Torsion of Shafts Civil Engineering (CE) Notes | EduRev

Civil Engineering SSC JE (Technical)

Civil Engineering (CE) : Torsion of Shafts Civil Engineering (CE) Notes | EduRev

The document Torsion of Shafts Civil Engineering (CE) Notes | EduRev is a part of the Civil Engineering (CE) Course Civil Engineering SSC JE (Technical).
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Chapter 8 

Torsion of Shafts

TORSION OF CIR CULAR  SHAFTS
 Theory of Pure Torsion

 Torsion of Shafts Civil Engineering (CE) Notes | EduRev

Torsional Moment of Resistance:
Torsion of Shafts Civil Engineering (CE) Notes | EduRev

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 Civil Engineering (CE) Notes | EduRev
Torsion of Shafts Civil Engineering (CE) Notes | EduRev

  • 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 Civil Engineering (CE) Notes | EduRev

for hollow shaft,
Torsion of Shafts Civil Engineering (CE) Notes | EduRev

Where, do = outer diameter
di = inner diameter

Torsional rigidity:

 Torsion of Shafts Civil Engineering (CE) Notes | EduRev

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 Civil Engineering (CE) Notes | EduRev

= 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 Civil Engineering (CE) Notes | EduRev
Torsion of Shafts Civil Engineering (CE) Notes | EduRev

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

 Torsion of Shafts Civil Engineering (CE) Notes | EduRev
Torsion of Shafts Civil Engineering (CE) Notes | EduRev
if l1 = l2 G1 = G2 them
Torsion of Shafts Civil Engineering (CE) Notes | EduRev

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 Civil Engineering (CE) Notes | EduRev

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

T = T1 + T2 =

 Torsion of Shafts Civil Engineering (CE) Notes | EduRev
Torsion of Shafts Civil Engineering (CE) Notes | EduRev

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 Civil Engineering (CE) Notes | EduRev
  • 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 Civil Engineering (CE) Notes | EduRev

  • 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 Civil Engineering (CE) Notes | EduRev

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 Civil Engineering (CE) Notes | EduRev

(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 Civil Engineering (CE) Notes | EduRev

  • for hollow shaft,

 Torsion of Shafts Civil Engineering (CE) Notes | EduRev

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

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