A beam on simple supports is subjected to a parabolically distributed load of intensity q(x) = 4q 0 x(L - x )/L 2 , where q 0  is the maximum intensity of the load (see figure). Derive the equation of...

A beam on simple supports is subjected to a parabolically distributed load of intensity q(x) = 4q₀
x(L - x )/L², where q₀
is the maximum intensity of the load (see figure).

Derive the equation of the deflection curve, and then determine the maximum deflection

_max. Use the fourth-order differential equation of the deflection curve (the load equation).