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).

 

ellipse-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 εand radius equal ε2 respectively. ( εis 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 εi.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.