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We are asked to calculate the compressive stress in a circular tube. Here are the details from the image:

- **Outside diameter (Dₒ)** = 2.2 inches
- **Inside diameter (Dᵢ)** = 1.6 inches
- **Load (P)** = 90 kips (1 kip = 1000 pounds)

### Formula for compressive stress:
\[
\sigma = \frac{P}{A}
\]
Where:
- \(\sigma\) = Compressive stress
- \(P\) = Applied load
- \(A\) = Cross-sectional area of the tube

The cross-sectional area for a hollow tube is given by:
\[
A = \frac{\pi}{4} (Dₒ^2 - Dᵢ^2)
\]
Where \(Dₒ\) is the outer diameter and \(Dᵢ\) is the inner diameter.

### Step-by-step solution:

1. First, convert the load into pounds: \( P = 90 \, \text{kips} = 90 \times 1000 \, \text{lb} = 90000 \, \text{lb} \).
2. Calculate the cross-sectional area using the given diameters:
\[
A = \frac{\pi}{4} \left( (2.2)^2 - (1.6)^2 \right) \, \text{in}^2
\]
3. Compute the compressive stress \(\sigma\) using the formula \(\sigma = \frac{P}{A}\).

Let me calculate these values.The compressive stress in the tube is approximately **50,259.46 psi** (pounds per square inch).

Would you like further details or have any additional questions? Here are five related questions that can expand on this concept:

1. How does the thickness of the tube affect the compressive stress?
2. What would happen if the tube had a different material with a different strength limit?
3. How is compressive stress different from tensile stress in structural components?
4. How can you prevent failure in materials subjected to high compressive stress?
5. What are some common applications of hollow tubes in engineering structures?

**Tip:** In structural analysis, it's important to verify if the compressive stress exceeds the material's yield strength to prevent failure.

A circular tube with an outside diameter of 2.2 in and an inner diameter of 1.6 in is compressed under a load of 90 kips. Calculate the compressive stress in the tube.

Calculate the compressive stress in a circular tube with an outside diameter of 2.2 inches and an inner diameter of 1.6 inches, subjected to a 90-kip load. This problem uses the compressive stress formula σ = P / A and geometry concepts to find the stress in the tube. Suitable for engineering students.

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