A 5 x 5 cm tubular with a square cross-section and wall thickness of 2 mm is subjected to a
tensile load of 100N. Determine the stress experienced by the bar.

To determine the stress experienced by the bar, we can use the formula for stress:

\[
\text{Stress} (\sigma) = \frac{\text{Force} (F)}{\text{Area} (A)}
\]

### Step 1: Determine the Cross-Sectional Area

Given that the tubular bar has a square cross-section with an outer side length of \( 5 \, \text{cm} \) and a wall thickness of \( 2 \, \text{mm} = 0.2 \, \text{cm} \), we need to calculate the cross-sectional area that resists the tensile load.

1. **Outer side length** = \( 5 \, \text{cm} \)
2. **Inner side length** = Outer side length - 2 × Wall thickness

\[
\text{Inner side length} = 5 \, \text{cm} - 2 \times 0.2 \, \text{cm} = 4.6 \, \text{cm}
\]

3. **Cross-sectional area** \( A \) is the difference between the area of the outer square and the inner square:

\[
A = (\text{Outer side length})^2 - (\text{Inner side length})^2 
\]

\[
A = (5 \, \text{cm})^2 - (4.6 \, \text{cm})^2 
\]

\[
A = 25 \, \text{cm}^2 - 21.16 \, \text{cm}^2 = 3.84 \, \text{cm}^2 
\]

### Step 2: Calculate the Stress

Convert the area from \(\text{cm}^2\) to \(\text{m}^2\) for consistency with the force (which is in newtons):

\[
A = 3.84 \, \text{cm}^2 \times 10^{-4} = 3.84 \times 10^{-4} \, \text{m}^2
\]

Now, using the formula for stress:

\[
\sigma = \frac{F}{A} = \frac{100 \, \text{N}}{3.84 \times 10^{-4} \, \text{m}^2}
\]

\[
\sigma = 260,416.67 \, \text{Pa} \, (\text{Pascals})
\]

Thus, the stress experienced by the bar is approximately **260,417 Pa** or **260.4 kPa**.

Would you like more details on any part of the solution?

### Related Questions:
1. What is the significance of wall thickness in calculating the stress in a tubular section?
2. How would the stress change if the tensile load were increased?
3. What are the units of stress and how do they relate to force and area?
4. How would the stress calculation differ if the cross-section were circular instead of square?
5. What other factors could influence the stress experienced by a material under load?

### Tip:
Always ensure that units are consistent when performing calculations, especially when converting between different unit systems.

Learn how to calculate stress in a tubular bar with a square cross-section and wall thickness using the formula for stress. Detailed step-by-step solution involving mechanics and material science concepts. Suitable for advanced high school or college-level 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