### Stress Analysis of Ductile Alloy ComponentThe stresses on the surface of a ductile alloy component are as illustrated in the provided diagram. The yield strength of the alloy (\(\sigma_y\)) is given as 190 MPa.**Objective:**1. Find the Principal Stresses.2. Calculate the Mises equivalent stress for the given state of plane stress.3. Calculate the Factor of Safety predicted by the maximum-distortion-energy theory using Mises stress.4. Calculate the Factor of Safety predicted by the maximum-shear-stress theory of failure.#### Problem Details:**Given:**- Yield Strength of the alloy \(\sigma_y = 190 \text{ MPa}\)**Principal Stresses:**\[\sigma_{\text{max}} = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \text{ MPa} \quad \sigma_{\text{min}} = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \text{ MPa}\]**Mises Equivalent Stress Calculation:**\[\sigma_M = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \text{ MPa}\]**Factor of Safety (FS) using Maximum-Distortion-Energy Theory:**\[FS = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\]**Failure Assessment:**Does the component fail according to this theory? \underline{Yes} or \underline{No}**Factor of Safety (FS) using Maximum-Shear-Stress Theory:**\[FS = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\]**Failure Assessment:**Does the component fail according to this theory? \underline{Yes} or \underline{No}#### Diagram Explanation:The provided diagram shows the state of plane stress on the surface of a ductile alloy component. The diagram includes:- **Stress values** along different directions on the component: - A vertical arrow pointing upwards indicating 50 MPa. - A vertical arrow pointing downwards indicating 50 MPa. - A horizontal arrow pointing to the right indicating 100 MPa. - A horizontal arrow pointing to the left indicating 0 MPa. The component is labelled with axes \(x\) and

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The stresses on the surface of a ductile alloy component 50 MPa are as pictured. The yield strength of the alloy is oy = 190MPA. 100 MPa Find Principal Stresses: Отах MPa Omin MPа 50 MPa Calculate Mises equivalent stress for the given state of plane stress: OM MPa Calculate Factor of Safety predicted by the maximum-distortion-energy theory using Mises stress: FS Does the component fail according to this theory? Yes or No Calculate Factor of Safety predicted by the maximum-shear-stress theory of failure: FS Does the component fail according to this theory? Yes or No

The stresses on the surface of a ductile alloy component 50 MPa are as pictured. The yield strength of the alloy is oy = 190MPA. 100 MPa Find Principal Stresses: Отах MPa Omin MPа 50 MPa Calculate Mises equivalent stress for the given state of plane stress: OM MPa Calculate Factor of Safety predicted by the maximum-distortion-energy theory using Mises stress: FS Does the component fail according to this theory? Yes or No Calculate Factor of Safety predicted by the maximum-shear-stress theory of failure: FS Does the component fail according to this theory? Yes or No

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

### Stress Analysis of Ductile Alloy Component

The stresses on the surface of a ductile alloy component are as illustrated in the provided diagram. The yield strength of the alloy (\(\sigma_y\)) is given as 190 MPa.

**Objective:**
1. Find the Principal Stresses.
2. Calculate the Mises equivalent stress for the given state of plane stress.
3. Calculate the Factor of Safety predicted by the maximum-distortion-energy theory using Mises stress.
4. Calculate the Factor of Safety predicted by the maximum-shear-stress theory of failure.

#### Problem Details:

**Given:**
- Yield Strength of the alloy \(\sigma_y = 190 \text{ MPa}\)

**Principal Stresses:**
\[
\sigma_{\text{max}} = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \text{ MPa} \quad \sigma_{\text{min}} = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \text{ MPa}
\]

**Mises Equivalent Stress Calculation:**
\[
\sigma_M = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \text{ MPa}
\]

**Factor of Safety (FS) using Maximum-Distortion-Energy Theory:**
\[
FS = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
\]

**Failure Assessment:**
Does the component fail according to this theory? \underline{Yes} or \underline{No}

**Factor of Safety (FS) using Maximum-Shear-Stress Theory:**
\[
FS = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
\]

**Failure Assessment:**
Does the component fail according to this theory? \underline{Yes} or \underline{No}

#### Diagram Explanation:
The provided diagram shows the state of plane stress on the surface of a ductile alloy component. The diagram includes:
- **Stress values** along different directions on the component:
- A vertical arrow pointing upwards indicating 50 MPa.
- A vertical arrow pointing downwards indicating 50 MPa.
- A horizontal arrow pointing to the right indicating 100 MPa.
- A horizontal arrow pointing to the left indicating 0 MPa.

The component is labelled with axes \(x\) and

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Please help explain all, thank you!
How would you solve this
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