W21×201 Steel Beam
A W21×201 is a wide flange steel beam 23 inches deep with 12.6-inch flanges, weighing 201 pounds per foot. In ASTM A992 steel (Fy = 50 ksi) it has a design bending strength of 1,988 kip-ft (LRFD) when its compression flange is braced, and a design shear strength of 628 kips.
Design a W21×201 beam Opens a 36 ft span in the free beam designer.
W21×201 dimensions
| Dimension | Value |
|---|---|
| Depth, d | 23.0 in |
| Flange width, bf | 12.6 in |
| Flange thickness, tf | 1.63 in |
| Web thickness, tw | 0.910 in |
| Distance to web toe of fillet, kdes | 2.13 in |
| Distance between flange centroids, ho | 21.37 in |
| Cross-sectional area, A | 59.2 in2 |
| Weight | 201 lb/ft |
Dimensions are AISC design values. Detailing dimensions are rounded to the nearest 1/16 in.
W21×201 section properties
| Property | Strong axis (x) | Weak axis (y) |
|---|---|---|
| Moment of inertia, I | 5310 in4 | 542 in4 |
| Elastic section modulus, S | 461 in3 | 86.1 in3 |
| Plastic section modulus, Z | 530 in3 | 133 in3 |
| Radius of gyration, r | 9.47 in | 3.02 in |
| Torsion and slenderness | Value |
|---|---|
| Torsional constant, J | 40.9 in4 |
| Warping constant, Cw | 62000 in6 |
| Effective radius of gyration, rts | 3.55 in |
| Flange slenderness, bf/2tf | 3.86 |
| Web slenderness, h/tw | 20.6 |
W21×201 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 = 1,988 kip-ft | Mn/Ω = 1,322 kip-ft |
| Shear | φVn = 628 kips | Vn/Ω = 419 kips |
If the compression flange isn't braced, the beam can buckle sideways before it yields. Up to Lp = 10.7 ft between braces it keeps its full strength; past Lr = 46.2 ft it buckles elastically. With uniform moment between braces (Cb = 1.0):
| Unbraced length, Lb | φMn (LRFD) | Mn/Ω (ASD) |
|---|---|---|
| Braced | 1,988 kip-ft | 1,322 kip-ft |
| 10 ft | 1,988 kip-ft | 1,322 kip-ft |
| 10.7 ft (Lp) | 1,987 kip-ft | 1,322 kip-ft |
| 20 ft | 1,783 kip-ft | 1,186 kip-ft |
| 30 ft | 1,564 kip-ft | 1,041 kip-ft |
| 40 ft | 1,345 kip-ft | 895 kip-ft |
| 46.2 ft (Lr) | 1,210 kip-ft | 805 kip-ft |
| 50 ft | 1,108 kip-ft | 737 kip-ft |
| 60 ft | 909 kip-ft | 605 kip-ft |
| 70 ft | 772 kip-ft | 514 kip-ft |
| 80 ft | 672 kip-ft | 447 kip-ft |
| 90 ft | 594 kip-ft | 395 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.
W21×201 load table by span
The largest uniform load a simply supported W21×201 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 0.201 kips per foot.
| Span | Factored load (LRFD) | Allowable load (ASD) | Load at span/360 | Load at span/240 |
|---|---|---|---|---|
| 12 ft | 104.7* | 69.8* | 132.0 | 198.0 |
| 14 ft | 81.1 | 54.0 | 83.1 | 124.7 |
| 16 ft | 62.1 | 41.3 | 55.7 | 83.5 |
| 18 ft | 49.1 | 32.7 | 39.1 | 58.7 |
| 20 ft | 39.8 | 26.4 | 28.5 | 42.8 |
| 22 ft | 32.9 | 21.9 | 21.4 | 32.1 |
| 24 ft | 27.6 | 18.4 | 16.5 | 24.8 |
| 26 ft | 23.5 | 15.6 | 13.0 | 19.5 |
| 28 ft | 20.3 | 13.5 | 10.4 | 15.6 |
| 30 ft | 17.7 | 11.8 | 8.45 | 12.7 |
| 32 ft | 15.5 | 10.3 | 6.96 | 10.4 |
| 34 ft | 13.8 | 9.15 | 5.80 | 8.71 |
| 36 ft | 12.3 | 8.16 | 4.89 | 7.33 |
| 38 ft | 11.0 | 7.33 | 4.16 | 6.24 |
| 40 ft | 9.94 | 6.61 | 3.56 | 5.35 |
| 42 ft | 9.01 | 6.00 | 3.08 | 4.62 |
| 44 ft | 8.21 | 5.46 | 2.68 | 4.02 |
| 46 ft | 7.51 | 5.00 | 2.34 | 3.52 |
| 48 ft | 6.90 | 4.59 | 2.06 | 3.09 |
| 50 ft | 6.36 | 4.23 | 1.83 | 2.74 |
| 52 ft | 5.88 | 3.91 | 1.62 | 2.43 |
| 54 ft | 5.45 | 3.63 | 1.45 | 2.17 |
| 56 ft | 5.07 | 3.37 | 1.30 | 1.95 |
| 58 ft | 4.73 | 3.14 | 1.17 | 1.75 |
- 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 36 ft span, a W21×201 carries a factored load of 12.3 kips per foot (LRFD) or an allowable load of 8.16 kips per foot (ASD). A live load of 4.89 kips per foot would deflect it span/360, which is 1.20 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.
W21×201 questions
What does W21×201 mean?
W means a wide flange shape. 21 is its nominal depth in inches (the actual depth is 23.0 in) and 201 is its weight in pounds per foot.
How much does a W21×201 weigh?
201 pounds per foot, so a 20 ft W21×201 weighs about 4,020 pounds.
How far can a W21×201 span?
It depends on the load. Braced along its length, it carries 104.7 kips per foot of factored load at 12 ft and 4.73 kips per foot at 58 ft; the load table has the spans in between. Floor beams are often 35 to 46 ft for this depth (span-to-depth ratios of about 18 to 24), where deflection usually governs.
Is a W21×201 a compact section?
Yes. Its flanges (bf/2tf = 3.86) and web (h/tw = 20.6) are both compact for bending in 50 ksi steel.