Hi,
I will explain here the concept of the plane strain.
Plane Strain is the strain occurring in a body under the action of the external loads along a plane only. The loads can be three dimensional but the strain must be only in two dimensions.
As you know, when we apply an axial load, there is change in the lateral dimensions also, i.e. if we apply the load in the x-axis of a cubical element, as a result, along with the strain along the x-axis, it is accompanied by the change in the width and height of the element.
This change can be found out by multiplying the longitudinal strain with the Poisson's ratio. So, to get the plane strain we have to restrict the deformation of the element along the one of the two other lateral dimensions.
By restricting the strain along one of the three direction, we get the state of plane strain. Let P, is the axial load along the x-axis, which will result in the longitudinal strain,
ex = P/E
also, there will be lateral strain along the y-axis and z-axis
ey= -1/m(P/E)
and ez = -1/m(P/E)
To get the condition of plane strain suppose we want to restrict the strain along the z-axis, Then will will have to apply a load of -E.ez along the z-axis,
So we have to apply a load equal to 1/m(P) along the z-axis.
Net strain along the z-axis is 0. Only ey and ex will exit with further modification due application of the load along the z-axis.
Thank you!
(Reference: nptel- online video lectures)
I will explain here the concept of the plane strain.
Plane Strain is the strain occurring in a body under the action of the external loads along a plane only. The loads can be three dimensional but the strain must be only in two dimensions.
As you know, when we apply an axial load, there is change in the lateral dimensions also, i.e. if we apply the load in the x-axis of a cubical element, as a result, along with the strain along the x-axis, it is accompanied by the change in the width and height of the element.
This change can be found out by multiplying the longitudinal strain with the Poisson's ratio. So, to get the plane strain we have to restrict the deformation of the element along the one of the two other lateral dimensions.
By restricting the strain along one of the three direction, we get the state of plane strain. Let P, is the axial load along the x-axis, which will result in the longitudinal strain,
ex = P/E
also, there will be lateral strain along the y-axis and z-axis
ey= -1/m(P/E)
and ez = -1/m(P/E)
To get the condition of plane strain suppose we want to restrict the strain along the z-axis, Then will will have to apply a load of -E.ez along the z-axis,
So we have to apply a load equal to 1/m(P) along the z-axis.
Net strain along the z-axis is 0. Only ey and ex will exit with further modification due application of the load along the z-axis.
Thank you!
(Reference: nptel- online video lectures)
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