A circular bar ACB of diameter d having a cylindrical hole of length x and diameter d/2 from A to C is held between rigid supports at A and B. A load P acts at L/2 from ends A and B. Assume E is constant.
(a) Obtain formulas for the reactions RA and RB at supports A and B, respectively, due to the load P (see figure part a).
(b) Obtain a formula for the displacement δ at the point of load application (see figure part a).
(c) For what value of x is RB = (6/5) RA? (See figure part a.)
(d) Repeat (a) if the bar is now tapered linearly from A to B as shown in figure part b and x = L/2.
(e) Repeat (a) if the bar is now rotated to a vertical position, load P is removed, and the bar is hanging under its own weight (assume mass density = p). (See figure part c.) Assume that x = L/2

P. RB dB RA L-Papplied - d-2 d