Two cables, each having a length L of approximately 40 m, support a loaded container of weight W (see figure). The cables, which have effective cross-sectional area A = 48.0 mm2 and effective modulus of elasticity E = 160 GPa, are identical except that one cable is longer than the other when they are hanging separately and unloaded. The difference in lengths is d = 100 mm. The cables are made of steel having an elastoplastic stress-strain diagram with σY = 500 MPa. Assume that the weight W is initially zero and is slowly increased by the addition of material to the container.
(a) Determine the weight WY that first produces yielding of the shorter cable. Also, determine the corresponding elongation δY of the shorter cable.
(b) Determine the weight WP that produces yielding of both cables. Also, determine the elongation δP of the shorter cable when the weight W just reaches the value WP.
(c) Construct a load-displacement diagram showing the weight W as ordinate and the elongation δ of the shorter cable as abscissa.

L W