Answer Happy

Problem 3 Consider the beam bending problem shown below. The cantilever beam is of length L, stiffness E and moment of inertia I. It has a symmetric cross-section, and is subjected to a transverse load of amplitude q (in N/m) applied over the first two-thirds of the beam. The elastic boundary condition at x=L is modeled by a linear spring of stiffness k. q (N/m) k X 2L/3 (a) Is this problem statically determinate or indeterminate, and why? (b) What is the degree of redundancy? (c) Write the boundary value problem (governing differential equation and boundary conditions) describing the bending response of the beam. (d) How do the boundary conditions change when k → 00? (e) Solve the beam bending problem described in d) (i.e., when k→ ∞o) and put your solution in a non-dimensional form.