Review The simply-supported beam is built-up from three boards by nailing them together as shown. The wood has an allowable shear stress of Tallow = 1.5 MPa, and an allowable bending stress of oallow = 9 MPa. The nails are spaced at s = 77 mm, and each has a shear strength of 1.5 kN. (Eigure 1) Part A Determine the maximum allowable force P that can be applied to the beam. Express your answer to three significant figures and include the appropriate units. HÀ ? P= 8.9 kN Submit Previous Answers Request Answer X Incorrect; Try Again; 3 attempts remaining Provide Feedback Next > Figure < 1 of 1> 1 m I m 100 mm 25 mm 25 mm 200 mm 25 mm

Elements Of Electromagnetics
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ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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The problem involves determining the maximum allowable force \( P \) that can be applied to a simply-supported beam composed of three boards nailed together. Here are the details provided:

### Beam Specifications:
- **Shear Stress**: The wood has an allowable shear stress of \( \tau_{\text{allow}} = 1.5 \, \text{MPa} \).
- **Bending Stress**: The allowable bending stress is \( \sigma_{\text{allow}} = 9 \, \text{MPa} \).
- **Nails**:
  - Spacing: \( s = 77 \, \text{mm} \).
  - Shear Strength: \( 1.5 \, \text{kN} \).

### Task:
Calculate the maximum force, \( P \), applying the above constraints, and express your answer to three significant figures including the units.

### User Input:
- The user attempted to input \( P = 8.9 \, \text{kN} \) and received feedback indicating the answer is incorrect with three attempts remaining.

### Beam Diagram Description:
The diagram shows:
- The beam is supported at points \( A \) and \( B \), with point \( P \) applied at the center of the span.
- Total span of the beam is \( 2 \, \text{m} \) (1 m from support \( A \) to \( P \) and 1 m from \( P \) to support \( B \)).
- Cross-sectional view displays three layers:
  - Top and bottom layers are \( 100 \, \text{mm} \) wide and \( 25 \, \text{mm} \) thick.
  - Middle layer is \( 200 \, \text{mm} \) wide and \( 25 \, \text{mm} \) thick.

### Interaction:
- Users can submit answers, request answers, or provide feedback.
- The interface confirms submissions and tracks attempts remaining.
Transcribed Image Text:The problem involves determining the maximum allowable force \( P \) that can be applied to a simply-supported beam composed of three boards nailed together. Here are the details provided: ### Beam Specifications: - **Shear Stress**: The wood has an allowable shear stress of \( \tau_{\text{allow}} = 1.5 \, \text{MPa} \). - **Bending Stress**: The allowable bending stress is \( \sigma_{\text{allow}} = 9 \, \text{MPa} \). - **Nails**: - Spacing: \( s = 77 \, \text{mm} \). - Shear Strength: \( 1.5 \, \text{kN} \). ### Task: Calculate the maximum force, \( P \), applying the above constraints, and express your answer to three significant figures including the units. ### User Input: - The user attempted to input \( P = 8.9 \, \text{kN} \) and received feedback indicating the answer is incorrect with three attempts remaining. ### Beam Diagram Description: The diagram shows: - The beam is supported at points \( A \) and \( B \), with point \( P \) applied at the center of the span. - Total span of the beam is \( 2 \, \text{m} \) (1 m from support \( A \) to \( P \) and 1 m from \( P \) to support \( B \)). - Cross-sectional view displays three layers: - Top and bottom layers are \( 100 \, \text{mm} \) wide and \( 25 \, \text{mm} \) thick. - Middle layer is \( 200 \, \text{mm} \) wide and \( 25 \, \text{mm} \) thick. ### Interaction: - Users can submit answers, request answers, or provide feedback. - The interface confirms submissions and tracks attempts remaining.
Expert Solution
Step 1 Foundamental about Bending Stress and Transverse Shear Stress Formula

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