3.2. DIMENSION DESIGN WITH REQUIRED RELIABILITY 123
Table 3.2: e preliminary stress concentration factors for a stepped bar/plate
Stepped Plate or Bar Bending Axial
Shoulder fi llet–sharp (r/W = 0.02) 2.7 3.0
Shoulder fi llet–well-rounded (r/W = 0.1) 1.7 1.9
Table 3.3: e preliminary stress concentration factors for a plate with a center hole
Plate with a Center Hole Bending Loading Axial Loading
Narrow plate (d/W = 2) 1 2.1
Plate (d/W = 3) 0.667 2.3
In fatigue design, the fatigue stress concentration factor is a dimension-dependent which
will be determined by dimension, fillet radius, and type of material. e fatigue stress concen-
tration factor can be calculated per Equations (2.22), (2.23), and (2.24) in Section 2.6 when the
static stress concentration factor, fillet radius, and ultimate strength are known. Tables 3.1, 3.2,
and 3.3 can help to determine the preliminary static stress concentration factor. As we mentioned
above, the fillet radius can be pre-determined by the type of fillets and its purpose according to
the sketched structure of the component. We can also pre-select the type of material. erefore,
we can determine a preliminary estimation of the fatigue stress concentration factor.
In fatigue design, the size modification factor is also a dimension-dependent parameter
and can be calculated per Equation (2.17) in Section 2.4. e size dimension factor for bending
or torsion has a value between 0.807–1.12. We can use 0.87 as its preliminary estimation:
k
b
D
8
<
:
0:87 For bending or torsion loading
1 For axial loading:
(3.3)
In the following sections, we will discuss how to determine the mean
d
of a normally dis-
tributed dimension with the required reliability R.
3.2.2 DIMENSION DESIGN BY THE FOSM METHOD
When all random variables are normally distributed random variables in the limit state func-
tion (1.1), we can use the FOSM method to estimate
d
with the required reliability R under
specified loading condition. e FOSM method for calculating the reliability of a component
has been discussed in Section 3.5 of Volume 1 [1]. Now, we will discuss how to use the FOSM
to conduct the dimension design with the required reliability. e procedure of the dimension
design by the FOSM method is as follows.
Step 1: Preliminary design for determining K
t
for static design or K
f
and k
b
for fatigue design.