The bxdxh rubber blocks shown are used in a double U shear mount to isolate the vibration of a machine from its supports. An applied load of P = 630 N causes the upper frame to be deflected downward by 7.9 mm. Determine the average shear strain and the shear stress in the rubber blocks. Assume b = 15 mm, d = 34 mm, and h = 20.
The bxdxh rubber blocks shown are used in a double U shear mount to isolate the vibration of a machine from its supports. An applied load of P = 630 N causes the upper frame to be deflected downward by 7.9 mm. Determine the average shear strain and the shear stress in the rubber blocks. Assume b = 15 mm, d = 34 mm, and h = 20.
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![### Shear Deformation in Rubber Blocks Used in Double U Shear Mounts
#### Introduction
In this example, rubber blocks with dimensions \( b \times d \times h \) are utilized in a double U shear mount to minimize the vibration of a machine from its supports. An applied load \( P = 630 \, N \) causes the upper frame to deflect downward by \( 7.9 \, mm \).
#### Objective
The objectives are to determine:
1. The average shear strain in the rubber blocks.
2. The average shear stress in the rubber blocks.
#### Given Data
- Applied load, \( P = 630 \, N \)
- Deflection, \( \delta = 7.9 \, mm \)
- Dimensions of rubber blocks:
- \( b = 15 \, mm \)
- \( d = 34 \, mm \)
- \( h = 20 \, mm \)
#### Diagram Explanation
1. **Upper Diagram**:
- Shows the overall structure of the double U anti-vibration shear mount with the rubber blocks (highlighted in red) inserted within the mount.
2. **Middle Diagram**:
- Demonstrates the application of load \( P \) downward onto the upper frame, which subsequently causes shear deformation in the rubber blocks.
3. **Lower Diagram** (Detailed View):
- Illustrates the critical dimensions of the rubber block—width \( b \), depth \( d \), and height \( h \).
#### Formulas and Calculation
1. **Average Shear Strain (\(\gamma\))**:
Shear strain is defined as the deformation per unit length.
\[
\gamma = \frac{\delta}{h}
\]
For the given data:
\[
\gamma = \frac{7.9 \, mm}{20 \, mm} = 0.395 \, \text{rad}
\]
2. **Average Shear Stress (\(\tau\))**:
Shear stress is calculated using the formula:
\[
\tau = \frac{P}{A}
\]
Where \( A \) is the area of the rubber surface affected by the load in shear deformation, which is \( 2 \times (b \times d) \) because there are two rubber blocks.
\[
A = 2 \times](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb0830934-b0ff-4672-88dc-560265a97e08%2Fc3e15715-e56c-48b7-95aa-75f7e867e07d%2Fgg4gu8h_processed.png&w=3840&q=75)
Transcribed Image Text:### Shear Deformation in Rubber Blocks Used in Double U Shear Mounts
#### Introduction
In this example, rubber blocks with dimensions \( b \times d \times h \) are utilized in a double U shear mount to minimize the vibration of a machine from its supports. An applied load \( P = 630 \, N \) causes the upper frame to deflect downward by \( 7.9 \, mm \).
#### Objective
The objectives are to determine:
1. The average shear strain in the rubber blocks.
2. The average shear stress in the rubber blocks.
#### Given Data
- Applied load, \( P = 630 \, N \)
- Deflection, \( \delta = 7.9 \, mm \)
- Dimensions of rubber blocks:
- \( b = 15 \, mm \)
- \( d = 34 \, mm \)
- \( h = 20 \, mm \)
#### Diagram Explanation
1. **Upper Diagram**:
- Shows the overall structure of the double U anti-vibration shear mount with the rubber blocks (highlighted in red) inserted within the mount.
2. **Middle Diagram**:
- Demonstrates the application of load \( P \) downward onto the upper frame, which subsequently causes shear deformation in the rubber blocks.
3. **Lower Diagram** (Detailed View):
- Illustrates the critical dimensions of the rubber block—width \( b \), depth \( d \), and height \( h \).
#### Formulas and Calculation
1. **Average Shear Strain (\(\gamma\))**:
Shear strain is defined as the deformation per unit length.
\[
\gamma = \frac{\delta}{h}
\]
For the given data:
\[
\gamma = \frac{7.9 \, mm}{20 \, mm} = 0.395 \, \text{rad}
\]
2. **Average Shear Stress (\(\tau\))**:
Shear stress is calculated using the formula:
\[
\tau = \frac{P}{A}
\]
Where \( A \) is the area of the rubber surface affected by the load in shear deformation, which is \( 2 \times (b \times d) \) because there are two rubber blocks.
\[
A = 2 \times
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