Biomedical Engineering Reference
In-Depth Information
3
Static equilibrium
3.1
Introduction
According to Newton's law the acceleration of the centroid of a body multiplied by
its mass equals the total force applied to the body and there will be a spin around
the centroid, when there is a resulting moment with respect to the centroid. But
in many cases bodies do not move at all when forces are applied to them. In that
case the bodies are in static equilibrium. A simple example is given in Fig.
3.1
.
In Fig.
3.1
(a) a body is loaded by two forces of equal size but with an opposite
direction. The lines-of-action of the two forces coincide and clearly the body is
in equilibrium. If the lines-of-action do not coincide, as in Fig.
3.1
(b), the forces
have a resulting moment and the body will rotate. To enforce static equilibrium a
counteracting moment should be applied to prevent the body rotating, as indicated
in Fig.
3.1
(c).
3.2
Static equilibrium conditions
If a body moves monotonously (no acceleration of the centroid, no rate of rotation
around the centroid), the body is in static equilibrium. If the velocities are zero
as well, the body is at rest. In both cases the sum of all forces
and
the sum of
all moments (with respect to any point) acting on the body are zero. Suppose
that
n
forces
F
i
(
i
1, 2, ...,
n
) are applied to the body. Each of these forces will
have a moment
M
i
with respect to an arbitrary point P. There may be a number
of additional moments
=
M
j
(
j
=
1, 2, ...,
m
) applied to the body. Static equilibrium
then requires that
i
=
1
F
i
n
=
0
n
m
M
i
+
M
j
=
0.
(3.1)
i
=
1
j
=
1
