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

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

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

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

$\sigma_o=\sqrt{\frac{1}{2}\left [ 94.16\right ]}$

$\sigma_o=6.86\ ksi$

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

Factor of safety $N=\dfrac{17.2}{6.86}$

$N=2.5$