W40×372 Steel Beam
A W40×372 is a wide flange steel beam 40.6 inches deep with 16.1-inch flanges, weighing 372 pounds per foot. In ASTM A992 steel (Fy = 50 ksi) it has a design bending strength of 6,300 kip-ft (LRFD) when its compression flange is braced, and a design shear strength of 1,413 kips.
Design a W40×372 beam Opens a 62 ft span in the free beam designer.
W40×372 dimensions
| Dimension | Value |
|---|---|
| Depth, d | 40.6 in |
| Flange width, bf | 16.1 in |
| Flange thickness, tf | 2.05 in |
| Web thickness, tw | 1.16 in |
| Distance to web toe of fillet, kdes | 3.23 in |
| Distance between flange centroids, ho | 38.55 in |
| Cross-sectional area, A | 109 in2 |
| Weight | 372 lb/ft |
Dimensions are AISC design values. Detailing dimensions are rounded to the nearest 1/16 in.
W40×372 section properties
| Property | Strong axis (x) | Weak axis (y) |
|---|---|---|
| Moment of inertia, I | 29600 in4 | 1420 in4 |
| Elastic section modulus, S | 1460 in3 | 177 in3 |
| Plastic section modulus, Z | 1680 in3 | 277 in3 |
| Radius of gyration, r | 16.5 in | 3.60 in |
| Torsion and slenderness | Value |
|---|---|
| Torsional constant, J | 116 in4 |
| Warping constant, Cw | 528000 in6 |
| Effective radius of gyration, rts | 4.33 in |
| Flange slenderness, bf/2tf | 3.93 |
| Web slenderness, h/tw | 29.5 |
W40×372 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 = 6,300 kip-ft | Mn/Ω = 4,192 kip-ft |
| Shear | φVn = 1,413 kips | Vn/Ω = 942 kips |
If the compression flange isn't braced, the beam can buckle sideways before it yields. Up to Lp = 12.7 ft between braces it keeps its full strength; past Lr = 44.5 ft it buckles elastically. With uniform moment between braces (Cb = 1.0):
| Unbraced length, Lb | φMn (LRFD) | Mn/Ω (ASD) |
|---|---|---|
| Braced | 6,300 kip-ft | 4,192 kip-ft |
| 10 ft | 6,300 kip-ft | 4,192 kip-ft |
| 12.7 ft (Lp) | 6,300 kip-ft | 4,191 kip-ft |
| 20 ft | 5,734 kip-ft | 3,815 kip-ft |
| 30 ft | 4,957 kip-ft | 3,298 kip-ft |
| 40 ft | 4,180 kip-ft | 2,781 kip-ft |
| 44.5 ft (Lr) | 3,829 kip-ft | 2,547 kip-ft |
| 50 ft | 3,300 kip-ft | 2,196 kip-ft |
| 60 ft | 2,645 kip-ft | 1,760 kip-ft |
| 70 ft | 2,212 kip-ft | 1,471 kip-ft |
| 80 ft | 1,903 kip-ft | 1,266 kip-ft |
| 90 ft | 1,671 kip-ft | 1,112 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.
W40×372 load table by span
The largest uniform load a simply supported W40×372 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 0.372 kips per foot.
| Span | Factored load (LRFD) | Allowable load (ASD) | Load at span/360 | Load at span/240 |
|---|---|---|---|---|
| 20 ft | 126.0 | 83.8 | 159.0 | 238.4 |
| 22 ft | 104.1 | 69.3 | 119.4 | 179.1 |
| 24 ft | 87.5 | 58.2 | 92.0 | 138.0 |
| 26 ft | 74.6 | 49.6 | 72.4 | 108.5 |
| 28 ft | 64.3 | 42.8 | 57.9 | 86.9 |
| 30 ft | 56.0 | 37.3 | 47.1 | 70.7 |
| 32 ft | 49.2 | 32.7 | 38.8 | 58.2 |
| 34 ft | 43.6 | 29.0 | 32.4 | 48.5 |
| 36 ft | 38.9 | 25.9 | 27.3 | 40.9 |
| 38 ft | 34.9 | 23.2 | 23.2 | 34.8 |
| 40 ft | 31.5 | 21.0 | 19.9 | 29.8 |
| 42 ft | 28.6 | 19.0 | 17.2 | 25.7 |
| 44 ft | 26.0 | 17.3 | 14.9 | 22.4 |
| 46 ft | 23.8 | 15.8 | 13.1 | 19.6 |
| 48 ft | 21.9 | 14.6 | 11.5 | 17.2 |
| 50 ft | 20.2 | 13.4 | 10.2 | 15.3 |
| 52 ft | 18.6 | 12.4 | 9.04 | 13.6 |
| 54 ft | 17.3 | 11.5 | 8.08 | 12.1 |
| 56 ft | 16.1 | 10.7 | 7.24 | 10.9 |
| 58 ft | 15.0 | 9.97 | 6.52 | 9.78 |
| 60 ft | 14.0 | 9.31 | 5.89 | 8.83 |
| 62 ft | 13.1 | 8.72 | 5.34 | 8.00 |
| 64 ft | 12.3 | 8.19 | 4.85 | 7.28 |
| 66 ft | 11.6 | 7.70 | 4.42 | 6.64 |
| 68 ft | 10.9 | 7.25 | 4.04 | 6.07 |
| 70 ft | 10.3 | 6.84 | 3.71 | 5.56 |
| 72 ft | 9.72 | 6.47 | 3.41 | 5.11 |
| 74 ft | 9.20 | 6.12 | 3.14 | 4.71 |
| 76 ft | 8.73 | 5.81 | 2.90 | 4.35 |
| 78 ft | 8.28 | 5.51 | 2.68 | 4.02 |
| 80 ft | 7.88 | 5.24 | 2.48 | 3.73 |
| 82 ft | 7.50 | 4.99 | 2.31 | 3.46 |
| 84 ft | 7.14 | 4.75 | 2.15 | 3.22 |
| 86 ft | 6.81 | 4.53 | 2.00 | 3.00 |
| 88 ft | 6.51 | 4.33 | 1.87 | 2.80 |
| 90 ft | 6.22 | 4.14 | 1.74 | 2.62 |
| 92 ft | 5.95 | 3.96 | 1.63 | 2.45 |
| 94 ft | 5.70 | 3.80 | 1.53 | 2.30 |
| 96 ft | 5.47 | 3.64 | 1.44 | 2.16 |
| 98 ft | 5.25 | 3.49 | 1.35 | 2.03 |
| 100 ft | 5.04 | 3.35 | 1.27 | 1.91 |
| 102 ft | 4.84 | 3.22 | 1.20 | 1.80 |
- 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 W40×372 carries a factored load of 13.1 kips per foot (LRFD) or an allowable load of 8.72 kips per foot (ASD). A live load of 5.34 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.
W40×372 questions
What does W40×372 mean?
W means a wide flange shape. 40 is its nominal depth in inches (the actual depth is 40.6 in) and 372 is its weight in pounds per foot.
How much does a W40×372 weigh?
372 pounds per foot, so a 20 ft W40×372 weighs about 7,440 pounds.
How far can a W40×372 span?
It depends on the load. Braced along its length, it carries 126.0 kips per foot of factored load at 20 ft and 4.84 kips per foot at 102 ft; the load table has the spans in between. Floor beams are often 61 to 81 ft for this depth (span-to-depth ratios of about 18 to 24), where deflection usually governs.
Is a W40×372 a compact section?
Yes. Its flanges (bf/2tf = 3.93) and web (h/tw = 29.5) are both compact for bending in 50 ksi steel.