Plane Strain

1
Plane Strain

• A state of plane strain exits when the strains
  are confined to a single plane, such as the x-y
  plane.
• This generally means that the stresses in the
  other direction eg., the z direction, are
  non-zero.
• Plane Strain occurs in thick sections that
  constrain out of plane deformations

2
Transformations in plane strain
e
e
,
g
,
Determine the
.
The state of plane strain at a point p is given
by
x
y
xy
principal strains and the maximum in-plane shear
strain and show the
orientations of the elements subjected to these
strains. Also determine the
absolute maximum shear strain.
e
3
Solution
g
xy
tan
2
q
p
e
e
x
y
g
-0.006
1
xy
1
.
.
q
atan
atan
p
(0.003-0.001)
e
e
2
2
x
y
4
Principal Strains
e
e
e
e
g
x
y
x
y
xy
.
.
.
.
e
'
cos
2
q
sin
2
q
x
p
p
2
2
2
e
e
e
e
g
x
y
x
y
xy
.
.
.
.
e
'
cos
2
q
sin
2
q
y
p
p
2
2
2
-0.006
0.004
0.002
-79.6º
.
sin
-79.6º
e
'
cos
x
2
2
2
0.005162
ey-0.001162
5
Maximum Shear Strain
e
'
e
'
x
y

e
'
g
x
test
e
'
y
gmax 0.006325
Use diameters of circles!, Mohrs circle plots
g/2, so g is the diameter (2x radius).
6
Max In-Plane Shear Strain
9.2º
-0.006325
7
Mohrs Circle

• Plot normal strain on the x-axis
• Plot ½ the shear strain on the y-axis
• Solve as you would for plane stress problem

g/2
e