https://file.aiquickdraw.com/mathbot/file/17268950851650rhibqad.jpg

To solve this problem, let's break it down:

We are asked to determine the maximum load \( P \) that can be applied to a connection involving bolts of 6 mm in diameter. The average shear stress in the bolts is limited to 124 MPa (MegaPascals). 

### Formula to use:
The average shear stress \( \tau \) in the bolts is given by:

\[
\tau = \frac{P}{A \cdot n}
\]

Where:
- \( P \) is the load applied (in Newtons or kN),
- \( A \) is the cross-sectional area of a single bolt,
- \( n \) is the number of bolts (in this case, \( n = 3 \)),
- \( \tau \) is the shear stress (124 MPa, or \( 124 \times 10^6 \, \text{Pa} \)).

The cross-sectional area \( A \) of a bolt is calculated from its diameter \( d \) using the formula for the area of a circle:

\[
A = \frac{\pi d^2}{4}
\]

Given:
- Diameter of the bolts \( d = 6 \, \text{mm} = 6 \times 10^{-3} \, \text{m} \),
- Shear stress \( \tau = 124 \times 10^6 \, \text{Pa} \),
- Number of bolts \( n = 3 \).

Let's calculate the maximum load \( P \).The maximum load \( P \) that can be applied to the connection is approximately \( 10.52 \, \text{kN} \).

It seems the given answer in the image is different (21.04 kN), which suggests either a different number of bolts, shear planes, or other factors were considered. However, based on the provided data (3 bolts, 6 mm diameter, 124 MPa shear stress), the result is \( 10.52 \, \text{kN} \).

Would you like more details or have any questions?

Here are 5 follow-up questions:
1. How does the number of bolts affect the maximum load \( P \)?
2. What would happen to the load if the bolt diameter was increased?
3. How do you calculate shear stress for a single bolt?
4. Why is shear stress used instead of tensile stress in bolt calculations?
5. Can bolts with different diameters be used in the same connection?

**Tip:** Always verify the number of bolts and their arrangement when calculating load distribution across fasteners.

For the connection shown, the average shear stress in the 6-mm-diameter bolts must be limited to 124 MPa. Determine the maximum load P that may be applied to the connection.

Calculate the maximum load that can be applied to a connection using bolts of 6 mm diameter, with the average shear stress limited to 124 MPa. This problem covers concepts in statics and mechanical engineering, including shear stress formulas.

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