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
icon
Related questions
icon
Concept explainers
Question

I cant figure out how to do this problem how do I do it?

**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 \( (\frac{\pi d^4}{32}) \)
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 \( (\frac{\pi d^4}{32}) \)
Expert Solution
Step 1: Given data

For the solution refer below images.

Mechanical Engineering homework question answer, step 1, image 1

steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question

where did the 16 come?

Solution
Bartleby Expert
SEE SOLUTION
Knowledge Booster
Combined Loading
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY