W40×503 Steel Beam
A W40×503 is a wide flange steel beam 42.1 inches deep with 16.4-inch flanges, weighing 503 pounds per foot. In ASTM A992 steel (Fy = 50 ksi) it has a design bending strength of 8,700 kip-ft (LRFD) when its compression flange is braced, and a design shear strength of 1,945 kips.
Design a W40×503 beam Opens a 63 ft span in the free beam designer.
W40×503 dimensions
| Dimension | Value |
|---|---|
| Depth, d | 42.1 in |
| Flange width, bf | 16.4 in |
| Flange thickness, tf | 2.76 in |
| Web thickness, tw | 1.54 in |
| Distance to web toe of fillet, kdes | 3.94 in |
| Distance between flange centroids, ho | 39.34 in |
| Cross-sectional area, A | 148 in2 |
| Weight | 503 lb/ft |
Dimensions are AISC design values. Detailing dimensions are rounded to the nearest 1/16 in.
W40×503 section properties
| Property | Strong axis (x) | Weak axis (y) |
|---|---|---|
| Moment of inertia, I | 41600 in4 | 2040 in4 |
| Elastic section modulus, S | 1980 in3 | 249 in3 |
| Plastic section modulus, Z | 2320 in3 | 394 in3 |
| Radius of gyration, r | 16.8 in | 3.72 in |
| Torsion and slenderness | Value |
|---|---|
| Torsional constant, J | 277 in4 |
| Warping constant, Cw | 789000 in6 |
| Effective radius of gyration, rts | 4.50 in |
| Flange slenderness, bf/2tf | 2.98 |
| Web slenderness, h/tw | 22.3 |
W40×503 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 = 8,700 kip-ft | Mn/Ω = 5,788 kip-ft |
| Shear | φVn = 1,945 kips | Vn/Ω = 1,297 kips |
If the compression flange isn't braced, the beam can buckle sideways before it yields. Up to Lp = 13.1 ft between braces it keeps its full strength; past Lr = 55.2 ft it buckles elastically. With uniform moment between braces (Cb = 1.0):
| Unbraced length, Lb | φMn (LRFD) | Mn/Ω (ASD) |
|---|---|---|
| Braced | 8,700 kip-ft | 5,788 kip-ft |
| 10 ft | 8,700 kip-ft | 5,788 kip-ft |
| 13.1 ft (Lp) | 8,700 kip-ft | 5,788 kip-ft |
| 20 ft | 8,129 kip-ft | 5,408 kip-ft |
| 30 ft | 7,296 kip-ft | 4,855 kip-ft |
| 40 ft | 6,464 kip-ft | 4,301 kip-ft |
| 50 ft | 5,631 kip-ft | 3,747 kip-ft |
| 55.2 ft (Lr) | 5,198 kip-ft | 3,458 kip-ft |
| 60 ft | 4,727 kip-ft | 3,145 kip-ft |
| 70 ft | 3,985 kip-ft | 2,651 kip-ft |
| 80 ft | 3,448 kip-ft | 2,294 kip-ft |
| 90 ft | 3,041 kip-ft | 2,024 kip-ft |
| 100 ft | 2,722 kip-ft | 1,811 kip-ft |
| 110 ft | 2,464 kip-ft | 1,639 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.
W40×503 load table by span
The largest uniform load a simply supported W40×503 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 0.503 kips per foot.
