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The maximum bending moment the beam must resist.
This is typically the maximum moment from your beam's load and span analysis (e.g. wL²/8 for a simply-supported uniformly loaded beam).
The beam's cross-sectional width (the narrower dimension).
The ACTUAL dressed width, not the nominal — a 2× timber is about 38 mm and calling it 50 over-states the section by a third. Width contributes linearly to bending strength while depth contributes as the square, which is why timber beams are deep and narrow and why doubling up a member is a weaker answer than a deeper one at the same volume of timber.
The beam's cross-sectional depth (the dimension parallel to the bending load).
The actual dressed depth, in the direction the load bends it — a beam laid flat is a different and far weaker member than the same timber on edge. Section modulus goes with the square of this, so 15% of depth is about 30% of strength: a beam ripped down or notched at mid-span loses capacity fast, which is what the notch calculation on this site is for.
Actual bending stress
1,442 psi
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Timber Beam Bending Stress Calculator: 1,442 psi — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
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How this was calculated
Formula source(s)
- Rectangular section bending stress: fb = 6M/(b×d²), the standard flexure formula (fb = Mc/I) applied to a rectangular cross-section
Inputs used
- Applied Bending Moment
- 11.06 kip·ft
- Beam Width
- 4 in
- Beam Depth
- 11.75 in
What this calculation does not cover
- The figure returned is the stress demand on the section, not a verdict on the beam. Nothing here compares it against the bending strength of your species and grade, and none of the modification factors are applied — load duration and wet service under the NDS, kmod and the material partial factor under Eurocode 5. Under Eurocode 5 those two alone typically cut the characteristic bending strength to around 60 percent of its value, and the factors themselves are jurisdictional.
- Bending is only one of the checks a timber beam has to pass. This page does not calculate shear stress, which for a rectangular section is 3V/(2bd) and commonly governs on short heavily loaded spans, nor deflection, which usually governs on long ones and is limited by span ratios such as span/360 for imposed load depending on the jurisdiction. Bearing stress at the supports is also outside its scope.
- The flexure formula assumes the compression edge is held against sideways movement. A deep, narrow beam loaded on edge with an unrestrained compression edge can fail by lateral torsional buckling at a moment well below the one this stress figure implies is safe, which is why codes apply a beam stability factor (CL in the NDS, kcrit in Eurocode 5). No such reduction is made here.
- The calculation uses the full uncut rectangle you type in. Notches, birdsmouths, bolt holes and drilled service holes reduce the section modulus, and a notch on the tension face adds a stress concentration that simply reducing the depth does not represent, which is why code rules restrict notch depth and position. Enter actual dressed dimensions as well: a nominal 2x10 measures 1.5 by 9.25 inches (38 by 235 mm), and using the nominal figures understates the bending stress by about a third.
- Depth must be the dimension in the plane of the load, not just the larger one. Entering a 100 by 300 mm joist the wrong way round — 300 wide by 100 deep, as if laid flat — triples the reported stress, and the calculator cannot tell which orientation you meant. Every box follows the unit switch — the moment in kN·m or kip·ft, the section in millimetres or inches — and the stress comes back in MPa or psi.
Add the equipment this sizes
This result is a specification — 1,442 psi — not a quantity. Put the thing it sizes into your project: how many, what you call it, and your supplier’s price.
Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.
Sources checked 2026-09-22 · v1.1.0
Regulatory standards & verification citations1
- Rectangular section bending stress: fb = 6M/(b×d²), the standard flexure formula (fb = Mc/I) applied to a rectangular cross-section
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