114 2. RELIABILITY OF A COMPONENT UNDER CYCLIC LOAD
2.13. A shaft with a diameter d D 1:500 ˙ 0:005
00
is subjected to a cyclic torsion loading.
e torque can be treated as a fully reversed cyclic torsion. e torque amplitude in the
unit of klb-in can be treated as lognormal distribution with a log mean
ln T
D 1:85
and log standard deviation
ln T
D 0:062. e component torsion endurance limit S
e
follows a normal distribution with a mean
S
e
D 12:4 (ksi) and a standard deviation
S
e
D 1:02 (ksi). is shaft is designed to have an infinite life. (1) Establish the limit
state function of this problem. (2) Calculate the reliability of the shaft under the cyclic
bending loading
2.14. What is the P-S-N curve approach? What are the two sets of curves that the P-S-N
curve can provide?
2.15. Conduct literature research and find an example where the P-S-N curves are presented.
2.16. A bar is subjected to cyclic axial stress with a mean stress
m
D 12:6 (ksi) and stress
amplitude
a
D 8:6 (ksi). According to the design specification, the bar has a design
life n
L
D 380;000 (cycles). e bar fatigue life N
C
at the stress level with a mean stress
m
D 12:6 (ksi) and stress amplitude
a
D 8:6 (ksi) follow a normal distribution with
a mean
N
C
D 440;000 (cycles) and a standard deviation
N
C
D 34;500. Calculate its
reliability.
2.17. A beam is subjected to a fully reversed cyclic bending stress with a constant num-
ber of cycles n
L
D 450;000 (cycles). e stress amplitude of this fully reversed cyclic
bending stress
a
follows a Weibull distribution with a scale parameter D 18:25 (ksi)
and a shape parameter ˇ D 1:5. e beam fatigue strength S
f
at the fatigue life N D
450;000 (cycles) follows a normal distribution with a mean
S
f
D 21:98 (ksi) and a
standard deviation
S
f
D 1:78 (ksi). Calculate its reliability
2.18. A square bar is subjected to cyclic fully reversed axial stress with a constant stress ampli-
tude
a
D 24:6 (ksi). Its number of cycles of this fully reversed axial stress can be treated
as a normal distribution with a mean
n
L
D 125;000 (cycles) and a standard deviation
n
L
D 5600 (cycles). e bar fatigue life N
C
at the fatigue strength level S
f
D 24:6 (ksi)
follows a lognormal distribution with a log mean
ln N
C
D 12:13 and a standard devi-
ation
ln N
C
D 0:249. Calculate its reliability.
2.19. A round bar is subjected to three constant cyclic stresses as listed in the 2nd and 3rd
columns of Table 2.64. e distributed fatigue life of this bar at the corresponding stress
levels are listed in the 4th and 5th columns of Table 2.64. Calculate its reliability.
2.20. A beam is subjected to three constant cyclic bending stresses with a distributed number
of cycles as listed in the 2nd, 3rd, and 4th columns of Table 2.65. e distributed fatigue
life of this bar at the corresponding stress levels are listed in the 5th and 6th columns of
Table 2.65. Calculate its reliability.