25. A frame is clamped on the left side and inclined roller supported on the right side, as shown in the figure. A uniformly distributed force q is applied and the roller contact surface is assumed to be non-frictional. When one frame finite element is used to approximate the structure, the nodal displacement vector can be defined as {d} = {m, vu 9i, 112, V2, qiY\ where u and v are x- and y-directional displacements, respectively, and 9 is the rotation with respect to z-direction.

(a) Construct the 6 x 6 FE matrix equation before applying boundary conditions.

(b) Reduce the dimension of FE matrix equation to 2 x 2 by applying boundary conditions.

You may need to use appropriate transformation.

(c) Solve the FE matrix equation and calculate nodal displacement vector {d}.

(d) Write the expression of FE vertical displacement v(x), 0