W40×331 Steel Beam
A W40×331 is a wide flange steel beam 40.8 inches deep with 12.2-inch flanges, weighing 331 pounds per foot. In ASTM A992 steel (Fy = 50 ksi) it has a design bending strength of 5,363 kip-ft (LRFD) when its compression flange is braced, and a design shear strength of 1,493 kips.
Design a W40×331 beam Opens a 62 ft span in the free beam designer.
W40×331 dimensions
| Dimension | Value |
|---|---|
| Depth, d | 40.8 in |
| Flange width, bf | 12.2 in |
| Flange thickness, tf | 2.13 in |
| Web thickness, tw | 1.22 in |
| Distance to web toe of fillet, kdes | 3.31 in |
| Distance between flange centroids, ho | 38.67 in |
| Cross-sectional area, A | 97.5 in2 |
| Weight | 331 lb/ft |
Dimensions are AISC design values. Detailing dimensions are rounded to the nearest 1/16 in.
W40×331 section properties
| Property | Strong axis (x) | Weak axis (y) |
|---|---|---|
| Moment of inertia, I | 24700 in4 | 644 in4 |
| Elastic section modulus, S | 1210 in3 | 106 in3 |
| Plastic section modulus, Z | 1430 in3 | 172 in3 |
| Radius of gyration, r | 15.9 in | 2.57 in |
| Torsion and slenderness | Value |
|---|---|
| Torsional constant, J | 105 in4 |
| Warping constant, Cw | 241000 in6 |
| Effective radius of gyration, rts | 3.21 in |
| Flange slenderness, bf/2tf | 2.86 |
| Web slenderness, h/tw | 28.0 |
W40×331 bending and shear strength
For ASTM A992 steel (Fy = 50 ksi, E = 29,000 ksi) per AISC 360-16. Its flanges and web are compact for bending, so with its compression flange braced it reaches its full plastic moment.
| Strength | LRFD | ASD |
|---|---|---|
| Bending, compression flange braced | φMn = 5,363 kip-ft | Mn/Ω = 3,568 kip-ft |
| Shear | φVn = 1,493 kips | Vn/Ω = 996 kips |
If the compression flange isn't braced, the beam can buckle sideways before it yields. Up to Lp = 9.1 ft between braces it keeps its full strength; past Lr = 33.7 ft it buckles elastically. With uniform moment between braces (Cb = 1.0):
| Unbraced length, Lb | φMn (LRFD) | Mn/Ω (ASD) |
|---|---|---|
| Braced | 5,363 kip-ft | 3,568 kip-ft |
| 9.1 ft (Lp) | 5,362 kip-ft | 3,568 kip-ft |
| 10 ft | 5,281 kip-ft | 3,513 kip-ft |
| 20 ft | 4,395 kip-ft | 2,924 kip-ft |
| 30 ft | 3,508 kip-ft | 2,334 kip-ft |
| 33.8 ft (Lr) | 3,173 kip-ft | 2,111 kip-ft |
| 40 ft | 2,574 kip-ft | 1,712 kip-ft |
| 50 ft | 1,982 kip-ft | 1,319 kip-ft |
| 60 ft | 1,616 kip-ft | 1,075 kip-ft |
| 70 ft | 1,366 kip-ft | 909 kip-ft |
A beam with a uniform load between braces has Cb above 1.0 (1.14 for a simple span braced only at its ends), so these values are conservative. The beam designer works out Cb for every segment between braces.
W40×331 load table by span
The largest uniform load a simply supported W40×331 can carry, in kips per foot, with its compression flange braced along its length (by a floor or roof deck, for example). The loads include the beam's own weight of 0.331 kips per foot.
