Bending Stress Calculator
Calculate bending stress in a beam from the applied bending moment, distance to the outer fiber, and moment of inertia.
How this calculator works
When a beam bends under load, the stress it carries is not the same throughout its depth — it is zero at the centerline and highest at the outer edges. This calculator takes the bending moment on the beam, the distance from the centerline to the outer edge, and the section’s moment of inertia, then finds that maximum bending stress.
Formula: Bending stress = (Moment × Distance from neutral axis) ÷ Moment of inertia (σ = Mc/I). Get I from the Moment of Inertia Calculator using your section’s dimensions.
Worked example
A 50,000 in-lb bending moment on a section with c = 4.625 in (half the depth of a 9.25-inch-deep section) and I = 300 in⁴:
- Moment: 50,000 in-lb
- Distance to outer fiber (c): 4.625 in
- Moment of inertia (I): 300 in⁴
- Bending stress: (50,000 × 4.625) ÷ 300 ≈ 770.83 psi
Notes
c is the distance from the beam’s neutral axis (its centerline) to the outer edge, where stress is highest. For a symmetric rectangular section, that is simply half the depth. The maximum bending stress always occurs at the outer fiber — the top or bottom edge — not at the centerline, which carries zero bending stress.
Compare the result against the material’s allowable bending stress to check that the section is adequate for the load it carries.
How to use
Enter the bending moment on the beam, the distance from the neutral axis to the outer fiber (c), and the section’s moment of inertia (I), all in consistent units. The calculator returns the maximum bending stress in psi, which you can compare against the material’s allowable bending stress.
This is a planning estimate using standard mechanics-of-materials formulas, not a substitute for engineering design. Confirm actual stress limits and material allowables with a licensed structural or mechanical engineer.
Frequently asked questions
What is bending stress?
Bending stress is the stress a beam experiences when it sags or flexes under load. As the beam bends, one side stretches (tension) and the other side compresses, with stress rising from zero at the centerline to a maximum at the outer edges. This calculator finds that maximum stress at the outer edge.
What is c, the distance from the neutral axis?
The neutral axis is the beam's centerline, where bending stress is zero no matter how much the beam bends. The value c is the distance from that centerline out to the beam's outer edge, where stress is highest. For a symmetric rectangular section, c is simply half the total depth of the beam.
Where do I get the moment of inertia for my beam?
Moment of inertia (I) describes how a cross-section's shape resists bending, and it depends on the beam's width, depth, and shape. Use the Moment of Inertia Calculator with your section's dimensions to find I, then bring that value into this calculator along with your moment and c.
Why does maximum stress occur at the outer fiber, not the center?
As a beam bends, material farther from the neutral axis stretches or compresses more than material close to it, so stress builds with distance from the centerline. The outer fiber, at the top or bottom edge of the section, is farthest from the neutral axis and therefore carries the most stress, while the centerline itself carries none.
Estimates only. Verify quantities with your supplier before purchasing.