4unit- Torsion of circular shaftsss.pptx

4unit- Torsion of circular shaft.pptx

1. TORSION OF CIRCULAR SHAFTS

2. UNIT IV Torsion of Circular Shafts - Theory of pure torsion, derivation of torsion equations, assumptions made in the theory of pure torsion, torsional moment of resistance, polarsection modulus. Deflection of Beams- Bending into a circular arc slope, deflection and radius of curvature , differential equation for the elastic line of a beam, double integration and Macaulay’s methods,determination of slope and deflection for cantilever and simply supported beams subjected to point loads.

3. J J J

4. T = Torsional moment τ = Shear stress ( N- m ) J = Polar moment of inertia (m 4 ) ( N/m 2 ) R = Radius of the shaft (m) G = Modulus of rigidity (N/m 2 ) θ = Angle of twist (radians) L = Length of the shaft (m) T = τ = G × θ J R L

5. POLAR MODULUS : T = τ × J = τ × Z P R T = τ J R Where Z P = J/R = polar modulus. Where τ is maximum shear stress (occurring at surface) and R is extreme fibre distance from centre. Thus polar modulus is the ratio of polar moment of inertia to extreme radial distance of the fibre from the centre. Unit : m 3

6. Solid Circular Section : I XX = I YY = πD 4 64 J = I XX + I YY = πD 4 32 R=D/2 Polar modulus, Z P = J = πD 3 R 16 POLAR MODULUS :

7. Hollow Circular Section : I XX = I YY = π(D 1 4 –D 2 4 ) 64 x x y D 1 y D 2 XX YY 1 2 J = I + I = π(D 4 – D 4 ) 32 R= D 1 /2 Polar modulus, Z P = J = π(D 1 4 –D 2 4 ) R 16D 1

8. Power, P = T × N × 2π = 2π NT 60 60 POWER TRANSMITTED BY SHAFTS : Consider a shaft subjected to torque ‘T’ and rotating at ‘N’ revolutions per minute (rpm). Taking second as the unit of time, we have, Angle through which shaft moves = N × 2π 60 Power, P = Work done per second. Unit : N- m/s or Watt. 1H.P = 736Watt = 736 N- m/s