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

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

Materials Science And Engineering Properties
Materials Science And Engineering Properties
1st Edition
ISBN:9781111988609
Author:Charles Gilmore
Publisher:Charles Gilmore
Chapter8: Engineering Materials
Section: Chapter Questions
Problem 85CQ
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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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