Biomedical Engineering Reference
In-Depth Information
in compression, which is only about 1 percent of the yield stress for stainless steel (see
Table 4.2). The maximum shear stress due to the axial load is
s
2
¼
t
max
¼
3
:
76 MPa
and occurs at 45
from the long axis. The axial strain can be computed using the elastic
modulus for stainless steel,
s
e
¼
F
=
A
E
¼
D
l
=
l
giving an expression for strain:
¼
F
EA
e
376 N
10
6
¼
Þ
¼
41
:
8
10
9
Pa
180
ð
0
:
005 m
Þð
0
:
01 m
From this strain the axial deformation can be computed
10
6
m
D
l
axial
¼
e
l
¼
2
:
51
which is negligible.
The transverse load causes the cantilever section to bend. The equations describing beam
bending can be found in any mechanics of materials text (e.g., [26]). Consider the beam in
the left panel of Figure 4.17. If this beam is fixed at the left-hand side and subjected to a
downward load on the right, it will bend with the top of the beam elongating and the
bottom shortening. Consequently, the top of the beam is in tension, and the bottom in
compression. The point of transition, where there is no bending force, is denoted the neutral
axis, located at distance
c
. For a symmetric rectangular beam of height
h
,
c
is located at the
midline
h
/2. The beam resists bending via its area moment of inertia
I
. For a rectangular
cross section of width
and height
,
I
¼
1
12
3
, depicted in the right panel of Figure 4.17.
b
h
bh
Beam tip deflection d
y
is equal to
2
y
¼
Fx
d
EI
ð
3
L
x
Þ
ð
4
:
53
Þ
6
y
I = 1/12 bh
3
c
Tension
x
h
c
Compression
b
FIGURE 4.17
(Left) A beam fixed on the left and subjected to a downward load on the right undergoes bend-
ing, with the top of the beam in tension and the bottom in compression. The position where tension changes to
compression is denoted the neutral axis, located at
c
. (Right) A beam of rectangular cross section with width
b
12
3
.
and height
h
resists bending via the area moment of inertia
I
¼
bh
