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It seems you've uploaded an image of a mechanical problem related to determining nodal displacements, element stresses, and support reactions. To assist in solving this problem using **Mathcad**, I can provide the structure of the necessary code. Here's a breakdown of the problem and the corresponding steps you'll need to follow for implementing it in Mathcad:

### Problem Overview:
The diagram seems to involve a **1D bar under axial load** with different material properties and boundary conditions. Based on this, the steps for solving it would involve:
1. Determining **nodal displacements** using stiffness matrices.
2. Computing **element stresses** based on displacements.
3. Finding the **support reactions**.

We can use the **direct stiffness method** to approach this, forming the global stiffness matrix, applying boundary conditions, and solving for unknowns.

### Mathcad Code Structure:
```plaintext
Given:
E := 200 × 10^9 Pa   (Modulus of Elasticity)
A := [A1, A2]        (Cross-sectional areas of each element)
L := [L1, L2]        (Lengths of each element)
P := 3000 N          (Axial load applied)

# Stiffness matrix for each element (EA/L)
k1 := (E × A1) / L1
k2 := (E × A2) / L2

# Global stiffness matrix (2 elements)
K := [
    [k1, -k1,  0],
    [-k1, k1 + k2, -k2],
    [0,   -k2,  k2]
]

# Force vector (load applied at the node)
F := [0, P, 0]  # Modify based on the location of the applied load

# Boundary conditions: Node 1 is fixed, so u1 = 0
u := [0, u2, u3]  # Unknown displacements

# Solve for the unknown displacements using the system of equations: K * u = F
u := lsolve(K, F)

# Element stresses are given by σ = E/L * (u_n+1 - u_n)
sigma1 := E / L1 * (u2 - u1)
sigma2 := E / L2 * (u3 - u2)

# Support reactions can be calculated by back-substitution into K*u = F
R := K * u - F
```

### Steps in the Code:
1. Define material properties like **Elastic Modulus (E)** and **Area (A)** for each element.
2. Create **stiffness matrices** for each element based on \( EA/L \).
3. Assemble the **global stiffness matrix** for the system.
4. Define the **force vector** considering the load \( P \).
5. Apply **boundary conditions** (fixed and free ends).
6. Solve the system \( K \cdot u = F \) for unknown displacements \( u_2, u_3 \).
7. Calculate **element stresses** and **support reactions**.

#### Mathcad Notes:
- Use **`lsolve()`** in Mathcad to solve systems of linear equations.
- Ensure proper units throughout the problem.
  
Would you like a detailed step-by-step explanation of how to input this into Mathcad, or any specific area expanded further?

### Related Questions:
1. How is the stiffness matrix formed for each element in a 1D axial load problem?
2. What are the typical boundary conditions in bar problems, and how do they affect the solution?
3. How do you calculate the stress in each element once the nodal displacements are known?
4. What adjustments would be made if additional loads or moments were applied?
5. How can Mathcad handle more complex element geometries?

### Tip:
Always check for unit consistency in Mathcad, especially when working with large numbers and multiple units like force (N) and length (m).

Consider the 1D bar under axial load in the given diagram. Determine the nodal displacements, element stresses, and support reactions using the direct stiffness method. Verify results using a program like FEMID.

Solve a 1D bar under axial load problem using the direct stiffness method. This tutorial covers nodal displacements, element stresses, and support reactions. Ideal for undergraduate mechanical engineering students.

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