### Required InformationThe torques shown are exerted on pulleys **A** and **B**. Consider $ T_A = 360 \, \text{N} \cdot \text{m} $ and $ T_B = 400 \, \text{N} \cdot \text{m} $.#### Diagram Description:- The diagram illustrates two solid shafts with pulleys labeled **A** and **B**.- Torque $ T_A $ is applied on pulley **A**, with a direction indicated by a clockwise arrow.- Torque $ T_B $ is applied on pulley **B**, also with a clockwise arrow.- The shaft between **A** and **B** has a diameter of 30 mm.- The shaft between **B** and the base **C** has a diameter of 46 mm.### Problem StatementKnowing that both shafts are solid, determine the maximum shearing stress in shaft $ AB $.The maximum shearing stress in shaft $ AB $ is ______ MPa.

Answered: Required information The torques shown…

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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### Required Information

The torques shown are exerted on pulleys **A** and **B**. Consider $ T_A = 360 \, \text{N} \cdot \text{m} $ and $ T_B = 400 \, \text{N} \cdot \text{m} $.

#### Diagram Description:
- The diagram illustrates two solid shafts with pulleys labeled **A** and **B**.
- Torque $ T_A $ is applied on pulley **A**, with a direction indicated by a clockwise arrow.
- Torque $ T_B $ is applied on pulley **B**, also with a clockwise arrow.
- The shaft between **A** and **B** has a diameter of 30 mm.
- The shaft between **B** and the base **C** has a diameter of 46 mm.

### Problem Statement

Knowing that both shafts are solid, determine the maximum shearing stress in shaft $ AB $.

The maximum shearing stress in shaft $ AB $ is ______ MPa.

Expert Solution

Step 1

Introduction

When the shaft or pulley experiences a twisting moment or torque, shear stress forms in the shaft or pulley in a direction perpendicular to the neutral axis and parallel to the shaft or pulley's cross section. With the use of the torsional equation, we will compute the maximum shear stress generated in the region AB in this case.

Given data:

$\begin{array}{rcl} torque on the top pulley A (T_{A}) & = & 360 N m \\ torque on the middle pulley B (T_{B}) & = & 400 N m \\ diameter of the shaft (d_{1}) & = & 30 mm \\ diameter of the shaft (d_{2}) & = & 46 mm \end{array}$

Find out:

The maximum shear stress in the AB ${(ζ)}_{\max}$ .

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