Using Method of Sections find 10 kips A 20′ – 0" F B 20'-0" 40 k G

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
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**Title: Determining the Force in Truss Member BC Using the Method of Sections**

**Objective:**
To find the force in the truss member BC by employing the Method of Sections.

**Procedure:**
1. **Diagram Analysis:**
   The truss structure presents a series of joints and members arranged as follows:
   - A triangular arrangement forms with points A, F, E, G, H, B, C, and D.
   - Horizontal members: AF, FG, GH, and HE.
   - Vertical/diagonal members: AB, BF, FC, CG, GD, DH, and DE.

2. **Loads and Supports:**
   - There are three vertical loads applied at:
     - B: 10 kips downwards
     - C: 40 kips downwards
     - D: 10 kips downwards
   - Horizontal distances between points: 20 feet each.
   - Vertical distance: 20 feet (distance between D and E).

3. **Support Reactions:**
   - Point A: Pinned support (provides both vertical and horizontal reactions).
   - Point E: Roller support (provides a vertical reaction only).

4. **Objective: Force in Member BC**
   - Use the Method of Sections: 
     - Cut through the truss to isolate member BC.
     - Form equilibrium equations (sum of forces and moments).

**Steps in Method of Sections:**
1. **Draw Free-Body Diagram (FBD)** of the section including members intersected by the cut: BC, CG, and GD.
2. **Apply Equilibrium Equations**:
   - Sum of vertical forces (ΣFy = 0)
   - Sum of horizontal forces (ΣFx = 0)
   - Sum of moments about any point within the section (ΣM = 0)

**Diagram Description:**
- **Structure**:
  - A truss with a horizontal span divided into four segments of 20 feet each.
  - It comprises vertical and diagonal members forming triangular shapes.

**Truss Description:**
- Identified Points: 
  - A: Pin support starting point
  - B & D: Points with downward loads of 10 kips each.
  - C: Point with a downward load of 40 kips.
  - E: Roller support
- Internal Signals: To determine the force in member BC.

**Conclusion:**
Using the
Transcribed Image Text:**Title: Determining the Force in Truss Member BC Using the Method of Sections** **Objective:** To find the force in the truss member BC by employing the Method of Sections. **Procedure:** 1. **Diagram Analysis:** The truss structure presents a series of joints and members arranged as follows: - A triangular arrangement forms with points A, F, E, G, H, B, C, and D. - Horizontal members: AF, FG, GH, and HE. - Vertical/diagonal members: AB, BF, FC, CG, GD, DH, and DE. 2. **Loads and Supports:** - There are three vertical loads applied at: - B: 10 kips downwards - C: 40 kips downwards - D: 10 kips downwards - Horizontal distances between points: 20 feet each. - Vertical distance: 20 feet (distance between D and E). 3. **Support Reactions:** - Point A: Pinned support (provides both vertical and horizontal reactions). - Point E: Roller support (provides a vertical reaction only). 4. **Objective: Force in Member BC** - Use the Method of Sections: - Cut through the truss to isolate member BC. - Form equilibrium equations (sum of forces and moments). **Steps in Method of Sections:** 1. **Draw Free-Body Diagram (FBD)** of the section including members intersected by the cut: BC, CG, and GD. 2. **Apply Equilibrium Equations**: - Sum of vertical forces (ΣFy = 0) - Sum of horizontal forces (ΣFx = 0) - Sum of moments about any point within the section (ΣM = 0) **Diagram Description:** - **Structure**: - A truss with a horizontal span divided into four segments of 20 feet each. - It comprises vertical and diagonal members forming triangular shapes. **Truss Description:** - Identified Points: - A: Pin support starting point - B & D: Points with downward loads of 10 kips each. - C: Point with a downward load of 40 kips. - E: Roller support - Internal Signals: To determine the force in member BC. **Conclusion:** Using the
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