W21×166 Steel Beam
A W21×166 is a wide flange steel beam 22.5 inches deep with 12.4-inch flanges, weighing 166 pounds per foot. In ASTM A992 steel (Fy = 50 ksi) it has a design bending strength of 1,620 kip-ft (LRFD) when its compression flange is braced, and a design shear strength of 506 kips.
Design a W21×166 beam Opens a 33 ft span in the free beam designer.
W21×166 dimensions
| Dimension | Value |
|---|---|
| Depth, d | 22.5 in |
| Flange width, bf | 12.4 in |
| Flange thickness, tf | 1.36 in |
| Web thickness, tw | 0.750 in |
| Distance to web toe of fillet, kdes | 1.86 in |
| Distance between flange centroids, ho | 21.14 in |
| Cross-sectional area, A | 48.8 in2 |
| Weight | 166 lb/ft |
Dimensions are AISC design values. Detailing dimensions are rounded to the nearest 1/16 in.
W21×166 section properties
| Property | Strong axis (x) | Weak axis (y) |
|---|---|---|
| Moment of inertia, I | 4280 in4 | 435 in4 |
| Elastic section modulus, S | 380 in3 | 70.0 in3 |
| Plastic section modulus, Z | 432 in3 | 108 in3 |
| Radius of gyration, r | 9.36 in | 2.99 in |
| Torsion and slenderness | Value |
|---|---|
| Torsional constant, J | 23.6 in4 |
| Warping constant, Cw | 48500 in6 |
| Effective radius of gyration, rts | 3.48 in |
| Flange slenderness, bf/2tf | 4.57 |
| Web slenderness, h/tw | 25.0 |
W21×166 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 = 1,620 kip-ft | Mn/Ω = 1,078 kip-ft |
| Shear | φVn = 506 kips | Vn/Ω = 338 kips |
If the compression flange isn't braced, the beam can buckle sideways before it yields. Up to Lp = 10.6 ft between braces it keeps its full strength; past Lr = 39.8 ft it buckles elastically. With uniform moment between braces (Cb = 1.0):
| Unbraced length, Lb | φMn (LRFD) | Mn/Ω (ASD) |
|---|---|---|
| Braced | 1,620 kip-ft | 1,078 kip-ft |
| 10 ft | 1,620 kip-ft | 1,078 kip-ft |
| 10.6 ft (Lp) | 1,620 kip-ft | 1,078 kip-ft |
| 20 ft | 1,419 kip-ft | 944 kip-ft |
| 30 ft | 1,206 kip-ft | 803 kip-ft |
| 39.8 ft (Lr) | 998 kip-ft | 664 kip-ft |
| 40 ft | 991 kip-ft | 660 kip-ft |
| 50 ft | 766 kip-ft | 510 kip-ft |
| 60 ft | 626 kip-ft | 416 kip-ft |
| 70 ft | 530 kip-ft | 353 kip-ft |
| 80 ft | 460 kip-ft | 306 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.
W21×166 load table by span
The largest uniform load a simply supported W21×166 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 0.166 kips per foot.
| Span | Factored load (LRFD) | Allowable load (ASD) | Load at span/360 | Load at span/240 |
|---|---|---|---|---|
| 11 ft | 92.0* | 61.4* | 138.2 | 207.2 |
| 13 ft | 76.7 | 51.0 | 83.7 | 125.5 |
| 15 ft | 57.6 | 38.3 | 54.5 | 81.7 |
| 17 ft | 44.8 | 29.8 | 37.4 | 56.1 |
| 19 ft | 35.9 | 23.9 | 26.8 | 40.2 |
| 21 ft | 29.4 | 19.6 | 19.9 | 29.8 |
| 23 ft | 24.5 | 16.3 | 15.1 | 22.7 |
| 25 ft | 20.7 | 13.8 | 11.8 | 17.7 |
| 27 ft | 17.8 | 11.8 | 9.34 | 14.0 |
| 29 ft | 15.4 | 10.3 | 7.54 | 11.3 |
| 31 ft | 13.5 | 8.97 | 6.17 | 9.26 |
| 33 ft | 11.9 | 7.92 | 5.12 | 7.68 |
| 35 ft | 10.6 | 7.04 | 4.29 | 6.43 |
| 37 ft | 9.47 | 6.30 | 3.63 | 5.45 |
| 39 ft | 8.52 | 5.67 | 3.10 | 4.65 |
| 41 ft | 7.71 | 5.13 | 2.67 | 4.00 |
| 43 ft | 7.01 | 4.66 | 2.31 | 3.47 |
| 45 ft | 6.40 | 4.26 | 2.02 | 3.03 |
| 47 ft | 5.87 | 3.90 | 1.77 | 2.66 |
| 49 ft | 5.40 | 3.59 | 1.56 | 2.34 |
| 51 ft | 4.98 | 3.32 | 1.39 | 2.08 |
| 53 ft | 4.61 | 3.07 | 1.24 | 1.85 |
| 55 ft | 4.28 | 2.85 | 1.11 | 1.66 |
- 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 33 ft span, a W21×166 carries a factored load of 11.9 kips per foot (LRFD) or an allowable load of 7.92 kips per foot (ASD). A live load of 5.12 kips per foot would deflect it span/360, which is 1.10 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.
W21×166 questions
What does W21×166 mean?
W means a wide flange shape. 21 is its nominal depth in inches (the actual depth is 22.5 in) and 166 is its weight in pounds per foot.
How much does a W21×166 weigh?
166 pounds per foot, so a 20 ft W21×166 weighs about 3,320 pounds.
How far can a W21×166 span?
It depends on the load. Braced along its length, it carries 92.0 kips per foot of factored load at 11 ft and 4.28 kips per foot at 55 ft; the load table has the spans in between. Floor beams are often 34 to 45 ft for this depth (span-to-depth ratios of about 18 to 24), where deflection usually governs.
Is a W21×166 a compact section?
Yes. Its flanges (bf/2tf = 4.57) and web (h/tw = 25.0) are both compact for bending in 50 ksi steel.