Difference between plane stress and plane strain problem

Presented by: Satyajit MhatreDIFFERENCE BETWEEN PLANE STRESS AND PLANE STRAIN PROBLEM11PLANE STRESSPlane stress is defined to be a state of stress in which the normal stress, and shear stress, directed to the x-y plane are assumed to be zero.The geometry of the body is that of a plate with one dimension much smaller than the others. The loads are applied uniformly over the thickness of the plate and act in the plane of the plate.The plane stress condition is the simplest form of behavior for continuum structures and represents situations frequently encountered in practice.2PLANE STRESS

3Typical loading and boundary conditions for a plane stress problem in 2-dimensional analysis:-

Loadings may be point forces or distributed forces applied over the thickness of the plate.Supports may be fixed points or fixed edges or roller supports.

4Loading and Boundary Conditions for a plane stress

52-D State of Plane Stress

62-D State of Plane Stress

72-D State of Plane Stress

8PLANE STRAINPlane strain is defined to be a state of strain in which the strain normal to the x-y plane, and shear strain are assumed to be zero. Dimension of the structure in one direction (say z direction ) is very large as compared to other two directions (x-y).Applied forces act in x-y plane and do not vary in the z direction i.e. the loads are uniformly distributed with respect to the large dimension and act perpendicular to it. 9PLANE STRAIN

10Typical loading and boundary conditions for a plane strain problem in 2-dimensional analysis:-

112-D State of Plane Strain

122-D State of Plane Strain

13Comparison of plane stress and plane strain

14Examples of 2-D Plane Stress AnalysisPlane stress case is a case of a thin plate, a cantilever plate or so.

15Examples of 2-D Plane Strain AnalysisPlane strain problem is used in case of long cylindrical or a prismatic body say a cylindrical tube, a culvert or tunnel, retaining wall etc.

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