Module 5 - E-Courses

Reliability Engineering Prof. G. L. Sivakumar Babu
Figure 11 - Design point and reliability index for highly nonlinear limit state
function.
The
iterative procedure requires us to solve a set of (2n + 1) simultaneous equation with
* * *
(2n + I) unknowns: β,α1, α2 ……., αn , Z1
, Z 2.......
Z n where
α =
∂g
−
∂Z
Indian Institute of Science Bangalore
i
∂g
∂Z
n
∑
i=
1
*
i
i
⎛
n
⎜ ∑ ⎜ k = 1 ∂Z
k evaluated at design po int
∂g
=
∂X
( α )
⎝
i
∂g
∂X
∂Z
i evaluated at design po int
i
i
∂g
= σ
∂X
* *
*
( z , z .......... ... z ) = 0
1
2
z = βα
g
i
2
i
n
i
X i
2
⎟ ⎟
⎞
⎠
Equation 5.23b is just an application of the chain rule of differentiation Equation 5.23c is
a requirement on the values of the αi variables, which can be confirmed by looking at
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