| Span | Factored load (LRFD) | Allowable load (ASD) | Load at span/360 | Load at span/240 |
|---|---|---|---|---|
| 21 ft | 157.8 | 105.0 | 193.0 | 289.5 |
| 23 ft | 131.6 | 87.5 | 146.9 | 220.3 |
| 25 ft | 111.4 | 74.1 | 114.4 | 171.6 |
| 27 ft | 95.5 | 63.5 | 90.8 | 136.2 |
| 29 ft | 82.8 | 55.1 | 73.3 | 109.9 |
| 31 ft | 72.4 | 48.2 | 60.0 | 90.0 |
| 33 ft | 63.9 | 42.5 | 49.7 | 74.6 |
| 35 ft | 56.8 | 37.8 | 41.7 | 62.5 |
| 37 ft | 50.8 | 33.8 | 35.3 | 52.9 |
| 39 ft | 45.8 | 30.4 | 30.1 | 45.2 |
| 41 ft | 41.4 | 27.5 | 25.9 | 38.9 |
| 43 ft | 37.6 | 25.0 | 22.5 | 33.7 |
| 45 ft | 34.4 | 22.9 | 19.6 | 29.4 |
| 47 ft | 31.5 | 21.0 | 17.2 | 25.8 |
| 49 ft | 29.0 | 19.3 | 15.2 | 22.8 |
| 51 ft | 26.8 | 17.8 | 13.5 | 20.2 |
| 53 ft | 24.8 | 16.5 | 12.0 | 18.0 |
| 55 ft | 23.0 | 15.3 | 10.7 | 16.1 |
| 57 ft | 21.4 | 14.3 | 9.65 | 14.5 |
| 59 ft | 20.0 | 13.3 | 8.70 | 13.1 |
| 61 ft | 18.7 | 12.4 | 7.87 | 11.8 |
| 63 ft | 17.5 | 11.7 | 7.15 | 10.7 |
| 65 ft | 16.5 | 11.0 | 6.51 | 9.76 |
| 67 ft | 15.5 | 10.3 | 5.94 | 8.91 |
| 69 ft | 14.6 | 9.73 | 5.44 | 8.16 |
| 71 ft | 13.8 | 9.19 | 4.99 | 7.49 |
| 73 ft | 13.1 | 8.69 | 4.59 | 6.89 |
| 75 ft | 12.4 | 8.23 | 4.24 | 6.35 |
| 77 ft | 11.7 | 7.81 | 3.91 | 5.87 |
| 79 ft | 11.2 | 7.42 | 3.62 | 5.44 |
| 81 ft | 10.6 | 7.06 | 3.36 | 5.04 |
| 83 ft | 10.1 | 6.72 | 3.13 | 4.69 |
| 85 ft | 9.63 | 6.41 | 2.91 | 4.37 |
| 87 ft | 9.20 | 6.12 | 2.71 | 4.07 |
| 89 ft | 8.79 | 5.85 | 2.54 | 3.80 |
| 91 ft | 8.40 | 5.59 | 2.37 | 3.56 |
| 93 ft | 8.05 | 5.35 | 2.22 | 3.33 |
| 95 ft | 7.71 | 5.13 | 2.08 | 3.13 |
| 97 ft | 7.40 | 4.92 | 1.96 | 2.94 |
| 99 ft | 7.10 | 4.72 | 1.84 | 2.76 |
| 101 ft | 6.82 | 4.54 | 1.73 | 2.60 |
| 103 ft | 6.56 | 4.36 | 1.64 | 2.45 |
| 105 ft | 6.31 | 4.20 | 1.54 | 2.32 |
- 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 63 ft span, a W40×503 carries a factored load of 17.5 kips per foot (LRFD) or an allowable load of 11.7 kips per foot (ASD). A live load of 7.15 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.
W40×503 questions
What does W40×503 mean?
W means a wide flange shape. 40 is its nominal depth in inches (the actual depth is 42.1 in) and 503 is its weight in pounds per foot.
How much does a W40×503 weigh?
503 pounds per foot, so a 20 ft W40×503 weighs about 10,060 pounds.
How far can a W40×503 span?
It depends on the load. Braced along its length, it carries 157.8 kips per foot of factored load at 21 ft and 6.31 kips per foot at 105 ft; the load table has the spans in between. Floor beams are often 63 to 84 ft for this depth (span-to-depth ratios of about 18 to 24), where deflection usually governs.
Is a W40×503 a compact section?
Yes. Its flanges (bf/2tf = 2.98) and web (h/tw = 22.3) are both compact for bending in 50 ksi steel.