Principal Strains & Direction From
Measurements
The equations for calculating principal strains
from three rosette strain measurements are derived
from what is known as a
"strain-transformation" relationship. As
employed here in its simplest form, such a
relationship expresses the normal strain in any
direction on a test surface in terms of the two
principal strains and the angle from the principal
axis to the direction of the specified strain. This
situation can be envisioned most readily with the aid
of the well-known Mohr's circle for strain
*
.
It can be seen from this figure (noting that the
angles in Mohr's circle are double the physical
angles on the test surface) that the normal strain at
any angle
from the major principal axis is simply expressed
by:
(515.1)
*
The Mohr's circle shown above is
constructed with positive shear strain plotted
downward. This is done so that the positive
rotational direction in Mohr's circle is the same
(CCW) as for the rosette, while maintaining the usual
sign convention for shear (i.e., positive shear
corresponds to a reduction in the initial right angle
at the origin of the X-Y axes).
(
continued ...
)
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Vishay Measurements Group
