MOHR DIAGRAM FOR THREE STRETCHES, MURPHY
If we have longitudinal strains known in three directions, we need to construct their relationship first in deformed state by drawing a triangle, and then restore this to undeformed state and find out two angular shear strains and then construct the Mohr circle. Please see the above problem solved in this manner in the book by Ramsay and Huber Vol I Techniques of Modern Structural Geology :Strain Analysis. However, Lisle in 1989 showed the Murphy's method for three stretches. You should simply draw two axes and plot on the horizontal axis or abscissa at the top. Scale the abscissa. Arrange the reciprocal quadratic extensions in increasing order and plot these according to scale on the abscissa. Draw lines through each parallel to the ordinate. Choose any point x on the middle line, and from here construct the angles that this elements with the two other elements on either side. These will intersect the two lines on either side parallel to ordinate in let us say P and Q. Find midpoint of P and of Q and erect normals to intersect in C which is the centre of the Mohr circle. Draw a line lambda ' axis parallel to abscissa on top. With C as centre and CP or CQ or Cx as radius, construct the Mohr circle. Read off the values of lambda'1 and of lambda'2.