Numerical/Fill in the Slank, \( +200,-0.00 \) A component is subjected to an axial stress of 250 MPa and shear stress of \( \cdot 150 \mathrm{MPa} \). The yield strength of the material is 400 MPa and ultimate strength of the material is 600 MPa . The factor of safety based on Von Mises criterion is \( \qquad \) (round off to two decimal places).

To find the factor of safety based on the Von Mises criterion, we first need to calculate the Von Mises stress (\( \sigma_{VM} \)) using the formula: \[ \sigma_{VM} = \sqrt{\sigma^2 + 3\tau^2} \] Where: - \( \sigma \) is the axial stress, - \( \tau \) is the shear stress. Substituting in the given values: \[ \sigma_{VM} = \sqrt{(250 \, \text{MPa})^2 + 3(150 \, \text{MPa})^2} = \sqrt{62500 + 3 \times 22500} = \sqrt{62500 + 67500} = \sqrt{130000} \] Calculating this gives: \[ \sigma_{VM} \approx 360.55 \, \text{MPa} \] Now, to find the factor of safety (FoS): \[ \text{FoS} = \frac{\text{Yield Strength}}{\sigma_{VM}} = \frac{400 \, \text{MPa}}{360.55 \, \text{MPa}} \approx 1.11 \] So the factor of safety based on the Von Mises criterion is approximately \( \mathbf{1.11} \).