Bending Stress

Calculate the internal stress in a beam subjected to a bending moment.

Stress Parameters

Bending Moment (lb-in)

Distance to Fiber (y) (in)

Moment of Inertia (I) (in⁴)

* Ensure your Moment is in force-length units (e.g. lb-in) and dimensions/inertia are in consistent units (e.g. in, in⁴).

Stress Analysis

Analyzing material stress?

Enter the bending moment, the beam's geometric properties, and the distance from the neutral axis to calculate the resulting internal stress.

About this calculator

Overview

Bending stress is the normal stress that an object encounters when it is subjected to a large load at a particular point. This stress is zero at the beam's neutral axis (the center for symmetrical beams) and reaches its maximum value at the top and bottom fibers. If this stress exceeds the material's yield strength, the beam will permanently deform or fail.

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Pro Tips

The value of 'y' is typically half of the beam's total depth (h/2) if you want to find the maximum stress at the surface.
Check your units carefully! If Moment is in lb-ft and dimensions are in inches, you must convert the Moment to lb-in (multiply by 12).
For a rectangular beam, Bending Stress can also be calculated as (6 × M) / (b × h²).

Fun Facts

"In a simply supported beam under a downward load, the top fibers are in compression and the bottom fibers are in tension."
"The 'Neutral Axis' is the line in a beam where there is no longitudinal stress or strain."
"I-beams are shaped as they are (with large flanges) to maximize the Moment of Inertia while minimizing weight."

Formula: σ = (M × y) / I; Section Modulus (S) = I / y