Biomedical Engineering Reference
In-Depth Information
intersection point of the network the molecules are (weakly) cross-linked. Within
each of the molecules a (tensile) force is present and at the interconnection point
force equilibrium must apply. In Fig.
3.3
the forces acting on one of the intercon-
nection points have been sketched, the sum of these force vectors has to be equal
to zero.
With respect to a Cartesian coordinate system equilibrium requires that the sum
of all forces in the
x
-,
y
- and
z
-direction is zero. With the decomposition of a force
F
, according to
F
=
F
x
e
x
+
F
y
e
y
+
F
z
e
z
, that is the case if:
n
F
x
,
i
=
0
i
=
1
n
F
y
,
i
=
0
i
=
1
n
F
z
,
i
=
0,
i
=
1
and that the sum of all moments in the
x
-,
y
- and
z
-direction with respect to an
arbitrarily selected point P is zero. Choosing point P to coincide with the point of
application of the forces, immediately reveals that the equilibrium of moments is
trivially satisfied.
Equilibrium of forces may also be expressed in column notation, according to:
n
∼
i
=
∼
.
i
=
1
3.3
Free body diagram
A free body diagram serves to specify and visualize the complete loading of a
body, including the reaction forces and moments acting on the body that is sup-
ported in one way or the other. The body may be part of a system of bodies and,
using the free body diagram, the reaction forces on the body under considera-
tion imposed by the other bodies may be identified. For this purpose the body
is isolated from its surroundings and the proper reaction forces and moments are
introduced such as to ensure equilibrium of the body. Clearly, these reaction forces
and moments are not known a priori, but the equilibrium conditions may be used to
try to compute these unknowns. A distinction must be made between the
statically
determinate
and the
statically indeterminate
case.
