HP 50g User Manual page 749

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