• Torsion force is a twisting force that is
applied on an object by twisting one end
when the other is held in position or
twisted in the opposite direction. Different
materials have a different way of
responding to torsion. Some will deform,
crack or even break depending on the
type of material.
• If a plastic ruler is twisted between both hands.
The ruler is said to be in a state of torsion.
• Whenever we turn a key in a lock the handle
/shank of the key is in torsion.
• Propeller shaft on a ship. The engine turns the
shaft, but the water resists the movement of the
propeller. That induces torsion in the propeller
• In solid mechanics torsion is the twisting of
an object due to applied torque.
• Twisting moments or torques are forces acting
through distance so as to promote rotation.
Simple torque : T = F * l
TORSIONAL DEFORMATION OF
Consider a cylindrical bar of
circular cross section twisted by
the torques T at both the ends.
Since every cross section of the
bar is symmetrical and is applied
to the same internal torque T we
can say that the bar is in pure
Under action of torque T the right
end of the bar will rotate through
small angle known as angle of
The angle of twist varies along the
axis of the bar at intermediate
cross section denoted byφ ( x )
φ ( x)
TORSIONAL FORCE FOR
• Rate of twist
• Shear Strain at the outer
surface of the bar
γ max =
bb | rdφ
• For pure torsion the rate of
twist is constant and equal
to the total angle of twist
divided by the length L of
γ max = rθ =
BEAMS ARE SUBJECTED TO
A member subjected to torsion moments would twist
about a longitudinal axis through the shear centre of the
cross section. It was also pointed out that when the
resultant of applied forces passed through the
longitudinal shear centre axis no torsion would occur. In
general, torsion moments would cause twisting and
BAR SUBJECTED TO TORSION
Let us now consider a straight bar
supported at one end and acted upon
by two pairs of equal and opposite
Then each pair of forces P and P2
form a couple that tend to twist the
bar about its longitudinal axis, thus
producing surface tractions and
Then we can write the moments as
T = 1 d1
T2 = 2 d 2
Since the stresses act continuously they have
a resultant in the form of moment.
The Moment of a small element dA located at
radial distance ρ and is given by
τ max 2
The resultant moment ( torque T ) is the
summation over the entire cross sectional
area of all such elemental moments.
T = ∫ dM =
Polar moment of inertia of circle with radius r
and diameter d
π r4 π d 4
Maximum Shear Stress
τ max =
• A solid steel bar of circular cross section has diameter
d=1.5in, l=54in,G=11.5*10^6psi.The bar is subjected to
torques T acting at the ends if the torques have magnitude
T=250 lbft.a) what is the maximum shear stress in the bar
b) what is the angle of twist between the ends?
• From torsion formula
τ max =
16T 16* 250*12
= 4530 psi
Angle of twist
π d 4 π *1.54
= .4970in 4
Ductile materials generally fail in shear.
Brittle materials are weaker in tension than shear.
• When subjected to torsion a ductile
specimen breaks along the plane of
maximum shear, i.e. a plane perpendicular
to the shaft axis.
• When subjected to torsion a brittle
material breaks along planes perpendicular
to the direction in which tension is
maximum, i.e. along surfaces at 45 to the
• Because of torsion force an object can be
turned and twisted.
• Because if torsion force we can tighten a
nut in a bolt by using a wrench.