A 3/4 in shaft uses sleeve bearings. The total load per bearing is 400 lb. An L/D ratio of 2.5 is desired. What is the bearing pressure in psi?

To find the bearing pressure, we can use the following formula:

\[
\text{Bearing Pressure} = \frac{\text{Load}}{\text{Bearing Area}}
\]

### Step 1: Determine the Bearing Area

The bearing area is the product of the bearing's length (L) and the shaft diameter (D). Since the length-to-diameter (L/D) ratio is provided, we can calculate the length as:

\[
L = \text{L/D} \times D
\]

Given that:

- Diameter (D) = 3/4 inches = 0.75 inches
- L/D ratio = 2.5

\[
L = 2.5 \times 0.75 = 1.875 \, \text{inches}
\]

### Step 2: Calculate the Bearing Area

The bearing area (A) is the product of the length and the diameter:

\[
A = L \times D = 1.875 \, \text{inches} \times 0.75 \, \text{inches} = 1.40625 \, \text{square inches}
\]

### Step 3: Calculate the Bearing Pressure

Now, we can calculate the bearing pressure:

\[
\text{Bearing Pressure} = \frac{400 \, \text{lb}}{1.40625 \, \text{square inches}} = 284.21 \, \text{psi}
\]

Thus, the bearing pressure is approximately **284.21 psi**.

Would you like further clarification on any part of this? 

Here are some related questions:
1. What are common L/D ratios for different applications?
2. How does bearing pressure affect bearing wear?
3. What materials are suitable for sleeve bearings in high-pressure situations?
4. How can increasing the bearing length affect the load capacity?
5. What are the effects of misalignment in sleeve bearings?

**Tip:** Maintaining proper lubrication in sleeve bearings is essential for minimizing wear and extending their life.

Learn how to calculate the bearing pressure for a 3/4 inch shaft using sleeve bearings under a 400 lb load. This problem involves calculating the bearing area with a specified L/D ratio of 2.5, and uses key concepts of geometry and pressure. Suitable for college-level engineering or physics students.

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