Torsion of circular cross section PowerPoint Presentation

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SIMPLE TORSION THEORY:

When a uniform circular shaft is subjected to a torque, it can be shown that every section of the shaft is subjected to a state of pure shear, the moment of resistance developed by the shear stresses being everywhere equal to the magnitude, and opposite in sense, to the applied torque.
For the purposes of deriving a simple theory to describe the behaviour of shafts subjected to torque it is necessary to make the following basic assumptions:

Assumptions

(1) The material is homogeneous, i.e. of uniform elastic properties throughout.

(2) The material is elastic, following Hooke's law with shear stress proportional
to shear strain.

(3) The stress does not exceed the elastic limit or limit of proportionality.

(4) Circular sections remain circular.

(5) Cross-sections remain plane. (This is certainly not the case with the torsion of non-circular sections.)

(6) Cross-sections rotate as if rigid, i.e. every diameter rotates through the same angle.
Practical tests carried out on circular shafts have shown that the theory developed below on the basis of these assumptions shows excellent correlation with experimental results.

Combined Stress Systems-Combined Bending and Torsion

In most practical transmission situations shafts which carry torque are also subjected to bending, if only by virtue of the self-weight of the gears they carry. Many other practical applications occur where bending and torsion arise simultaneously so that this type of loading represents one of the major sources of complex stress situations.

Combined Bending and Torsion-Equivalent Bending Moment

For shafts subjected to the simultaneous application of a bending moment M and torque T the principal stresses set up in the shaft can beshown to be equal to those produced by an equivalent bending moment,of a certain value Me acting alone.