Biomedical Engineering Reference
In-Depth Information
The horizontal reaction forces
H
A
and
H
B
can, incidentally, still be calculated,
giving, as before:
H
A
=
0[N],
H
B
=−
20 [N].
But, there is insufficient information to compute
V
A
and
V
B
. In fact, there are only
three equations to determine the four unknowns (
H
A
,
H
B
,
V
A
and
V
B
).
The nature of the support defines the possible set of reaction forces that have to
be introduced. In the above given two-dimensional statically indeterminate exam-
ple the supports are assumed to be hinges or pin-connections. Effectively this
means that no moments can be exerted on the support and only forces in the
x
-
and
y
-direction have to be introduced.
Example 3.5
An example of a fixed support is given in Fig.
3.7
(a), showing a beam that is
clamped at one end and loaded at a distance
L
from this fixation (cantilever beam).
The reaction forces and moment can be computed by enforcing force and moment
equilibrium. The sum of the forces in the
x
- and
y
-direction has to be equal to zero:
H
A
=
0
−
F
+
V
A
=
0,
while the sum of the moments has to be zero, for instance, with respect to point A:
M
A
−
LF
=
0.
L
F
A
y
x
(a)
F
V
A
V
A
H
A
H
A
M
A
M
A
(b)
Figure 3.7
Free body diagram of bar fixed at one end and loaded at the other.
