Equal and opposite shear forces, as applied to acylinder constrained in space, cause the cylinderto twist. This is known as a torsional or torqueforce. If we substitute the cylinder for a tibia,then the following discussion can be applied tounderstanding how a skier sustains a spiralfracture in the tibia when the skis twist around.
The twisting of the skis applies a torsional
force.Similar to bending forces, graduations of thetorque force apply through the cylinder, fromthe surfaces edges, where the torque is maximal, to the centre of the cylinder, where
the resultant force of the two opposite shearingforces is zero. A line connecting areas of zeronet force throughout a structure is termed theaxis of twist. The formula for calculating theshear stress force generated by the torque forcesat any given point is shown in the figure below
The polar moment of inertia, or polar
moment area (PMA), similar to the SMA, is a
variable parameter related to the size and shapeof a structure but not the material from whichit is constructed. Figure 17.6 shows the
formulae for calculating the PMA for cylindricalshapes.
Returning to the skiing example, the ski tip
is a long distance from the tibia of the skier. Asa result of the long moment arm, the force
applied to the tibia is high. Using the formula
below for a hollow cylinder, we can calculate
the order of magnitude of forces required to
fracture the tibia. Again, it is clear from the
formulae that in terms of the dimensions of the
cylinder, the radius (i.e. the distance from the
axis of twist) affects the PMA to the fourth
power.The rigidity of materials to torsion is
calculated in a similar way to that of bending
rigidity.
Torsional rigidity is a measure of the
resistance of a material in a particular size andshape to torsional forces. From Figure 17.6, wesee that for a cylinder, the polar moment variesto the fourth power of the radius. Therefore,an intramedullary rod that is twice as thick has
2 square 4 (16) times the rigidity. Considering
intramedullary nail types, note that when
comparing nails of the same diameter and
length, cannulation or slotting of the nail
decreases the polar moment area according to
the earlier formula. As a result, torsional
rigidity of slotted or cannulated nails is
lessened, although bending rigidity is affected
only minimally.