13. In this chapter, we derived the beam finite element equation using the principle of minimum potential energy. However, the same finite element equation can be derived from the Galerkin method, as in Section 3.3. The governing differential equation of the beam is El^4= f(x), xe{0,L]

where fix) is the distributed load. In the case of a clamped beam, the boundary conditions are given by <<0) = «(L)=£(0)=£(L) = 0 Using the Galerkin method and the interpolation scheme in Eq. (4.44), derive the finite element matrix equation when a constant distributed load f(x) = q is applied along the beam.