A nonprismatic bar ABC is composed of two segments: AB of length L1 and cross-sectional area A1;

Question:

A nonprismatic bar ABC is composed of two segments: AB of length L1 and cross-sectional area A1; and BC of length L2 and cross-sectional area A2.
The modulus of elasticity E, mass density p, and acceleration of gravity g are constants. Initially, bar ABC is horizontal and then is restrained at A and C and rotated to a vertical position. The bar then hangs vertically under its own weight (see figure). Let A1 = 2A2 = A and L1 = 3/5 L, L2 = 2/5 L.
(a) Obtain formulas for the reactions RA and RC at supports A and C, respectively, due to gravity.
(b) Derive a formula for the downward displacement B of point B.
(c) Find expressions for the axial stresses a small distance above points B and C, respectively.