202 3. THE DIMENSION OF A COMPONENT WITH REQUIRED RELIABILITY
dimension-dependent parameters need to be updated in each iterative step by the newly available
dimension.
When the limit state function of a component under a specified loading is established, and
initial dimension-dependent parameters are selected through the preliminary design, we can use
four different computational methods to iteratively determine component dimension with the
required reliability under the specified loadings. ese four methods are as follows.
• e FOSM method. When all random variables in the limit state function are normal
distributions, the FOSM method provides an equation to link the reliability index ˇ with
the means and the standard deviations of all normally distributed random variables. In
this equation, the only one unknown is the dimension and so can be solved. is is an
approximate result. is method has been discussed in Section 3.2.2.
• e modified H-L method. When all random variables in the limit state function are
normal distributions, the modified H-L method can be used to determine the component
dimension iteratively. e detailed procedure and the program flowchart of the modified
H-L method have been discussed in Section 3.2.3.
• e modified R-F method. When there is at least one non-normal distribution in the
limit state function, the modified R-F can be used to determine the component dimension
iteratively. e detailed procedure and the program flowchart of the modified R-F method
have been discussed in Section 3.2.4.
• e modified Monte Carlo Method. For any type of distribution in a limit state func-
tion, the modified Monet Carlo method can always be used to determine the component
dimension iteratively. is method might take a little longer computing time to get the
result when it is compared with the modified H-L and modified R-F methods. e de-
tailed procedure and the program flowchart of the modified Monet Carlo method have
been discussed in Section 3.2.5.
e dimension design of the component under static loading is discussed in Section 3.3.
Several examples are provided and discussed, including bars under axial loading, pins under di-
rect shearing, shafts under torsion and beams under bending, and components under combined
loadings.
It is difficult to use the P-S-N curves approach to conduct the dimension design because
stress is the dimension-dependent, and the corresponding P-S-N curves could not be selected.
erefore, the dimension design of component under cyclic loadings is based on the K-D prob-
abilistic fatigue damage model in this chapter and is fully demonstrated and discussed in Sec-
tion 3.4. Several examples are presented including bars under cyclic axial loadings, pins under
cyclic direct shearing loading, shafts under cyclic torsion loadings, beam under cyclic bending
loadings, rotating shaft under cyclic combined-bending-torsion loading.