ELLIPSE OF STRAIN
It is the locus of the resultant strain on the infinite inclined planes within a body under principle strains. It is a graphical method to find the resultant strain and the angle of obliquity on a given inclined plane (with the plane of major principal strain).
Being a graphical method, there are a few steps of construction.
(x) Taking O as center, draw two concentric circles with radius equal to ε1 and radius equal ε2 respectively. ( ε1 is the greater principal strain). Principal strains are the axis of the ellipse.
(xi) Draw x-axis and y-axis as usual. X-axis as the plane of ε2 and y-axis as the plane of ε1.
(xii) Draw a line LM at an angle of θ with the plane of ε1 i.e. with the y-axis.
(xiii) From O draw perpendicular to LM to cut the inner circle at P and the outer circle at N respectively.
(xiv) From N draw a line NR perpendicular to X-axis.
(xv) From point P draw a perpendicular to meet NR at point Q.
(xvi) Join OQ.
(xvii) OQ Will be resultant strain on the inclined plane and point Q will trace its locus which will be an ellipse for different inclinations of the inclined plane.
(xviii) Measure angle QON which is the angle of obliquity.