W21×182 Steel Beam
A W21×182 is a wide flange steel beam 22.7 inches deep with 12.5-inch flanges, weighing 182 pounds per foot. In ASTM A992 steel (Fy = 50 ksi) it has a design bending strength of 1,785 kip-ft (LRFD) when its compression flange is braced, and a design shear strength of 565 kips.
Design a W21×182 beam Opens a 35 ft span in the free beam designer.
W21×182 dimensions
| Dimension | Value |
|---|---|
| Depth, d | 22.7 in |
| Flange width, bf | 12.5 in |
| Flange thickness, tf | 1.48 in |
| Web thickness, tw | 0.830 in |
| Distance to web toe of fillet, kdes | 1.98 in |
| Distance between flange centroids, ho | 21.22 in |
| Cross-sectional area, A | 53.6 in2 |
| Weight | 182 lb/ft |
Dimensions are AISC design values. Detailing dimensions are rounded to the nearest 1/16 in.
W21×182 section properties
| Property | Strong axis (x) | Weak axis (y) |
|---|---|---|
| Moment of inertia, I | 4730 in4 | 483 in4 |
| Elastic section modulus, S | 417 in3 | 77.2 in3 |
| Plastic section modulus, Z | 476 in3 | 119 in3 |
| Radius of gyration, r | 9.40 in | 3.00 in |
| Torsion and slenderness | Value |
|---|---|
| Torsional constant, J | 30.7 in4 |
| Warping constant, Cw | 54400 in6 |
| Effective radius of gyration, rts | 3.51 in |
| Flange slenderness, bf/2tf | 4.22 |
| Web slenderness, h/tw | 22.6 |
W21×182 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 = 1,785 kip-ft | Mn/Ω = 1,188 kip-ft |
| Shear | φVn = 565 kips | Vn/Ω = 377 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 = 42.6 ft it buckles elastically. With uniform moment between braces (Cb = 1.0):
| Unbraced length, Lb | φMn (LRFD) | Mn/Ω (ASD) |
|---|---|---|
| Braced | 1,785 kip-ft | 1,188 kip-ft |
| 10 ft | 1,785 kip-ft | 1,188 kip-ft |
| 10.6 ft (Lp) | 1,785 kip-ft | 1,188 kip-ft |
| 20 ft | 1,582 kip-ft | 1,053 kip-ft |
| 30 ft | 1,367 kip-ft | 909 kip-ft |
| 40 ft | 1,151 kip-ft | 766 kip-ft |
| 42.6 ft (Lr) | 1,094 kip-ft | 728 kip-ft |
| 50 ft | 913 kip-ft | 608 kip-ft |
| 60 ft | 748 kip-ft | 498 kip-ft |
| 70 ft | 634 kip-ft | 422 kip-ft |
| 80 ft | 551 kip-ft | 367 kip-ft |
| 90 ft | 487 kip-ft | 324 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.
W21×182 load table by span
The largest uniform load a simply supported W21×182 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 0.182 kips per foot.
| Span | Factored load (LRFD) | Allowable load (ASD) | Load at span/360 | Load at span/240 |
|---|---|---|---|---|
| 11 ft | 102.8* | 68.5* | 152.7 | 229.0 |
| 13 ft | 84.5 | 56.2 | 92.5 | 138.7 |
| 15 ft | 63.5 | 42.2 | 60.2 | 90.3 |
| 17 ft | 49.4 | 32.9 | 41.4 | 62.0 |
| 19 ft | 39.6 | 26.3 | 29.6 | 44.4 |
| 21 ft | 32.4 | 21.5 | 21.9 | 32.9 |
| 23 ft | 27.0 | 18.0 | 16.7 | 25.1 |
| 25 ft | 22.8 | 15.2 | 13.0 | 19.5 |
| 27 ft | 19.6 | 13.0 | 10.3 | 15.5 |
| 29 ft | 17.0 | 11.3 | 8.33 | 12.5 |
| 31 ft | 14.9 | 9.89 | 6.82 | 10.2 |
| 33 ft | 13.1 | 8.72 | 5.65 | 8.48 |
| 35 ft | 11.7 | 7.76 | 4.74 | 7.11 |
| 37 ft | 10.4 | 6.94 | 4.01 | 6.02 |
| 39 ft | 9.39 | 6.25 | 3.43 | 5.14 |
| 41 ft | 8.49 | 5.65 | 2.95 | 4.42 |
| 43 ft | 7.72 | 5.14 | 2.56 | 3.83 |
| 45 ft | 7.05 | 4.69 | 2.23 | 3.35 |
| 47 ft | 6.46 | 4.30 | 1.96 | 2.94 |
| 49 ft | 5.95 | 3.96 | 1.73 | 2.59 |
| 51 ft | 5.49 | 3.65 | 1.53 | 2.30 |
| 53 ft | 5.08 | 3.38 | 1.36 | 2.05 |
| 55 ft | 4.72 | 3.14 | 1.22 | 1.83 |
| 57 ft | 4.40 | 2.92 | 1.10 | 1.65 |
- 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 35 ft span, a W21×182 carries a factored load of 11.7 kips per foot (LRFD) or an allowable load of 7.76 kips per foot (ASD). A live load of 4.74 kips per foot would deflect it span/360, which is 1.17 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.
W21×182 questions
What does W21×182 mean?
W means a wide flange shape. 21 is its nominal depth in inches (the actual depth is 22.7 in) and 182 is its weight in pounds per foot.
How much does a W21×182 weigh?
182 pounds per foot, so a 20 ft W21×182 weighs about 3,640 pounds.
How far can a W21×182 span?
It depends on the load. Braced along its length, it carries 102.8 kips per foot of factored load at 11 ft and 4.40 kips per foot at 57 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 W21×182 a compact section?
Yes. Its flanges (bf/2tf = 4.22) and web (h/tw = 22.6) are both compact for bending in 50 ksi steel.