402 Appendix A: Stress and strain analysis
az ao az,
ax ay az-+-+-+y=o
the equilibrium equations.Each equation contains increments of the stress components in one
direction. In these equations the vector (X, Y and Z) is the body force vector,
that is the force (mass x acceleration) produced by the body itself. Normally
we will be dealing with bodies at rest in the Earths gravitional field, with
the z-axis vertically downwards. In this case the body force vector is
simply (O,O, rz).Transformation of the stress tensor
It is often the case that we may know applied stresses relative to one set
of axes (the global axes), but may wish to know the stress state relative to
another set (the local axes). For example, suppose we are dealing with a
discontinuity in a rock mass:Given oy and zyx, what are oy* and
zyxT?Unfortunately, stresses are tensors, not vectors like forces, and so cannot
be simply resolved: they must be transformed. We will limit ourselves to
this case:
Z,d, % w
.+. X' I' Y Y'The global system is x, y, z.
The local system is x', y', z'.
In this case z and z' are coincident.