Biomedical Engineering Reference
In-Depth Information
5.36
There has been an increased interest in using translucent fiber reinforced com-
posites in prosthodontics. Narva et al. [7] evaluated electrical-glass fiber (15
to 17
m thick, the elastic modulus is 73 GPa, and the density of the fiber is
2.54 g/cm
3
) and reinforced urethane dimethacrylate (the elastic modulus is 3.9
GPa and the density of the polymer is 1.19 g/cm
3
) composites as a possibility.
They tested for flexural rigidity of these composites using cylindrical unidirec-
tionally reinforced samples that were 2 mm in diameter and 60 mm long. A
one-way constant deflection test was performed by fixing the sample. Apply-
ing a load of 40N at a 11-mm span from the fixed end showed a deflection of
1 mm. An independent analysis of the fiber content in the composite showed
53.5 % by wt. Do you think these results are consistent? If not, why not? State
your reasons and show your calculations.
μ
5.37
Suppose a tendon is modeled as a cylindrical structure (see the figure) of length
L
, a cross-sectional area
A
, and a modulus of elasticity
E
, which is subject to
equal and opposite axial loads of magnitude
F
. The amount of the tendon ex-
tension under the load
P
is
Δ
L
.
(a) What is the stiffness
k
of the tendon (the slope of the force-deflection curve)
in terms of
A
,
E
, and
L
?
(b) For a given magnitude of
P
, how would the extension
Δ
L
be affected if
A
is doubled? If
E
is
doubled? If
L
is
doubled?
(c) Let the symbol
W
represent body weight in Newtons. Assume that the
tendon cross-sectional area
A
is proportional to 2
W
/3, the tendon length
L
is proportional to
W
/3, and the tendon modulus of elasticity
E
does not
vary with
W
. How would the tendon stiffness
k
then vary with
W
?
5.38
A common technique for replacing a torn anterior cruciate ligament involves
constructing a graft from a removed section of the patient's patellar tendon.
A surgeon is interested in understanding how much of the patellar tendon can
by removed before its strength is compromised. The surgeon initially consid-
ers the common but strenuous activity of rising from a chair. He conducts a
free-body diagram analysis, which indicates that for the 700N patient, the
tensile force in each of the right and left patellar tendons during this activity
is approximately 410N. The surgeon also considers the published data on the
adult patellar tendon [4], which are as follows: the average length is 30 mm,
the average cross-sectional area is 74 mm
2
(and does not vary substantially
along its length), the elastic modulus is 400 MPa, and the ultimate stress is 58
MPa.
(a) What is the axial stress in an intact tendon under 410N of axial force and
the “factor of safety” (the ratio of ultimate stress divided by working stress)
associated with this activity?
