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Determine the force in member AB for the truss using the method of joints. 10 ft DO 5 k O a. 13 k compression O b. 13 k tension O c. 24 k tension O d. 24 k compression 12ft- E B 10 k - 12 ft- 10 k

Determine the force in member AB for the truss using the method of joints. 10 ft DO 5 k O a. 13 k compression O b. 13 k tension O c. 24 k tension O d. 24 k compression 12ft- E B 10 k - 12 ft- 10 k

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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Determine the force in member AB for the truss using the method of joints.

### Determining the Force in Member AB Using the Method of Joints In this example, we are tasked with finding the force in member \( AB \) of a truss using the method of joints. The truss structure depicted is supported at points \( A \) and \( C \), with forces applied at various joints. Here's a detailed description of the diagram and the problem: #### Diagram Explanation 1. **Structural Elements:** - **Members**: The truss consists of individual members connecting points \( D, E, A, B, \) and \( C \) in a triangular and linear pattern. - **Joints**: Nodes are denoted by letters \( A, B, C, D, \) and \( E \). 2. **Support and Forces:** - **Support at A**: This is a fixed support capable of reactions both horizontally and vertically. - **Support at C**: This is a roller support allowing vertical reaction only. - **External Forces**: - A vertical downward force of \( 5 \, \text{k} \) at joint \( A \). - A vertical downward force of \( 10 \, \text{k} \) at joint \( C \). 3. **Dimensions**: - The horizontal distance between each pair of joints, starting from \( A \) to \( B \) and \( B \) to \( C \), is \( 12 \, \text{ft} \). - The vertical height from \( A \) to \( D \) is \( 10 \, \text{ft} \). #### Required: Determine the force in member \( AB \) and specify whether it is in tension or compression. ### Answer Options: a. \( 13 \, \text{k} \) compression b. \( 13 \, \text{k} \) tension c. \( 24 \, \text{k} \) tension d. \( 24 \, \text{k} \) compression --- To solve this problem using the method of joints, you would typically: 1. **Calculate the Reaction Forces** at Supports \( A \) and \( C \). 2. **Analyze Each Joint** to solve for the forces in each truss member using equilibrium equations (\(\sum F_x = 0\) and \(\sum F_y = 0\))
Transcribed Image Text:### Determining the Force in Member AB Using the Method of Joints In this example, we are tasked with finding the force in member \( AB \) of a truss using the method of joints. The truss structure depicted is supported at points \( A \) and \( C \), with forces applied at various joints. Here's a detailed description of the diagram and the problem: #### Diagram Explanation 1. **Structural Elements:** - **Members**: The truss consists of individual members connecting points \( D, E, A, B, \) and \( C \) in a triangular and linear pattern. - **Joints**: Nodes are denoted by letters \( A, B, C, D, \) and \( E \). 2. **Support and Forces:** - **Support at A**: This is a fixed support capable of reactions both horizontally and vertically. - **Support at C**: This is a roller support allowing vertical reaction only. - **External Forces**: - A vertical downward force of \( 5 \, \text{k} \) at joint \( A \). - A vertical downward force of \( 10 \, \text{k} \) at joint \( C \). 3. **Dimensions**: - The horizontal distance between each pair of joints, starting from \( A \) to \( B \) and \( B \) to \( C \), is \( 12 \, \text{ft} \). - The vertical height from \( A \) to \( D \) is \( 10 \, \text{ft} \). #### Required: Determine the force in member \( AB \) and specify whether it is in tension or compression. ### Answer Options: a. \( 13 \, \text{k} \) compression b. \( 13 \, \text{k} \) tension c. \( 24 \, \text{k} \) tension d. \( 24 \, \text{k} \) compression --- To solve this problem using the method of joints, you would typically: 1. **Calculate the Reaction Forces** at Supports \( A \) and \( C \). 2. **Analyze Each Joint** to solve for the forces in each truss member using equilibrium equations (\(\sum F_x = 0\) and \(\sum F_y = 0\))
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