What is the equation for calculating normal stress in a beam under combined axial and bending stress?

The calculation of normal stress in a beam subjected to combined axial and bending stresses is guided by established principles from mechanics of materials. The correct equation to express this relationship is derived from the superposition principle, which allows us to combine the effects of axial loading and bending moments.

The general expression for normal stress (σ) in this context can be represented as the sum of the axial stress and the bending stress. Axial stress is determined by the axial force (P) divided by the cross-sectional area (A), specifically as P/A. The bending stress is calculated as the moment (M) multiplied by the distance from the neutral axis (y) divided by the moment of inertia (I), resulting in the term My/I.

Therefore, when you combine these two components, the correct formula becomes: σ = P/A + My/I

This means that both the axial force and the bending moment contribute positively to the overall normal stress in the beam, leading to an increase in tensile or compressive stress depending on their respective directions.

The choice labeled as the correct answer aligns precisely with the conventional formulation used in structural engineering, which is derived from fundamental mechanics of materials concepts and reflects real-world scenarios engineers face when analyzing beam behavior under loads.