Page 61 - Rock Mechanics For Underground Mining

PROBLEMS

of the circle diagram yields
(OS 1 − OD)
tan 1 =
DF
( 1 − xx )
=
xy
This expression is completely consistent with that for orientations of principal axes
established analytically (equation 2.24b).

Problems

(The geomechanics convention for stress and strain is to be assumed in the following
exercises.)

1 The rectangular plate shown in the figure below has the given loads uniformly
distributed over the edges. The plate is 50 mm thick, AB is 500 mm and BC is
400 mm.
(a) Determine the shear forces which must operate on the edges BC, DA, to maintain
the equilibrium of the plate.

(b) Relative to the x, y reference axes, determine the state of stress at any point P
in the interior of the plate.
(c) For the l, m axes oriented as shown, determine the stress components
ll , mm , lm .
(d) Determine the magnitudes of the principal stresses, and the orientation of the
major principal stress axis to the x axis.
◦
(e) For the surface GH, whose outward normal is inclined at
to the x axis,
determine expressions for the component tractions, t x , t y , operating on it as a
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