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FIGURE 2.4
Pulley system.
nonoperator matrix (the stiffness matrix) which is the central ingredient of the displacement
method. As indicated in Chapter 4, the stiffness matrix follows from k D upon introduction
of unit displacement functions or appropriate trial functions.
EXAMPLE 2.3 Pulley
Determine the force P required to raise a weight W if the pulley of Fig. 2.4 consists of four
frictionless rollers.
From the principle of virtual work or virtual displacements,
δ
W i δ
W e =
W
δ
z
P
δ
V
=
0or P
δ
V
=
W
δ
z
(1)
The mechanics of the pulley system dictates that geometrically admissible virtual displace-
ments
δ
V a nd
δ
z are related according to
δ
V
=
4
δ
z . Substitution of this relationship into
(1) gives P
=
W
/
4 as the force required for equilibrium. Any greater force will raise the
weight.
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