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1
Lecture Date
: 04.11.2009
Prepared By
:
(01) Anas Abdulrahim
(02)
Engin Usta
2D PROBLEMS IN STRESS ANALYSIS
In stress or strain analysis we can model most the problems as 2D, instead of 3D
analysis it is oftentimes better
to use 1D or 2D representations of the actual stress or strain
case.We can categorize the models as in the following diagram and we apply can employ
these models under appropriate conditions.
Fundamental 2D StressStrain Models
Plane stress
: Assume infinitely thin plate (xy plane), loading is uniformly distrubuted over
the thickness parallel to the plane of stress.
Plane strain:
Assume element infinitely thin along z (xy plane),all cross sections experience
same deformation.
Axisymetric:
Axisymmetric geometry and loads (rz plane),at a constant radii load or strain
conditions are the same along the circumference.In this problems polar coordinates are used.
PLANE STRESS
PROBLEMS
σ
zz
=
0
σ
yz
=
0
σ
xz
=
0
PLANE STRAIN
PROBLEMS
Є
zz
=
0
Є
yz
=
0
Є
xz
=
0
∂/∂z= 0
AXISYMMETRIC
PROBLEMS
∂/∂θ= 0
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(Axisymmetric figure)
PLANE STRESS PROBLEMS
The body has dimensions are such that
h << a, b
Thus, the plate is thin enough such that there is no variation of
displacement (and
temperature) with respect to z, it depends on x and y.Also the stresses in z direction are zero.
Equilibrium Equations
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 Spring '11
 Daglas

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