W21×50 Steel Beam
A W21×50 is a wide flange steel beam 20.8 inches deep with 6.53-inch flanges, weighing 50 pounds per foot. In ASTM A992 steel (Fy = 50 ksi) it has a design bending strength of 413 kip-ft (LRFD) when its compression flange is braced, and a design shear strength of 237 kips.
Design a W21×50 beam Opens a 32 ft span in the free beam designer.
W21×50 dimensions
| Dimension | Value |
|---|---|
| Depth, d | 20.8 in |
| Flange width, bf | 6.53 in |
| Flange thickness, tf | 0.535 in |
| Web thickness, tw | 0.380 in |
| Distance to web toe of fillet, kdes | 1.04 in |
| Distance between flange centroids, ho | 20.27 in |
| Cross-sectional area, A | 14.7 in2 |
| Weight | 50 lb/ft |
Dimensions are AISC design values. Detailing dimensions are rounded to the nearest 1/16 in.
W21×50 section properties
| Property | Strong axis (x) | Weak axis (y) |
|---|---|---|
| Moment of inertia, I | 984 in4 | 24.9 in4 |
| Elastic section modulus, S | 94.5 in3 | 7.64 in3 |
| Plastic section modulus, Z | 110 in3 | 12.2 in3 |
| Radius of gyration, r | 8.18 in | 1.30 in |
| Torsion and slenderness | Value |
|---|---|
| Torsional constant, J | 1.14 in4 |
| Warping constant, Cw | 2570 in6 |
| Effective radius of gyration, rts | 1.64 in |
| Flange slenderness, bf/2tf | 6.10 |
| Web slenderness, h/tw | 49.4 |
W21×50 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 = 413 kip-ft | Mn/Ω = 274 kip-ft |
| Shear | φVn = 237 kips | Vn/Ω = 158 kips |
If the compression flange isn't braced, the beam can buckle sideways before it yields. Up to Lp = 4.6 ft between braces it keeps its full strength; past Lr = 13.6 ft it buckles elastically. With uniform moment between braces (Cb = 1.0):
| Unbraced length, Lb | φMn (LRFD) | Mn/Ω (ASD) |
|---|---|---|
| Braced | 413 kip-ft | 274 kip-ft |
| 2 ft | 413 kip-ft | 274 kip-ft |
| 4 ft | 413 kip-ft | 274 kip-ft |
| 4.6 ft (Lp) | 413 kip-ft | 274 kip-ft |
| 6 ft | 387 kip-ft | 257 kip-ft |
| 8 ft | 350 kip-ft | 233 kip-ft |
| 10 ft | 313 kip-ft | 208 kip-ft |
| 12 ft | 277 kip-ft | 184 kip-ft |
| 13.6 ft (Lr) | 248 kip-ft | 165 kip-ft |
| 14 ft | 235 kip-ft | 156 kip-ft |
| 16 ft | 189 kip-ft | 125 kip-ft |
| 18 ft | 157 kip-ft | 104 kip-ft |
| 20 ft | 133 kip-ft | 88.7 kip-ft |
| 22 ft | 116 kip-ft | 77.0 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.
W21×50 load table by span
The largest uniform load a simply supported W21×50 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 0.050 kips per foot.
| Span | Factored load (LRFD) | Allowable load (ASD) | Load at span/360 | Load at span/240 |
|---|---|---|---|---|
| 10 ft | 33.0 | 22.0 | 42.3 | 63.4 |
| 12 ft | 22.9 | 15.2 | 24.5 | 36.7 |
| 14 ft | 16.8 | 11.2 | 15.4 | 23.1 |
| 16 ft | 12.9 | 8.58 | 10.3 | 15.5 |
| 18 ft | 10.2 | 6.78 | 7.25 | 10.9 |
| 20 ft | 8.25 | 5.49 | 5.28 | 7.93 |
| 22 ft | 6.82 | 4.54 | 3.97 | 5.96 |
| 24 ft | 5.73 | 3.81 | 3.06 | 4.59 |
| 26 ft | 4.88 | 3.25 | 2.41 | 3.61 |
| 28 ft | 4.21 | 2.80 | 1.93 | 2.89 |
| 30 ft | 3.67 | 2.44 | 1.57 | 2.35 |
| 32 ft | 3.22 | 2.14 | 1.29 | 1.94 |
| 34 ft | 2.85 | 1.90 | 1.08 | 1.61 |
| 36 ft | 2.55 | 1.69 | 0.91 | 1.36 |
| 38 ft | 2.29 | 1.52 | 0.77 | 1.16 |
| 40 ft | 2.06 | 1.37 | 0.66 | 0.99 |
| 42 ft | 1.87 | 1.24 | 0.57 | 0.86 |
| 44 ft | 1.70 | 1.13 | 0.50 | 0.74 |
| 46 ft | 1.56 | 1.04 | 0.43 | 0.65 |
| 48 ft | 1.43 | 0.95 | 0.38 | 0.57 |
| 50 ft | 1.32 | 0.88 | 0.34 | 0.51 |
| 52 ft | 1.22 | 0.81 | 0.30 | 0.45 |
- 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 32 ft span, a W21×50 carries a factored load of 3.22 kips per foot (LRFD) or an allowable load of 2.14 kips per foot (ASD). A live load of 1.29 kips per foot would deflect it span/360, which is 1.07 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.
W21×50 questions
What does W21×50 mean?
W means a wide flange shape. 21 is its nominal depth in inches (the actual depth is 20.8 in) and 50 is its weight in pounds per foot.
How much does a W21×50 weigh?
50 pounds per foot, so a 20 ft W21×50 weighs about 1,000 pounds.
How far can a W21×50 span?
It depends on the load. Braced along its length, it carries 33.0 kips per foot of factored load at 10 ft and 1.22 kips per foot at 52 ft; the load table has the spans in between. Floor beams are often 31 to 42 ft for this depth (span-to-depth ratios of about 18 to 24), where deflection usually governs.
Is a W21×50 a compact section?
Yes. Its flanges (bf/2tf = 6.10) and web (h/tw = 49.4) are both compact for bending in 50 ksi steel.