if a bar is subjected to a direct load, and hence a stress the bar will change in length. If the bar has an original length L and changes by an amount dL, the strain produce is defined as follows:Strain is thus, a measure of the deformation of the material and is a nondimensional Quantity i.e. it has no units. It is simply a ratio of two quantities with the same unit.
shear strain(due to shear stress&torsional stress)
This is a measure of the internal resistance in
a material to an externally applied load.
Stress is designated and is defined as:
When a body is subjected to some external force, there is some
change of dimension of the body. The ratio of change of
dimension of the body to its original dimension is known as
Strain may be:- a) Tensile strain
b) Compressive strain
c) Volumetric strain d) Shear strain
Tensile strain- Ratio of increase in length to original length of
the body when it is subjected to a pull force
Compressive strain- Ratio of decrease in length to original
length of the body when it is subjected to a push force
Volumetric strain- Ratio of change of volume of the body to the
Shear strain-Strain due to shear stress`
Sign convention for strain:
• Tensile strains are positive whereas
compressive strains are negative.
• The strain defined earlier was known as linear
strain or normal strain or the longitudinal
Similarly in shear the shear stress is a measure
of the internal resistance of a material to an
externally applied shear load.
area resisting shear A
Concept of 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.
Shear stress and strain
Shear displacement (x)
Shear strain is angle
Shear stress tends to change the shape of a body without changing its volume
Note: we apply shear force and shear stresses develop in the interior of the material
Sign convention of shear stress
The sign convention for shear force and
stress is based on how it shears the materials
as shown below.
Hooke’s Law for Shear
By conducting a similar material testing to normal stress (Section 2.4), there
is a linear
relationship (for most engineering materials) between the shear stress and
Fig : Relationship of shear stress τ – shear strain γ for linear elastic material
Torsion occurs when an external torque is
applied and an internal torque, shear
stress, and deformation .
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.