JNTU B.Tech III Year FINITE ELEMENT METHODS Previous Question Paper (August - 2022 - R18)

In a state of plane stress, the stress components acting in the thickness direction (z-direction) are assumed to be zero. Specifically, the normal stress in the z-direction is defined as:

By definition, for a plane stress condition, the stress tensor is reduced such that σz = 0, τxz = 0, and τyz = 0. While the strain in the z-direction (εz) is non-zero due to the Poisson effect, the stress σz itself is negligible and is taken as zero for the purpose of analysis.

Plane Stress is a state of stress in which the normal stress and shear stresses directed perpendicular to the plane of the body are assumed to be zero. It typically occurs in thin plates loaded in their own plane. The stress state is defined by σx, σy, and τxy, while σz = τxz = τyz = 0.

Plane Strain is a state of strain in which the strain components normal to the plane of the body and the shear strains involving the z-direction are assumed to be zero. It typically occurs in long prismatic members (like dams or tunnels) where the cross-section is constant and the length is significantly larger than the cross-sectional dimensions. The strain state is defined by εx, εy, and γxy, while εz = γxz = γyz = 0.