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).

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To determine the factor of safety based on the Von Mises criterion, follow these steps:

### Given:
- **Axial Stress ($$\sigma$$)**: 250 MPa
- **Shear Stress ($$\tau$$)**: 150 MPa
- **Yield Strength ($$S_y$$)**: 400 MPa

### Von Mises Equivalent Stress ($$\sigma_V$$):
The Von Mises stress is calculated using the formula:
$$
\sigma_V = \sqrt{\sigma^2 + 3\tau^2}
$$

Plugging in the values:
$$
\sigma_V = \sqrt{(250)^2 + 3 \times (150)^2} = \sqrt{62,500 + 67,500} = \sqrt{130,000} \approx 360.56 \text{ MPa}
$$

### Factor of Safety ($$n$$):
The factor of safety based on the Von Mises criterion is:
$$
n = \frac{S_y}{\sigma_V}
$$

Substituting the values:
$$
n = \frac{400}{360.56} \approx 1.11
$$

### **Answer:**
1.11
The factor of safety based on the Von Mises criterion is **1.11**.

Numerical/Fill in the Slank,

A component is subjected to an axial stress of 250 MPa and shear stress of . 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 (round off to two decimal places).

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Numerical/Fill in the Slank, A component is subjected to an axial stress of 250 MPa and shear stress of . 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 (round off to two decimal places).