Engineering Rock Mechanics

424 Appendix A: Stress and strain analysis

It is not possible to measure shear strains in practice, so for two-
dimensional strain three normal strains are measured at known relative
angles. This permits solution of the strain transformation equation for three
unknowns-El,
Strain gauge rosettes are the devices used to measure strain. They consist
of three strain gauges mounted on an epoxy backing, such that the mutual
angles between the gauges is 45" or 60" (so-called rectangular and delta
rosettes):

and the angle between one gauge and cl.

Three-element (rectangular) Three-element (delta)

rosette, 45" planar, foil rosette, 60" shear planar, foil

For the purposes of analysis we can

assume this geometry, where

a = p = 45" for rectangular rosette

a = p = 60" for a delta rosette.

E2

t

We measure ~p, % and E~, we know a and p, and hence we can calculate

E~, and 8.

Substituting ~1 = E,, cZ = ~y and yrJ = 0 into the strain transformation

equation for direct strain gives us three equations:

In general we have

E~ = c + r cos 2@

where c = centre distance of Mohr's circle = Yz (~1 + EZ)

r = radius of Mohr/s circle = M (EX - EZ)

@ = angle between gauge and E~.