Why we perform Torsion test?

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• Torque or turning moment or twisting moment
1. In Factories and workshops, shafts is used to transmit energy from one end to other end.
2. To transmit the energy, a turning force is applied either to the rim of a pulley, keyed to the shafts, or to any other suitable point at some distance from the axis of the shaft.
3. The moment of couple acting on the shaft is called torque or turning moment or twisting moment.
4. Torque = turning force * diameter of shaft
   T = F * 2R
   where,
   T= Torque
   F= Turning force
   S= Radius of the shaft
   Unit of torque(T) is N-mm or kN-mm

• Angle of TWIST
1. When the shaft is subjected to Torque(T), point $A$ on the surface of the shaft comes to ${{A}^{'}}$ position. The angle ${{AOA}^{'}}$ at the centre of of the shaft is called the angle of twist.
2. ${{AOA}^{'}}$ = $\theta$ = Angle of twist.
   Angle of twist is measured in radians.

• Shear stress in Shaft($\tau$)
1. When a shaft is subjected to equals and opposite end couples, whose axes coincide with the axis of the shaft, the shaft is said to be in pure torsion and at any point in the section of the shaft stress will be induce.
2. That stress is called shear stress in shaft.

• Strength of shafts:
Maximum torque or power the shaft can transmit from one pulley to another, is called strength of shaft.
1. For Solid circular shafts:
   maximum torque (T) is given by: ${T}={\frac{\pi}{16}*{\tau}*{D}^3}$
   Where,
   D = Dia of the shaft,
   $\tau$ = Shear stress in the shaft
2. For Hollow circular shaft.
   maximum torque(T) is given by: ${T}={\frac{\pi}{16}*\tau*\frac{{D^4}-{d^4}}{D}}$
   Where, D = Outer dia of shaft
   d= inner dia of shaft.

• Polar moment of inertia:
1. The moment of inertia of a plane area, with respect to an axis perpendicular to the plane of the figure is called polar moment of inertia.
2. As per the perpendicular axis theorem. \[{{J}={I_{zz}}={{I_{xx}}+{I_{yy}}}}\] \[={{\frac{\pi}{64}}*{D^4}}+{{\frac{\pi}{64}}*{D^4}}\] \[ J = {\frac{\pi}{32}}*{D^4} \]

• Torsion Rigidity
1. Let twisting moment Produce a twist radians in length L. \[{\frac{T}{J}}={\frac{G\theta}{L}}\]