Identify given parameters

The beam length $L$ is given as $4\text{ m}$ and the intensity of the uniformly distributed load $w$ is $20\text{ kN/m}$.

$L = 4\text{ m}, w = 20\text{ kN/m}$

Select the fixed end moment formula

For a fixed beam subjected to a UDL over the entire span, the fixed end moment $M_F$ at both supports is calculated using the standard structural mechanics formula.

$M_F = \frac{wL^2}{12}$

Calculate the fixed end moment

Substitute the given values into the formula: $M_F = \frac{20 \times 4^2}{12} = \frac{20 \times 16}{12} = \frac{320}{12}$.

$M_F = 26.666...\text{ kNm} \approx 26.66\text{ kNm}$