Answer to Question #144707 in Mechanical Engineering for phoebe jewelle agoo

Question

A steel rotating-beam test specimen has an ultimate strength of 1600 MPa. Estimate the life of the

specimen if it is tested at a completely reversed stress amplitude of 900 MPa.

Answer 1

Ultimate strength of rotating component is ,S_ut=1600 MPa, Reversed amplitude =900 MPa= $\sigma_a$

We know that for endurance limit for specimen is

$S_e=0.5 \times \sigma_u=0.5\times 1600=800$ MPa

Now we know that for, $\sigma_u>1400 MPa$

we take endurance limit as 700 MPa and strength friction,f=0.77

Now,

we will find value of constant a and b

$a=\frac{(f\times \sigma_u)^2}{S_e}$

$a=a=\frac{(0.77\times 1600)^2}{700}=2169 MPa$

$b=\frac{1}{3}\times log (\frac{f\times \sigma_u}{S_e})$

b=-0.08

Now we know that for Number of cycles or for life span of specimen

$N=(\frac{\sigma_a}{a})^b=(\frac{900}{2169})^{(-0.08)}$

N= 46401