A solid 40 mm diameter shaft is subjected to the torques shown. The bearings shown allow the shaft to turn freely. Assume TA= 395 N·m, TB = 987.5 N·m, Tc = 790 N·m, and Tp 197.5 N.m. Determine the magnitude of the maximum shear stress in the shaft. D TD Tc B TB TA
A solid 40 mm diameter shaft is subjected to the torques shown. The bearings shown allow the shaft to turn freely. Assume TA= 395 N·m, TB = 987.5 N·m, Tc = 790 N·m, and Tp 197.5 N.m. Determine the magnitude of the maximum shear stress in the shaft. D TD Tc B TB TA
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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![**Problem Statement:**
A solid 40 mm diameter shaft is subjected to the torques shown. The bearings allow the shaft to turn freely.
**Given Torques:**
- \( T_A = 395 \, \text{N} \cdot \text{m} \)
- \( T_B = 987.5 \, \text{N} \cdot \text{m} \)
- \( T_C = 790 \, \text{N} \cdot \text{m} \)
- \( T_D = 197.5 \, \text{N} \cdot \text{m} \)
**Task:**
Determine the magnitude of the maximum shear stress in the shaft.
**Diagram Explanation:**
The diagram shows a shaft supported by two bearings at points A and D. There are four torques applied at various segments along the shaft, i.e., \(T_A\), \(T_B\), \(T_C\), and \(T_D\), represented by circular arrows around the shaft indicating the direction and location of each torque.
**Incorrect Answer Indicated:**
\[
T_{\text{max}} = 0.000079577 \, \text{MPa}
\]
**Notes:**
The problem requires calculating the maximum shear stress, often approached using formulas related to torsion in cylindrical shafts. This involves using the equation for shear stress due to a torque:
\[
\tau = \frac{Tc}{J}
\]
Where:
- \(T\) is the applied torque
- \(c\) is the outer radius of the shaft
- \(J\) is the polar moment of inertia \( (\frac{\pi d^4}{32}) \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F919fc4f8-bc37-4123-8b2a-9ca8cd02385f%2Ff9f95dfe-4e47-4329-a70f-73008f658c4a%2Fpphw9mn_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A solid 40 mm diameter shaft is subjected to the torques shown. The bearings allow the shaft to turn freely.
**Given Torques:**
- \( T_A = 395 \, \text{N} \cdot \text{m} \)
- \( T_B = 987.5 \, \text{N} \cdot \text{m} \)
- \( T_C = 790 \, \text{N} \cdot \text{m} \)
- \( T_D = 197.5 \, \text{N} \cdot \text{m} \)
**Task:**
Determine the magnitude of the maximum shear stress in the shaft.
**Diagram Explanation:**
The diagram shows a shaft supported by two bearings at points A and D. There are four torques applied at various segments along the shaft, i.e., \(T_A\), \(T_B\), \(T_C\), and \(T_D\), represented by circular arrows around the shaft indicating the direction and location of each torque.
**Incorrect Answer Indicated:**
\[
T_{\text{max}} = 0.000079577 \, \text{MPa}
\]
**Notes:**
The problem requires calculating the maximum shear stress, often approached using formulas related to torsion in cylindrical shafts. This involves using the equation for shear stress due to a torque:
\[
\tau = \frac{Tc}{J}
\]
Where:
- \(T\) is the applied torque
- \(c\) is the outer radius of the shaft
- \(J\) is the polar moment of inertia \( (\frac{\pi d^4}{32}) \)
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