Question

A rotating beam is subject to an alternating stress of 48 kpsi and a mean stress of 24 kpsi. The ultimate strength of the material is 100 kpsi and the fully correctly endurance limit is 40 kspi. Calculate the factor of safety using the Goodman fatigue failure theory to show this is finite life. Then, calculate the life of the beam in number of cycles.

Answer 1

goodman = 0.694

life of beam = 211597

Step-by-step explanation:

alternating stress = 48 kpsi

mean stress = 24 kpsi

ultimate strength = 100 kpsi

endurance limit = 40 kpsi

goodman:

=
`(mean stress)/(ultimate stress) +(alternating stress)/(endurance limit) =(1)/(N)`

=
`(24)/(100) +(48)/(40) =(1)/(N)`

= 0.24 + 1.2 =
`(1)/(N)`

N = 1/1.44

N = 0.694

2. check attachment for diagram

Log(N)-3/3 = log90 - log48/log90 - log40

Log(N)-3/3 = 0.77517

Log N = 5.325509

N = 10^(5.325509)

N = 211597