Chapter 6: Torsion

Prepaired BySANJAY KUMAR

Assistant Professor Department of Mechanical EngineeringDepartment of Mechanical Engineering

YMCA University of Science & Technology, Faridabad

DEPARTMENT OF MECHANICAL ENGINEERINGYMCA UNIVERSITY OF SCIENCE & TECHNOLOGY, FARIDABAD

To understand the difference between torsion and bending.

To derive and explain the torsion equations for a section.

To calculate the stresses in composite shafts and design such shafts.

To design flanged couplings in shafts.To design flanged couplings in shafts.

To calculate torsion of a tapering shaft.

To calculate strain energy in torsion.

To know derivation of torsion formula and strain energy in closed coiled helical spring.

Assumptions in Theory of Pure Torsion The material is homogeneous and isotropic.

The stresses are within the elastic limit.

Cross-sections which are plane before applying twisting moment remain plane even after the application of twisting

Cross-sections which are plane before applying twisting moment remain plane even after the application of twisting moment.

Radial lines remain radial even after applying torsional moment.

The twist along the shaft is uniform.

Polar Modulus for Standard Cross-sections

For solid circular section Zp = 3

16

d

For hollow circular section Zp = 4 4

1 2

116

d d

d

Polar Modulus

Torque Transmitted by Different Shafts

T = qs D3 for solid circular shaft of dia D16

T = qs for hollow circular shaft.4 4

1 2

116

s

D Dq

D

Torque Transmitted by Different Shafts (Contd…)

If torque T is acting at distance L1 from end 1, the torquetransferred to end 1 and end 2 may be determined from theequations

T1 + T2 = T

1 2 2

1 1 2 2

TL T L

G J G J

….. (Contd..) For closed coil helical spring

T = WR

316WR nd =

Stiffness of spring

3

4

16WR n

Gd

4

364

W Gd

R n