A prismatic bar has a cross-section of 25 mm x 50 mm and a length of 2000 mm. Under an axial load of 100 kN, the measured elongation of the bar is 2 mm. The tensile stress and % strain in the bar
A prismatic bar has a cross-section of 25 mm x 50 mm and a length of 2000 mm. Under an axial load of 100 kN, the measured elongation of the bar is 2 mm. The tensile stress and % strain in the bar
Principles of Foundation Engineering (MindTap Course List)
8th Edition
ISBN:9781305081550
Author:Braja M. Das
Publisher:Braja M. Das
Chapter6: Vertical Stress Increase In Soil
Section: Chapter Questions
Problem 6.4P: Refer to Figure P6.4. A strip load of q = 900 lb/ft2 is applied over a width B = 36 ft. Determine...
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![**Problem Statement:**
A prismatic bar has a cross-section of \(25 \, \text{mm} \times 50 \, \text{mm}\) and a length of \(2000 \, \text{mm}\). Under an axial load of \(100 \, \text{kN}\), the measured elongation of the bar is \(2 \, \text{mm}\). The tensile stress and percentage strain in the bar are required to be calculated.
**Solution:**
1. **Calculate the Tensile Stress:**
- **Formula:** Tensile stress \( \sigma = \frac{F}{A} \)
- **Given:**
- Axial load \( F = 100 \, \text{kN} = 100,000 \, \text{N} \)
- Cross-sectional area \( A = 25 \, \text{mm} \times 50 \, \text{mm} = 1250 \, \text{mm}^2 \)
- **Convert \( A \) to \( \text{m}^2\) for consistency:** \( 1250 \, \text{mm}^2 = 1250 \times 10^{-6} \, \text{m}^2 \)
- **Calculation:**
\[
\sigma = \frac{100,000 \, \text{N}}{1250 \times 10^{-6} \, \text{m}^2} = 80 \, \text{MPa}
\]
2. **Calculate the Percentage Strain:**
- **Formula:** Percentage strain \( \epsilon \% = \left(\frac{\Delta L}{L_0}\right) \times 100 \)
- **Given:**
- Elongation \( \Delta L = 2 \, \text{mm} \)
- Original length \( L_0 = 2000 \, \text{mm} \)
- **Calculation:**
\[
\epsilon \% = \left(\frac{2 \, \text{mm}}{2000 \, \text{mm}}\right) \times 100 = 0.1\%
\]
**Results:**
- **Tensile Stress:** 80 MPa
- **Percentage Strain:** 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fef49af5c-9039-416f-bcaa-34814d7a1303%2Fe7e5f27b-b4ba-41d0-ba2a-77a83ea7d018%2F4if8kjr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A prismatic bar has a cross-section of \(25 \, \text{mm} \times 50 \, \text{mm}\) and a length of \(2000 \, \text{mm}\). Under an axial load of \(100 \, \text{kN}\), the measured elongation of the bar is \(2 \, \text{mm}\). The tensile stress and percentage strain in the bar are required to be calculated.
**Solution:**
1. **Calculate the Tensile Stress:**
- **Formula:** Tensile stress \( \sigma = \frac{F}{A} \)
- **Given:**
- Axial load \( F = 100 \, \text{kN} = 100,000 \, \text{N} \)
- Cross-sectional area \( A = 25 \, \text{mm} \times 50 \, \text{mm} = 1250 \, \text{mm}^2 \)
- **Convert \( A \) to \( \text{m}^2\) for consistency:** \( 1250 \, \text{mm}^2 = 1250 \times 10^{-6} \, \text{m}^2 \)
- **Calculation:**
\[
\sigma = \frac{100,000 \, \text{N}}{1250 \times 10^{-6} \, \text{m}^2} = 80 \, \text{MPa}
\]
2. **Calculate the Percentage Strain:**
- **Formula:** Percentage strain \( \epsilon \% = \left(\frac{\Delta L}{L_0}\right) \times 100 \)
- **Given:**
- Elongation \( \Delta L = 2 \, \text{mm} \)
- Original length \( L_0 = 2000 \, \text{mm} \)
- **Calculation:**
\[
\epsilon \% = \left(\frac{2 \, \text{mm}}{2000 \, \text{mm}}\right) \times 100 = 0.1\%
\]
**Results:**
- **Tensile Stress:** 80 MPa
- **Percentage Strain:** 0.
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