A shaft transmits power and rotational motion. Machine elements like gears and pulleys are mounted on shafts using press fits, keys, or splines. Shafts experience shear stresses from torque and bending stresses from forces on machine elements. Shafts are designed based on strength to withstand torque only, bending only, or combined loads. Their dimensions are determined using formulas relating stress to torque or bending moment based on the shaft's moment of inertia. Combined loads require considering maximum shear or normal stresses.

1. Design of Shaft
• A shaft is a rotating member usually of circular cross-section, which
transmits power and rotational motion.
• Machine elements such as gears , pulleys (sheaves),flywheels ,
clutches are mounted on the shaft and are used to transmit power from
the driving device(motor or engine )through a machine.
• Press fit , keys ,dowel , pins and splines are used to attach these
machine elements on the shaft.
• The shaft rotates on rolling contact bearings or bush bearings.
• Couplings are used to transmit power from drive shaft(eg. motor) to
the driven shaft (eg. gearbox, wheels).

2. • A shaft is a rotating machine element which is used to transmit power
from one place to another.
• In order to transfer the power from one shaft to another , the various
members such as pulleys , gears etc., are mounted on it .these
members along with the forces exerted upon them causes the shaft to
bending.
• In other words, we may say that a shaft is used for transmission of
torque and bending moment. The various members are mounted on
the shaft by means of keys.

3. Stresses in Shaft
• Shear stresses due to the transmission of torque (i.e. due to torsional
load).
• Bending stresses (tensile or compressive) due to the forces acting upon
machine elements like gears, pulleys etc. as well as due to the weight
of the shaft itself.
• Stresses due to combined torsional and bending loads.

4. Design of Shaft
The shafts may be designed on the basis of
1. Strength, and 2. Rigidity & Stiffness.
In designing shafts on the basis of strength, the following cases may be
considered:
a) Shafts subjected to twisting moment or torque only,
b) Shafts subjected to bending moment only,
c) Shafts subjected to combined twisting and bending moments,
d) Shafts subjected to axial loads in addition to combined torsional and bending
loads.

5. BASED ON TORSION ONLY
Shafts Subjected to Torque
• Maximum shear stress developed in a shaft subjected to torque is
given by,
where T = Twisting moment (or torque) acting upon the shaft,
J = Polar moment of inertia of the shaft about the axis of
rotation
for solid shafts with diameter d

6. = for hollow shafts with do and di as outer and inner
diameter.
r = Distance from neutral axis to the outer most fibre = d/2
(or do/2)
So, dimensions of the shaft subjected to torque can be
determined from above relation for a known value of
allowable shear stress, [τ].

7. BASED ON BENDING MOMENT
Shafts Subjected to Bending Moment
• Maximum bending stress developed in a shaft is given by,
where M = Bending Moment acting upon the shaft,
I = Moment of inertia of cross-sectional area of the shaft about the
axis of rotation
for solid shafts with diameter d

8. = for hollow shafts with do and di as outer and inner diameter.
y = Distance from neutral axis to the outer most fibre = d / 2 (or do/2)
So, dimensions of the shaft subjected to bending moment can be
determined from above relation for a known value of allowable
tensile stress.

9. Shafts Subjected to Combined Twisting
Moment & Bending Moment
• When the shaft is subjected to combined twisting moment and
bending, then the shaft must be designed on the basic of the two
moments simultaneously. Various theories have been suggested to
accounts for the elastic failure of the materials when they are
subjected to various types of combined stresses.
• Maximum shear stress theory or Guest’s theory. It is used for
ductile materials such as mild steel.
• Maximum normal stress theory or Rankine’s theory. It is used for
brittle materials such as cast iron.

10. Maximum Shear Stress Theory
• Maximum Shear Stress is given by, σx = σb, σy = 0, 𝜏xy = 𝜏
is called equivalent torque, Te, such that

11. Maximum Principal Stress Theory
• Maximum Principal Stress is given by, σx = σb, σy = 0, 𝜏xy = 𝜏
is called equivalent bending moment, Me, such that

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