JNTU B.Tech II FUNDAMENTALS OF STRUCTURAL ANALYSIS Previous Question Paper (November/December - 2020 - R16)

In structural mechanics, two-dimensional idealizations are used to simplify three-dimensional problems. These are categorized based on the state of stress or strain within the body.

Plane Stress: A state of plane stress exists when the stress components in the direction of the thickness (z-direction) are zero. This typically occurs in thin plates subjected to forces acting in the plane of the plate. The non-zero stress components are σx, σy, and τxy, while σz = τxz = τyz = 0. Because the plate is thin, it cannot sustain significant stress through its thickness.

Example of Plane Stress: A thin metal sheet or a thin plate subjected to in-plane tensile or shear forces. The stress variation through the thickness is negligible, making the 2D assumption highly accurate.

Plane Strain: A state of plane strain exists when the strain components in the direction of the longitudinal axis (z-direction) are zero. This occurs in long, prismatic bodies where the cross-section is constant and the loading is uniform along the length, such that the body is constrained from deforming in the z-direction. The non-zero strain components are εx, εy, and γxy, while εz = γxz = γyz = 0.

Example of Plane Strain: A long retaining wall, a dam, or a long cylindrical pipe subjected to internal pressure. In these cases, the longitudinal strain is prevented by the surrounding material or the geometry of the structure, meaning the deformation behavior is identical in every cross-sectional slice.

The fundamental distinction lies in the boundary conditions: plane stress assumes the faces are free of stress, whereas plane strain assumes the longitudinal displacement is restricted by the geometry or constraints of the structural member.