The sectional modulus $S$ for a rectangular cross-section is given by the formula:

$S = \frac{b \cdot h^2}{6}$

where:

• $b$ is the width of the beam,
• $h$ is the height of the beam.

Given:

• $b = 240 \, \text{mm}$
• $h = 450 \, \text{mm}$

Calculation

$S = \frac{240 \, \text{mm} \cdot (450 \, \text{mm})^2}{6}$

1. First, calculate $h^2$: $h^2 = 450^2 = 202500 \, \text{mm}^2$

2. Substitute values: $S = \frac{240 \times 202500}{6} = \frac{48600000}{6} = 8100000 \, \text{mm}^3$

Result

The sectional modulus $S$ for the rectangular beam is:

$S = 8,100,000 \, \text{mm}^3$

Would you like more details, or do you have any questions?

---

Here are some additional related questions:

1. What is the moment of inertia for the same rectangular beam?
2. How would the sectional modulus change if the beam were rotated?
3. How does the sectional modulus affect beam strength?
4. What are the units of sectional modulus in different measurement systems?
5. Can you compare this beam's sectional modulus with a circular section of similar area?

Tip: Sectional modulus is crucial in determining the flexural strength of a beam—the higher it is, the more bending load the beam can withstand.