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0 Consider the given image. Assume h=16 ft, L = 6 ft, B=9 ft. The plate width is 5 ft. Wall Pa Seawater: 64 lbf/ft³ Gate Hinge BY Pa

0 Consider the given image. Assume h=16 ft, L = 6 ft, B=9 ft. The plate width is 5 ft. Wall Pa Seawater: 64 lbf/ft³ Gate Hinge BY Pa

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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I got 13.23 ft but it’s incorrect
### Educational Website Content --- ### Title: Analysis of Hydrostatic Forces on An Inclined Gate #### Context of the Problem: Given a setup involving a gate submerged in seawater, the aim is to understand the forces acting on the gate due to the water's pressure. The diagram below illustrates a side view of the setup. #### Problem Statement: Consider the given image. Assume the following dimensions: - \( h = 16 \) ft (height of the seawater column above the hinge) - \( L = 6 \) ft (distance from the hinge to point A) - \( B = 9 \) ft (length of the gate from the hinge to the end) - Plate width is 5 ft - Seawater density is \( 64 \, \text{lbf/ft}^3 \) #### Diagram Explanation: The image depicts the side view of a gate that is hinged at the bottom and inclined at an angle \(\theta\) from the horizontal. The setup includes: - **Seawater**: represented with its density. - **Hinge**: located at the bottom-left corner of the gate. The gate rotates around this hinge. - **Gate**: represented by an inclined line extending from the hinge. Lengths \( B \) and \( L \) are identified along this gate. - **Wall**: depicted on the right side, against which point A makes contact. From point A, a vertical line extends downward showing distance \( L \) from the hinge. - **Pressure Forces \(P_a\)**: Represented by arrows indicating the pressure exerted by the seawater on the gate. Pressure acts perpendicularly to the surface of the gate. **Note**: The angle \( \theta \) is implicitly defined by the inclination of the gate. #### Key Parameters: 1. **Height (h)**: Vertical distance from the water surface to the hinge. 2. **Distances (L and B)**: - \( L \): Distance from point A to the hinge measured along the gate. - \( B \): Full length of the gate from hinge vertically upwards to the end of the gate. 3. **Seawater Density**: Given as \( 64 \, \text{lbf/ft}^3 \). 4. **Plate Width**: Is 5 ft wide, suggesting a three-dimensional aspect, although depicted in 2D. #### Analysis
Transcribed Image Text:### Educational Website Content --- ### Title: Analysis of Hydrostatic Forces on An Inclined Gate #### Context of the Problem: Given a setup involving a gate submerged in seawater, the aim is to understand the forces acting on the gate due to the water's pressure. The diagram below illustrates a side view of the setup. #### Problem Statement: Consider the given image. Assume the following dimensions: - \( h = 16 \) ft (height of the seawater column above the hinge) - \( L = 6 \) ft (distance from the hinge to point A) - \( B = 9 \) ft (length of the gate from the hinge to the end) - Plate width is 5 ft - Seawater density is \( 64 \, \text{lbf/ft}^3 \) #### Diagram Explanation: The image depicts the side view of a gate that is hinged at the bottom and inclined at an angle \(\theta\) from the horizontal. The setup includes: - **Seawater**: represented with its density. - **Hinge**: located at the bottom-left corner of the gate. The gate rotates around this hinge. - **Gate**: represented by an inclined line extending from the hinge. Lengths \( B \) and \( L \) are identified along this gate. - **Wall**: depicted on the right side, against which point A makes contact. From point A, a vertical line extends downward showing distance \( L \) from the hinge. - **Pressure Forces \(P_a\)**: Represented by arrows indicating the pressure exerted by the seawater on the gate. Pressure acts perpendicularly to the surface of the gate. **Note**: The angle \( \theta \) is implicitly defined by the inclination of the gate. #### Key Parameters: 1. **Height (h)**: Vertical distance from the water surface to the hinge. 2. **Distances (L and B)**: - \( L \): Distance from point A to the hinge measured along the gate. - \( B \): Full length of the gate from hinge vertically upwards to the end of the gate. 3. **Seawater Density**: Given as \( 64 \, \text{lbf/ft}^3 \). 4. **Plate Width**: Is 5 ft wide, suggesting a three-dimensional aspect, although depicted in 2D. #### Analysis
### Calculating the Center of Pressure **Problem Statement:** Integrate the moments about point A to find the position of the center of pressure. **Result:** The position of the center of pressure is located at: \[ \boxed{13.23} \text{ ft} \] This result is obtained by integrating the moments about the specified point A. Understanding the process of how to perform this integration will help in solving similar problems in mechanics and fluid dynamics. **Additional Resources:** For further learning on how to integrate moments, refer to our detailed tutorials and examples sections. (![Link Image])[Link to Resource]
Transcribed Image Text:### Calculating the Center of Pressure **Problem Statement:** Integrate the moments about point A to find the position of the center of pressure. **Result:** The position of the center of pressure is located at: \[ \boxed{13.23} \text{ ft} \] This result is obtained by integrating the moments about the specified point A. Understanding the process of how to perform this integration will help in solving similar problems in mechanics and fluid dynamics. **Additional Resources:** For further learning on how to integrate moments, refer to our detailed tutorials and examples sections. (![Link Image])[Link to Resource]
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