02-07ChapGere.0019 - 178 A-PDF Axially Loaded Purchase...

Problem 2.12-10 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 mm 2 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
Y
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
W
Y
that first produces yielding of the shorter cable. Also,
determine the corresponding elongation
Y
of the shorter cable.
(b) Determine the weight
W
P
that produces yielding of both cables. Also, determine the
elongation
P
of the shorter cable when the weight W just reaches the value W
P
.
(c) Construct a load-displacement diagram showing the weight
W
as ordinate and the
elongation of the shorter cable as abscissa. (