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To calculate the resultant shear stress in rivet 1, we need to analyze the forces acting on the rivets and determine the area over which the shear force is distributed.

### Given Data:
- Diameter of rivets = 25 mm
- Load = 25 kN at 30° from horizontal
- Horizontal distance between rivet 1 and 2 = 80 mm
- Vertical distance between rivet 1 and 2 = 50 mm

The force acting on the bracket is resolved into two components:
- Horizontal component of the load, \( F_x \): 
  \[
  F_x = 25 \, \text{kN} \times \cos(30^\circ)
  \]
- Vertical component of the load, \( F_y \): 
  \[
  F_y = 25 \, \text{kN} \times \sin(30^\circ)
  \]

Now, these forces create direct shear forces in both rivets, as well as a moment around the center of the rivets, which causes additional shear stress due to the distance from the center.

To proceed:
1. Calculate the area of each rivet: \( A = \frac{\pi}{4} \times d^2 \), where \( d = 25 \, \text{mm} \).
2. Resolve the force into \( F_x \) and \( F_y \).
3. Determine the distribution of forces between rivets based on the geometry and calculate the total shear stress in rivet 1.

I will now compute these values.The resultant shear stress in rivet 1 is approximately **25.46 MPa**, rounded to two decimal places.

Would you like more details on the calculation or have any other questions?

Here are five related questions you might find helpful:
1. How does the angle of the applied force affect the shear stress in the rivets?
2. What happens if the rivets have different diameters? How would the stress distribution change?
3. How do you calculate the bending moment caused by this force?
4. What are the assumptions behind distributing the force equally between the two rivets?
5. How would the shear stress change if the load were applied at a different point on the bracket?

**Tip:** Shear stress is directly proportional to the applied force and inversely proportional to the cross-sectional area. Reducing the area or increasing the force will increase the shear stress.

A bracket is attached to a steel column by two identical rivets of diameter 25 mm. It is subjected to loading as shown in the figure. The resultant shear stress in rivet 1 is _____ MPa (round off to two decimal places).

Learn how to calculate the resultant shear stress in a rivet of 25 mm diameter subjected to a 25 kN load at 30 degrees. This problem involves the resolution of forces, shear stress formula, and statics principles. Suitable for undergraduate engineering students.

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