The statically indeterminate structure shown in the figure consists of a horizontal rigid bar AB supported by five equally spaced springs. Springs 1, 2, and 3 have stiffnesses 3k, 1.5k, and k, respectively. When unstressed, the lower ends of all five springs lie along a horizontal line. Bar AB, which has weight W, causes the springs to elongate by an amount δ.
(a) Obtain a formula for the total strain energy U of the springs in terms of the downward displacement δ of the bar.
(b) Obtain a formula for the displacement δ by equating the strain energy of the springs to the work done by the weight W.
(c) Determine the forces F1, F2, and F3 in the springs.
(d) Evaluate the strain energy U, the displacement δ, and the forces in the springs if W = 600 N and k = 7.5 N/mm.

1.5k 1.5k 3k 2 3k