In plane stress conditions, the stresses are associated with which of the following?

• A. The primary forces acting on the member
• B. Stresses that exist in two principal directions of the plane
• C. All directions of stress
• D. Thermal expansion stresses

Answer: (B)

Plane stress means the material’s thickness is small and the load produces stresses mainly in the plane of the member, with negligible through-thickness stress components. In this state the in-plane stress components are sigma in one in-plane direction, sigma in the orthogonal in-plane direction, and the in-plane shear tau_xy. You can rotate the in-plane axes to find two directions where the shear disappears and the normal stresses reach their principal values. Those two directions are the principal directions in the plane, so the stresses are associated with two directions within the plane.

The other ideas don’t describe the essence of plane stress: stresses tied to the overall external force direction aren’t about the in-plane confinement; asking about stresses in all directions would imply a three-dimensional state; and thermal expansion stresses are simply a specific cause, not the defining feature.