Question

The stress components at a given point in an engineering component are estimated to be xx= 4.1 ksi, yy= 0 ksi, zz= 0.9 ksi, xy= −3.1ksi, yz= 1.2 ksi, xz= 0 ksi. Estimate the factor of safety against yielding using Von Mises theory if the uniaxial yield stress of the material is SY = 17.2 ksi.

Answer 1

Answer:2.5

Step-by-step explanation:

Given

`\sigma_(xx)=4.1\ ksi`

`\sigma_(yy)=0\ ksi`

`\sigma_(zz)=0.9\ ksi`

`\sigma_(xy)=-3.1\ ksi`

`\sigma_(yz)=1.2\ ksi`

`\sigma_(xz)=0\ ksi`

According to Von-mises working stress is given by

`\sigma_o=\sqrt{(1)/(2)\left [ (\sigma_(xx)-\sigma_(yy))^2+(\sigma_(yy)-\sigma_(zz))^2(\sigma_(zz)-\sigma_(xx))^2+6(\sigma_(xy)^2+\sigma_(xy)^2+\sigma_(yz)^2+\sigma_(xz)^2)\right ]}`

`\sigma_o=\sqrt{(1)/(2)\left [ (4.1-0)^2+(0-0.9)^2+(0.9-4.1)^2+6(3.1^2+0^2+1.2^2)\right ]}`

`\sigma_o=\sqrt{(1)/(2)\left [ 94.16\right ]}`

`\sigma_o=6.86\ ksi`

and Yield stress is
`\sigma _y=17.2\ ksi`

Factor of safety
`N=(17.2)/(6.86)`

`N=2.5`