Biomedical Engineering Reference
In-Depth Information
Suppose that
l
x
=
2[m],
l
y
=
1[m],
H
P
=
20[N],
V
P
=
10[N].
Substitution of these values into the equation above, renders:
−
20
−
H
A
−
H
B
=
0
10
+
V
B
=
0
−
2
H
B
−
20
−
20
=
0.
Clearly, from the second equation it follows immediately that
V
B
=−
10 [N],
while from the last equation it is clear that
H
B
=−
20 [N], which leaves the first
equation to calculate
H
A
as
H
A
=
0 [N]. Hence we have the solution:
H
A
=
0[N],
H
B
=−
20 [N],
V
B
=−
10 [N].
Example 3.4
An example of a statically indeterminate case appears if the rolling support at
point A of Fig.
3.4
is replaced by a hinge as in point B. In that case an additional
reaction force in the vertical direction must be introduced at point A, see Fig.
3.6
.
With the same values of the parameters as before, force and moment equilibrium
yields
−
20
−
H
A
−
H
B
=
0
10
+
V
A
+
V
B
=
0
−
2
H
B
−
20
−
20
=
0.
V
A
V
A
A
H
A
H
A
V
P
l
y
V
B
V
B
P
H
P
l
y
H
B
H
B
B
l
x
y
x
Figure 3.6
Free body diagram of the simple loaded body, statically indeterminate case.
