Torsion of Fibers

The torque of the fiber often is studied by twisting a fiber. Torque basically is the measure of how much a torsional force acting on a fiber causes that fiber to twist In mechanics, when the force is applied on a lever arm, the torque can be defined by  

Fiber Tensile Strength (grams per denier) Shear Strength (grams per denier) 

Source. Warner, Fiber Science, Prentice Hall, 1995.  

According to Equation 15.32, under a torsional force, the fiber resists the torsional displacement (6/L) by a factor of ttR G/I. Therefore, the torsional rigidity can be defined as  

The torsional rigidity of a fiber contains a material term (G) and a geometric term (h RV2). The geometric term contains the fiber radius to the fourth power, and hence the radius or diameter of a fiber has a significant effect on its torsional rigidity. Equation 15.33 can only be used for calculating the torsional rigidities of circular fibers, i.e., those with circular cross-sections. When a non-circular fiber is studied, the shape factor (A. ), i.e., the ratio of the perimeter of the non-circular fiber to that of a circular fiber of the same cross-sectional area, should be used  

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