To analyze the situation, we assume the tube you mentioned is cylindrical and is subjected to a shear force of 25 kN. We'll compute the shear stress in the tube, which is critical for understanding the load the tube can handle.

Given Data:

• Outer diameter ($D_{\text{outer}}$): 60 mm
• Thickness ($t$): 3 mm
• Shear Force ($F$): 25 kN = 25,000 N

Step 1: Calculate the Inner Diameter

The inner diameter ($D_{\text{inner}}$) can be found by subtracting twice the thickness from the outer diameter:

$D_{\text{inner}} = D_{\text{outer}} - 2 \times t$

$D_{\text{inner}} = 60\,\text{mm} - 2 \times 3\,\text{mm} = 54\,\text{mm}$

Step 2: Calculate the Cross-Sectional Area

For a tube, the shear stress is typically distributed over the cross-sectional area of the wall, which is annular (i.e., the area of the tube wall). The formula for the cross-sectional area ($A$) is:

$A = \frac{\pi}{4} \left( D_{\text{outer}}^2 - D_{\text{inner}}^2 \right)$

Substituting the values:

$A = \frac{\pi}{4} \left( 60^2 - 54^2 \right) \text{mm}^2$

Let's calculate this area.

The cross-sectional area of the tube wall is approximately $537.21 \, \text{mm}^2$.

Step 3: Calculate the Shear Stress

Shear stress ($\tau$) is calculated by dividing the shear force by the cross-sectional area:

$\tau = \frac{F}{A}$

Substituting the values:

$\tau = \frac{25,000 \, \text{N}}{537.21 \, \text{mm}^2}$

Let's compute this shear stress.The shear stress in the tube is approximately $46.54 \, \text{N/mm}^2$ or $46.54 \, \text{MPa}$.

Summary:

• Outer diameter: 60 mm
• Inner diameter: 54 mm
• Cross-sectional area: 537.21 mm²
• Shear force: 25 kN
• Shear stress: 46.54 MPa

Let me know if you would like further details!

Here are 5 related questions for further exploration:

1. What is the maximum shear stress the material of the tube can withstand?
2. How would increasing the thickness affect the shear stress?
3. How does the shear stress change if the shear force increases to 30 kN?
4. How is shear stress related to torsional loads on the same tube?
5. What are the failure modes of a tube under high shear stress?

Tip: Always ensure the material’s yield stress is higher than the calculated stress to avoid failure.