W21×57 Steel Beam
A W21×57 is a wide flange steel beam 21.1 inches deep with 6.56-inch flanges, weighing 57 pounds per foot. In ASTM A992 steel (Fy = 50 ksi) it has a design bending strength of 484 kip-ft (LRFD) when its compression flange is braced, and a design shear strength of 256 kips.
Design a W21×57 beam Opens a 33 ft span in the free beam designer.
W21×57 dimensions
| Dimension | Value |
|---|---|
| Depth, d | 21.1 in |
| Flange width, bf | 6.56 in |
| Flange thickness, tf | 0.650 in |
| Web thickness, tw | 0.405 in |
| Distance to web toe of fillet, kdes | 1.15 in |
| Distance between flange centroids, ho | 20.45 in |
| Cross-sectional area, A | 16.7 in2 |
| Weight | 57 lb/ft |
Dimensions are AISC design values. Detailing dimensions are rounded to the nearest 1/16 in.
W21×57 section properties
| Property | Strong axis (x) | Weak axis (y) |
|---|---|---|
| Moment of inertia, I | 1170 in4 | 30.6 in4 |
| Elastic section modulus, S | 111 in3 | 9.35 in3 |
| Plastic section modulus, Z | 129 in3 | 14.8 in3 |
| Radius of gyration, r | 8.36 in | 1.35 in |
| Torsion and slenderness | Value |
|---|---|
| Torsional constant, J | 1.77 in4 |
| Warping constant, Cw | 3190 in6 |
| Effective radius of gyration, rts | 1.68 in |
| Flange slenderness, bf/2tf | 5.04 |
| Web slenderness, h/tw | 46.3 |
W21×57 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 = 484 kip-ft | Mn/Ω = 322 kip-ft |
| Shear | φVn = 256 kips | Vn/Ω = 171 kips |
If the compression flange isn't braced, the beam can buckle sideways before it yields. Up to Lp = 4.8 ft between braces it keeps its full strength; past Lr = 14.3 ft it buckles elastically. With uniform moment between braces (Cb = 1.0):
| Unbraced length, Lb | φMn (LRFD) | Mn/Ω (ASD) |
|---|---|---|
| Braced | 484 kip-ft | 322 kip-ft |
| 2 ft | 484 kip-ft | 322 kip-ft |
| 4 ft | 484 kip-ft | 322 kip-ft |
| 4.8 ft (Lp) | 484 kip-ft | 322 kip-ft |
| 6 ft | 459 kip-ft | 305 kip-ft |
| 8 ft | 419 kip-ft | 279 kip-ft |
| 10 ft | 378 kip-ft | 252 kip-ft |
| 12 ft | 338 kip-ft | 225 kip-ft |
| 14 ft | 298 kip-ft | 198 kip-ft |
| 14.3 ft (Lr) | 291 kip-ft | 194 kip-ft |
| 16 ft | 244 kip-ft | 162 kip-ft |
| 18 ft | 204 kip-ft | 136 kip-ft |
| 20 ft | 174 kip-ft | 116 kip-ft |
| 22 ft | 152 kip-ft | 101 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.
W21×57 load table by span
The largest uniform load a simply supported W21×57 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 0.057 kips per foot.
| Span | Factored load (LRFD) | Allowable load (ASD) | Load at span/360 | Load at span/240 |
|---|---|---|---|---|
| 11 ft | 32.0 | 21.3 | 37.8 | 56.6 |
| 13 ft | 22.9 | 15.2 | 22.9 | 34.3 |
| 15 ft | 17.2 | 11.4 | 14.9 | 22.3 |
| 17 ft | 13.4 | 8.91 | 10.2 | 15.3 |
| 19 ft | 10.7 | 7.13 | 7.33 | 11.0 |
| 21 ft | 8.78 | 5.84 | 5.43 | 8.14 |
| 23 ft | 7.32 | 4.87 | 4.13 | 6.20 |
| 25 ft | 6.19 | 4.12 | 3.22 | 4.83 |
| 27 ft | 5.31 | 3.53 | 2.55 | 3.83 |
| 29 ft | 4.60 | 3.06 | 2.06 | 3.09 |
| 31 ft | 4.03 | 2.68 | 1.69 | 2.53 |
| 33 ft | 3.55 | 2.36 | 1.40 | 2.10 |
| 35 ft | 3.16 | 2.10 | 1.17 | 1.76 |
| 37 ft | 2.83 | 1.88 | 0.99 | 1.49 |
| 39 ft | 2.54 | 1.69 | 0.85 | 1.27 |
| 41 ft | 2.30 | 1.53 | 0.73 | 1.09 |
| 43 ft | 2.09 | 1.39 | 0.63 | 0.95 |
| 45 ft | 1.91 | 1.27 | 0.55 | 0.83 |
| 47 ft | 1.75 | 1.17 | 0.48 | 0.73 |
| 49 ft | 1.61 | 1.07 | 0.43 | 0.64 |
| 51 ft | 1.49 | 0.99 | 0.38 | 0.57 |
| 53 ft | 1.38 | 0.92 | 0.34 | 0.51 |
- 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 W21×57 carries a factored load of 3.55 kips per foot (LRFD) or an allowable load of 2.36 kips per foot (ASD). A live load of 1.40 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.
W21×57 questions
What does W21×57 mean?
W means a wide flange shape. 21 is its nominal depth in inches (the actual depth is 21.1 in) and 57 is its weight in pounds per foot.
How much does a W21×57 weigh?
57 pounds per foot, so a 20 ft W21×57 weighs about 1,140 pounds.
How far can a W21×57 span?
It depends on the load. Braced along its length, it carries 32.0 kips per foot of factored load at 11 ft and 1.38 kips per foot at 53 ft; the load table has the spans in between. Floor beams are often 32 to 42 ft for this depth (span-to-depth ratios of about 18 to 24), where deflection usually governs.
Is a W21×57 a compact section?
Yes. Its flanges (bf/2tf = 5.04) and web (h/tw = 46.3) are both compact for bending in 50 ksi steel.