### Analysis of Shear Stress in Coupled Circular Shafts**Problem Statement:**Two solid circular shafts, denoted as \( AB \) and \( BC \), are fixed to rigid walls at points \( A \) and \( C \), respectively. Members \( AB \) and \( BC \) are coupled together through a rigid plate at point \( B \). An external torque is applied at point \( B \) as depicted in the accompanying figure. The task is to determine the absolute maximum shear stress developed in the complete structure spanning from \( A \) to \( C \). Both members \( AB \) and \( BC \) are composed of an aluminum alloy with a shear modulus \( G = 60 \, \text{GPa} \).**Note:** Disregard the effect of stress concentration in this analysis.**Figure Explanation:**- The diagram illustrates two segments of a shaft, \( AB \) and \( BC \), connected at a central point \( B \) by a rigid plate.- The total length of \( AB \) is \( 100 \, \text{mm} \), and the length of \( BC \) is \( 150 \, \text{mm} \).- The diameter of the shafts is indicated as \( 20 \, \text{mm} \).- A torque of \( 5 \, \text{kN} \cdot \text{m} \) is applied at the junction \( B \).- The shafts are fixed at their respective ends, \( A \) and \( C \), to rigid supports.This setup is designed to analyze the distribution and intensity of shear stress in the shafts due to the applied torque.

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Two solid circular shafts (i.e., AB and BC) are fixed to rigid walls at point A and C, respectively. Members AB and BC are coupled together through a rigid plate at B. As shown in the figure, an external torque is applied at point B. Determine the absolute maximum shear stress developed in the whole structure AC. Both members AB and BC are made of the aluminum alloy with shear modulus G = 60 GPa. 150 mm 100 mm B 10 mm Note: ignore the effect of stress concentration. 5 kN-m 20 mm

Two solid circular shafts (i.e., AB and BC) are fixed to rigid walls at point A and C, respectively. Members AB and BC are coupled together through a rigid plate at B. As shown in the figure, an external torque is applied at point B. Determine the absolute maximum shear stress developed in the whole structure AC. Both members AB and BC are made of the aluminum alloy with shear modulus G = 60 GPa. 150 mm 100 mm B 10 mm Note: ignore the effect of stress concentration. 5 kN-m 20 mm

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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Question

### Analysis of Shear Stress in Coupled Circular Shafts

**Problem Statement:**

Two solid circular shafts, denoted as \( AB \) and \( BC \), are fixed to rigid walls at points \( A \) and \( C \), respectively. Members \( AB \) and \( BC \) are coupled together through a rigid plate at point \( B \). An external torque is applied at point \( B \) as depicted in the accompanying figure. The task is to determine the absolute maximum shear stress developed in the complete structure spanning from \( A \) to \( C \). Both members \( AB \) and \( BC \) are composed of an aluminum alloy with a shear modulus \( G = 60 \, \text{GPa} \).

**Note:** Disregard the effect of stress concentration in this analysis.

**Figure Explanation:**

- The diagram illustrates two segments of a shaft, \( AB \) and \( BC \), connected at a central point \( B \) by a rigid plate.
- The total length of \( AB \) is \( 100 \, \text{mm} \), and the length of \( BC \) is \( 150 \, \text{mm} \).
- The diameter of the shafts is indicated as \( 20 \, \text{mm} \).
- A torque of \( 5 \, \text{kN} \cdot \text{m} \) is applied at the junction \( B \).
- The shafts are fixed at their respective ends, \( A \) and \( C \), to rigid supports.

This setup is designed to analyze the distribution and intensity of shear stress in the shafts due to the applied torque.

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