Chapter 9, Problem 9.4.6P

-6 A cantilever beam .4B is subjected to a parabolically valying load of intensity $q(x)=q_0(L^2-x^2)/L^2$ where q₀is the maximum intensity of the load (see figure).

Derive the equation of the deflection curve, and then determine the deflection ${\delta }_B$and angle of rotation ${\theta }_B$at the free end. Use the fourth-order differential equation of the deflection curve (the load equation).