Consider a beam L units long subjected to the force f(x). At the left end of the beam (x = 0), the beam is attached to a hinge on the ground. At the right end of the beam (x = L), the beam is horizontally attached to the structure 1m above the ground. This problem can be written as the boundary value problem.
∂4h/∂x4 = f(x) for 0 < x < L
h(x) = 0, ∂2h/∂x2 = 0atx = 0
h(x) = 0, ∂h/∂x = 0atx = L
where h(x) is the deflection of the beam off of the ground.
1. Solve the BVP for the beam where the force is given by f(x) = cos x and the beam is L = π units in length.
2. Determine the location(s) throughout the beam where the deflection is the largest.
3. The bending moment of a beam is defined to be the second derivative of the deflection. At what location(s) throughout the beam is the bending moment the largest in absolute value?
4. The shear force of a beam is defined to be the third derivative of the deflection. At what location(s) throughout the beam is the shear force the largest?