W40×278 Steel Beam
A W40×278 is a wide flange steel beam 40.2 inches deep with 12-inch flanges, weighing 278 pounds per foot. In ASTM A992 steel (Fy = 50 ksi) it has a design bending strength of 4,463 kip-ft (LRFD) when its compression flange is braced, and a design shear strength of 1,242 kips.
Design a W40×278 beam Opens a 60 ft span in the free beam designer.
W40×278 dimensions
| Dimension | Value |
|---|---|
| Depth, d | 40.2 in |
| Flange width, bf | 12.0 in |
| Flange thickness, tf | 1.81 in |
| Web thickness, tw | 1.03 in |
| Distance to web toe of fillet, kdes | 2.99 in |
| Distance between flange centroids, ho | 38.39 in |
| Cross-sectional area, A | 82.0 in2 |
| Weight | 278 lb/ft |
Dimensions are AISC design values. Detailing dimensions are rounded to the nearest 1/16 in.
W40×278 section properties
| Property | Strong axis (x) | Weak axis (y) |
|---|---|---|
| Moment of inertia, I | 20500 in4 | 521 in4 |
| Elastic section modulus, S | 1020 in3 | 87.1 in3 |
| Plastic section modulus, Z | 1190 in3 | 140 in3 |
| Radius of gyration, r | 15.8 in | 2.52 in |
| Torsion and slenderness | Value |
|---|---|
| Torsional constant, J | 65.0 in4 |
| Warping constant, Cw | 192000 in6 |
| Effective radius of gyration, rts | 3.13 in |
| Flange slenderness, bf/2tf | 3.31 |
| Web slenderness, h/tw | 33.3 |
W40×278 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 = 4,463 kip-ft | Mn/Ω = 2,969 kip-ft |
| Shear | φVn = 1,242 kips | Vn/Ω = 828 kips |
If the compression flange isn't braced, the beam can buckle sideways before it yields. Up to Lp = 8.9 ft between braces it keeps its full strength; past Lr = 30.4 ft it buckles elastically. With uniform moment between braces (Cb = 1.0):
| Unbraced length, Lb | φMn (LRFD) | Mn/Ω (ASD) |
|---|---|---|
| Braced | 4,463 kip-ft | 2,969 kip-ft |
| 8.9 ft (Lp) | 4,463 kip-ft | 2,969 kip-ft |
| 10 ft | 4,371 kip-ft | 2,908 kip-ft |
| 20 ft | 3,542 kip-ft | 2,357 kip-ft |
| 30 ft | 2,713 kip-ft | 1,805 kip-ft |
| 30.4 ft (Lr) | 2,678 kip-ft | 1,782 kip-ft |
| 40 ft | 1,874 kip-ft | 1,247 kip-ft |
| 50 ft | 1,431 kip-ft | 952 kip-ft |
| 60 ft | 1,160 kip-ft | 772 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.
W40×278 load table by span
The largest uniform load a simply supported W40×278 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 0.278 kips per foot.
| Span | Factored load (LRFD) | Allowable load (ASD) | Load at span/360 | Load at span/240 |
|---|---|---|---|---|
| 20 ft | 89.3 | 59.4 | 110.1 | 165.1 |
| 22 ft | 73.8 | 49.1 | 82.7 | 124.1 |
| 24 ft | 62.0 | 41.2 | 63.7 | 95.6 |
| 26 ft | 52.8 | 35.1 | 50.1 | 75.2 |
| 28 ft | 45.5 | 30.3 | 40.1 | 60.2 |
| 30 ft | 39.7 | 26.4 | 32.6 | 48.9 |
| 32 ft | 34.9 | 23.2 | 26.9 | 40.3 |
| 34 ft | 30.9 | 20.5 | 22.4 | 33.6 |
| 36 ft | 27.5 | 18.3 | 18.9 | 28.3 |
| 38 ft | 24.7 | 16.4 | 16.1 | 24.1 |
| 40 ft | 22.3 | 14.8 | 13.8 | 20.6 |
| 42 ft | 20.2 | 13.5 | 11.9 | 17.8 |
| 44 ft | 18.4 | 12.3 | 10.3 | 15.5 |
| 46 ft | 16.9 | 11.2 | 9.05 | 13.6 |
| 48 ft | 15.5 | 10.3 | 7.96 | 11.9 |
| 50 ft | 14.3 | 9.50 | 7.05 | 10.6 |
| 52 ft | 13.2 | 8.78 | 6.26 | 9.40 |
| 54 ft | 12.2 | 8.15 | 5.59 | 8.39 |
| 56 ft | 11.4 | 7.57 | 5.02 | 7.52 |
| 58 ft | 10.6 | 7.06 | 4.51 | 6.77 |
| 60 ft | 9.92 | 6.60 | 4.08 | 6.12 |
| 62 ft | 9.29 | 6.18 | 3.70 | 5.54 |
| 64 ft | 8.72 | 5.80 | 3.36 | 5.04 |
| 66 ft | 8.20 | 5.45 | 3.06 | 4.60 |
| 68 ft | 7.72 | 5.14 | 2.80 | 4.20 |
| 70 ft | 7.29 | 4.85 | 2.57 | 3.85 |
| 72 ft | 6.89 | 4.58 | 2.36 | 3.54 |
| 74 ft | 6.52 | 4.34 | 2.17 | 3.26 |
| 76 ft | 6.18 | 4.11 | 2.01 | 3.01 |
| 78 ft | 5.87 | 3.90 | 1.86 | 2.78 |
| 80 ft | 5.58 | 3.71 | 1.72 | 2.58 |
| 82 ft | 5.31 | 3.53 | 1.60 | 2.40 |
| 84 ft | 5.06 | 3.37 | 1.49 | 2.23 |
| 86 ft | 4.83 | 3.21 | 1.38 | 2.08 |
| 88 ft | 4.61 | 3.07 | 1.29 | 1.94 |
| 90 ft | 4.41 | 2.93 | 1.21 | 1.81 |
| 92 ft | 4.22 | 2.81 | 1.13 | 1.70 |
| 94 ft | 4.04 | 2.69 | 1.06 | 1.59 |
| 96 ft | 3.87 | 2.58 | 1.00 | 1.49 |
| 98 ft | 3.72 | 2.47 | 0.94 | 1.40 |
| 100 ft | 3.57 | 2.38 | 0.88 | 1.32 |
- 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 60 ft span, a W40×278 carries a factored load of 9.92 kips per foot (LRFD) or an allowable load of 6.60 kips per foot (ASD). A live load of 4.08 kips per foot would deflect it span/360, which is 2.00 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.
W40×278 questions
What does W40×278 mean?
W means a wide flange shape. 40 is its nominal depth in inches (the actual depth is 40.2 in) and 278 is its weight in pounds per foot.
How much does a W40×278 weigh?
278 pounds per foot, so a 20 ft W40×278 weighs about 5,560 pounds.
How far can a W40×278 span?
It depends on the load. Braced along its length, it carries 89.3 kips per foot of factored load at 20 ft and 3.57 kips per foot at 100 ft; the load table has the spans in between. Floor beams are often 60 to 80 ft for this depth (span-to-depth ratios of about 18 to 24), where deflection usually governs.
Is a W40×278 a compact section?
Yes. Its flanges (bf/2tf = 3.31) and web (h/tw = 33.3) are both compact for bending in 50 ksi steel.