Steel beam size is the lightest W-shape whose bending, shear and sag all pass: a 14 ft span carrying 400 plf of live load and 100 plf of dead load takes a W8x13. Enter your span and load above and the calculator lists the lightest W-shapes that work, with the beam's own weight in the load.
How the steel beam size is found
For every compact W-shape in the AISC Shapes Database, the calculator checks a simple span with a uniform load (and an optional point load at the center) against three limits, using allowable strength design and 50 ksi steel:
- Bending: the moment w × L² ÷ 8 must not exceed Fy × Zx ÷ 1.67, where Zx is the plastic section modulus (AISC 360-16 Section F2.1, Ω = 1.67).
- Shear: the end reaction must not exceed 0.6 × Fy × d × tw ÷ 1.50 (Section G2.1, Ω = 1.50, for webs that qualify for Cv1 = 1.0).
- Sag: live load at most span ÷ 360 (floors) or ÷ 240 (roofs), total load at most span ÷ 240, with E = 29,000 ksi and the shape's Ix.
Bending capacity (lb-ft) = 50,000 psi × Zx (in³) ÷ 1.67 ÷ 12. Sag = 5 × w × L⁴ ÷ (384 × E × Ix).
The lightest shape that passes all three, with its own weight added to the load, is the answer. Shapes that are not compact at 50 ksi, or whose web is too slender for the simple shear check, are left out rather than approximated.
Worked example: a 14 ft span
Span 14 ft, 10 ft tributary width, live load 40 psf, dead load 10 psf, so 400 plf live and 100 plf dead.
- A W8x13 adds 13 plf, so the load is 513 plf.
- Bending: 513 × 14² ÷ 8 = 12,569 lb-ft against 28,443 lb-ft allowed (50,000 × 11.4 ÷ 1.67 ÷ 12 for its Zx of 11.4 in³), 44 percent.
- Live load sag: 0.30 in against a 0.47 in limit (168 in ÷ 360).
- Total load sag: 0.39 in against a 0.70 in limit (168 in ÷ 240).
The next lightest shapes that pass are W8x15, W10x15 and W6x16. Sag, not strength, is what picks a light beam like this: bending is only 44 percent used. Choosing a deeper W10x15 for the same weight class drops the sag from 0.39 to 0.22 in.
Limit the depth
Beams that must hide in a floor or ceiling are depth-limited. Choose "Up to 8 in" for the same load and the answer is still W8x13 (8.0 in deep); the next choice at that limit is W6x16. Depth is the actual depth from the AISC database, not the number in the name: a W8x13 is 7.99 in deep and a W10x15 is 9.99 in.
Braced flange, or not
The bending capacity above assumes the compression flange is held from moving sideways by decking or joists along the span (unbraced length Lb no more than Lp, where Lp = 1.76 × ry × the square root of E ÷ Fy, AISC F2-5). For a W8x13 that is 36 in. Turn the brace option off and the calculator only offers shapes whose Lp is at least the span, which at 14 ft means very wide shapes such as a W14x145. Longer unbraced lengths reduce the capacity under AISC F2.2, which this tool does not compute; brace the beam or ask an engineer.
W-shape names
The number after the X is the weight in pounds per foot: a W8x13 weighs 13 lb/ft. The number after the W is the nominal depth in inches. See every shape with its depth, flange and web in the I-beam size chart and the weight of your run in the steel weight calculator.
Next questions
- Sag for a section or material of your own, or other supports: the beam deflection calculator.
- A wood alternative: the LVL beam calculator, or the sawn-lumber girder tables in the beam span calculator.
- A steel header over a wide opening: the header span calculator.
- Footings under the posts that hold the beam: the concrete footing calculator.
- More span tools: framing and lumber calculators.
This is a first sizing for a simple, uniformly loaded span. Bearing, web crippling, connections, holes, camber, floor vibration and the columns and footings that carry the beam are not checked. Have a structural engineer verify any steel beam before you buy it, and get a permit where your building department requires one.