Problem 1: Largest vertical load $P$ at $C$

To solve this, we need to consider:

1. Stress in the steel rod at $B$: $\text{Stress} = \frac{\text{Force}}{\text{Area}} \leq 40 \, \text{ksi}$

2. Vertical movement limitation at $C$: $\Delta_C = \frac{PL}{AE} \leq 0.15 \, \text{in}$ Where:

   • $P$: Load applied
   • $L$: Length of the steel rod
   • $A$: Cross-sectional area of the rod
   • $E$: Young's modulus for steel

By combining these constraints and any equilibrium conditions provided by the geometry of the system (e.g., lever arm moments), we can solve for $P$.

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Problem 2: Change in length of the steel shaft $ABCD$

The formula for axial deformation under axial load is: $\Delta = \sum \frac{P_i L_i}{A_i E}$ Where:

• $P_i$: Axial load on segment $i$
• $L_i$: Length of segment $i$
• $A_i$: Cross-sectional area of segment $i$
• $E$: Young's modulus for steel

Steps:

1. Break the shaft $ABCD$ into segments based on where the loads are applied.
2. Calculate the deformation for each segment separately.
3. Sum the deformations to find the total change in length.

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To solve both problems completely, I need details such as:

• Lengths, areas, and geometric properties of the members.
• Specific axial loads and their application points.
• Any additional constraints or dimensions.

Would you like me to assume reasonable values or provide a detailed example?