Question

Cyclic Stresses A fatigue test was conducted in which the mean stress was 46.2 MPa and the stress amplitude was 219 MPa. (a) Calculate the maximum stress level (in MPa). (b) Calculate the minimum stress level (in MPa). (c) Calculate the stress ratio. (d) Calculate the magnitude of the stress range (in MPa). (a) MPa (b) MPa (c) (d) MPa

Answer 1

Answer:

a) 265.2 MPa

b)-172.8 MPa

c) -0.6541

d) 438 MPa

Explanation:

$\sigma_{mean}= 46.2 MPa$

$\sigma_{amplitude}= 219 MPa$

we know that

$\sigma_{mean} = \frac{\sigma_{max}+\sigma_{min}}{2}$

$46.2 = \frac{\sigma_{max}-\sigma_{min}}{2}$..............(1)

$\sigma_{amplitude} = \frac{\sigma_{max}-\sigma_{min}}{2}$

$219 = \frac{\sigma_{max}-\sigma_{min}}{2}$.................(2)

solving equ (1) and equ (2) we get

$\sigma_{max}$ = 265.2 MPa

$\sigma_{min}$= -172.8 MPa

stress ratio = $\frac{\sigma_{min}}{\sigma_{max}}$

= $\frac{-172.8}{265.2}$ = -0.6515

now stress range = $\sigma_{max}$-$\sigma_{min}$

= 265.2 -(-172.8) = 438 MPa