W40×392 Steel Beam
A W40×392 is a wide flange steel beam 41.6 inches deep with 12.4-inch flanges, weighing 392 pounds per foot. In ASTM A992 steel (Fy = 50 ksi) it has a design bending strength of 6,413 kip-ft (LRFD) when its compression flange is braced, and a design shear strength of 1,772 kips.
Design a W40×392 beam Opens a 63 ft span in the free beam designer.
W40×392 dimensions
| Dimension | Value |
|---|---|
| Depth, d | 41.6 in |
| Flange width, bf | 12.4 in |
| Flange thickness, tf | 2.52 in |
| Web thickness, tw | 1.42 in |
| Distance to web toe of fillet, kdes | 3.70 in |
| Distance between flange centroids, ho | 39.08 in |
| Cross-sectional area, A | 115 in2 |
| Weight | 392 lb/ft |
Dimensions are AISC design values. Detailing dimensions are rounded to the nearest 1/16 in.
W40×392 section properties
| Property | Strong axis (x) | Weak axis (y) |
|---|---|---|
| Moment of inertia, I | 29900 in4 | 803 in4 |
| Elastic section modulus, S | 1440 in3 | 130 in3 |
| Plastic section modulus, Z | 1710 in3 | 212 in3 |
| Radius of gyration, r | 16.1 in | 2.64 in |
| Torsion and slenderness | Value |
|---|---|
| Torsional constant, J | 172 in4 |
| Warping constant, Cw | 306000 in6 |
| Effective radius of gyration, rts | 3.30 in |
| Flange slenderness, bf/2tf | 2.45 |
| Web slenderness, h/tw | 24.1 |
W40×392 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 = 6,413 kip-ft | Mn/Ω = 4,266 kip-ft |
| Shear | φVn = 1,772 kips | Vn/Ω = 1,181 kips |
If the compression flange isn't braced, the beam can buckle sideways before it yields. Up to Lp = 9.3 ft between braces it keeps its full strength; past Lr = 38.3 ft it buckles elastically. With uniform moment between braces (Cb = 1.0):
| Unbraced length, Lb | φMn (LRFD) | Mn/Ω (ASD) |
|---|---|---|
| Braced | 6,413 kip-ft | 4,266 kip-ft |
| 9.3 ft (Lp) | 6,412 kip-ft | 4,266 kip-ft |
| 10 ft | 6,351 kip-ft | 4,226 kip-ft |
| 20 ft | 5,443 kip-ft | 3,621 kip-ft |
| 30 ft | 4,535 kip-ft | 3,017 kip-ft |
| 38.3 ft (Lr) | 3,777 kip-ft | 2,513 kip-ft |
| 40 ft | 3,591 kip-ft | 2,389 kip-ft |
| 50 ft | 2,786 kip-ft | 1,854 kip-ft |
| 60 ft | 2,281 kip-ft | 1,518 kip-ft |
| 70 ft | 1,934 kip-ft | 1,287 kip-ft |
| 80 ft | 1,680 kip-ft | 1,118 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.
W40×392 load table by span
The largest uniform load a simply supported W40×392 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 0.392 kips per foot.
| Span | Factored load (LRFD) | Allowable load (ASD) | Load at span/360 | Load at span/240 |
|---|---|---|---|---|
| 21 ft | 116.3 | 77.4 | 138.7 | 208.1 |
| 23 ft | 97.0 | 64.5 | 105.6 | 158.4 |
| 25 ft | 82.1 | 54.6 | 82.2 | 123.3 |
| 27 ft | 70.4 | 46.8 | 65.3 | 97.9 |
| 29 ft | 61.0 | 40.6 | 52.7 | 79.0 |
| 31 ft | 53.4 | 35.5 | 43.1 | 64.7 |
| 33 ft | 47.1 | 31.3 | 35.7 | 53.6 |
| 35 ft | 41.9 | 27.9 | 30.0 | 44.9 |
| 37 ft | 37.5 | 24.9 | 25.4 | 38.0 |
| 39 ft | 33.7 | 22.4 | 21.7 | 32.5 |
| 41 ft | 30.5 | 20.3 | 18.6 | 28.0 |
| 43 ft | 27.7 | 18.5 | 16.2 | 24.2 |
| 45 ft | 25.3 | 16.9 | 14.1 | 21.1 |
| 47 ft | 23.2 | 15.5 | 12.4 | 18.6 |
| 49 ft | 21.4 | 14.2 | 10.9 | 16.4 |
| 51 ft | 19.7 | 13.1 | 9.68 | 14.5 |
| 53 ft | 18.3 | 12.2 | 8.63 | 12.9 |
| 55 ft | 17.0 | 11.3 | 7.72 | 11.6 |
| 57 ft | 15.8 | 10.5 | 6.94 | 10.4 |
| 59 ft | 14.7 | 9.81 | 6.25 | 9.38 |
| 61 ft | 13.8 | 9.17 | 5.66 | 8.49 |
| 63 ft | 12.9 | 8.60 | 5.14 | 7.71 |
| 65 ft | 12.1 | 8.08 | 4.68 | 7.02 |
| 67 ft | 11.4 | 7.60 | 4.27 | 6.41 |
| 69 ft | 10.8 | 7.17 | 3.91 | 5.87 |
| 71 ft | 10.2 | 6.77 | 3.59 | 5.38 |
| 73 ft | 9.63 | 6.40 | 3.30 | 4.95 |
| 75 ft | 9.12 | 6.07 | 3.04 | 4.57 |
| 77 ft | 8.65 | 5.76 | 2.81 | 4.22 |
| 79 ft | 8.22 | 5.47 | 2.61 | 3.91 |
| 81 ft | 7.82 | 5.20 | 2.42 | 3.63 |
| 83 ft | 7.45 | 4.95 | 2.25 | 3.37 |
| 85 ft | 7.10 | 4.72 | 2.09 | 3.14 |
| 87 ft | 6.78 | 4.51 | 1.95 | 2.93 |
| 89 ft | 6.48 | 4.31 | 1.82 | 2.73 |
| 91 ft | 6.19 | 4.12 | 1.70 | 2.56 |
| 93 ft | 5.93 | 3.95 | 1.60 | 2.40 |
| 95 ft | 5.68 | 3.78 | 1.50 | 2.25 |
| 97 ft | 5.45 | 3.63 | 1.41 | 2.11 |
| 99 ft | 5.23 | 3.48 | 1.32 | 1.99 |
| 101 ft | 5.03 | 3.35 | 1.25 | 1.87 |
| 103 ft | 4.84 | 3.22 | 1.18 | 1.76 |
- 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 63 ft span, a W40×392 carries a factored load of 12.9 kips per foot (LRFD) or an allowable load of 8.60 kips per foot (ASD). A live load of 5.14 kips per foot would deflect it span/360, which is 2.10 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.
W40×392 questions
What does W40×392 mean?
W means a wide flange shape. 40 is its nominal depth in inches (the actual depth is 41.6 in) and 392 is its weight in pounds per foot.
How much does a W40×392 weigh?
392 pounds per foot, so a 20 ft W40×392 weighs about 7,840 pounds.
How far can a W40×392 span?
It depends on the load. Braced along its length, it carries 116.3 kips per foot of factored load at 21 ft and 4.84 kips per foot at 103 ft; the load table has the spans in between. Floor beams are often 62 to 83 ft for this depth (span-to-depth ratios of about 18 to 24), where deflection usually governs.
Is a W40×392 a compact section?
Yes. Its flanges (bf/2tf = 2.45) and web (h/tw = 24.1) are both compact for bending in 50 ksi steel.