all normally distributed and uncorrelated, then the above formula is exact.
Otherwise, it provides only an approximate estimate on the failure probability.
MVFOSM — Mean Value First Order Second Moment Method …3
Example
Please refer to the textbook “Reliability of Structures” by Professor A. S. Nowak.
Turn to Page 102, look at the example carefully!
MVFOSM — Mean Value First Order Second Moment Method …4
Nonlinear Limit State Functions
1. Assumptions
where,
the terms are uncorrelated random variables,
2. Formula
We can obtain an approxi