Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Document Description: Torsion of Shafts for Civil Engineering (CE) 2022 is part of Civil Engineering SSC JE (Technical) preparation. The notes and questions for Torsion of Shafts have been prepared according to the Civil Engineering (CE) exam syllabus. Information about Torsion of Shafts covers topics like and Torsion of Shafts Example, for Civil Engineering (CE) 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Torsion of Shafts.

Introduction of Torsion of Shafts in English is available as part of our Civil Engineering SSC JE (Technical) for Civil Engineering (CE) & Torsion of Shafts in Hindi for Civil Engineering SSC JE (Technical) course. Download more important topics related with notes, lectures and mock test series for Civil Engineering (CE) Exam by signing up for free. Civil Engineering (CE): Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
1 Crore+ students have signed up on EduRev. Have you?

Chapter 8 

Torsion of Shafts

TORSION OF CIR CULAR  SHAFTS
 Theory of Pure Torsion

 Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Torsional Moment of Resistance:
Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

ts= Shear intensity at the surface of the shaft
R = Radius of shaft
G = Modulus of rigidity of shaft material
l = Length of shaft
θ = Angular movement due to strain in length of the shaft
T = total moment of resistance offered by the cross-section of the shaft
I|p= Polar moment of Inertia of the section of the shaft

Assumptions in the theory of pure torsion: 

  • The material of the shaft is uniform throughout. 
  • Twist along the shaft is uniform. 
  • Shaft is of uniform circular section throughout, which may be hollow or solid. 
  • Cross section of the shaft, which are plane before  twist remain plane after twist. 
  • All radii which are straight  before twist remain straight after twist: Polar modulus:

Polar modulus = Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • The greatest twisting moment which a given shaft section can resist = Max. permissible shear stress × Polar Modulus

Þ T = δs Zp 

  • For solid shaft,

 Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

for hollow shaft,
Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Where, do = outer diameter
di = inner diameter

Torsional rigidity:

 Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Where, G = rigidity modulus
Ip = Polar moment of Inertia

The quantity GIp is called torsional rigidity. It is the torque required to produce a  twist of 1 radian per unit length of the shaft.
Power Transmitted by a shaft:

 Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

= Torque × angle turned per second Where,
P = Power transmitted (kW)

N = rotation per minute (rpm)
T = mean torque (kNm)

SHAFTS IN SERIES AND SHAFTS IN PARALLEL
(a) shafts in series: 

  • Torque T will be same for both the shafts. 
  • The  twists q1 and q 2 will be different for both the shafts.

 Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Where, T = Torque G1, G2 = Modulus of rigidity for shafts 1& 2 l1, l2 = length of shaft 1&2

 Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
if l1 = l2 G1 = G2 them
Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Where, q1, q2 = angle of twist Ip1, Ip2 = polar moments of inertia

(b) Shafts in parallel: 

  • In this case applied torque T is distributed to two shafts.

 Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

T = T1 + T2
 The angle of twist will be same for each shaft, 
q1 = q2=q 

T = T1 + T2 =

 Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

COMPARISON BETWEEN SOLID AND HOLLOW SHAFTS
Let hollow shaft and solid shafts have same material and length.
D0 = external diameter of hollow shaft
Di = nD0 = Internal diameter of hollow shaft
D = Diameter of the solid shaft

Case (i): When the hollow and solid  shafts have the same torsional strength.

  • Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)
  • In this case polar modulus section of two shafts would be equal.
  •  
  • USE: % Saving  in weight can be calculated for same torsional strength.

Case (ii): When the hollow and solid shafts are of equal weights. 

  • In this case torsional strength is compared.

 Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • USE: ratio of strength for same weight can be calculated.

 Case (iii) : When the diameter of solid shaft is equal  to the external diameter of the hollow shaft.

  •  Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

SHEAR AND TORSIONAL RESILIENCE
Shear resilience: Let t = shear stress intensity at faces of a square block 

  • Strain energy stored per unit volume

 Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

(uniform through the section)

Where G = rigidity modulus.

Torsional resilience: 

  • In this case shear stress due to torsion varies uniformly form zero at the axis to the maximum value ζs at the surface. 
  • Strain energy stored, per unit volume

 Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

  • for hollow shaft,

 Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

Where, D = outer diameter of hollow shaft
d = internal diameter of hollow shaft

The document Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE) is a part of the Civil Engineering (CE) Course Civil Engineering SSC JE (Technical).
All you need of Civil Engineering (CE) at this link: Civil Engineering (CE)
Download as PDF

Download free EduRev App

Track your progress, build streaks, highlight & save important lessons and more!

Related Searches

Previous Year Questions with Solutions

,

Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

,

past year papers

,

shortcuts and tricks

,

Extra Questions

,

ppt

,

study material

,

Semester Notes

,

MCQs

,

Sample Paper

,

mock tests for examination

,

pdf

,

Viva Questions

,

Objective type Questions

,

practice quizzes

,

Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

,

Summary

,

Exam

,

Free

,

Torsion of Shafts Notes | Study Civil Engineering SSC JE (Technical) - Civil Engineering (CE)

,

video lectures

,

Important questions

;