Civil Engineering Reference
In-Depth Information
Figure 2.6
Shear strains in an element.
Secondly, while stresses in soils are almost always positive (particulate materials cannot
usually sustain tensile stresses unless the grains are attached to one another), strains
may be positive (compressive) or negative (tensile) and in an increment of strain there
will usually be compressive and tensile strains in different directions. Thirdly, we must
be careful to distinguish between pure shear strains and engineers' shear strains
δγ
and
take account of any displacements of the centre of area of distorted elements.
Figure 2.6(a) shows an element OABC strained by
δγ
zh
to a new shape OA
1
B
1
C.
It can be seen that the diagonal OB has rotated to OB
1
through
2
δγ
zh
. Figure 2.6(b)
shows the strained element rotated and translated to O
2
A
2
B
2
C
2
so that the centre and
the diagonals coincide and the edges have now all strained through the same angle
δε
zh
=
δε
hz
=
1
2
δγ
zh
.
Figure 2.7(a) shows a plane element with principal strains
δε
h
(which is
negative), while Fig. 2.7(b) is the corresponding Mohr circle of strain. The pole is at P
δε
z
and
Figure 2.7
Analysis of strain using a Mohr circle.
