Determine the smallest diameter of the shaft. Use the maximum shear stress theory of failure with Tallow Express your answer to three significant figures and include appropriate units. = 8 ksi

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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**Transcription for Educational Website:**

**The Shaft and Journal Bearings Analysis**

The shaft is supported by journal bearings at points \( A \) and \( B \), which exert force components only in the \( x \) and \( z \) directions.

**Diagram Explanation:**

The diagram illustrates a shaft supported by two journal bearings, labeled \( A \) and \( B \). The system includes components and forces as follows:

- A force \( F_{x} = 200 \, \text{lb} \) is applied at a distance of 8 inches from the bearing \( A \), on a gear wheel located on the left side.
- The shaft spans a total distance with segments of 8 inches, marked between force applications and bearings.
- A second gear, located in the middle, experiences a force \( F_{y} = 50 \, \text{lb} \), applied in the \( y \) direction.
- On the right side, another force \( F_{z} = 250 \, \text{lb} \) acts perpendicular to the position of bearing \( B \), again 8 inches away from it.
- Each gear wheel is spaced at equal intervals of 8 inches along the shaft, with an additional 4 inches extending beyond the gears at each end.

**Part A: Calculation Task**

**Objective:**
Determine the smallest diameter of the shaft using the maximum shear stress theory of failure with an allowable shear stress \( \tau_{\text{allow}} = 8 \, \text{ksi} \).

**Instructions:**
Express the calculated diameter to three significant figures and include appropriate units in your response.
Transcribed Image Text:**Transcription for Educational Website:** **The Shaft and Journal Bearings Analysis** The shaft is supported by journal bearings at points \( A \) and \( B \), which exert force components only in the \( x \) and \( z \) directions. **Diagram Explanation:** The diagram illustrates a shaft supported by two journal bearings, labeled \( A \) and \( B \). The system includes components and forces as follows: - A force \( F_{x} = 200 \, \text{lb} \) is applied at a distance of 8 inches from the bearing \( A \), on a gear wheel located on the left side. - The shaft spans a total distance with segments of 8 inches, marked between force applications and bearings. - A second gear, located in the middle, experiences a force \( F_{y} = 50 \, \text{lb} \), applied in the \( y \) direction. - On the right side, another force \( F_{z} = 250 \, \text{lb} \) acts perpendicular to the position of bearing \( B \), again 8 inches away from it. - Each gear wheel is spaced at equal intervals of 8 inches along the shaft, with an additional 4 inches extending beyond the gears at each end. **Part A: Calculation Task** **Objective:** Determine the smallest diameter of the shaft using the maximum shear stress theory of failure with an allowable shear stress \( \tau_{\text{allow}} = 8 \, \text{ksi} \). **Instructions:** Express the calculated diameter to three significant figures and include appropriate units in your response.
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