This document discusses the design of shafts and couplings. It provides equations and procedures for: 1. Designing solid and hollow shafts subjected to twisting moment, bending moment, or combined loads based on shear and bending stress equations. 2. Designing common types of shaft couplings like sleeve, muff, flange, and flexible couplings. Dimensions are provided in terms of the shaft diameter and procedures outline designing the sleeve, keys, bolts. 3. Calculating torque in shafts using twisting moment equations and providing types and dimensions of common keys used to transmit torque between shafts and sleeves.

1. ME8593- DESIGN OF MACHINE ELEMENTS
KONGUNADU
COLLEGE OF ENGINEERING AND TECHNOLOGY
UNIT -II
DESIGN OF SHAFT AND COUPLINGS
1. SHAFTS SUBJECTED TO TWISTING MOMENT ONLY
For hollow section
Where
Design of shaft based on strength against static loads:
1. Shear strength for solid shaft = Ʈ =
П
(or) T =
П
x Ʈs x d3
2. Shear strength for Hollow shaft = Ʈ =
П (( )/ )
di=inside diameter, do= outside diameter
Twisting moment may be obtained by using the following relation
Mt =
× ×
N/mm or in terms of T.
In case of belt drives
T= (T1-T2) R , T1- Tension in the tight side
T2- Tension in the slack side , R- Radius of the pulley
2. SHAFT SUBJECTED TO BENDING MOMENT ONLY
The bending moment equation is
Bending stress (σb) = Mb /Z = Mb *y /I
M- Bending moment
I- moment of inertia of cross sectional area of the shaft about the axis of rotation
σb- Bending stress

2. ME8593- DESIGN OF MACHINE ELEMENTS
Shaft subjected to simple bending moment for solid shaft
σb = 32Mb / П
Shaft subjected to simple bending moment for Hollow shaft
σb = 32Mb / П (D3
-d3
)
3.SHAFT SUBJECTED TO COMBINED TWISTING MOMENT AND
BENDING MOMENT
When the shaft is subjected to combined twisting moment ad bending moment then
the shaft must be designed on the basic of two moments simultaneously
Shaft subjected to combined torque & bending moment:
For solid shaft = Ʈmax =
П
√ +
For hollow shaft = Ʈmax =
П( ) √ +
Design of keys:
S.N Key Name Width (b) Thickness (h) Length (L)
1 Saddle key b= d/4 h=d/12 L = 1.5to 3d
2 Tangent key b= d/4 h=d/4 L = 1.5d
3 Sunk key b= d/4 h=d/6 L = 1.5to 3d
4 parallel & square sunk
key
b= d/4 h=d/6 L = 1.5d
5 Gib head key b= d/4 h=d/6,h1= 1.75h L = 1.5d
6. Woodruff key b=0.16d h=0.35 to 0.4d L=0.15 to 0.4d

3. ME8593- DESIGN OF MACHINE ELEMENTS
Design procedure of Key:
Sunk key:
F = 2Mt / d, Mt = Fd / 2
A key may fail due to Shear or crushings,
a)Shear Failure:
Ʈ = F/L x b, F = Ʈ x L x b , A= L x b
Crushing Failure:
A = L x (h/2)
F = σc x L x (h/2)
Shear strength of the key = Ʈ x L x b x (d/2)
Shear strength of the shaft = (П / 16) x d3
x Ʈ
TYPES OF SHAFT COUPLINGS
A) Rigid coupling
It is used to connect two shafts which are perfectly aligned. The types are
1 ) Sleeve (or) muff coupling
2 ) Clamp(or) split muff (or) compression coupling
3 ) Flange coupling
B). Flexible coupling
It is used to connect two shafts having lateral and angular misalignments.
The types are
1) Bushed pin type coupling
2) Universal coupling
3) Oldham coupling

