Determine the forces in each member of the space truss. Detailed solution please. ### Analysis of a 3D Truss Structure Under LoadIn 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 ExplanationThis 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

Given Data - Space Truss P = 4 KNFind out - Force in each member of the Truss.

Answered: P = 4 kN A 2 m N 45° 2 m 2 kN D B E 2 m…

Engineering

Civil Engineering

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

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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A: Given:- a space truss as shown below

Concept explainers

System of Forces

A force is an external influence or agent that changes the state of a system. According to Newton's second law, the force applied to a body is proportional to the change in momentum of a body. Hence, whenever a force is applied to a body, its momentum changes. If the body is at rest, under the action of force, its state of rest changes to motion. In other words, the magnitude of the momentum of the body changes from zero to a measurable value. Similarly, if the body possesses some initial velocity, it has some associated momentum, the effect of force can cause the body to halt or come to rest, that is, the momentum reduces to zero.

Question

Determine the forces in each member of the space truss.

Detailed solution please.

### 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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