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The image shows a problem involving a rigid bar \(AB\) supported by two vertical rods: one made of steel and the other made of aluminum. The bar is initially horizontal, and a vertical load \(P = 70 \, \text{kN}\) is applied at the center of the bar. The task is to determine the vertical movement of the bar due to this load.

The parameters provided are as follows:

- **Steel rod**:
  - Length, \(L_s = 4 \, \text{m}\)
  - Cross-sectional area, \(A_s = 300 \, \text{mm}^2\)
  - Modulus of elasticity, \(E_s = 200 \, \text{GPa}\)
  
- **Aluminum rod**:
  - Length, \(L_a = 5 \, \text{m}\)
  - Cross-sectional area, \(A_a = 500 \, \text{mm}^2\)
  - Modulus of elasticity, \(E_a = 70 \, \text{GPa}\)
  
The load is applied at the center of the rigid bar (distance of 2 m from each rod), and we need to calculate the deflection of the bar.

To approach this:

1. **Compatibility condition**: Since the bar is rigid, the vertical deflection at both rods must result in equal displacements to maintain the bar's equilibrium.
   
2. **Equilibrium of forces**: The sum of the forces in the vertical direction must equal the applied load \(P = 70 \, \text{kN}\).

3. **Deformation of each rod**: The deformation \( \delta \) of each rod is given by the formula \( \delta = \frac{PL}{AE} \), where \(P\) is the force in the rod, \(L\) is the length, \(A\) is the cross-sectional area, and \(E\) is the modulus of elasticity.

Would you like me to proceed with solving this step-by-step?



Determine the vertical movement of a rigid bar attached to two vertical rods (one made of steel and the other made of aluminum) when a load of P = 70 kN is applied at the center.

Calculate the vertical movement of a rigid bar supported by steel and aluminum rods when a load of 70 kN is applied. This problem involves concepts in structural mechanics, including force equilibrium, deformation of materials, and compatibility conditions. Suitable for undergraduate engineering students.

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