W33×291 Steel Beam
A W33×291 is a wide flange steel beam 34.8 inches deep with 15.9-inch flanges, weighing 291 pounds per foot. In ASTM A992 steel (Fy = 50 ksi) it has a design bending strength of 4,350 kip-ft (LRFD) when its compression flange is braced, and a design shear strength of 1,002 kips.
Design a W33×291 beam Opens a 53 ft span in the free beam designer.
W33×291 dimensions
| Dimension | Value |
|---|---|
| Depth, d | 34.8 in |
| Flange width, bf | 15.9 in |
| Flange thickness, tf | 1.73 in |
| Web thickness, tw | 0.960 in |
| Distance to web toe of fillet, kdes | 2.52 in |
| Distance between flange centroids, ho | 33.07 in |
| Cross-sectional area, A | 85.7 in2 |
| Weight | 291 lb/ft |
Dimensions are AISC design values. Detailing dimensions are rounded to the nearest 1/16 in.
W33×291 section properties
| Property | Strong axis (x) | Weak axis (y) |
|---|---|---|
| Moment of inertia, I | 17700 in4 | 1160 in4 |
| Elastic section modulus, S | 1020 in3 | 146 in3 |
| Plastic section modulus, Z | 1160 in3 | 226 in3 |
| Radius of gyration, r | 14.4 in | 3.68 in |
| Torsion and slenderness | Value |
|---|---|
| Torsional constant, J | 65.1 in4 |
| Warping constant, Cw | 319000 in6 |
| Effective radius of gyration, rts | 4.34 in |
| Flange slenderness, bf/2tf | 4.60 |
| Web slenderness, h/tw | 31.0 |
W33×291 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 = 4,350 kip-ft | Mn/Ω = 2,894 kip-ft |
| Shear | φVn = 1,002 kips | Vn/Ω = 668 kips |
If the compression flange isn't braced, the beam can buckle sideways before it yields. Up to Lp = 13.0 ft between braces it keeps its full strength; past Lr = 43.8 ft it buckles elastically. With uniform moment between braces (Cb = 1.0):
| Unbraced length, Lb | φMn (LRFD) | Mn/Ω (ASD) |
|---|---|---|
| Braced | 4,350 kip-ft | 2,894 kip-ft |
| 10 ft | 4,350 kip-ft | 2,894 kip-ft |
| 13 ft (Lp) | 4,350 kip-ft | 2,894 kip-ft |
| 20 ft | 3,970 kip-ft | 2,641 kip-ft |
| 30 ft | 3,427 kip-ft | 2,280 kip-ft |
| 40 ft | 2,884 kip-ft | 1,919 kip-ft |
| 43.8 ft (Lr) | 2,678 kip-ft | 1,781 kip-ft |
| 50 ft | 2,258 kip-ft | 1,502 kip-ft |
| 60 ft | 1,806 kip-ft | 1,201 kip-ft |
| 70 ft | 1,507 kip-ft | 1,003 kip-ft |
| 80 ft | 1,295 kip-ft | 862 kip-ft |
| 90 ft | 1,137 kip-ft | 756 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.
W33×291 load table by span
The largest uniform load a simply supported W33×291 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 0.291 kips per foot.
| Span | Factored load (LRFD) | Allowable load (ASD) | Load at span/360 | Load at span/240 |
|---|---|---|---|---|
| 17 ft | 117.9* | 78.6* | 154.8 | 232.2 |
| 19 ft | 96.4 | 64.1 | 110.9 | 166.3 |
| 21 ft | 78.9 | 52.5 | 82.1 | 123.2 |
| 23 ft | 65.8 | 43.8 | 62.5 | 93.8 |
| 25 ft | 55.7 | 37.0 | 48.7 | 73.0 |
| 27 ft | 47.7 | 31.8 | 38.6 | 58.0 |
| 29 ft | 41.4 | 27.5 | 31.2 | 46.8 |
| 31 ft | 36.2 | 24.1 | 25.5 | 38.3 |
| 33 ft | 32.0 | 21.3 | 21.2 | 31.7 |
| 35 ft | 28.4 | 18.9 | 17.7 | 26.6 |
| 37 ft | 25.4 | 16.9 | 15.0 | 22.5 |
| 39 ft | 22.9 | 15.2 | 12.8 | 19.2 |
| 41 ft | 20.7 | 13.8 | 11.0 | 16.6 |
| 43 ft | 18.8 | 12.5 | 9.56 | 14.3 |
| 45 ft | 17.2 | 11.4 | 8.35 | 12.5 |
| 47 ft | 15.8 | 10.5 | 7.32 | 11.0 |
| 49 ft | 14.5 | 9.64 | 6.46 | 9.70 |
| 51 ft | 13.4 | 8.90 | 5.73 | 8.60 |
| 53 ft | 12.4 | 8.24 | 5.11 | 7.66 |
| 55 ft | 11.5 | 7.65 | 4.57 | 6.86 |
| 57 ft | 10.7 | 7.13 | 4.11 | 6.16 |
| 59 ft | 10.00 | 6.65 | 3.70 | 5.55 |
| 61 ft | 9.35 | 6.22 | 3.35 | 5.03 |
| 63 ft | 8.77 | 5.83 | 3.04 | 4.56 |
| 65 ft | 8.24 | 5.48 | 2.77 | 4.15 |
| 67 ft | 7.75 | 5.16 | 2.53 | 3.79 |
| 69 ft | 7.31 | 4.86 | 2.31 | 3.47 |
| 71 ft | 6.90 | 4.59 | 2.12 | 3.19 |
| 73 ft | 6.53 | 4.34 | 1.95 | 2.93 |
| 75 ft | 6.19 | 4.12 | 1.80 | 2.70 |
| 77 ft | 5.87 | 3.91 | 1.67 | 2.50 |
| 79 ft | 5.58 | 3.71 | 1.54 | 2.31 |
| 81 ft | 5.30 | 3.53 | 1.43 | 2.15 |
| 83 ft | 5.05 | 3.36 | 1.33 | 1.99 |
| 85 ft | 4.82 | 3.20 | 1.24 | 1.86 |
| 87 ft | 4.60 | 3.06 | 1.15 | 1.73 |
- 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 53 ft span, a W33×291 carries a factored load of 12.4 kips per foot (LRFD) or an allowable load of 8.24 kips per foot (ASD). A live load of 5.11 kips per foot would deflect it span/360, which is 1.77 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.
W33×291 questions
What does W33×291 mean?
W means a wide flange shape. 33 is its nominal depth in inches (the actual depth is 34.8 in) and 291 is its weight in pounds per foot.
How much does a W33×291 weigh?
291 pounds per foot, so a 20 ft W33×291 weighs about 5,820 pounds.
How far can a W33×291 span?
It depends on the load. Braced along its length, it carries 117.9 kips per foot of factored load at 17 ft and 4.60 kips per foot at 87 ft; the load table has the spans in between. Floor beams are often 52 to 70 ft for this depth (span-to-depth ratios of about 18 to 24), where deflection usually governs.
Is a W33×291 a compact section?
Yes. Its flanges (bf/2tf = 4.60) and web (h/tw = 31.0) are both compact for bending in 50 ksi steel.