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It looks like you've uploaded a problem that involves structural analysis, specifically focusing on determining nodal displacements, element stresses, and support reactions. Here's a breakdown of how to approach the problem:

### Problem Summary:
1. **Given Data:**
   - The structure is a bar loaded with forces.
   - Dimensions and force values are provided: 
     - \( P = 300 \, \text{kN} \)
     - Lengths: 150 mm, 150 mm, and 450 mm.
   - Material properties: 
     - \( E = 200 \times 10^3 \, \text{MPa} \).

2. **Objective:**
   - Solve for:
     - Nodal displacements.
     - Element stresses.
     - Support reactions.
   - Use **Citerion Method** to handle boundary conditions.

3. **Verification:**
   - Results are to be verified using the FEM program **PMI/ID**.

### Steps to Solve:
1. **Determine Element Stiffness Matrices:**
   - The structure seems to involve two bar elements. For each element, use the stiffness matrix for a bar in 1D axial loading:
     \[
     k = \frac{EA}{L}
     \]
   - \( E \) is Young's modulus, \( A \) is the cross-sectional area, and \( L \) is the length of each element.

2. **Assemble Global Stiffness Matrix:**
   - Combine the stiffness matrices of the individual elements into a global stiffness matrix. Apply the **Citerion Method** to handle boundary conditions, which typically involves modifying the global matrix to account for fixed nodes or prescribed displacements.

3. **Solve for Displacements:**
   - Once the global stiffness matrix is set up, solve for nodal displacements using:
     \[
     \mathbf{K} \mathbf{u} = \mathbf{F}
     \]
   - Where \( \mathbf{K} \) is the global stiffness matrix, \( \mathbf{u} \) is the vector of unknown displacements, and \( \mathbf{F} \) is the vector of applied forces.

4. **Calculate Element Stresses:**
   - Stresses in each element can be found using:
     \[
     \sigma = \frac{E}{L}(u_B - u_A)
     \]
   - Where \( u_B \) and \( u_A \) are the displacements at the ends of the element.

5. **Support Reactions:**
   - Once displacements are known, use them to compute the reactions at the supports by substituting them back into the equilibrium equations.

Would you like me to proceed with specific calculations or explain a particular step in more detail? 

### Related Questions:
1. How do you compute the stiffness matrix for a bar element under axial loading?
2. What is the **Citerion Method** for boundary condition handling in FEM?
3. Can you describe the process of assembling the global stiffness matrix from individual element matrices?
4. How do you calculate stresses in structural elements based on nodal displacements?
5. What role do boundary conditions play in finite element analysis?

### Tip:
When assembling the global stiffness matrix, always pay attention to the boundary conditions, as incorrect handling can lead to errors in displacement and reaction calculations.

Consider the structure in Fig. 3.7 loaded as shown. Determine the nodal displacements, element stresses, and support reactions. Solve this problem by hand calculation, adopting the Citerion method for handling boundary conditions. Verify your results using program PMI/ID.

Learn how to solve a structural mechanics problem involving nodal displacements, element stresses, and support reactions. Using the Citerion method for boundary conditions and solving by hand calculation, this problem covers key FEM concepts. Suitable for university-level engineering students.

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