Shear Stress
Shear stress is defined a the component of
force that acts parallel to a surface area
 Shear stress is a stress state where the shape
of a material tends to change (usually by
"sliding" forces – torque by transversely-acting
forces) without particular volume change.
 The shape change is evaluated by measuring
the change of the angle's magnitude (shear
strain).

Examples of Shear Stress
Structural members in pure shear stress
are the torsion bars and the driveshafts in
automobiles.
 Riveted and bolted may also be mainly
subjected to shear stress.

Shear Stress Formula
Shear Strain

Shear strain is the displacement that
occurs in a body that is parallel to the
forces applied.
Shear Strain Formula
Shear strain is the displacement that
occurs in a body that is parallel to the
forces applied.
 Shear Strain = DL / L
 Where:

– DL = Horizontal Displacement from Vertical
– L = Original Length
Modulus of Rigidity (G)
Also referred to as the Shear Modulus
 Ratio of shear stress to shear strain

Shear Stress
G=
Shear Strain
Bearing Stress
Bearing stress is the stress caused by one
part acting directly on another.
 Bearing stress is a compressive stress and
is equal to the bearing force divided by
the bearing area.

Bearing Stress
Bearing stress is a compressive stress and
is equal to the bearing force divided by
the bearing area.
 s (bearing) = Compressive Forces/Area

Torque
Torque is a measure of how much a force
acting on an object causes that object to
rotate.
 The object rotates about a pivot point.
 A force is applied at a distance from that
pivot point.
 The distance from the pivot point to the
point where the force acts is the moment
arm.

Torsion
Torsion occurs when an external torque is
applied and an internal torque, shear
stress, and deformation (twist) develops in
response to the externally applied torque.
 There is a corresponding deformation
(angle of twist) which results from the
applied torque and the resisting internal
torque causing the shaft to twist.

Torsion and Shearing Stress
There is also an internal shear stress
which develops inside the shaft.
 This shearing stress on the cross sectional
area varies from zero at the center of the
shaft linearly to a maximum at the outer
edge.
 This may be thought of as being due to
the adjacent cross sectional areas of the
shaft trying to twist passed each other.

Torsion

The angle of twist can be found by using:

Where:
– Theta is the angle of twist in radians
– T is the torque ( N * m or ft * lbs ).
– L is the length of the object the torque is being applied to or
over.
– G is the shear modulus or more commonly the modulus of
rigidity
– J is the polar moment of inertia
Torsion Example





A steel, cylindrical bar has a 20,000 in-lb torque applied to it.
The radius of the bar is .5 inches and it is 5 feet in length
The steel used in this example has a shear modulus of 11 X 106 psi
The polar moment of inertia for a circular object is calculated using:
– J = (p r 4)/ 2 = .10 in 4
The torsion can be calculated using:
 Q = (20,000 in-lb)(60 in)/(.10 in 4)(11 X 106 psi) = 1.09 radians
– Angle in degrees = Angle in Radians * 180 / Pi
– Converting radians into degrees, the steel bar is expected to
twist 62.5 degrees