17.6 : Stress: General Loading Conditions

To grasp the intricacy of real-world conditions where multiple loads are applied simultaneously to a structure, one might visualize a section passing through a specific point within a body, aligned parallel to the xy plane. This section is subjected to various forces, including original loads, normal forces, and shearing forces.

The shearing force, possessing potential directionality within the plane of the section, is simplified into two component forces running parallel to the x and y axes. Each force is divided by the area, and as it approaches zero, three distinct stress components (σ_z, τ_zx, and τ_zy) are defined. The initial subscript in these components signifies that the stresses are exerted on a surface perpendicular to the z-axis, whereas the second subscript identifies the direction of the component.

The signs of these stress components indicate tension (positive) or compression (negative). A similar analysis on the right portion of the body results in identical stress components but in opposite directions. Additional stress components can be determined by passing sections through the point parallel to the yz and zx planes. This analysis aids in unraveling the complex interplay of forces and stresses under intricate loading conditions.