A RIVET WITH A DIAMETER OF 12 MM IS USED TO JOIN TWO PLATES SUBJECTED TO A SHEAR FORCE OF 8 KN.
CALCULATE THE SHEAR STRESS IN THE RIVET.

To calculate the shear stress in the rivet, we can use the formula for shear stress:

\[
\text{Shear Stress}, \ \tau = \frac{F}{A}
\]

Where:
- \( F \) is the shear force applied (in Newtons).
- \( A \) is the cross-sectional area of the rivet (in square meters).

### Step 1: Convert Force to Newtons
The force is given in kilonewtons (kN), so convert it to Newtons:
\[
8 \, \text{kN} = 8 \times 10^3 \, \text{N} = 8000 \, \text{N}
\]

### Step 2: Calculate the Cross-Sectional Area of the Rivet
The rivet has a circular cross-section with a diameter of 12 mm. The formula for the area \( A \) of a circle is:

\[
A = \pi \left(\frac{d}{2}\right)^2
\]

Where \( d = 12 \, \text{mm} = 0.012 \, \text{m} \) is the diameter of the rivet.

Substituting this in:

\[
A = \pi \left(\frac{0.012}{2}\right)^2 = \pi (0.006)^2
\]

\[
A = \pi \times 3.6 \times 10^{-5} \, \text{m}^2 = 1.131 \times 10^{-4} \, \text{m}^2
\]

### Step 3: Calculate the Shear Stress
Now, substitute the force and area into the shear stress formula:

\[
\tau = \frac{8000 \, \text{N}}{1.131 \times 10^{-4} \, \text{m}^2}
\]

\[
\tau = 7.07 \times 10^7 \, \text{N/m}^2 = 70.7 \, \text{MPa}
\]

### Final Answer:
The shear stress in the rivet is \( 70.7 \, \text{MPa} \).

Would you like further details on any step?

---

Here are 5 related questions for deeper understanding:
1. How does the shear stress change if the diameter of the rivet increases?
2. What is the relationship between force and shear stress in different materials?
3. How would shear stress be affected if the plates were subjected to multiple forces?
4. What is the significance of the rivet material’s yield strength in relation to shear stress?
5. How can rivet joints be optimized to reduce shear stress in high-load applications?

**Tip:** Always ensure units are consistent when applying formulas, especially in engineering problems where precision is crucial.

A RIVET WITH A DIAMETER OF 12 MM IS USED TO JOIN TWO PLATES SUBJECTED TO A SHEAR FORCE OF 8 KN. CALCULATE THE SHEAR STRESS IN THE RIVET.

Calculate the shear stress in a 12 mm diameter rivet subjected to an 8 kN force. Learn how to use the shear stress formula and calculate the area of the rivet's circular cross-section to arrive at a solution of 70.7 MPa. This step-by-step guide covers geometry and stress analysis concepts for engineering students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation