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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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