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?