Definition of Strain
The ratio of change in a dimension that
takes place with a material under stress.
Strain is a measurement of stress.
O The Cauchy strain or engineering strain is
expressed as the ratio of total deformation to the
initial dimension of the material body in which the
forces are being applied. The engineering normal
strain or engineering extensional strain or nominal
strain e of a material line element or fiber axially
loaded is expressed as the change in length
ΔL per unit of the original length L of the line
element or fibers. The normal strain is positive if
the material fibers are stretched and negative if
they are compressed. Thus, we have
O where is the engineering normal strain, is the
original length of the fiber and is the final length of
Definition of Shear Strain
O Shear strain is defined as the strain
accompanying a shearing action. It is the
angle in radian measure through which
the body gets distorted when subjected to
an external shearing action.
We can define shear strain exactly the way
we do longitudinal strain: the ratio of
deformation to original dimensions. In the
case of shear strain, though, it's the amount of
deformation perpendicular to a given line
rather than parallel to it. The ratio turns out to
be tan A, where A is the angle the sheared
line makes with its original orientation. Note
that if A equals 90 degrees, the shear strain is
Any time an object is deformed, shear occurs.
For example, in the top row a block is
deformed without changing area. It looks like
the only deformation involved is compression
Directions of greatest compression and
extension are constant. The major and minor
axes of the deforming ellipse remain constant.
All other lines rotate.
Shear stress developed in a material subjected to a specified torque in torsion test. It is calculated
by the equation:
where T is torque, r is the distance from the axis of twist to the outermost fiber of the specimen,
and J is the polar moment of inertia.
Formulas for bars of circular section
Formulas for bars of non - circular section.
Bars of non -circular section tend to behave non-symmetrically when under torque and plane
sections to not remain plane. Also the distribution of stress in a section is not necessarily linear.
The general formula of torsional stiffness of bars of non-circular section are as shown below the
factor J' is dependent of the dimensions of the section and some typical values are shown
below. For the circular section J' = J.