W40×397 Steel Beam
A W40×397 is a wide flange steel beam 41 inches deep with 16.1-inch flanges, weighing 397 pounds per foot. In ASTM A992 steel (Fy = 50 ksi) it has a design bending strength of 6,750 kip-ft (LRFD) when its compression flange is braced, and a design shear strength of 1,501 kips.
Design a W40×397 beam Opens a 63 ft span in the free beam designer.
W40×397 dimensions
| Dimension | Value |
|---|---|
| Depth, d | 41.0 in |
| Flange width, bf | 16.1 in |
| Flange thickness, tf | 2.20 in |
| Web thickness, tw | 1.22 in |
| Distance to web toe of fillet, kdes | 3.38 in |
| Distance between flange centroids, ho | 38.80 in |
| Cross-sectional area, A | 117 in2 |
| Weight | 397 lb/ft |
Dimensions are AISC design values. Detailing dimensions are rounded to the nearest 1/16 in.
W40×397 section properties
| Property | Strong axis (x) | Weak axis (y) |
|---|---|---|
| Moment of inertia, I | 32000 in4 | 1540 in4 |
| Elastic section modulus, S | 1560 in3 | 191 in3 |
| Plastic section modulus, Z | 1800 in3 | 300 in3 |
| Radius of gyration, r | 16.6 in | 3.64 in |
| Torsion and slenderness | Value |
|---|---|
| Torsional constant, J | 142 in4 |
| Warping constant, Cw | 579000 in6 |
| Effective radius of gyration, rts | 4.38 in |
| Flange slenderness, bf/2tf | 3.66 |
| Web slenderness, h/tw | 28.0 |
W40×397 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 = 6,750 kip-ft | Mn/Ω = 4,491 kip-ft |
| Shear | φVn = 1,501 kips | Vn/Ω = 1,000 kips |
If the compression flange isn't braced, the beam can buckle sideways before it yields. Up to Lp = 12.9 ft between braces it keeps its full strength; past Lr = 46.6 ft it buckles elastically. With uniform moment between braces (Cb = 1.0):
| Unbraced length, Lb | φMn (LRFD) | Mn/Ω (ASD) |
|---|---|---|
| Braced | 6,750 kip-ft | 4,491 kip-ft |
| 10 ft | 6,750 kip-ft | 4,491 kip-ft |
| 12.9 ft (Lp) | 6,750 kip-ft | 4,491 kip-ft |
| 20 ft | 6,188 kip-ft | 4,117 kip-ft |
| 30 ft | 5,402 kip-ft | 3,594 kip-ft |
| 40 ft | 4,616 kip-ft | 3,071 kip-ft |
| 46.6 ft (Lr) | 4,095 kip-ft | 2,725 kip-ft |
| 50 ft | 3,753 kip-ft | 2,497 kip-ft |
| 60 ft | 3,018 kip-ft | 2,008 kip-ft |
| 70 ft | 2,528 kip-ft | 1,682 kip-ft |
| 80 ft | 2,179 kip-ft | 1,449 kip-ft |
| 90 ft | 1,916 kip-ft | 1,275 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.
W40×397 load table by span
The largest uniform load a simply supported W40×397 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 0.397 kips per foot.
| Span | Factored load (LRFD) | Allowable load (ASD) | Load at span/360 | Load at span/240 |
|---|---|---|---|---|
| 21 ft | 122.4 | 81.5 | 148.5 | 222.7 |
| 23 ft | 102.1 | 67.9 | 113.0 | 169.5 |
| 25 ft | 86.4 | 57.5 | 88.0 | 132.0 |
| 27 ft | 74.1 | 49.3 | 69.8 | 104.8 |
| 29 ft | 64.2 | 42.7 | 56.4 | 84.6 |
| 31 ft | 56.2 | 37.4 | 46.1 | 69.2 |
| 33 ft | 49.6 | 33.0 | 38.3 | 57.4 |
| 35 ft | 44.1 | 29.3 | 32.1 | 48.1 |
| 37 ft | 39.4 | 26.2 | 27.1 | 40.7 |
| 39 ft | 35.5 | 23.6 | 23.2 | 34.8 |
| 41 ft | 32.1 | 21.4 | 19.9 | 29.9 |
| 43 ft | 29.2 | 19.4 | 17.3 | 25.9 |
| 45 ft | 26.7 | 17.7 | 15.1 | 22.6 |
| 47 ft | 24.4 | 16.3 | 13.2 | 19.9 |
| 49 ft | 22.5 | 15.0 | 11.7 | 17.5 |
| 51 ft | 20.8 | 13.8 | 10.4 | 15.5 |
| 53 ft | 19.2 | 12.8 | 9.23 | 13.9 |
| 55 ft | 17.9 | 11.9 | 8.26 | 12.4 |
| 57 ft | 16.6 | 11.1 | 7.42 | 11.1 |
| 59 ft | 15.5 | 10.3 | 6.69 | 10.0 |
| 61 ft | 14.5 | 9.66 | 6.06 | 9.09 |
| 63 ft | 13.6 | 9.05 | 5.50 | 8.25 |
| 65 ft | 12.8 | 8.50 | 5.01 | 7.51 |
| 67 ft | 12.0 | 8.00 | 4.57 | 6.86 |
| 69 ft | 11.3 | 7.55 | 4.19 | 6.28 |
| 71 ft | 10.7 | 7.13 | 3.84 | 5.76 |
| 73 ft | 10.1 | 6.74 | 3.53 | 5.30 |
| 75 ft | 9.60 | 6.39 | 3.26 | 4.89 |
| 77 ft | 9.11 | 6.06 | 3.01 | 4.52 |
| 79 ft | 8.65 | 5.76 | 2.79 | 4.18 |
| 81 ft | 8.23 | 5.48 | 2.59 | 3.88 |
| 83 ft | 7.84 | 5.22 | 2.40 | 3.61 |
| 85 ft | 7.47 | 4.97 | 2.24 | 3.36 |
| 87 ft | 7.13 | 4.75 | 2.09 | 3.13 |
| 89 ft | 6.82 | 4.54 | 1.95 | 2.93 |
| 91 ft | 6.52 | 4.34 | 1.82 | 2.74 |
| 93 ft | 6.24 | 4.15 | 1.71 | 2.56 |
| 95 ft | 5.98 | 3.98 | 1.60 | 2.41 |
| 97 ft | 5.74 | 3.82 | 1.51 | 2.26 |
| 99 ft | 5.51 | 3.67 | 1.42 | 2.13 |
| 101 ft | 5.29 | 3.52 | 1.33 | 2.00 |
| 103 ft | 5.09 | 3.39 | 1.26 | 1.89 |
- 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 W40×397 carries a factored load of 13.6 kips per foot (LRFD) or an allowable load of 9.05 kips per foot (ASD). A live load of 5.50 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.
W40×397 questions
What does W40×397 mean?
W means a wide flange shape. 40 is its nominal depth in inches (the actual depth is 41.0 in) and 397 is its weight in pounds per foot.
How much does a W40×397 weigh?
397 pounds per foot, so a 20 ft W40×397 weighs about 7,940 pounds.
How far can a W40×397 span?
It depends on the load. Braced along its length, it carries 122.4 kips per foot of factored load at 21 ft and 5.09 kips per foot at 103 ft; the load table has the spans in between. Floor beams are often 62 to 82 ft for this depth (span-to-depth ratios of about 18 to 24), where deflection usually governs.
Is a W40×397 a compact section?
Yes. Its flanges (bf/2tf = 3.66) and web (h/tw = 28.0) are both compact for bending in 50 ksi steel.