Biomedical Engineering Reference
In-Depth Information
X
M z ¼ I zz a z þð I yy I xx Þ
o x o y
ð
4
:
46
Þ
M i
is the net moment,
I ii
is the body's moment of inertia with respect to the principal axes,
and a i
are the body's angular acceleration and angular velocity, respectively. Euler's
equations require angular measurements in radians. Their derivation is outside the scope
of this chapter but may be found in an intermediate dynamics topic—for example, [12].
Equations (4.44)-(4.46) will be used in Section 4.6 to compute intersegmental or joint
moments.
and o i
4.3 MECHANICS OF MATERIALS
Just as kinematic and kinetic relations may be applied to biological bodies to describe
their motion and its associated forces, concepts from mechanics of materials may be used
to quantify tissue deformation, to study distributed orthopedic forces, and to predict the
performance of orthopedic implants and prostheses and of surgical corrections. Since this
topic is very broad, some representative concepts will be illustrated with the following
examples.
An orthopedic bone plate is a flat segment of stainless steel used to screw two failed
sections of bone together. The bone plate in Figure 4.13 has a rectangular cross section,
A
, measuring 4.17 mm by 12 mm and made of 316L stainless steel. An applied axial load,
F
, of 500 N produces axial
stress
, s, (force/area):
¼ F
A
s
ð
4
:
47
Þ
500 N
¼
Þ ¼
10 MPa
10 3 m
10 3 m
ð
4
:
17
Þð
12
The maximum shear stress, t max , occurs at a 45 angle to the applied load
¼ F 45
A
t max
45
cos 45
ð
500 N
Þ
ð
4
:
48
Þ
2
3
¼
¼
5 MPa
ð
0
:
00417 m
Þð
0
:
012 m
Þ
4
5
cos 45
which is 0
5s, as expected from mechanics of materials principles. Prior to loading, two
points were punched 15 mm apart on the long axis of the plate, as shown. After the 500 N
load is applied, those marks are an additional 0.00075 mm apart. The plate's
:
strain
, e,relates
the change in length,
D l
to the original length,
l
:
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