This question asks for the maximum bending moment in a simply supported beam subjected to a uniformly distributed load (UDL).

Beam Parameters Analysis

We are given the following information about the beam:

• Beam Type: Simply supported
• Span Length ($L$): 4 m
• Load: Uniformly distributed load (UDL) specified as 20 kN over the entire span. This implies the intensity of the UDL ($w$) is the total load divided by the span length.

To find the UDL intensity ($w$):

$$ w = \frac{\text{Total Load}}{\text{Span Length}} = \frac{20 \text{ kN}}{4 \text{ m}} = 5 \text{ kN/m} $$

Maximum Bending Moment Calculation

For a simply supported beam carrying a uniformly distributed load ($w$) over its entire span ($L$), the maximum bending moment ($M_{max}$) occurs at the center of the span. The standard formula is:

$$ M_{max} = \frac{wL^2}{8} $$

Step-by-Step Calculation

Now, we substitute the values into the formula:

1. Identify the values:
   • $w = 5$ kN/m
   • $L = 4$ m
2. Apply the formula:

   $$ M_{max} = \frac{(5 \text{ kN/m}) \times (4 \text{ m})^2}{8} $$

3. Calculate the square of the span:

   $$ L^2 = (4 \text{ m})^2 = 16 \text{ m}^2 $$

4. Calculate the numerator:

   $$ wL^2 = (5 \text{ kN/m}) \times (16 \text{ m}^2) = 80 \text{ kN-m}^2 $$

5. Divide by 8 to find $M_{max}$:

   $$ M_{max} = \frac{80 \text{ kN-m}^2}{8} = 10 \text{ kN-m} $$

Conclusion

The calculated maximum bending moment for the simply supported beam is 10 kN-m. This value corresponds to one of the options provided.