HP F2226A - 48GII Graphic Calculator User Manual page 750

side figure shows the state of stresses when the element is rotated by an angle
φ. In this case, the normal stresses are σ' and σ'
, while the shear stresses
xx yy
are τ' and τ'
.
xy yx
, σ , τ , τ
The relationship between the original state of stresses (σ ) and the
xx yy xy yx
, σ' , τ'
state of stress when the axes are rotated counterclockwise by f (σ' ,
xx yy xy
τ'
), can be represented graphically by the construct shown in the figure
yx
below.
To construct Mohr's circle we use a Cartesian coordinate system with the x-
axis corresponding to the normal stresses (σ), and the y-axis corresponding to
) and B (σ , τ
the shear stresses (τ). Locate the points A(σ ,τ ), and draw
xx xy yy xy
the segment AB. The point C where the segment AB crosses the σ
axis will
n
be the center of the circle. Notice that the coordinates of point C are (½⋅(σ
yy
+ σ
), 0). When constructing the circle by hand, you can use a compass to
xy
trace the circle since you know the location of the center C and of two points,
A and B.
Let the segment AC represent the x-axis in the original state of stress. If you
want to determine the state of stress for a set of axes x'-y', rotated
counterclockwise by an angle with respect to the original set of axes x-y,
draw segment A'B', centered at C and rotated clockwise by and angle
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