Biomedical Engineering Reference
In-Depth Information
e
z
F
z
M
x
a
A
M
y
F
y
e
y
F
x
P
P
b
e
x
M
z
(a)
(b)
Figure 3.8
Abeamconstructionloadedbyaforce
P
and the free body diagram.
Example 3.6
Consider the beam construction, sketched in Fig.
3.8
(a), loaded by a force
P
. The
beam is clamped at point A and we want to determine the reaction loads at point A.
First of all a coordinate system is introduced and a free body diagram of the loaded
beam construction is drawn, as in Fig.
3.8
(b). The applied load is represented by
the vector:
P
=−
Pe
z
.
The reaction force vector on the beam construction at point A is denoted by
F
and
is decomposed according to:
F
=
F
x
e
x
+
F
y
e
y
+
F
z
e
z
,
while the reaction moment vector at point A is written as
M
=
M
x
e
x
+
M
y
e
y
+
M
z
e
z
.
The requirement that the sum of all forces is equal to zero implies that
F
+
P
=
0,
and consequently
F
x
=
0,
F
y
=
0,
F
z
−
P
=
0.
The requirement that the sum of all moments with respect to A equals zero
leads to:
M
+
d
×
P
=
0,
