# Ellipse of Strain

**Ellipse of Strain**

**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).**

**CONSTRUCTION**

Being a graphical method, there are a few steps of construction.

(x) Taking O as center, draw two concentric circles with radius equal to ε_{1 }and radius equal ε_{2} respectively. ( ε_{1 }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 ε_{2} and y-axis as the plane of ε_{1}.

(xii) Draw a line LM at an angle of θ with the plane of ε_{1 }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.