| Span | Factored load (LRFD) | Allowable load (ASD) | Load at span/360 | Load at span/240 |
|---|---|---|---|---|
| 20 ft | 107.3 | 71.4 | 132.6 | 199.0 |
| 22 ft | 88.6 | 59.0 | 99.7 | 149.5 |
| 24 ft | 74.5 | 49.6 | 76.8 | 115.1 |
| 26 ft | 63.5 | 42.2 | 60.4 | 90.6 |
| 28 ft | 54.7 | 36.4 | 48.3 | 72.5 |
| 30 ft | 47.7 | 31.7 | 39.3 | 59.0 |
| 32 ft | 41.9 | 27.9 | 32.4 | 48.6 |
| 34 ft | 37.1 | 24.7 | 27.0 | 40.5 |
| 36 ft | 33.1 | 22.0 | 22.7 | 34.1 |
| 38 ft | 29.7 | 19.8 | 19.3 | 29.0 |
| 40 ft | 26.8 | 17.8 | 16.6 | 24.9 |
| 42 ft | 24.3 | 16.2 | 14.3 | 21.5 |
| 44 ft | 22.2 | 14.7 | 12.5 | 18.7 |
| 46 ft | 20.3 | 13.5 | 10.9 | 16.4 |
| 48 ft | 18.6 | 12.4 | 9.60 | 14.4 |
| 50 ft | 17.2 | 11.4 | 8.49 | 12.7 |
| 52 ft | 15.9 | 10.6 | 7.55 | 11.3 |
| 54 ft | 14.7 | 9.79 | 6.74 | 10.1 |
| 56 ft | 13.7 | 9.10 | 6.04 | 9.06 |
| 58 ft | 12.8 | 8.48 | 5.44 | 8.16 |
| 60 ft | 11.9 | 7.93 | 4.91 | 7.37 |
| 62 ft | 11.2 | 7.43 | 4.45 | 6.68 |
| 64 ft | 10.5 | 6.97 | 4.05 | 6.07 |
| 66 ft | 9.85 | 6.55 | 3.69 | 5.54 |
| 68 ft | 9.28 | 6.17 | 3.37 | 5.06 |
| 70 ft | 8.76 | 5.83 | 3.09 | 4.64 |
| 72 ft | 8.28 | 5.51 | 2.84 | 4.26 |
| 74 ft | 7.83 | 5.21 | 2.62 | 3.93 |
| 76 ft | 7.43 | 4.94 | 2.42 | 3.63 |
| 78 ft | 7.05 | 4.69 | 2.24 | 3.35 |
| 80 ft | 6.70 | 4.46 | 2.07 | 3.11 |
| 82 ft | 6.38 | 4.24 | 1.92 | 2.89 |
| 84 ft | 6.08 | 4.05 | 1.79 | 2.69 |
| 86 ft | 5.80 | 3.86 | 1.67 | 2.50 |
| 88 ft | 5.54 | 3.69 | 1.56 | 2.34 |
| 90 ft | 5.30 | 3.52 | 1.46 | 2.18 |
| 92 ft | 5.07 | 3.37 | 1.36 | 2.04 |
| 94 ft | 4.86 | 3.23 | 1.28 | 1.92 |
| 96 ft | 4.65 | 3.10 | 1.20 | 1.80 |
| 98 ft | 4.47 | 2.97 | 1.13 | 1.69 |
| 100 ft | 4.29 | 2.85 | 1.06 | 1.59 |
| 102 ft | 4.12 | 2.74 | 1.00 | 1.50 |
- Factored and allowable loads are limited by bending, or by shear where marked *.
- The deflection columns are the service loads that make the beam sag span/360 or span/240. Compare span/360 with the live load alone and span/240 with dead plus live load, the usual floor limits in IBC Table 1604.3.
Reading the table
At a 62 ft span, a W40×331 carries a factored load of 11.2 kips per foot (LRFD) or an allowable load of 7.43 kips per foot (ASD). A live load of 4.45 kips per foot would deflect it span/360, which is 2.07 in. The beam works if the factored load is under the first number and the live and total loads are under the deflection numbers. For other spans, supports or loads, open it in the beam designer, or follow the steel beam design guide to check one by hand.
W40×331 questions
What does W40×331 mean?
W means a wide flange shape. 40 is its nominal depth in inches (the actual depth is 40.8 in) and 331 is its weight in pounds per foot.
How much does a W40×331 weigh?
331 pounds per foot, so a 20 ft W40×331 weighs about 6,620 pounds.
How far can a W40×331 span?
It depends on the load. Braced along its length, it carries 107.3 kips per foot of factored load at 20 ft and 4.12 kips per foot at 102 ft; the load table has the spans in between. Floor beams are often 61 to 82 ft for this depth (span-to-depth ratios of about 18 to 24), where deflection usually governs.
Is a W40×331 a compact section?
Yes. Its flanges (bf/2tf = 2.86) and web (h/tw = 28.0) are both compact for bending in 50 ksi steel.