Sketch a free-body diagram of each element in the figure. Compute the magnitude and direction of each force. Φ AC B 10 in 100 lbf 10 in 10 in 10 in →→→→

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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### Mechanics: Analyzing Forces on a Beam

#### Problem Statement:
**Sketch a free-body diagram of each element in the figure. Compute the magnitude and direction of each force.**

#### Diagram Description:
The diagram illustrates a beam with multiple forces and pivots. The beam is horizontally aligned and fixed at one end (O) to a wall. The distance from O to point A is 10 inches, from A to B is another 10 inches, and from B to C is 10 inches.

- **Dimensions:** 
  - O to A: 10 inches
  - A to B: 10 inches
  - B to C: 10 inches

- **Forces:**
  - A vertical force of 100 lbf is acting downward at point C.
  
- **Other Elements:**
  - The beam is supported by a curved member connected at point B.
  - The vertical distance from point B to the beam at point C is 10 inches.

#### Steps for Solving the Problem:

1. **Sketch a Free-Body Diagram:**
   - Identify and indicate all forces acting on the beam.
   - Include reaction forces at the support point O.
   - Mark the applied load at point C and the directions of the forces.
   - Show the points of application of forces and distances between these points.

2. **Compute the Magnitude and Direction of Each Force:**
   - Apply the equations of static equilibrium to solve for unknown forces:
     - Sum of Vertical Forces (`ΣFy = 0`)
     - Sum of Horizontal Forces (`ΣFx = 0`)
     - Sum of Moments about any point (`ΣM = 0`)

3. **Detailed Analysis:**
   - Calculate the reactions at the fixed support (O).
   - Calculate the forces in the curved member connected at point B by considering the geometry and the external force applied at point C.
   - Break down forces into their components if necessary, especially if calculating moments around a point.

#### Graph/Diagram Explanation:
- **Graph:** The beam is shown with a horizontal alignment. Each measurement and force is labeled for clarity.
- **Connections:** The beam is fixed at one end (O) with a pin support and has a curved member at B, stressing the beam through C.
- **Load Applied:** A vertical force of 100 lbf acting downward at point C.

By carefully analyzing the forces and using principles of statics,
Transcribed Image Text:### Mechanics: Analyzing Forces on a Beam #### Problem Statement: **Sketch a free-body diagram of each element in the figure. Compute the magnitude and direction of each force.** #### Diagram Description: The diagram illustrates a beam with multiple forces and pivots. The beam is horizontally aligned and fixed at one end (O) to a wall. The distance from O to point A is 10 inches, from A to B is another 10 inches, and from B to C is 10 inches. - **Dimensions:** - O to A: 10 inches - A to B: 10 inches - B to C: 10 inches - **Forces:** - A vertical force of 100 lbf is acting downward at point C. - **Other Elements:** - The beam is supported by a curved member connected at point B. - The vertical distance from point B to the beam at point C is 10 inches. #### Steps for Solving the Problem: 1. **Sketch a Free-Body Diagram:** - Identify and indicate all forces acting on the beam. - Include reaction forces at the support point O. - Mark the applied load at point C and the directions of the forces. - Show the points of application of forces and distances between these points. 2. **Compute the Magnitude and Direction of Each Force:** - Apply the equations of static equilibrium to solve for unknown forces: - Sum of Vertical Forces (`ΣFy = 0`) - Sum of Horizontal Forces (`ΣFx = 0`) - Sum of Moments about any point (`ΣM = 0`) 3. **Detailed Analysis:** - Calculate the reactions at the fixed support (O). - Calculate the forces in the curved member connected at point B by considering the geometry and the external force applied at point C. - Break down forces into their components if necessary, especially if calculating moments around a point. #### Graph/Diagram Explanation: - **Graph:** The beam is shown with a horizontal alignment. Each measurement and force is labeled for clarity. - **Connections:** The beam is fixed at one end (O) with a pin support and has a curved member at B, stressing the beam through C. - **Load Applied:** A vertical force of 100 lbf acting downward at point C. By carefully analyzing the forces and using principles of statics,
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