HP 49g+ User Manual page 746

Graphing calculator
Hide thumbs Also See for 49g+:
Table of Contents

Advertisement

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
), 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
Page 22-34

Advertisement

Table of Contents
loading

Table of Contents