### Problem StatementA shaft of different diameters is embedded in the wall at point A and subjected to torque loadings as illustrated. Determine the maximum shear stress in the shaft. A fillet weld with a radius of 5 mm is used to connect the shafts at point B.### Diagram Explanation#### Shaft Diagram- The shaft is fixed to the wall at point A.- It has varying diameters: - Diameter from A to B: 50 mm - Diameter from B to C: 30 mm- Torque is applied at various points: - 1000 N·m at A - 400 N·m at B - 250 N·m at C#### Stress Concentration Diagram- The graph shows the stress concentration factor \( K \) against the ratio \( \frac{r}{d} \), where \( r \) is the fillet radius and \( d \) is the smaller diameter of the shaft.- Lines on the graph represent different \( \frac{D}{d} \) ratios: - \( \frac{D}{d} = 2.5 \) - \( \frac{D}{d} = 2.0 \) - \( \frac{D}{d} = 1.67 \) - \( \frac{D}{d} = 1.25 \) - \( \frac{D}{d} = 1.11 \)The graph can be used to find the stress concentration factor \( K \) for specific shaft dimensions and fillet parameters.

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6. A shaft of different diameters is planted to the wall at A and is subjected to torque loadings, as shown. Determine the maximum shear stress in the shaft. A fillet weld having a radius of 5 mm is used to connect the shafts at B. (note: the stress concentration diagram is given) 1000 N·m. 50 mm B 400N.m 30 mm 250 N·m 2.0 1.9 1.8 1.7 1.6 K 1.5 1.4 1.3 1.2 1.1 1.0 0.00 0.05 0.10 ▬▬▬▬▬▬▬▬▬▬▬ T D 0.15 LE 0.20 D/d 0.25 = 2.5 2.0 1.67 1.25 1.11 0.30

6. A shaft of different diameters is planted to the wall at A and is subjected to torque loadings, as shown. Determine the maximum shear stress in the shaft. A fillet weld having a radius of 5 mm is used to connect the shafts at B. (note: the stress concentration diagram is given) 1000 N·m. 50 mm B 400N.m 30 mm 250 N·m 2.0 1.9 1.8 1.7 1.6 K 1.5 1.4 1.3 1.2 1.1 1.0 0.00 0.05 0.10 ▬▬▬▬▬▬▬▬▬▬▬ T D 0.15 LE 0.20 D/d 0.25 = 2.5 2.0 1.67 1.25 1.11 0.30

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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Question

### Problem Statement

A shaft of different diameters is embedded in the wall at point A and subjected to torque loadings as illustrated. Determine the maximum shear stress in the shaft. A fillet weld with a radius of 5 mm is used to connect the shafts at point B.

### Diagram Explanation

#### Shaft Diagram

- The shaft is fixed to the wall at point A.
- It has varying diameters:
- Diameter from A to B: 50 mm
- Diameter from B to C: 30 mm
- Torque is applied at various points:
- 1000 N·m at A
- 400 N·m at B
- 250 N·m at C

#### Stress Concentration Diagram

- The graph shows the stress concentration factor \( K \) against the ratio \( \frac{r}{d} \), where \( r \) is the fillet radius and \( d \) is the smaller diameter of the shaft.
- Lines on the graph represent different \( \frac{D}{d} \) ratios:
- \( \frac{D}{d} = 2.5 \)
- \( \frac{D}{d} = 2.0 \)
- \( \frac{D}{d} = 1.67 \)
- \( \frac{D}{d} = 1.25 \)
- \( \frac{D}{d} = 1.11 \)

The graph can be used to find the stress concentration factor \( K \) for specific shaft dimensions and fillet parameters.

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