| Axes systems,
etc. (See diagram) |
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Local, regional
(spinal) and global axis systems |
(Figure 1) |
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|
Vector |
A quantity that possesses both a magnitude and a
direction (e.g. force; velocity; displacement). |
| Loading |
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Force |
An action that causes a body to displace or deform. (SI
Unit of measure = Newton, i.e., N) |
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Tension Force |
A force that tends to elongate a structure of
material. |
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Compression Force |
A force that tends to shorten a structure or material. |
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Moment or Torque |
The sum of the forces applied to a structure
multiplied by their perpendicular distance from a reference point or axis. (SI
Unit of measure = Newton- metre, i.e., Nm). Bending Moment at a point within
a structure. (See Figure 2). The moment that tends
to bend a structure. It is usually the sum of the moments due to several
forces. |
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Couple |
Two equal non-collinear forces producing a torque. |
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3-Point Bending (Figure
3) |
A structure is loaded in 3-point bending when a single
force is applied on one side and two forces are applied on the other side
acting in opposite directions. |
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|
4-Point Bending (Figure
3) |
A long structure is loaded in 4-point bending when two
transverse forces are applied on one side and two on the other. |
| Stress |
The force per unit area of a structure and a
measurement of the intensity of force (SI Units are Newtons/m2=Pascals.
Hence 1 N/m2 = 106 N/mm2 = 1 MPa). |
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Normal Stress |
The intensity of force perpendicular to the surface on
which it acts. |
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Shear Stress |
The intensity of force parallel to the surface on
which it acts. |
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Compressive Stress |
A normal stress that tends to shorten a material. |
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Tensile Stress |
A normal stress that tends to elongate a material. |
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Principal Stresses |
The stresses normal to the principal planes of a
material are called principal stresses. |
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Stress Concentration |
A site of stress that is high compared to that of
nearby sites in a structure or material. It is often caused by a sharp
change in shape. |
| Center of
Gravity |
The point in a body in which the body mass is
centered. |
|
Displacement/Deformation |
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| |
Absolute Motion |
Motion of a rigid body relative to the global axis
system. |
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Relative Motion |
Motion of a rigid body relative to the local axis
system of an adjacent body. |
| |
Rotation (Figure
4) |
Motion of a rigid body in which a certain straight
line within or adjacent to the body remains motionless. (That straight
line is the axis of rotation) |
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Translation (Figure
4) |
Motion of a rigid body in which a straight line in the
body always remains parallel to itself. |
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Plane Motion |
A motion of a rigid body in which the body moves in a
single plane. |
| |
Degrees of Freedom (Figure
5) |
The number of independent displacements that can occur
in a mechanism (e.g. the spine and instrumentation) - total of possible
displacements and rotations at all of the joints. |
| |
Instantaneous Axis of
Rotation (Figure 5) |
When a rigid body moves at every instant there is a
line in the body or some hypothetical extension of it that does not move.
For plane motion the axis of rotation becomes the center of rotation. Note:
This applies to absolute motion of a single body, also to the relative
motion of two bodies such as two vertebrae. |
| |
Bending |
Deformation of a structure in response to a bending
moment. |
| |
Neutral Axis |
Line or axis within a beam or other structure about
which bending occurs. |
| |
Strain (Figure
6) |
Deformation divided by original length or thickness.
Normal Strain is defined as the change in length divided by the original
length. Normal strain can be tensile or compressive. |
| |
Shear Strain |
Shear deformation divided by the thickness
perpendicular to the shear. |
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Plastic Deformation (Figure
7) |
Deformation that remains after the deforming load is
removed. |
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Load-Displacement, Stress-Strain Relationships |
| Elastic
Behavior: |
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| |
Stiffness |
Relationship between load and deformation – the force
applied divided by the deformation it produces. |
| |
Modulus of Elasticity
|
Relationship between stress and strain. (e.g., Young’s
modulus = normal stress divided by normal strain) |
| |
Torsional Rigidity |
The applied moment or torque divided by the rotational
deformation (torsion) that it produces. |
| Time
Dependent Behavior: |
|
| |
Creep |
Time dependent deformation of a material resulting
from the application of a constant load. |
| |
Viscoelasticity |
Material behavior in which the resistance to
deformation depends on the amount of deformation (elastic) and the rate of
deformation (viscous). |
| Failure |
|
| |
Yield Stress (Figure
7) |
Magnitude of stress on the stress-strain curve at
which appreciable deformation takes place without any appreciable increase
in the stress. |
| |
Ductility |
Property of a material in which there is a large
amount of deformation possible after the yield point. This implies that a
large amount of deformation energy is absorbed by the material before
failure. (opposite of brittle) |
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Fatigue |
Eventual failure after repeated cycles of sub-failure
loading. This usually occurs as a result of the process of the growth of
cracks in structures subjected to repetitive load cycles. |
| Equilibrium
|
State of a system in which all forces and moments are
balanced, hence it does not displace. |
| |
Free Body Analysis (Figure
8) |
Equilibrium analysis in which a system is split into
real or imagined components (free bodies), in order to check that each part
is in equilibrium. It is also used for determining the internal stresses in
a structure subjected to external loads. |
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Statics |
The branch of mechanics that deals with the
equilibrium of bodies at rest or in motion with zero acceleration. |
| |
Dynamics |
The branch of mechanics that deals with motion of
systems in which the accelerations of masses have significant effect. |
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Kinematics |
The branch of mechanics that deals with motion. |
| Stability |
Behavior of a system whereby it returns to its
equilibrium position after being disturbed. |
| |
Buckling |
A kind of instability in which a structure suddenly
bends and collapses when a certain critical load is applied. The stable
equilibrium position is a position of minimum potential energy – any
displacement of the structure requires a net input of energy. Although
stiffness or rigidity of a structure can contribute to its stability,
stiffness and stability are not the same thing. When referring to the
rigidity of, for example an instrumentation construct, use the term
stiffness or rigidity, not stability. |
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Figure 1. |
Local, regional (spinal) and global axis systems. Note: these are Cartesian
systems, defined by three mutually perpendicular lines (axes).
|
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Figure 2. |
Bending moment (produced here by the force in a Harrington rod) is the force
multiplied by its perpendicular distance from a point in the structure
(spine).
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Figure 3. |
3 and 4 point bending. For 3 point bending, the maximum bending moment is at
point ‘B’. For 4 point bending with four equal forces, the bending moment
between forces ‘B’ and ‘C’ is uniform (constant).
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Figure 4. |
Rotation and translation motion. The motion form A to B is a pure rotation,
with an axis of rotation lying outside the vertebra. The motion from A to C
is a pure translation.
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Figure 5. |
A motion segment has six degrees of freedom (i.e., six possible relative
displacements of one vertebrae relative to its neighbor). The motion at any
instant can be described as a translation along and a rotation about an
instantaneous axis rotation.
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Figure 6. |
Stress is the standardized measure of loading (force/unit area) and strain
is the standardized measure of deformation (deformation divided by original
length). (a) Normal stress and strain. (b) Shear stress and strain. |
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Figure 7. |
Stress-strain graph of a typical material. A sample was loaded past its
elastic limit, unloaded to demonstrate plastic deformation, then loaded
again to failure.
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Figure 8. |
Simple static analysis (no motion occurring) of lifting mechanics to
determine forces at the thoracolumbar junction. Here a free-body analysis is
used. All forces acting on the upper part of the body must be in equilibrium
(i.e., no net force or moment acting on the upper body) – otherwise it would
be forced to accelerate. |
