Solve all parts completelyEETIEET. ORE Re ra Ne SR Am rE AE SNe] eS IS mn tN TCI RRL SANE SNE SR
A camshaft in a small engine is supported by two bearings.
A cam lobe applies a side thrust force of

Question

Solve all parts completelyEETIEET. ORE Re ra Ne SR Am rE AE SNe] eS IS mn tN TCI RRL SANE SNE SR
A camshaft in a small engine is supported by two bearings.
A cam lobe applies a side thrust force of 220 N on the shaft during operation.
This force acts at a point 90 mm away from the nearest bearing.
The camshaft is made from alloy steel and has a diameter of 28 mm.
The engineer needs to evaluate the bending stress caused by the side thrust.
For bending of a circular shaft:
M=FxL
32M
re
wd?

Where:

oF = side thrust force (N)

« L = distance from bearing (mm)

d= shaft diameter (mm)

« M = bending moment (N-mm)

«0 = bending stress (MPa)
Tasks

1. Compute the bending moment generated by the cam thrust force.

2. Calculate the bending stress in the 28 mm camshaft.

3. Report the final answer in MPa.

VIPSolutions · Accepted Answer

# Solution to Camshaft Bending Stress Problem

Let's solve each task step by step.

---

## 1. **Compute the Bending Moment (M)**

$$
M = F \times L
$$

Given:
- $ F = 220 $ N  
- $ L = 90 $ mm

$$
M = 220 \times 90 = 19,\!800 \text{ N·mm}
$$

---

## 2. **Calculate the Bending Stress (σ) in the 28 mm Camshaft**

The formula is:

$$
\sigma = \frac{32M}{\pi d^3}
$$

Where:
- $ M = 19,\!800 $ N·mm
- $ d = 28 $ mm

Substitute values:

$$
\sigma = \frac{32 \times 19,800}{\pi \times (28)^3}
$$

Calculate $ 28^3 $:

$$
28^3 = 21,952
$$

Now plug in the values:

$$
\sigma = \frac{32 \times 19,800}{\pi \times 21,952}
$$
$$
= \frac{633,600}{68,972.6}
$$
$$
\approx 9.18 \text{ MPa}
$$

---

## 3. **Report the Final Answer in MPa**

**Final Answers:**

- **Bending Moment, $ M $:** 19,800 N·mm
- **Bending Stress, $ \sigma $:** 9.18 MPa

---

### **Summary Table**

| Task                                 | Value         | Units  |
|-------------------------------------- |:-------------:|:------:|
| Bending Moment ($ M $)              | 19,800        | N·mm   |
| Bending Stress ($ \sigma $)         | 9.18          | MPa    |

---

**The maximum bending stress in the camshaft is approximately** **9.18 MPa**.

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