A simply supported beam of length 2L is subjected to a moment M at the mid-point x = 0 as shown in the figure. The deflection in the domain 0 ≤ x ≤ L is given by

\(w = \frac{{ - Mx}}{{12EIL}}\left( {L - x} \right)\left( {x + c} \right)\)

Where E is Young’s modulus, I is the area moment of inertia and c is a constant (to be determined).

The slope at the centre x = 0 is