3. Buckling of Column: Under a uniform load, small deflections y of a simply supported beam

are given by

where L = 10 feet is the length of the beam, EI = 1900 is modulus of elasticity times moment

of inertia, and q = -0.6 is load distribution. The beam extends from z = 0 to z = L. The

goal is to find y at every 0.02 foot using the Direct Method and plot y(z) versus I.

(a) Using centered-differencing, formulate the finite difference approximation. To illustrate

your work, use 5 grid points (2 of them are on the boundaries, y = 0 and y = L).

Write down finite-difference approximations for the interior points, for a general uniform

grid spacing of Ar. Then write your algebraic equations in the matrix-vector form with

unknown vector on the left hand side and all known quantities on the right hand side.

(b) Using a computer program for N + 1 total points, solve the above equation using the

direct method with the grid spacing of 0.02 foot. Plot y(z) versus z. Compare your

solution with the Exact Solution (clearly label your graphs).