 # Equal and opposite shear forces, as applied to acylinder constrained in space

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.