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2. Determine the force in each member of the truss. State whether the members are in tension or compression. Set P = 8 kN. 60° B 4 m 4 m 4 m 60⁰

2. Determine the force in each member of the truss. State whether the members are in tension or compression. Set P = 8 kN. 60° B 4 m 4 m 4 m 60⁰

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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2.) please help with problem and provide free body diagrams when needed
**Truss Analysis Problem** **Objective:** Determine the force in each member of the truss. State whether the members are in tension or compression. Set \( P = 8 \, \text{kN} \). **Description:** The truss is arranged in a triangular configuration with two symmetrical halves and a horizontal base across the bottom. It consists of four triangular sections ABC, ABE, ECD, and ADE. **Details:** - The truss is anchored at point \( A \) on the horizontal plane and has a roller support at point \( E \). - The leftmost section of the truss \( ABA \) and the rightmost section \( ECD \) are symmetrical. - Each of these triangular sections forms an isosceles triangle with a \( 60^\circ \) angle at points \( B \) and \( D \). - There is a vertical load \( P = 8 \, \text{kN} \) applied downward at point \( D \), the rightmost corner of the truss. - The base of the truss is horizontally aligned, with \( AB = 4 \, \text{m} \), \( BC = 4 \, \text{m} \), and \( CD = 4 \,\text{m} \). **Diagram:** The truss is composed of the following components: - Triangle elements \( AB \), \( BC \), and \( BD \) - A horizontal member \( E \) connecting into triangles with \( BE \) and \( CE \) - Support reactions at \( A \) (fixed support) and \( E \) (roller support) **Analysis Approach:** 1. **Determine Support Reactions:** - Calculate the reaction forces at supports \( A \) and \( E \). 2. **Member Forces:** - Use methods such as method of joints or method of sections to calculate the force in each member. - Determine if each member is in tension (pulling apart) or compression (pushing together). 3. **Equilibrium Equations:** - Apply equilibrium equations (ΣFx = 0, ΣFy = 0, ΣM = 0) to solve for unknown forces. The analysis will reveal the internal forces within the truss and whether these forces induce tension or compression in each member.
Transcribed Image Text:**Truss Analysis Problem** **Objective:** Determine the force in each member of the truss. State whether the members are in tension or compression. Set \( P = 8 \, \text{kN} \). **Description:** The truss is arranged in a triangular configuration with two symmetrical halves and a horizontal base across the bottom. It consists of four triangular sections ABC, ABE, ECD, and ADE. **Details:** - The truss is anchored at point \( A \) on the horizontal plane and has a roller support at point \( E \). - The leftmost section of the truss \( ABA \) and the rightmost section \( ECD \) are symmetrical. - Each of these triangular sections forms an isosceles triangle with a \( 60^\circ \) angle at points \( B \) and \( D \). - There is a vertical load \( P = 8 \, \text{kN} \) applied downward at point \( D \), the rightmost corner of the truss. - The base of the truss is horizontally aligned, with \( AB = 4 \, \text{m} \), \( BC = 4 \, \text{m} \), and \( CD = 4 \,\text{m} \). **Diagram:** The truss is composed of the following components: - Triangle elements \( AB \), \( BC \), and \( BD \) - A horizontal member \( E \) connecting into triangles with \( BE \) and \( CE \) - Support reactions at \( A \) (fixed support) and \( E \) (roller support) **Analysis Approach:** 1. **Determine Support Reactions:** - Calculate the reaction forces at supports \( A \) and \( E \). 2. **Member Forces:** - Use methods such as method of joints or method of sections to calculate the force in each member. - Determine if each member is in tension (pulling apart) or compression (pushing together). 3. **Equilibrium Equations:** - Apply equilibrium equations (ΣFx = 0, ΣFy = 0, ΣM = 0) to solve for unknown forces. The analysis will reveal the internal forces within the truss and whether these forces induce tension or compression in each member.
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