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P = 4 kN A 2 m N 45° 2 m 2 kN D B E 2 m X

P = 4 kN A 2 m N 45° 2 m 2 kN D B E 2 m X

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 forces in each member of the space truss. 

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### Analysis of a 3D Truss Structure Under Load In this diagram, a 3D truss structure is depicted with various forces and dimensions provided for analysis. Let's go through the details of this structure step by step. #### Structure Configuration: - The truss consists of six members connected at five nodes: A, B, C, D, and E. - The base of the truss forms a right-angled triangle on the \(x\)-\(y\) plane with the following points: - Point C at the origin (0, 0, 0) - Point E at coordinates (2 m, 2 m, 0) - Point D at coordinates (2 m, 0, 0) - Points A and B are elevated above the base with heights specified along the \(z\)-axis. #### Dimensions: - The length of member CD is 2 meters along the \(x\)-axis. - The vertical distance from C to A along the \(z\)-axis is 2 meters. - The horizontal distance from E to B along the \(y\)-axis is 2 meters. #### Applied Forces: - A force \(P = 4 \text{kN}\) is applied horizontally to node A in the negative \(x\) direction. - A vertical force of \(2 \text{kN}\) is applied upwards at node B. - The same node B is subjected to an additional force which makes an angle of \(45^\circ\) with the \(z\)-axis in the \(x\)-\(z\) plane. #### Coordinates: - Node A (\(0,0,2\)) - Node B (\(0,2,2\)) - Node C (\(0,0,0\)) - Node D (\(2,0,0\)) - Node E (\(2,2,0\)) ### Diagram Explanation This detailed structural diagram is typical for demonstrating the principles of static equilibrium in engineering mechanics. Here are the notable points for further analysis: 1. **Joint Analysis**: Each joint where members meet must satisfy equilibrium conditions. At joints, the sum of all forces in each of the \(x\), \(y\), and \(z\) directions must be zero. 2. **Method of Joints**: Utilizing the method of joints, each joint can be isolated to analyze the forces acting through each member connected to it
Transcribed Image Text:### Analysis of a 3D Truss Structure Under Load In this diagram, a 3D truss structure is depicted with various forces and dimensions provided for analysis. Let's go through the details of this structure step by step. #### Structure Configuration: - The truss consists of six members connected at five nodes: A, B, C, D, and E. - The base of the truss forms a right-angled triangle on the \(x\)-\(y\) plane with the following points: - Point C at the origin (0, 0, 0) - Point E at coordinates (2 m, 2 m, 0) - Point D at coordinates (2 m, 0, 0) - Points A and B are elevated above the base with heights specified along the \(z\)-axis. #### Dimensions: - The length of member CD is 2 meters along the \(x\)-axis. - The vertical distance from C to A along the \(z\)-axis is 2 meters. - The horizontal distance from E to B along the \(y\)-axis is 2 meters. #### Applied Forces: - A force \(P = 4 \text{kN}\) is applied horizontally to node A in the negative \(x\) direction. - A vertical force of \(2 \text{kN}\) is applied upwards at node B. - The same node B is subjected to an additional force which makes an angle of \(45^\circ\) with the \(z\)-axis in the \(x\)-\(z\) plane. #### Coordinates: - Node A (\(0,0,2\)) - Node B (\(0,2,2\)) - Node C (\(0,0,0\)) - Node D (\(2,0,0\)) - Node E (\(2,2,0\)) ### Diagram Explanation This detailed structural diagram is typical for demonstrating the principles of static equilibrium in engineering mechanics. Here are the notable points for further analysis: 1. **Joint Analysis**: Each joint where members meet must satisfy equilibrium conditions. At joints, the sum of all forces in each of the \(x\), \(y\), and \(z\) directions must be zero. 2. **Method of Joints**: Utilizing the method of joints, each joint can be isolated to analyze the forces acting through each member connected to it
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