W40×431 Steel Beam
A W40×431 is a wide flange steel beam 41.3 inches deep with 16.2-inch flanges, weighing 431 pounds per foot. In ASTM A992 steel (Fy = 50 ksi) it has a design bending strength of 7,350 kip-ft (LRFD) when its compression flange is braced, and a design shear strength of 1,660 kips.
Design a W40×431 beam Opens a 63 ft span in the free beam designer.
W40×431 dimensions
| Dimension | Value |
|---|---|
| Depth, d | 41.3 in |
| Flange width, bf | 16.2 in |
| Flange thickness, tf | 2.36 in |
| Web thickness, tw | 1.34 in |
| Distance to web toe of fillet, kdes | 3.54 in |
| Distance between flange centroids, ho | 38.94 in |
| Cross-sectional area, A | 127 in2 |
| Weight | 431 lb/ft |
Dimensions are AISC design values. Detailing dimensions are rounded to the nearest 1/16 in.
W40×431 section properties
| Property | Strong axis (x) | Weak axis (y) |
|---|---|---|
| Moment of inertia, I | 34800 in4 | 1690 in4 |
| Elastic section modulus, S | 1690 in3 | 208 in3 |
| Plastic section modulus, Z | 1960 in3 | 328 in3 |
| Radius of gyration, r | 16.6 in | 3.65 in |
| Torsion and slenderness | Value |
|---|---|
| Torsional constant, J | 177 in4 |
| Warping constant, Cw | 638000 in6 |
| Effective radius of gyration, rts | 4.41 in |
| Flange slenderness, bf/2tf | 3.44 |
| Web slenderness, h/tw | 25.5 |
W40×431 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 = 7,350 kip-ft | Mn/Ω = 4,890 kip-ft |
| Shear | φVn = 1,660 kips | Vn/Ω = 1,107 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 = 49.0 ft it buckles elastically. With uniform moment between braces (Cb = 1.0):
| Unbraced length, Lb | φMn (LRFD) | Mn/Ω (ASD) |
|---|---|---|
| Braced | 7,350 kip-ft | 4,890 kip-ft |
| 10 ft | 7,350 kip-ft | 4,890 kip-ft |
| 12.9 ft (Lp) | 7,350 kip-ft | 4,890 kip-ft |
| 20 ft | 6,777 kip-ft | 4,509 kip-ft |
| 30 ft | 5,970 kip-ft | 3,972 kip-ft |
| 40 ft | 5,164 kip-ft | 3,436 kip-ft |
| 49.0 ft (Lr) | 4,436 kip-ft | 2,952 kip-ft |
| 50 ft | 4,328 kip-ft | 2,880 kip-ft |
| 60 ft | 3,492 kip-ft | 2,324 kip-ft |
| 70 ft | 2,933 kip-ft | 1,951 kip-ft |
| 80 ft | 2,531 kip-ft | 1,684 kip-ft |
| 90 ft | 2,228 kip-ft | 1,482 kip-ft |
| 100 ft | 1,991 kip-ft | 1,325 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.
W40×431 load table by span
The largest uniform load a simply supported W40×431 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 0.431 kips per foot.
| Span | Factored load (LRFD) | Allowable load (ASD) | Load at span/360 | Load at span/240 |
|---|---|---|---|---|
| 21 ft | 133.3 | 88.7 | 161.4 | 242.2 |
| 23 ft | 111.2 | 74.0 | 122.9 | 184.3 |
| 25 ft | 94.1 | 62.6 | 95.7 | 143.5 |
| 27 ft | 80.7 | 53.7 | 76.0 | 113.9 |
| 29 ft | 69.9 | 46.5 | 61.3 | 92.0 |
| 31 ft | 61.2 | 40.7 | 50.2 | 75.3 |
| 33 ft | 54.0 | 35.9 | 41.6 | 62.4 |
| 35 ft | 48.0 | 31.9 | 34.9 | 52.3 |
| 37 ft | 43.0 | 28.6 | 29.5 | 44.3 |
| 39 ft | 38.7 | 25.7 | 25.2 | 37.8 |
| 41 ft | 35.0 | 23.3 | 21.7 | 32.5 |
| 43 ft | 31.8 | 21.2 | 18.8 | 28.2 |
| 45 ft | 29.0 | 19.3 | 16.4 | 24.6 |
| 47 ft | 26.6 | 17.7 | 14.4 | 21.6 |
| 49 ft | 24.5 | 16.3 | 12.7 | 19.1 |
| 51 ft | 22.6 | 15.0 | 11.3 | 16.9 |
| 53 ft | 20.9 | 13.9 | 10.0 | 15.1 |
| 55 ft | 19.4 | 12.9 | 8.99 | 13.5 |
| 57 ft | 18.1 | 12.0 | 8.07 | 12.1 |
| 59 ft | 16.9 | 11.2 | 7.28 | 10.9 |
| 61 ft | 15.8 | 10.5 | 6.59 | 9.88 |
| 63 ft | 14.8 | 9.86 | 5.98 | 8.97 |
| 65 ft | 13.9 | 9.26 | 5.44 | 8.17 |
| 67 ft | 13.1 | 8.72 | 4.97 | 7.46 |
| 69 ft | 12.4 | 8.22 | 4.55 | 6.83 |
| 71 ft | 11.7 | 7.76 | 4.18 | 6.27 |
| 73 ft | 11.0 | 7.34 | 3.84 | 5.76 |
| 75 ft | 10.5 | 6.95 | 3.54 | 5.32 |
| 77 ft | 9.92 | 6.60 | 3.27 | 4.91 |
| 79 ft | 9.42 | 6.27 | 3.03 | 4.55 |
| 81 ft | 8.96 | 5.96 | 2.81 | 4.22 |
| 83 ft | 8.54 | 5.68 | 2.61 | 3.92 |
| 85 ft | 8.14 | 5.41 | 2.43 | 3.65 |
| 87 ft | 7.77 | 5.17 | 2.27 | 3.41 |
| 89 ft | 7.42 | 4.94 | 2.12 | 3.18 |
| 91 ft | 7.10 | 4.72 | 1.98 | 2.98 |
| 93 ft | 6.80 | 4.52 | 1.86 | 2.79 |
| 95 ft | 6.52 | 4.33 | 1.74 | 2.62 |
| 97 ft | 6.25 | 4.16 | 1.64 | 2.46 |
| 99 ft | 6.00 | 3.99 | 1.54 | 2.31 |
| 101 ft | 5.76 | 3.84 | 1.45 | 2.18 |
| 103 ft | 5.54 | 3.69 | 1.37 | 2.05 |
- 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 W40×431 carries a factored load of 14.8 kips per foot (LRFD) or an allowable load of 9.86 kips per foot (ASD). A live load of 5.98 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.
W40×431 questions
What does W40×431 mean?
W means a wide flange shape. 40 is its nominal depth in inches (the actual depth is 41.3 in) and 431 is its weight in pounds per foot.
How much does a W40×431 weigh?
431 pounds per foot, so a 20 ft W40×431 weighs about 8,620 pounds.
How far can a W40×431 span?
It depends on the load. Braced along its length, it carries 133.3 kips per foot of factored load at 21 ft and 5.54 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 W40×431 a compact section?
Yes. Its flanges (bf/2tf = 3.44) and web (h/tw = 25.5) are both compact for bending in 50 ksi steel.