17.7 : Components of Stress

Stress analysis under multiple loading conditions is intricate, necessitating a comprehensive grasp of normal and shearing stresses. Consider a small cube at point O, subjected to stress on all six faces, visible or not. Normal stress components σ_x, σ_y, σ_z act perpendicularly to the x, y, and z axes. Shearing stress components τ_xy and τ_xz are exerted on faces perpendicular to these axes.

Interestingly, the hidden cube faces also experience these stresses, equal and opposite to those on the visible faces, ensuring equilibrium. As the cube's side length nears zero, the difference between the stresses at O and those on the cube's faces becomes negligible.

Examining the forces acting on the cube leads to crucial relations among shearing stress components: τ_xy equals τ_yx, τ_yz equals τ_zy, and τ_zx equals τ_xz, indicating that only six stress components, not nine, define the stress condition at a point.

Importantly, shear cannot occur in only one plane. An equal shearing stress must be applied on another plane perpendicular to the first. Finally, the interpreted stress situation can vary depending on the orientation of the considered element, highlighting the complexity of stress analysis under multiple loading conditions.