Saint Venant Torsion Theory Summary

The important results from the Saint–Venant torsion [110] theory can be summarized in terms of stress function as below.

General torsion equation is …..3.1

Where,

G is the shear modulus and θ is the angle of twist.

Boundary condition: ∅ = 0 on a boundary …..3.2

By using 3.1 and 3.2 we can get torque T as follows …..3.3

L Prandtl [111] introduced membrane analogy to solve torsional problem. In case of narrow rectangular cross section this analogy gives very simple solution as provided by equation 3.3.

Maximum shear stress …..3.4

In which b is the longer side and c the shorter side of the rectangular cross section and α is a numerical factor depends on ratio of b/c.

The angle of twist per

A Torque sensor is a transducer that converts a torsional mechanical input into an electrical output signal. There are two types of torque sensors a reaction sensor that measures static torque, and rotary sensor that measures dynamic torque. Reaction torque sensors convert the torque applied to a fixed sensor into a useable measurement signal. Rotary torque sensors typically measure the torque generated by rotating devices. In this instrument we have used reaction torque sensor. Reaction torque sensors are machined with single piece of rigid steel that is integrated with strain gauges in Wheatstone bridge circuit. Their output signal varies proportionally to an applied torsional force. They have no moving parts and are typically flange mounted into a fixed position. The capacity of toque sensor is 1 kg of Unitech with a model no UITM- 06. Calibration of torque sensor is done by direct loading at 1meter arm length to

The samples of required length are prepared in warp and weft direction. The distance between two jaws is adjusted for required gauge length. Fabric specimen is mounted firmly between fixed and rotating jaw. Set the torque indicator to zero and also set number of turns required. Switch the motor which will stops at 180 intervals, to note down corresponding angle and torque value. Curve may be plotted, drawn between angle of twist and torque for further analysis.

The fig 3.5 shows the typical torque v/s angle of twist of one specimen sample at two gauge lengths and that of corresponding stitched samples. Curves show typical behavior and also are indicating the differences when the gauge length is changed and sample