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Determine the force in each member of the truss. State if the members are in tension or compression.

Determine the force in each member of the truss. State if the members are in tension or compression.

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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### Problem Statement **3.** Determine the force in each member of the truss. State if the members are in tension or compression. ### Diagram Description The diagram features a typical truss structure. Here's a detailed breakdown: 1. **Nodes and Connections:** - The truss has nodes labeled \( A \), \( B \), \( C \), \( D \), \( E \), and \( F \). - The truss forms a series of triangles and is supported at nodes \( C \) (pin connection) and \( E \) (roller support). 2. **Dimensions:** - Horizontal distances between nodes are \( AB = 3 \, \text{ft} \), \( BC = 3 \, \text{ft} \), \( BD = 3 \, \text{ft} \), and \( DF = 3 \, \text{ft} \). - Vertical distances specified are \( AC = 4 \, \text{ft} \) and \( DE = 4 \, \text{ft} \). - Overall horizontal measurement from \( A \) to \( F \) sums up to \( 12 \, \text{ft} \) (3 segments of 3 feet each + vertical drops measured). 3. **Load Details:** - At vertex \( A \), there's a force vector pointing downwards and to the left at a \( 13/5 \) slope, indicating the ratio of vertical to horizontal components of the force. This force has a magnitude of \( 130 \, \text{lb} \). ### Analyzing the Truss The objective is to find the force in each member and determine whether each member is under tension or compression. This typically involves: 1. **Breaking down forces into components.** 2. **Using equilibrium equations:** - Sum of forces in the \( x \)-direction should be zero. - Sum of forces in the \( y \)-direction should be zero. - Sum of moments about any point should be zero. ### Steps to Solve: 1. **Identify Support Reactions:** - Calculate the reactions at supports \( C \) and \( E \). 2. **Method of Joints or Sections:** - Apply either the method of joints (analyzing equilibrium at each node) or the method of sections (cutting through the tr
Transcribed Image Text:### Problem Statement **3.** Determine the force in each member of the truss. State if the members are in tension or compression. ### Diagram Description The diagram features a typical truss structure. Here's a detailed breakdown: 1. **Nodes and Connections:** - The truss has nodes labeled \( A \), \( B \), \( C \), \( D \), \( E \), and \( F \). - The truss forms a series of triangles and is supported at nodes \( C \) (pin connection) and \( E \) (roller support). 2. **Dimensions:** - Horizontal distances between nodes are \( AB = 3 \, \text{ft} \), \( BC = 3 \, \text{ft} \), \( BD = 3 \, \text{ft} \), and \( DF = 3 \, \text{ft} \). - Vertical distances specified are \( AC = 4 \, \text{ft} \) and \( DE = 4 \, \text{ft} \). - Overall horizontal measurement from \( A \) to \( F \) sums up to \( 12 \, \text{ft} \) (3 segments of 3 feet each + vertical drops measured). 3. **Load Details:** - At vertex \( A \), there's a force vector pointing downwards and to the left at a \( 13/5 \) slope, indicating the ratio of vertical to horizontal components of the force. This force has a magnitude of \( 130 \, \text{lb} \). ### Analyzing the Truss The objective is to find the force in each member and determine whether each member is under tension or compression. This typically involves: 1. **Breaking down forces into components.** 2. **Using equilibrium equations:** - Sum of forces in the \( x \)-direction should be zero. - Sum of forces in the \( y \)-direction should be zero. - Sum of moments about any point should be zero. ### Steps to Solve: 1. **Identify Support Reactions:** - Calculate the reactions at supports \( C \) and \( E \). 2. **Method of Joints or Sections:** - Apply either the method of joints (analyzing equilibrium at each node) or the method of sections (cutting through the tr
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