4. ME8593- DESIGN OF MACHINE ELEMENTS
SLEEVE (or) MUFF (or) BOX COUPLING
Design procedure for Muff (or) Box (or) Sleeve couplings (Refer PSGDB 7.133)
Step-1 Design for shaft
Mt =
П
×Ʈs × d3
N-mm
Where Mt =
× ×
N/mm
Step-2 Dimensions of Muff Coupling
Outer diameter of sleeve D=2d+13mm
Length of sleeve L=3.5d
Where d- diameter of shaft
Step-3 Design for sleeve
The sleeve is designed by considering it as a hollow shaft
Design of sleeve = Mt =
П
Ʈ
Step-4 Design of Key
Check for shear = Mt = l x b x Ʈ x d/2
Check for crushing = Mt = σc x l x x

5. ME8593- DESIGN OF MACHINE ELEMENTS
SPLIT MUFF COUPLINGS
Design Procedure Split Muff (Or) Clamp (Or) Compression Coupilng
(Refer PSGDB 7.133)
Step-1 Design for shaft
Mt =
П
×Ʈs × d3
N-mm
Where Mt =
× ×
N/mm
Step-2 Dimensions of Split Muff Coupling
Outer diameter of sleeve D=2d+13mm
Length of sleeve L=3.5d
Where d- diameter of shaft
Step-3 Design for sleeve
The sleeve is designed by considering it as a hollow shaft
Mt =
П
Ʈ
Step-4 Design of Key
The length of coupling key is at least equal to the length of the sleeve. The coupling
key is usually made into two parts so that the length of key in each shaft l = L/2 after
that the induced shearing and crushing stresses may be checked.
Check for shear = Mt = l x b x Ʈ x d/2
Check for crushing = Mt = σc x l x x

6. ME8593- DESIGN OF MACHINE ELEMENTS
Step-4 Design of clamping bolts
Design for Clamping Bolt = Mt =
П
µ (db)2
σ n d
Torque transmitted by the coupling
Where
T-torque transmitted by the shaft
d-diameter of shaft , db- root or effective diameter of bolt
n- number of bolt , σ-Permissible stress for bolt
μ-coefficent of friction between the muff and shaft
L- length of muff
FLANGE COUPLING
flange coupling
(For protected, Unprotected, Marine types)

7. ME8593- DESIGN OF MACHINE ELEMENTS
Various proportions in terms of shaft diameter d:
S.n Terms Un protected Protected Marine
1 Outer dia of hub
D = 2d D = 2d D = 2d
2 Length of hub L = 1.5 d L = 1.5 d L =1.5d
3 PCD of bolts D1 = 3d D1 = 3d D1 =1.6d
4 Outside dia of the
Flange
D2 = 4d D2 = 4d D2 = 2.2d
5 Thickness of flange tf = 0.5d tf =0.5d tf = d/3
6 Thickness of
protective layer
tp=0.25d
Design procedure for flange couplings (Refer PSGDB 7.134 & 7.135)
Step-1 Design for shaft
Mt =
П
×Ʈs × d3
N-mm
Where Mt =
× ×
N/mm
Step-2 Dimensions of Split Muff Coupling
Refer PSGDB 7.134
Step-3 Design for hub
The hub is designed by considering it as a hollow shaft
Mt =
П
Ʈh
Length of hub L=1.5d , D=2*d
Step-3 Design for key
A key may fail due to Shear or crushings,
Check for shear = Mt = l ×w × Ʈ × d/2
Check for crushing = Mt = σc × l × ×

8. ME8593- DESIGN OF MACHINE ELEMENTS
Step-4 Design of Flange
Design for flange = Mt =
П
x Ʈc x tf
tf - thickness of flange (d/2)
Step-5 Design of Bolts:
The bolts are subjected to shear stress due to torque transmitted. The number of bolts
(n) depends upon the diameter of shaft and pitch circle diameter is taken D1=3d
Torque transmitted d1- diameter of bolt for crushing
For shear = n ×
П
d1
2
x Ʈb ×
For crushing = n x d1 x tf x σcb x