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with respect to segment AB. The coordinates of point A’ will give the values
(σ’
xx
,τ’
xy
), while those of B’ will give the values (σ’
yy
,τ’
xy
).
The stress condition for which the shear stress, τ’
xy
, is zero, indicated by
segment D’E’, produces the so-called principal stresses, σ
P
xx
(at point D’) and
σ
P
yy
(at point E’). To obtain the principal stresses you need to rotate the
coordinate system x’-y’ by an angle φ
n
, counterclockwise, with respect to the
system x-y. In Mohr’s circle, the angle between segments AC and D’C
measures 2φ
n
.
The stress condition for which the shear stress, τ’
xy
, is a maximum, is given by
segment F’G’. Under such conditions both normal stresses, σ’
xx
= σ’
yy
, are
equal. The angle corresponding to this rotation is φ
s
. The angle between
segment AC and segment F’C in the figure represents 2φ
s
.
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