When a structural member is subjected simultaneously to more than one type of loading — axial force, bending moment, shear force, and/or torsion — the resulting stress state at a point is obtained by superposing the individual normal and shear stresses computed independently for each loading type (axial: P/A; bending: My/I; shear: VQ/I; torsion: Tρ/J), then combining the total normal and shear stress at that point via principal-stress methods (e.g., Mohr's circle) to determine the resultant maximum stresses. This principle of superposition is valid only under small-deformation conditions where secondary (P-delta) moment effects are negligible relative to primary bending moments. This is a topic in mechanics of materials (strength of materials), specifically combined-loading stress analysis, which synthesizes the previously derived individual stress formulas for axial, torsional, bending, and pressure-vessel loading into a unified framework for members under compound loading.
When a structural member is subjected simultaneously to more than one type of loading — axial force, bending moment, shear force, and/or torsion — the resulting stress state at a point is obtained by…