Shear Strength of Soils - Elements of Soil Mechanics - page 93

Major principal plane

(b)

Minor principal plane

(a)

Fig. 4.3 Stress induced by two principal stresses, σ 1 and σ 3 , on a plane inclined at θ to σ 3 .

Fig. 4.4 Mohr circle diagram.

These formulae lend themselves to graphical representation, and it can be shown that the locus of stress
conditions for all planes through a point is a circle (generally called a Mohr circle). In order to draw a Mohr
circle diagram a specific convention must be followed, all normal stresses (including principal stresses)
being plotted along the axis OX while shear stresses are plotted along the axis OY. For most cases the
axis OX is horizontal and OY is vertical, but the diagram is sometimes rotated to give correct orientation.
The convention also assumes that the direction of the major principal stress is parallel to axis OY, i.e. the
direction of the major principal plane is parallel to axis OX.
To draw the diagram, first lay down the axes OX and OY, then set off OA and OB along the OX axis
to represent the magnitudes of the minor and major principal stresses respectively, and finally construct
the circle with diameter AB. This circle is the locus of stress conditions for all planes passing through the
point A, i.e. a plane passing through A and inclined to the major principal plane at angle θ cuts the circle
at D. The coordinates of the point D are the normal and shear stresses on the plane (Fig. 4.4) .

Normal stress

= =

σ OE OA AE = + = + σ AD cos θ

3

AB cos

2

= +
= + −

σ θ 3

σ ( σ σ )cos 2 θ

3 1 3