Bending Stress Calculator

The Bending Stress Calculator computes maximum normal bending stress in a beam cross-section from applied moment and geometry. Choose square, rectangle, tube, circle, pipe, or I-beam sections. The tool calculates area moment of inertia $I$, section modulus $S$, and stress $\sigma$.

Bending stress equation

$$\sigma = \frac{M \cdot c}{I} = \frac{M}{S}$$

$M$ is bending moment, $c$ is distance from neutral axis to outer fiber, $I$ is area moment of inertia, and $S = I/c$ is section modulus.

Rectangle example

For width $b$ and depth $d$, $I = bd^3/12$ and $c = d/2$. A 200 mm by 300 mm section with 10 kN·m moment gives about 3.33 MPa maximum stress at top and bottom fibers.

Frequently Asked Questions

What is bending stress?

Bending stress is normal stress from flexure. The top fiber is in compression and the bottom in tension (for downward loading). Maximum stress occurs at the outer fibers farthest from the neutral axis.

How is bending stress different from shear stress?

Bending stress acts normal to the cross-section along the beam length. Shear stress acts parallel to the cross-section and is largest near supports.

Why does a deeper beam have lower stress?

Moment of inertia grows with the cube of depth for a rectangle. Deeper sections have much larger $I$, so the same moment produces lower $\sigma = Mc/I$.

What moment of inertia formula is used for an I-beam?

For equal flanges: $I = [b_f h^3 - (b_f - t_w)(h - 2t_f)^3]/12$, where $b_f$ is flange width, $h$ is overall height, $t_f$ is flange thickness, and $t_w$ is web thickness.

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Bending Stress Calculator