The image describes a homework problem regarding the design of a compression bushing involving a solid 4340 HR Steel tie rod and a Naval Brass bushing. Let's break down the key information given:

• Rod Length (L_rod) = 850 mm
• Bushing Length (L_bushing) = 625 mm
• Rod Diameter (d_rod) = 25 mm
• Bushing Outer Diameter (d_o) = 80 mm
• Force (F) = 50 kN
• Total Displacement (δ_total) = 1 mm (maximum allowable)
• The normal stress in the bushing should not exceed the yield strength of the material (Naval Brass).

Problem Objective:

Determine the minimum wall thickness of the bushing (t_min), given the constraints on total displacement and stress.

Steps to Approach:

1. Displacement Constraint: The total displacement (δ_total = 1 mm) includes elastic deformation of both the tie rod and the bushing. You need to ensure the wall thickness results in this maximum displacement.

2. Stress Calculation: The normal stress in the bushing should not exceed the yield strength. The stress in a cylindrical bushing can be found using: $\sigma = \frac{F}{A}$ where $A = \frac{\pi (d_o^2 - d_i^2)}{4}$ is the cross-sectional area of the bushing, and $d_i$ is the inner diameter (related to the wall thickness).

3. Deformation Compatibility: You would also need to account for the elastic modulus of the materials (steel for the rod, brass for the bushing) in calculating the displacements.

Would you like a detailed solution for calculating the minimum wall thickness $t_{min}$?

Related Questions:

1. How do you calculate the normal stress in a hollow cylindrical bushing?
2. What is the relationship between the displacement and elastic modulus in this setup?
3. How can the yield strength of Naval Brass affect the design constraints?
4. What formulas are used to compute the cross-sectional area of a hollow circular bushing?
5. How does the length of the rod impact the overall deformation in this case?

Tip:

When dealing with stress and displacement, always ensure the material properties (like yield strength and elastic modulus) are incorporated into both calculations.