(shear strain).
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Transcript (shear strain).
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