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The solid shaft is subjected to the distributed and concentrated torsional loadings shown, where T=740 N⋅m. The allowable shear stress for the material is τallow=68 MPa. determine the required diameter d of the shaft.

The solid shaft is subjected to the distributed and concentrated torsional loadings shown, where T=740 N⋅m. The allowable shear stress for the material is τallow=68 MPa. determine the required diameter d of the shaft.

Elements Of Electromagnetics
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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The solid shaft is subjected to the distributed and concentrated torsional loadings shown, where T=740 N⋅m.

The allowable shear stress for the material is τallow=68 MPa.

determine the required diameter d of the shaft.

The diagram illustrates a cylindrical shaft subjected to various torsional loads and is supported at the end by a bearing at point C. The shaft is divided into sections with different forces and moments acting upon it. ### Key Elements of the Diagram: 1. **Torsional Torque at T:** - A torque labeled as \( T \) is applied at the left end of the shaft. 2. **Distributed Torque:** - A distributed torque of \( 4 \, \text{kN} \cdot \text{m/m} \) is applied over a segment of the shaft. 3. **Point Loads:** - A concentrated torque of \( 400 \, \text{N} \cdot \text{m} \) is applied just before the shaft reaches point C. 4. **Distances:** - Measurements between different points on the shaft are marked: - The distance from the left end to point A is \( 0.5 \, \text{m} \). - The distance from A to B is also \( 0.5 \, \text{m} \). - A short segment at the end, from B to C, is \( 0.2 \, \text{m} \). 5. **Diameter:** - The shaft has a diameter labeled as \( d \) at point A, indicating a measurement needed for calculating stress or deflection. 6. **Reactions at C:** - A reaction force or moment at point C counteracts the applied loads to maintain equilibrium. ### Explanation: This diagram is a visual representation for analyzing the distribution of torsional stresses along a cylindrical shaft. The distribution of applied torques and their concentrations will affect the deformation and stress within the shaft material. Calculations based on this diagram could involve determining the shaft's angle of twist, shear stress distribution, and reactions at point C, which are essential for mechanical design and analysis.
Transcribed Image Text:The diagram illustrates a cylindrical shaft subjected to various torsional loads and is supported at the end by a bearing at point C. The shaft is divided into sections with different forces and moments acting upon it. ### Key Elements of the Diagram: 1. **Torsional Torque at T:** - A torque labeled as \( T \) is applied at the left end of the shaft. 2. **Distributed Torque:** - A distributed torque of \( 4 \, \text{kN} \cdot \text{m/m} \) is applied over a segment of the shaft. 3. **Point Loads:** - A concentrated torque of \( 400 \, \text{N} \cdot \text{m} \) is applied just before the shaft reaches point C. 4. **Distances:** - Measurements between different points on the shaft are marked: - The distance from the left end to point A is \( 0.5 \, \text{m} \). - The distance from A to B is also \( 0.5 \, \text{m} \). - A short segment at the end, from B to C, is \( 0.2 \, \text{m} \). 5. **Diameter:** - The shaft has a diameter labeled as \( d \) at point A, indicating a measurement needed for calculating stress or deflection. 6. **Reactions at C:** - A reaction force or moment at point C counteracts the applied loads to maintain equilibrium. ### Explanation: This diagram is a visual representation for analyzing the distribution of torsional stresses along a cylindrical shaft. The distribution of applied torques and their concentrations will affect the deformation and stress within the shaft material. Calculations based on this diagram could involve determining the shaft's angle of twist, shear stress distribution, and reactions at point C, which are essential for mechanical design and analysis.
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