W33×387 Steel Beam
A W33×387 is a wide flange steel beam 36 inches deep with 16.2-inch flanges, weighing 387 pounds per foot. In ASTM A992 steel (Fy = 50 ksi) it has a design bending strength of 5,850 kip-ft (LRFD) when its compression flange is braced, and a design shear strength of 1,361 kips.
Design a W33×387 beam Opens a 54 ft span in the free beam designer.
W33×387 dimensions
| Dimension | Value |
|---|---|
| Depth, d | 36.0 in |
| Flange width, bf | 16.2 in |
| Flange thickness, tf | 2.28 in |
| Web thickness, tw | 1.26 in |
| Distance to web toe of fillet, kdes | 3.07 in |
| Distance between flange centroids, ho | 33.72 in |
| Cross-sectional area, A | 114 in2 |
| Weight | 387 lb/ft |
Dimensions are AISC design values. Detailing dimensions are rounded to the nearest 1/16 in.
W33×387 section properties
| Property | Strong axis (x) | Weak axis (y) |
|---|---|---|
| Moment of inertia, I | 24300 in4 | 1620 in4 |
| Elastic section modulus, S | 1350 in3 | 200 in3 |
| Plastic section modulus, Z | 1560 in3 | 312 in3 |
| Radius of gyration, r | 14.6 in | 3.77 in |
| Torsion and slenderness | Value |
|---|---|
| Torsional constant, J | 148 in4 |
| Warping constant, Cw | 459000 in6 |
| Effective radius of gyration, rts | 4.49 in |
| Flange slenderness, bf/2tf | 3.55 |
| Web slenderness, h/tw | 23.7 |
W33×387 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 = 5,850 kip-ft | Mn/Ω = 3,892 kip-ft |
| Shear | φVn = 1,361 kips | Vn/Ω = 907 kips |
If the compression flange isn't braced, the beam can buckle sideways before it yields. Up to Lp = 13.3 ft between braces it keeps its full strength; past Lr = 53.3 ft it buckles elastically. With uniform moment between braces (Cb = 1.0):
| Unbraced length, Lb | φMn (LRFD) | Mn/Ω (ASD) |
|---|---|---|
| Braced | 5,850 kip-ft | 3,892 kip-ft |
| 10 ft | 5,850 kip-ft | 3,892 kip-ft |
| 13.3 ft (Lp) | 5,850 kip-ft | 3,892 kip-ft |
| 20 ft | 5,465 kip-ft | 3,636 kip-ft |
| 30 ft | 4,889 kip-ft | 3,253 kip-ft |
| 40 ft | 4,312 kip-ft | 2,869 kip-ft |
| 50 ft | 3,736 kip-ft | 2,486 kip-ft |
| 53.3 ft (Lr) | 3,541 kip-ft | 2,356 kip-ft |
| 60 ft | 3,094 kip-ft | 2,059 kip-ft |
| 70 ft | 2,605 kip-ft | 1,733 kip-ft |
| 80 ft | 2,252 kip-ft | 1,498 kip-ft |
| 90 ft | 1,985 kip-ft | 1,321 kip-ft |
| 100 ft | 1,776 kip-ft | 1,181 kip-ft |
| 110 ft | 1,607 kip-ft | 1,069 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.
W33×387 load table by span
The largest uniform load a simply supported W33×387 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 0.387 kips per foot.
| Span | Factored load (LRFD) | Allowable load (ASD) | Load at span/360 | Load at span/240 |
|---|---|---|---|---|
| 18 ft | 144.4 | 96.1 | 179.0 | 268.5 |
| 20 ft | 117.0 | 77.8 | 130.5 | 195.8 |
| 22 ft | 96.7 | 64.3 | 98.0 | 147.1 |
| 24 ft | 81.3 | 54.1 | 75.5 | 113.3 |
| 26 ft | 69.2 | 46.1 | 59.4 | 89.1 |
| 28 ft | 59.7 | 39.7 | 47.6 | 71.3 |
| 30 ft | 52.0 | 34.6 | 38.7 | 58.0 |
| 32 ft | 45.7 | 30.4 | 31.9 | 47.8 |
| 34 ft | 40.5 | 26.9 | 26.6 | 39.8 |
| 36 ft | 36.1 | 24.0 | 22.4 | 33.6 |
| 38 ft | 32.4 | 21.6 | 19.0 | 28.5 |
| 40 ft | 29.3 | 19.5 | 16.3 | 24.5 |
| 42 ft | 26.5 | 17.7 | 14.1 | 21.1 |
| 44 ft | 24.2 | 16.1 | 12.3 | 18.4 |
| 46 ft | 22.1 | 14.7 | 10.7 | 16.1 |
| 48 ft | 20.3 | 13.5 | 9.44 | 14.2 |
| 50 ft | 18.7 | 12.5 | 8.35 | 12.5 |
| 52 ft | 17.3 | 11.5 | 7.42 | 11.1 |
| 54 ft | 16.0 | 10.7 | 6.63 | 9.95 |
| 56 ft | 14.9 | 9.93 | 5.94 | 8.92 |
| 58 ft | 13.9 | 9.26 | 5.35 | 8.03 |
| 60 ft | 13.0 | 8.65 | 4.83 | 7.25 |
| 62 ft | 12.2 | 8.10 | 4.38 | 6.57 |
| 64 ft | 11.4 | 7.60 | 3.98 | 5.97 |
| 66 ft | 10.7 | 7.15 | 3.63 | 5.45 |
| 68 ft | 10.1 | 6.73 | 3.32 | 4.98 |
| 70 ft | 9.55 | 6.35 | 3.04 | 4.57 |
| 72 ft | 9.03 | 6.01 | 2.80 | 4.20 |
| 74 ft | 8.55 | 5.69 | 2.58 | 3.86 |
| 76 ft | 8.10 | 5.39 | 2.38 | 3.57 |
| 78 ft | 7.69 | 5.12 | 2.20 | 3.30 |
| 80 ft | 7.31 | 4.87 | 2.04 | 3.06 |
| 82 ft | 6.96 | 4.63 | 1.89 | 2.84 |
| 84 ft | 6.63 | 4.41 | 1.76 | 2.64 |
| 86 ft | 6.33 | 4.21 | 1.64 | 2.46 |
| 88 ft | 6.04 | 4.02 | 1.53 | 2.30 |
| 90 ft | 5.78 | 3.84 | 1.43 | 2.15 |
- 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 54 ft span, a W33×387 carries a factored load of 16.0 kips per foot (LRFD) or an allowable load of 10.7 kips per foot (ASD). A live load of 6.63 kips per foot would deflect it span/360, which is 1.80 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.
W33×387 questions
What does W33×387 mean?
W means a wide flange shape. 33 is its nominal depth in inches (the actual depth is 36.0 in) and 387 is its weight in pounds per foot.
How much does a W33×387 weigh?
387 pounds per foot, so a 20 ft W33×387 weighs about 7,740 pounds.
How far can a W33×387 span?
It depends on the load. Braced along its length, it carries 144.4 kips per foot of factored load at 18 ft and 5.78 kips per foot at 90 ft; the load table has the spans in between. Floor beams are often 54 to 72 ft for this depth (span-to-depth ratios of about 18 to 24), where deflection usually governs.
Is a W33×387 a compact section?
Yes. Its flanges (bf/2tf = 3.55) and web (h/tw = 23.7) are both compact for bending in 50 ksi steel.