W33×221 Steel Beam
A W33×221 is a wide flange steel beam 33.9 inches deep with 15.8-inch flanges, weighing 221 pounds per foot. In ASTM A992 steel (Fy = 50 ksi) it has a design bending strength of 3,214 kip-ft (LRFD) when its compression flange is braced, and a design shear strength of 788 kips.
Design a W33×221 beam Opens a 51 ft span in the free beam designer.
W33×221 dimensions
| Dimension | Value |
|---|---|
| Depth, d | 33.9 in |
| Flange width, bf | 15.8 in |
| Flange thickness, tf | 1.28 in |
| Web thickness, tw | 0.775 in |
| Distance to web toe of fillet, kdes | 2.06 in |
| Distance between flange centroids, ho | 32.62 in |
| Cross-sectional area, A | 65.2 in2 |
| Weight | 221 lb/ft |
Dimensions are AISC design values. Detailing dimensions are rounded to the nearest 1/16 in.
W33×221 section properties
| Property | Strong axis (x) | Weak axis (y) |
|---|---|---|
| Moment of inertia, I | 12900 in4 | 840 in4 |
| Elastic section modulus, S | 759 in3 | 106 in3 |
| Plastic section modulus, Z | 857 in3 | 164 in3 |
| Radius of gyration, r | 14.1 in | 3.59 in |
| Torsion and slenderness | Value |
|---|---|
| Torsional constant, J | 27.8 in4 |
| Warping constant, Cw | 224000 in6 |
| Effective radius of gyration, rts | 4.25 in |
| Flange slenderness, bf/2tf | 6.20 |
| Web slenderness, h/tw | 38.5 |
W33×221 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 = 3,214 kip-ft | Mn/Ω = 2,138 kip-ft |
| Shear | φVn = 788 kips | Vn/Ω = 525 kips |
If the compression flange isn't braced, the beam can buckle sideways before it yields. Up to Lp = 12.7 ft between braces it keeps its full strength; past Lr = 38.2 ft it buckles elastically. With uniform moment between braces (Cb = 1.0):
| Unbraced length, Lb | φMn (LRFD) | Mn/Ω (ASD) |
|---|---|---|
| Braced | 3,214 kip-ft | 2,138 kip-ft |
| 10 ft | 3,214 kip-ft | 2,138 kip-ft |
| 12.7 ft (Lp) | 3,214 kip-ft | 2,138 kip-ft |
| 20 ft | 2,864 kip-ft | 1,905 kip-ft |
| 30 ft | 2,385 kip-ft | 1,587 kip-ft |
| 38.2 ft (Lr) | 1,990 kip-ft | 1,324 kip-ft |
| 40 ft | 1,859 kip-ft | 1,237 kip-ft |
| 50 ft | 1,355 kip-ft | 902 kip-ft |
| 60 ft | 1,065 kip-ft | 708 kip-ft |
| 70 ft | 877 kip-ft | 584 kip-ft |
| 80 ft | 747 kip-ft | 497 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.
W33×221 load table by span
The largest uniform load a simply supported W33×221 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 0.221 kips per foot.
| Span | Factored load (LRFD) | Allowable load (ASD) | Load at span/360 | Load at span/240 |
|---|---|---|---|---|
| 17 ft | 89.0 | 59.2 | 112.8 | 169.2 |
| 19 ft | 71.2 | 47.4 | 80.8 | 121.2 |
| 21 ft | 58.3 | 38.8 | 59.8 | 89.8 |
| 23 ft | 48.6 | 32.3 | 45.6 | 68.3 |
| 25 ft | 41.1 | 27.4 | 35.5 | 53.2 |
| 27 ft | 35.3 | 23.5 | 28.2 | 42.2 |
| 29 ft | 30.6 | 20.3 | 22.7 | 34.1 |
| 31 ft | 26.8 | 17.8 | 18.6 | 27.9 |
| 33 ft | 23.6 | 15.7 | 15.4 | 23.1 |
| 35 ft | 21.0 | 14.0 | 12.9 | 19.4 |
| 37 ft | 18.8 | 12.5 | 10.9 | 16.4 |
| 39 ft | 16.9 | 11.2 | 9.34 | 14.0 |
| 41 ft | 15.3 | 10.2 | 8.04 | 12.1 |
| 43 ft | 13.9 | 9.25 | 6.97 | 10.5 |
| 45 ft | 12.7 | 8.45 | 6.08 | 9.12 |
| 47 ft | 11.6 | 7.74 | 5.34 | 8.01 |
| 49 ft | 10.7 | 7.12 | 4.71 | 7.07 |
| 51 ft | 9.88 | 6.58 | 4.18 | 6.27 |
| 53 ft | 9.15 | 6.09 | 3.72 | 5.58 |
| 55 ft | 8.50 | 5.65 | 3.33 | 5.00 |
| 57 ft | 7.91 | 5.26 | 2.99 | 4.49 |
| 59 ft | 7.39 | 4.91 | 2.70 | 4.05 |
| 61 ft | 6.91 | 4.60 | 2.44 | 3.66 |
| 63 ft | 6.48 | 4.31 | 2.22 | 3.32 |
| 65 ft | 6.09 | 4.05 | 2.02 | 3.03 |
| 67 ft | 5.73 | 3.81 | 1.84 | 2.76 |
| 69 ft | 5.40 | 3.59 | 1.69 | 2.53 |
| 71 ft | 5.10 | 3.39 | 1.55 | 2.32 |
| 73 ft | 4.82 | 3.21 | 1.42 | 2.14 |
| 75 ft | 4.57 | 3.04 | 1.31 | 1.97 |
| 77 ft | 4.34 | 2.89 | 1.21 | 1.82 |
| 79 ft | 4.12 | 2.74 | 1.12 | 1.69 |
| 81 ft | 3.92 | 2.61 | 1.04 | 1.56 |
| 83 ft | 3.73 | 2.48 | 0.97 | 1.45 |
| 85 ft | 3.56 | 2.37 | 0.90 | 1.35 |
- 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 51 ft span, a W33×221 carries a factored load of 9.88 kips per foot (LRFD) or an allowable load of 6.58 kips per foot (ASD). A live load of 4.18 kips per foot would deflect it span/360, which is 1.70 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.
W33×221 questions
What does W33×221 mean?
W means a wide flange shape. 33 is its nominal depth in inches (the actual depth is 33.9 in) and 221 is its weight in pounds per foot.
How much does a W33×221 weigh?
221 pounds per foot, so a 20 ft W33×221 weighs about 4,420 pounds.
How far can a W33×221 span?
It depends on the load. Braced along its length, it carries 89.0 kips per foot of factored load at 17 ft and 3.56 kips per foot at 85 ft; the load table has the spans in between. Floor beams are often 51 to 68 ft for this depth (span-to-depth ratios of about 18 to 24), where deflection usually governs.
Is a W33×221 a compact section?
Yes. Its flanges (bf/2tf = 6.20) and web (h/tw = 38.5) are both compact for bending in 50 ksi steel.