W21×111 Steel Beam
A W21×111 is a wide flange steel beam 21.5 inches deep with 12.3-inch flanges, weighing 111 pounds per foot. In ASTM A992 steel (Fy = 50 ksi) it has a design bending strength of 1,046 kip-ft (LRFD) when its compression flange is braced, and a design shear strength of 355 kips.
Design a W21×111 beam Opens a 33 ft span in the free beam designer.
W21×111 dimensions
| Dimension | Value |
|---|---|
| Depth, d | 21.5 in |
| Flange width, bf | 12.3 in |
| Flange thickness, tf | 0.875 in |
| Web thickness, tw | 0.550 in |
| Distance to web toe of fillet, kdes | 1.38 in |
| Distance between flange centroids, ho | 20.63 in |
| Cross-sectional area, A | 32.7 in2 |
| Weight | 111 lb/ft |
Dimensions are AISC design values. Detailing dimensions are rounded to the nearest 1/16 in.
W21×111 section properties
| Property | Strong axis (x) | Weak axis (y) |
|---|---|---|
| Moment of inertia, I | 2670 in4 | 274 in4 |
| Elastic section modulus, S | 249 in3 | 44.5 in3 |
| Plastic section modulus, Z | 279 in3 | 68.2 in3 |
| Radius of gyration, r | 9.05 in | 2.90 in |
| Torsion and slenderness | Value |
|---|---|
| Torsional constant, J | 6.83 in4 |
| Warping constant, Cw | 29200 in6 |
| Effective radius of gyration, rts | 3.37 in |
| Flange slenderness, bf/2tf | 7.05 |
| Web slenderness, h/tw | 34.1 |
W21×111 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 = 1,046 kip-ft | Mn/Ω = 696 kip-ft |
| Shear | φVn = 355 kips | Vn/Ω = 237 kips |
If the compression flange isn't braced, the beam can buckle sideways before it yields. Up to Lp = 10.2 ft between braces it keeps its full strength; past Lr = 31.2 ft it buckles elastically. With uniform moment between braces (Cb = 1.0):
| Unbraced length, Lb | φMn (LRFD) | Mn/Ω (ASD) |
|---|---|---|
| Braced | 1,046 kip-ft | 696 kip-ft |
| 10 ft | 1,046 kip-ft | 696 kip-ft |
| 10.2 ft (Lp) | 1,046 kip-ft | 696 kip-ft |
| 20 ft | 864 kip-ft | 575 kip-ft |
| 30 ft | 677 kip-ft | 450 kip-ft |
| 31.2 ft (Lr) | 653 kip-ft | 434 kip-ft |
| 40 ft | 464 kip-ft | 309 kip-ft |
| 50 ft | 349 kip-ft | 232 kip-ft |
| 60 ft | 280 kip-ft | 187 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.
W21×111 load table by span
The largest uniform load a simply supported W21×111 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 0.111 kips per foot.
| Span | Factored load (LRFD) | Allowable load (ASD) | Load at span/360 | Load at span/240 |
|---|---|---|---|---|
| 11 ft | 64.5* | 43.0* | 86.2 | 129.3 |
| 13 ft | 49.5 | 33.0 | 52.2 | 78.3 |
| 15 ft | 37.2 | 24.8 | 34.0 | 51.0 |
| 17 ft | 29.0 | 19.3 | 23.3 | 35.0 |
| 19 ft | 23.2 | 15.4 | 16.7 | 25.1 |
| 21 ft | 19.0 | 12.6 | 12.4 | 18.6 |
| 23 ft | 15.8 | 10.5 | 9.43 | 14.1 |
| 25 ft | 13.4 | 8.91 | 7.34 | 11.0 |
| 27 ft | 11.5 | 7.64 | 5.83 | 8.74 |
| 29 ft | 9.95 | 6.62 | 4.70 | 7.06 |
| 31 ft | 8.71 | 5.79 | 3.85 | 5.78 |
| 33 ft | 7.69 | 5.11 | 3.19 | 4.79 |
| 35 ft | 6.83 | 4.55 | 2.68 | 4.01 |
| 37 ft | 6.11 | 4.07 | 2.26 | 3.40 |
| 39 ft | 5.50 | 3.66 | 1.93 | 2.90 |
| 41 ft | 4.98 | 3.31 | 1.66 | 2.50 |
| 43 ft | 4.53 | 3.01 | 1.44 | 2.16 |
| 45 ft | 4.13 | 2.75 | 1.26 | 1.89 |
| 47 ft | 3.79 | 2.52 | 1.10 | 1.66 |
| 49 ft | 3.49 | 2.32 | 0.98 | 1.46 |
| 51 ft | 3.22 | 2.14 | 0.86 | 1.30 |
| 53 ft | 2.98 | 1.98 | 0.77 | 1.16 |
- 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 W21×111 carries a factored load of 7.69 kips per foot (LRFD) or an allowable load of 5.11 kips per foot (ASD). A live load of 3.19 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.
W21×111 questions
What does W21×111 mean?
W means a wide flange shape. 21 is its nominal depth in inches (the actual depth is 21.5 in) and 111 is its weight in pounds per foot.
How much does a W21×111 weigh?
111 pounds per foot, so a 20 ft W21×111 weighs about 2,220 pounds.
How far can a W21×111 span?
It depends on the load. Braced along its length, it carries 64.5 kips per foot of factored load at 11 ft and 2.98 kips per foot at 53 ft; the load table has the spans in between. Floor beams are often 32 to 43 ft for this depth (span-to-depth ratios of about 18 to 24), where deflection usually governs.
Is a W21×111 a compact section?
Yes. Its flanges (bf/2tf = 7.05) and web (h/tw = 34.1) are both compact for bending in 50 ksi steel.