W40×199 Steel Beam
A W40×199 is a wide flange steel beam 38.7 inches deep with 15.8-inch flanges, weighing 199 pounds per foot. In ASTM A992 steel (Fy = 50 ksi) it has a design bending strength of 3,259 kip-ft (LRFD) when its compression flange is braced, and a design shear strength of 755 kips.
Design a W40×199 beam Opens a 59 ft span in the free beam designer.
W40×199 dimensions
| Dimension | Value |
|---|---|
| Depth, d | 38.7 in |
| Flange width, bf | 15.8 in |
| Flange thickness, tf | 1.07 in |
| Web thickness, tw | 0.650 in |
| Distance to web toe of fillet, kdes | 2.25 in |
| Distance between flange centroids, ho | 37.63 in |
| Cross-sectional area, A | 58.5 in2 |
| Weight | 199 lb/ft |
Dimensions are AISC design values. Detailing dimensions are rounded to the nearest 1/16 in.
W40×199 section properties
| Property | Strong axis (x) | Weak axis (y) |
|---|---|---|
| Moment of inertia, I | 14900 in4 | 695 in4 |
| Elastic section modulus, S | 770 in3 | 88.2 in3 |
| Plastic section modulus, Z | 869 in3 | 137 in3 |
| Radius of gyration, r | 16.0 in | 3.45 in |
| Torsion and slenderness | Value |
|---|---|
| Torsional constant, J | 18.3 in4 |
| Warping constant, Cw | 246000 in6 |
| Effective radius of gyration, rts | 4.12 in |
| Flange slenderness, bf/2tf | 7.39 |
| Web slenderness, h/tw | 52.6 |
W40×199 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 = 3,259 kip-ft | Mn/Ω = 2,168 kip-ft |
| Shear | φVn = 755 kips | Vn/Ω = 503 kips |
If the compression flange isn't braced, the beam can buckle sideways before it yields. Up to Lp = 12.2 ft between braces it keeps its full strength; past Lr = 34.3 ft it buckles elastically. With uniform moment between braces (Cb = 1.0):
| Unbraced length, Lb | φMn (LRFD) | Mn/Ω (ASD) |
|---|---|---|
| Braced | 3,259 kip-ft | 2,168 kip-ft |
| 10 ft | 3,259 kip-ft | 2,168 kip-ft |
| 12.2 ft (Lp) | 3,259 kip-ft | 2,168 kip-ft |
| 20 ft | 2,822 kip-ft | 1,878 kip-ft |
| 30 ft | 2,264 kip-ft | 1,506 kip-ft |
| 34.4 ft (Lr) | 2,018 kip-ft | 1,343 kip-ft |
| 40 ft | 1,574 kip-ft | 1,047 kip-ft |
| 50 ft | 1,115 kip-ft | 742 kip-ft |
| 60 ft | 857 kip-ft | 570 kip-ft |
| 70 ft | 694 kip-ft | 462 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.
W40×199 load table by span
The largest uniform load a simply supported W40×199 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 0.199 kips per foot.
| Span | Factored load (LRFD) | Allowable load (ASD) | Load at span/360 | Load at span/240 |
|---|---|---|---|---|
| 19 ft | 72.2 | 48.0 | 93.3 | 140.0 |
| 21 ft | 59.1 | 39.3 | 69.1 | 103.7 |
| 23 ft | 49.3 | 32.8 | 52.6 | 78.9 |
| 25 ft | 41.7 | 27.8 | 41.0 | 61.5 |
| 27 ft | 35.8 | 23.8 | 32.5 | 48.8 |
| 29 ft | 31.0 | 20.6 | 26.2 | 39.4 |
| 31 ft | 27.1 | 18.0 | 21.5 | 32.2 |
| 33 ft | 23.9 | 15.9 | 17.8 | 26.7 |
| 35 ft | 21.3 | 14.2 | 14.9 | 22.4 |
| 37 ft | 19.0 | 12.7 | 12.6 | 19.0 |
| 39 ft | 17.1 | 11.4 | 10.8 | 16.2 |
| 41 ft | 15.5 | 10.3 | 9.29 | 13.9 |
| 43 ft | 14.1 | 9.38 | 8.05 | 12.1 |
| 45 ft | 12.9 | 8.57 | 7.02 | 10.5 |
| 47 ft | 11.8 | 7.85 | 6.17 | 9.25 |
| 49 ft | 10.9 | 7.22 | 5.44 | 8.16 |
| 51 ft | 10.0 | 6.67 | 4.83 | 7.24 |
| 53 ft | 9.28 | 6.17 | 4.30 | 6.45 |
| 55 ft | 8.62 | 5.73 | 3.85 | 5.77 |
| 57 ft | 8.02 | 5.34 | 3.46 | 5.18 |
| 59 ft | 7.49 | 4.98 | 3.12 | 4.68 |
| 61 ft | 7.01 | 4.66 | 2.82 | 4.23 |
| 63 ft | 6.57 | 4.37 | 2.56 | 3.84 |
| 65 ft | 6.17 | 4.11 | 2.33 | 3.50 |
| 67 ft | 5.81 | 3.86 | 2.13 | 3.19 |
| 69 ft | 5.48 | 3.64 | 1.95 | 2.92 |
| 71 ft | 5.17 | 3.44 | 1.79 | 2.68 |
| 73 ft | 4.89 | 3.25 | 1.65 | 2.47 |
| 75 ft | 4.63 | 3.08 | 1.52 | 2.28 |
| 77 ft | 4.40 | 2.93 | 1.40 | 2.10 |
| 79 ft | 4.18 | 2.78 | 1.30 | 1.95 |
| 81 ft | 3.97 | 2.64 | 1.20 | 1.81 |
| 83 ft | 3.78 | 2.52 | 1.12 | 1.68 |
| 85 ft | 3.61 | 2.40 | 1.04 | 1.56 |
| 87 ft | 3.44 | 2.29 | 0.97 | 1.46 |
| 89 ft | 3.29 | 2.19 | 0.91 | 1.36 |
| 91 ft | 3.15 | 2.09 | 0.85 | 1.27 |
| 93 ft | 3.01 | 2.01 | 0.80 | 1.19 |
| 95 ft | 2.89 | 1.92 | 0.75 | 1.12 |
| 97 ft | 2.77 | 1.84 | 0.70 | 1.05 |
- 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 59 ft span, a W40×199 carries a factored load of 7.49 kips per foot (LRFD) or an allowable load of 4.98 kips per foot (ASD). A live load of 3.12 kips per foot would deflect it span/360, which is 1.97 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.
W40×199 questions
What does W40×199 mean?
W means a wide flange shape. 40 is its nominal depth in inches (the actual depth is 38.7 in) and 199 is its weight in pounds per foot.
How much does a W40×199 weigh?
199 pounds per foot, so a 20 ft W40×199 weighs about 3,980 pounds.
How far can a W40×199 span?
It depends on the load. Braced along its length, it carries 72.2 kips per foot of factored load at 19 ft and 2.77 kips per foot at 97 ft; the load table has the spans in between. Floor beams are often 58 to 77 ft for this depth (span-to-depth ratios of about 18 to 24), where deflection usually governs.
Is a W40×199 a compact section?
Yes. Its flanges (bf/2tf = 7.39) and web (h/tw = 52.6) are both compact for bending in 50 ksi steel.