### Torsion in shafts

ASSUMPTIONS:
1. The material is isotropic, homogeneous and linearly elastic in which hooks law is valid.
2. The plane section before twisting remains plane even after twisting. It means the radii which are straight before twisting remains straight even after twisting.
3. The section of the shafts is assumed to be circular which may be solid or hollow and area is prismatic.

## NOTE: If section is non-circular then shear stress distribution will ne non-linear. Hence there may occur warping and plain section may not remain plain.

SIGN CONVENTION:
• The torque is taken as positive which produces +ve shear stress element on the surface of shafts and vice- versa
• RIGHT HAND THUMB RULE: If right hand direction of torque applied towards the section thr torque is taken +ve.
In this table, NA stands for neutral axis
Effect of torsion:

1. Under pure tension, ductile materials fail in shear and failure plane is the plane of maximum shear stress which is at 90° to longitudinal axis.
2. In brittle materials, failure is due to principal tension and failure plane is at 45° to longitudinal axis.
3. In the brittle metals failure plane is a rough, fractured plane whereas in ductile metals failure plan is at 45° to the longitudinal axis.
4. On the cross- section of the shaft, shear stress is developed in the circumferential direction and normal to the circumferential in longitudinal direction.
TORSIONAL MOMENT EQUATION

T= torque applied
G =modulus of rigidity (shear modulus)
J =polar moment of inertia
θ = angle of twist over a length 'L' under a torque T
τ = shear stress at a distance of 'r' from the center

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