https://file.aiquickdraw.com/mathbot/file/1727403709878ev2rzfud.jpg

Note the n=assigned number x 2000 Newton(N) is 21 solve it step by step in a very detailed way especially number 4

Let's go through the problem step by step with a focus on solving for the final rectangular size of members AB and DE. Based on the image and instructions, the load "n" is given as \( n = 21 \), so the force is \( 21 \times 2000 = 42000 \, \text{N} \).

### Step 1: Solve for the Reactions at the Supports

The given truss structure is symmetric, supported at two points:
- A hinge support at \( A \), which provides reactions \( A_x \) and \( A_y \),
- A roller support at \( E \), providing reaction \( E_y \).

**Loads:** A vertical load of \( 42,000 \, \text{N} \) at joints \( B \), \( C \), and \( D \).

#### Equilibrium equations:
1. **Sum of Forces in \( x \)-direction:** \( \Sigma F_x = 0 \)
   \[
   A_x = 0 \quad (\text{since there is no horizontal load applied})
   \]

2. **Sum of Forces in \( y \)-direction:** \( \Sigma F_y = 0 \)
   \[
   A_y + E_y = 42,000 \times 3 = 126,000 \, \text{N}
   \]

3. **Sum of Moments about \( A \):** \( \Sigma M_A = 0 \)
   Taking moment about point \( A \):
   \[
   -42,000 \times 2 \, \text{m} - 42,000 \times 4 \, \text{m} - 42,000 \times 6 \, \text{m} + E_y \times 8 \, \text{m} = 0
   \]
   \[
   E_y = \frac{42,000 \times (2 + 4 + 6)}{8} = \frac{42,000 \times 12}{8} = 63,000 \, \text{N}
   \]
   Now using \( A_y + E_y = 126,000 \, \text{N} \):
   \[
   A_y = 126,000 - 63,000 = 63,000 \, \text{N}
   \]

Thus, the reactions are:
- \( A_x = 0 \),
- \( A_y = 63,000 \, \text{N} \),
- \( E_y = 63,000 \, \text{N} \).

### Step 2: Joint Method to Solve for Member Forces

We are tasked with determining the forces in members \( AB \) and \( DE \). This can be done using the joint method by analyzing the forces at each joint (B and D) and

Learn how to solve a truss analysis problem step-by-step, including calculating the reactions at supports, using the joint method to find forces in members, and determining the final rectangular size for members AB and DE. This guide is designed for engineering students with a focus on equilibrium equations and stress calculations.

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