Biomedical Engineering Reference
In-Depth Information
where
x
is the axial distance along the beam,
L
is the total beam length, and
I
is the beam's
cross-sectional area moment of inertia. For this example,
1
12
ð
3
10
3
m
10
3
m
10
10
m
4
I
¼
10
Þð
5
Þ
¼
1
:
042
Maximum deflection will occur at
x
¼
L
,
3
¼
FL
d
y
max
3
EI
3
137 N
ð
0
:
06 m
Þ
ð
4
:
54
Þ
¼
10
9
N
10
10
m
4
3
ð
180
=
m
2
Þð
1
:
042
Þ
10
4
m
¼
5
:
26
¼
0
:
526 mm
which is also negligible.
Computation of maximum shear and bending stresses requires maximum shear force
V
and bending moment
M
. Starting by static analysis of the entire free-body
P
F
x
:
A
x
376 N
¼
0
P
F
y
:
A
y
137 N
¼
0
P
M
A
:
M
a
137 N
ð
0
:
06 m
Þ¼
0
Solving these equations gives
A
x
¼
376 N,
A
y
¼
137 N, and
M
a
¼
8
:
22 N m. Taking a cut
at any point
and isolating the left-hand section gives the free-body in
Figure 4.16 (right, bottom). Applying the equations of static equilibrium to this isolated
section yields
x
to the right of
A
P
F
x
:
376 N
N
¼
0
N
ð
x
Þ¼
376 N
P
F
y
:
137 N
V
¼
0
V
ð
x
Þ¼
137 N
P
M
A
:
8
:
22 N m
ð
137 N
Þð
x
m
Þþ
M
¼
0
M
ð
x
Þ¼ð
137 N m
Þ
x
8
:
22 N m
These last equations can be plotted easily using MATLAB, giving the axial force, shear
force, and bending moment diagrams shown in Figure 4.18.
% Use MATLAB to plot axial force, shear force and bending moment
% diagrams for Example Problem 9
¼
x
[0:0.01:0.06];
¼
þ
N
x.*0
376;
