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Torsion Torsional Deformation in Circular Shaft Circular Solid Shaft Circular Solid Shaft To visualize the deformation later After deformation Rectangular grid become Ilgm shape Characterization of Angle of twist and shear strain  = Arbitrary radian position measured from central position measured from Centre of disc Shear Strain Small length of arc, ,is constant for the same cross section, (varies with position x ) According to Hooke’s law, , G = Modulus of Rigidity (Total Internal Torsional Moments) Torsion Formula (Shear stress at any arbitrar Position ) Polar Moment of Inertia For a circle of a radius c, Polar moment of Inertia about the centre (Differential Element) Angle of twist •Deformation under applied torques Angle of twist Denotation may be different in some books, Torsional Rigidity/ Stiffness of Shaft Here, the term GJ may be looked as torque required to introduce unit angle of twist in unit Length, and is called as torsional rigidity or stiffness of shaft. Stepped Shaft and Composite Shaft • A shaft may consist of a number of small shaft of different cross-sections or of different materials. • To analyze, first torque resisted by each portion is found and then individual effect are clubbed • Points to be noted • At fixed end torques of required magnitude develops to deep the shaft in equilibrium. • Torques developed at ends of any portion are equal and opposite • At common point between two portion angle of twi ...
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