# Stress and Strain Direction of Stress (Force) Bending

```Direction of Stress (Force)
Stress and Strain
Compression Tension
Shear
Course Text: Hamill &amp; Knutzen (Ch 2)
Nordin &amp; Frankel (Ch 1) or Hall (Ch. 4)
Axial compression of the spinal unit results in a loss
of height measured between the vertebrae. As the
disc material itself is essentially incompressible,
height decrease must result in a radial bulge of the
disc and a corresponding axial disc bulge (an inward
deformation of the vertebral end plates).
Bending
Tension
Compression
1
Stress analysis of the proximal
end of the femur (Koch)
Torsion
Strength &amp; Stiffness
Neutral Axis
&Oslash; Strength
Shear
&Oslash; Defined by the failure point. Also can
be assessed by energy storage (area
under curve).
&Oslash; Stiffness (modulus of elasticity)
&Oslash; determined by the slope of the load
deformation curve
2
Stiffness
Stress
Stiffness = &quot;force &quot;displ.
Strain
Force/Area
Δlength
original length
Force
Δy
!
Same units as
pressure
Δx
Ratio,
no units.
Displacement
Elastic Response
Stress/Strain Curves
Failure
Yield
Stress
Elastic
Region
Plastic
Region
Metal (ductile)
Glass (brittle)
Bone
Strain
3
Young’s Modulus
Flexible, Strong
Stiff, Strong
fiberglass
steel
Young’s Modulus is the ratio of:
stress / strain (stiffness)
Young’s
Modulus
Tendon
2 x 109
Bone
1.7 x 1010
Carbon Steel
2 x 1011
6
Soft rubber c.10
Tensile
Strength
1 x 108
1.8 x 108
3 x 109
iron
gold
silk
spider web
BONE
copper
oak
glass
Flexible, Weak
Stiff, Weak
Question
a)  In a fall a ligament has 2500 N of tensile
force exerted on it. If the area of the crosssectional area of the ligament is 2 cm2 what
is the tensile stress on the ligament?
b)  If the force rises to 3000 N and 10% of the
collagen fibers fail (break), what would the
tensile stress be now?
c)  What may happen to the ligament in this
strain curve for human ligament tissue.
4
Viscosity
&Oslash;  The mechanical response of human tissues
to applied force is not simply elastic.
&Oslash;  Human tissues also have fluid in them and
hence they have a viscous response also.
&Oslash;  Viscosity can be thought of as the &quot;internal
friction” when a fluid is subject to shearing.
&Oslash;  In simple terms viscosity is related to the the
&quot;thickness&quot; of the fluid.
Viscoelastic Characteristics
of Human Bone
Fracture
Quick
Slow
Fracture
Deformation
Viscoelastic Characteristics
a
Lo
d
(d
or
ef
)
m
U
nl
d
oa
ur
et
n)
(r
Hysteresis loop
represents lost
energy (heat)
Thixotropy
&Oslash;  By agitating or heating a material you can make it less
viscous.
&Oslash;  Obviously the example is the last bit of tomato ketchup
in the bottle (which you can make less viscous by
shaking it). Not really applicable to many materials.
&Oslash;  Although heating steel will make it more flexible such
that it may flow, it would take a lot of shaking to disrupt
the molecular bonds!
&Oslash;  With human tissue, the warm-up prior to athletic events
does increase flexibility, but could reduce connective
tissue strength (more later).
Deformation
5
Qualitative Tissue Tolerance Graph
Acute
Trauma
Tissue strength (conditioning)
is also a factor in risk of injury
Keep the big picture
in mind. If you have
little movement/
exercise then the
tissues become more
susceptible to injury
due to poor
conditioning.
Risk of
Injury
Injury Threshold
Tolerance
Chronic
Repetitive Injury
Repetition
(regulation)
&Oslash;  Disuse is an issue…loose bone mass at a rate
of 1.5% a month
too little
too much
Movement (repetition), force (lifting)
physical activity, sitting or standing
Hippocrates (460-377 B.C.)
“All parts of the body which have a function,
if used in moderation and exercises in
labours to which each are accustomed,
thereby become healthy and well-developed:
but if unused and left idle, they become liable
to disease, defective in growth, and age
quickly. This is especially the case with
joints and ligaments, if one doe not use
them.”
LeVay 1990. p30.
6
Acute vs. Chronic Injuries
Acute
Force
If you had a force vs
time graph the area
under the curve would
be an impulse (Ft =&gt;
of that tissue)
Chronic
a difficult thing.
&Oslash;  If there is adequate recovery time then even
high cumulative loads may be safe.
&Oslash;  On the other hand a one time high peak
force over a very short period of time (low
cumulative load) may exceed the strength of
the tissue and cause injury.
Time
Biomechanical Factors
Tissue Biomechanics
&Oslash;  Kumar (1999) proposed a theory of overexertion
that states overexertion can be created by
exceeding the normal physical and physiological
in any one of: force (Fx), exposure time (Dy),
range of motion (Mz).
&Oslash;  The weighting of these three functions is
obscure but Kumar symbolically represents
overexertion (OE) with the equation below.
&Oslash;  Any deformation or residual deformation alters
the mechanical response of the tissue reducing
its stress bearing capacity.
&Oslash;  Tissues that frequently get injured due to
occupational and athletic biomechanical hazards
are ligaments, tendons, muscle and nerves
(cartilage and bones are injured infrequently in
occupational settings but more frequently in
sports due to impacts and falls).
&Oslash;  We will look more closely at human tissue’s