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Calculation Example: Introduction to Static Failure Theories

1. Problem Statement

A machine component is subjected to loads resulting in the following principal stresses: $\sigma_1 = 150 \text{ MPa}$ , $\sigma_2 = 50 \text{ MPa}$ , and $\sigma_3 = 0 \text{ MPa}$ . Calculate the von Mises Equivalent Stress ( $\sigma^\prime$ ) to evaluate whether this component will fail according to Static Failure Theory.

2. Given Information

Principal Stress 1 (σ₁)

MPa

Principal Stress 2 (σ₂)

MPa

Principal Stress 3 (σ₃)

MPa

3. Calculation

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Introduction to Static Failure Theories

Introduction to static failure criteria for ductile materials, covering von Mises and Maximum Shear Stress theories.

1. Problem Statement

2. Given Information

Principal Stress 1 (σ₁)

MPa

Principal Stress 2 (σ₂)

MPa

Principal Stress 3 (σ₃)

MPa

3. Calculation

\sigma^\prime = \sqrt{\frac{(\sigma_1 - \sigma_2)^2 + (\sigma_2 - \sigma_3)^2 + (\sigma_3 - \sigma_1)^2}{2}}

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4. Engineering Interpretation

From the calculation, the von Mises Equivalent Stress is MPa. This value is the combined equivalent stress that engineers use to analyze the safety of ductile materials, such as steel.

In engineering practice, we compare $\sigma^\prime$ with the Yield Strength ( $S_y$ ) of the chosen material. If the calculated stress ( MPa) is less than $S_y$ , it indicates that the component remains safe without permanent deformation (yielding). The Factor of Safety ( $n$ ) can be calculated from the equation $n = \frac{S_y}{\sigma^\prime}$ .

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\sigma^\prime = \sqrt{\frac{(\sigma_1 - \sigma_2)^2 + (\sigma_2 - \sigma_3)^2 + (\sigma_3 - \sigma_1)^2}{2}}

4. Engineering Interpretation

From the calculation, the von Mises Equivalent Stress is MPa. This value is the combined equivalent stress that engineers use to analyze the safety of ductile materials, such as steel.

Calculation Example: Introduction to Static Failure Theories

1. Problem Statement

2. Given Information

3. Calculation

Related Content

Articles

Introduction to Static Failure Theories

1. Problem Statement

2. Given Information

3. Calculation

von Mises Stress (Static Failure Theories)

Where:

Calculation:

4. Engineering Interpretation

von Mises Stress (Static Failure Theories)

Where:

Calculation:

4. Engineering Interpretation