The correct answer is $\boxed{\frac{{\text{L}}}{2}}$.
A plastic hinge is a region in a beam where the material has yielded and is undergoing plastic deformation. The length of the plastic hinge is determined by the following equation:
$$L_p = \frac{M_p}{\sigma_y}$$
where $M_p$ is the plastic moment of the beam, $\sigma_y$ is the yield stress of the material, and $L_p$ is the length of the plastic hinge.
For a simply supported I-section beam of span $L$ and loaded with a central load $W$, the plastic moment is given by the following equation:
$$M_p = \frac{WL^2}{8}$$
The yield stress of steel is typically 250 MPa. Therefore, the length of the plastic hinge is given by the following equation:
$$L_p = \frac{\frac{WL^2}{8}}{{250 \text{ MPa}}} = \frac{{\text{L}}}{2}$$
The other options are incorrect because they do not represent the correct length of the plastic hinge.