420 Appendix A: Stress and strain analysis
E~ = 2E -4Mohr’ circle of strain for struin guuge rosettes
Consider three arbitrarily orientated gauges, and their associated Mohr’s
circle:&e +a + p &e +a €0The points P, Q, R represent the state of strain in the directions of the
gauges. Of particular interest are the dotted lines to the point X, and the
angles PXQ = a and QXR = 0. These angles arise from the geometry of a
circle, and allow us to construct Mohr’s circle when the angle 8is unknown.
The procedure is:
(a) draw the shear strain axis and a temporary horizontal axis;
(b) mark off the strains €0, €e+a and Ee+a+D on this axis, and draw vertical
construction lines through them;
(c) select any point X on the line through &e+,, and draw lines inclined at
a and p to intersect the other construction lines at P and R,
respectively;
(d)draw the perpendicular bisectors to PX and RX, and mark their
intersection. This is the centre of Mohr’s circle;
(e) the true direct strain axis can be drawn through the centre of the circle,
and q, and 8 measured off.