How this instrument works
When a beam bends under load, the material at its top and bottom edges stretches or compresses more than the material near its center — that internal stress is called bending stress, and every beam material has a maximum allowable value it can withstand before it's considered overstressed or at risk of failure.
For a simply supported beam with a single point load at midspan, the bending moment reaches its maximum at the center: M = P x L/4. That moment is then converted to a stress using the beam's section modulus S = b x d²/6 (where b is width and d is depth): sigma = M/S. Combined and simplified into inch-pound units for a rectangular section, the working formula is sigma = 18 x P x L(ft) / (b x d²).
This calculator tells you the resulting stress for a given load, span, and section — it's on you (or your structural engineer) to compare that number against the correct allowable stress for your actual material, species, and grade. This is a preliminary mechanics-of-materials estimate for planning purposes only; before finalizing any real structure, have the design checked by a licensed structural engineer or reviewed against your local building department's requirements.
- Enter the center point load in pounds-force.
- Enter the span between supports in feet.
- Enter the section width and depth in inches (actual dimensions).
- Read the resulting bending stress in psi and compare it against your material's allowable bending stress (Fb).
A 2x10 overloaded past a common lumber allowable stress
A single 2x10 (1.5 in x 9.25 in actual) spans 8 ft and carries a 1,000 lbf point load at its center — a fairly heavy point load for that section. Moment: M = 1,000 x 8/4 = 2,000 ft-lb, or 24,000 in-lb. Section modulus: S = 1.5 x 9.25² / 6 = 21.3906 in³. Bending stress: sigma = 24,000 / 21.3906 = 1,121.99 psi — which exceeds both Spruce-Pine-Fir No.2's (875 psi) and Douglas Fir-Larch No.2's (900 psi) published reference allowable stresses, meaning this configuration would be inadequate for either species at this load and span.
Drop the load to a lighter 500 lbf on a shorter 6 ft span using a 2x8 (1.5 in x 7.25 in), and the picture reverses: M = 500 x 6/4 = 750 ft-lb (9,000 in-lb), S = 1.5 x 7.25² / 6 = 13.1406 in³, giving sigma = 684.90 psi — comfortably within the 875 psi SPF No.2 allowable. This is a preliminary estimate only; confirm the correct allowable stress for your actual material and have the final design reviewed by a licensed structural engineer.
Questions
What do I do with the bending stress number once I have it?
Compare it against the allowable bending stress (Fb) published for your specific material, species, and grade. If your computed stress is below Fb, that particular beam clears this one strength check at this load and span; if it's above Fb, the beam is overstressed and needs to be larger, shorter-spanned, or made from a stronger material.
How is this different from the beam-load calculator?
This calculator starts from a known load and section and solves for the resulting stress. The beam-load calculator runs the same physics in reverse — starting from a known allowable stress and section, it solves for the maximum load the beam can carry. Use whichever direction matches the question you're actually asking.
Why does the formula only use a center point load, not a uniform load?
A center point load is the governing case this specific formula is built around (M = PL/4). A beam carrying a uniform load instead — like its own weight or an evenly distributed floor load — follows a different moment formula (M = wL²/8), which is what the beam-load calculator uses.
Does a stress result under the allowable limit guarantee the beam is safe?
No — it only clears the bending-stress check. A complete beam design also needs a deflection check (see beam-deflection) and a shear check, plus proper end support and connection details. This calculator is a preliminary estimate covering one part of the picture, not a full structural design.