Calculating Flexural Stress in Cast Iron Pipe

This question asks us to find the maximum flexural stress ($\sigma_{\text{max}}$) in a cast iron pipe, given the maximum bending moment ($M$) and the section modulus ($Z$). Flexural stress, also known as bending stress, is the stress experienced by a material when it is subjected to bending. It occurs because different parts of the beam experience different levels of tension and compression.

Flexural Stress Formula Explained

The formula used to calculate the maximum flexural stress at any point in a beam is:

$$ \sigma_{\text{max}} = \frac{M}{Z} $$

Where:

• $ \sigma_{\text{max}} $ is the maximum flexural stress (in N/mm² or Pascals).
• $ M $ is the maximum bending moment acting on the cross-section (in N-mm).
• $ Z $ is the section modulus of the cross-section (in mm³).

The section modulus is a geometric property that represents the strength of a cross-section's shape with regard to bending. A larger section modulus indicates a greater resistance to bending stress.

Given Values for Calculation

From the question, we have the following values:

• Maximum bending moment, $ M = 125000 \text{ N-mm} $
• Section modulus, $ Z = 17017 \text{ mm}^3 $

Step-by-Step Calculation

Now, we can substitute the given values into the flexural stress formula:

1. Formula: $ \sigma_{\text{max}} = \frac{M}{Z} $
2. Substitution: $ \sigma_{\text{max}} = \frac{125000 \text{ N-mm}}{17017 \text{ mm}^3} $
3. Calculation: $ \sigma_{\text{max}} \approx 7.344508... \text{ N/mm}^2 $

Result Interpretation

The calculated maximum flexural stress is approximately $ 7.34 \text{ N/mm}^2 $. Comparing this result with the given options:

• Option 1: $ 17.23 \text{ N/mm}^2 $
• Option 2: $ 7.34 \text{ N/mm}^2 $
• Option 3: $ 9.21 \text{ N/mm}^2 $
• Option 4: $ 14.32 \text{ N/mm}^2 $

The calculated value closely matches Option 2.