W24×84 Steel Beam
A W24×84 is a wide flange steel beam 24.1 inches deep with 9.02-inch flanges, weighing 84 pounds per foot. In ASTM A992 steel (Fy = 50 ksi) it has a design bending strength of 840 kip-ft (LRFD) when its compression flange is braced, and a design shear strength of 340 kips.
Design a W24×84 beam Opens a 36 ft span in the free beam designer.
W24×84 dimensions
| Dimension | Value |
|---|---|
| Depth, d | 24.1 in |
| Flange width, bf | 9.02 in |
| Flange thickness, tf | 0.770 in |
| Web thickness, tw | 0.470 in |
| Distance to web toe of fillet, kdes | 1.27 in |
| Distance between flange centroids, ho | 23.33 in |
| Cross-sectional area, A | 24.7 in2 |
| Weight | 84 lb/ft |
Dimensions are AISC design values. Detailing dimensions are rounded to the nearest 1/16 in.
W24×84 section properties
| Property | Strong axis (x) | Weak axis (y) |
|---|---|---|
| Moment of inertia, I | 2370 in4 | 94.4 in4 |
| Elastic section modulus, S | 196 in3 | 20.9 in3 |
| Plastic section modulus, Z | 224 in3 | 32.6 in3 |
| Radius of gyration, r | 9.79 in | 1.95 in |
| Torsion and slenderness | Value |
|---|---|
| Torsional constant, J | 3.70 in4 |
| Warping constant, Cw | 12800 in6 |
| Effective radius of gyration, rts | 2.37 in |
| Flange slenderness, bf/2tf | 5.86 |
| Web slenderness, h/tw | 45.9 |
W24×84 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 = 840 kip-ft | Mn/Ω = 559 kip-ft |
| Shear | φVn = 340 kips | Vn/Ω = 227 kips |
If the compression flange isn't braced, the beam can buckle sideways before it yields. Up to Lp = 6.9 ft between braces it keeps its full strength; past Lr = 20.3 ft it buckles elastically. With uniform moment between braces (Cb = 1.0):
| Unbraced length, Lb | φMn (LRFD) | Mn/Ω (ASD) |
|---|---|---|
| Braced | 840 kip-ft | 559 kip-ft |
| 5 ft | 840 kip-ft | 559 kip-ft |
| 6.9 ft (Lp) | 840 kip-ft | 559 kip-ft |
| 10 ft | 764 kip-ft | 509 kip-ft |
| 15 ft | 643 kip-ft | 428 kip-ft |
| 20 ft | 522 kip-ft | 347 kip-ft |
| 20.3 ft (Lr) | 515 kip-ft | 342 kip-ft |
| 25 ft | 372 kip-ft | 247 kip-ft |
| 30 ft | 285 kip-ft | 190 kip-ft |
| 35 ft | 231 kip-ft | 154 kip-ft |
| 40 ft | 194 kip-ft | 129 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.
W24×84 load table by span
The largest uniform load a simply supported W24×84 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 0.084 kips per foot.
| Span | Factored load (LRFD) | Allowable load (ASD) | Load at span/360 | Load at span/240 |
|---|---|---|---|---|
| 12 ft | 46.7 | 31.0 | 58.9 | 88.4 |
| 14 ft | 34.3 | 22.8 | 37.1 | 55.7 |
| 16 ft | 26.3 | 17.5 | 24.9 | 37.3 |
| 18 ft | 20.7 | 13.8 | 17.5 | 26.2 |
| 20 ft | 16.8 | 11.2 | 12.7 | 19.1 |
| 22 ft | 13.9 | 9.24 | 9.56 | 14.3 |
| 24 ft | 11.7 | 7.76 | 7.37 | 11.0 |
| 26 ft | 9.94 | 6.61 | 5.79 | 8.69 |
| 28 ft | 8.57 | 5.70 | 4.64 | 6.96 |
| 30 ft | 7.47 | 4.97 | 3.77 | 5.66 |
| 32 ft | 6.56 | 4.37 | 3.11 | 4.66 |
| 34 ft | 5.81 | 3.87 | 2.59 | 3.89 |
| 36 ft | 5.19 | 3.45 | 2.18 | 3.27 |
| 38 ft | 4.65 | 3.10 | 1.86 | 2.78 |
| 40 ft | 4.20 | 2.79 | 1.59 | 2.39 |
| 42 ft | 3.81 | 2.53 | 1.37 | 2.06 |
| 44 ft | 3.47 | 2.31 | 1.20 | 1.79 |
| 46 ft | 3.18 | 2.11 | 1.05 | 1.57 |
| 48 ft | 2.92 | 1.94 | 0.92 | 1.38 |
| 50 ft | 2.69 | 1.79 | 0.81 | 1.22 |
| 52 ft | 2.49 | 1.65 | 0.72 | 1.09 |
| 54 ft | 2.30 | 1.53 | 0.65 | 0.97 |
| 56 ft | 2.14 | 1.43 | 0.58 | 0.87 |
| 58 ft | 2.00 | 1.33 | 0.52 | 0.78 |
| 60 ft | 1.87 | 1.24 | 0.47 | 0.71 |
- 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 36 ft span, a W24×84 carries a factored load of 5.19 kips per foot (LRFD) or an allowable load of 3.45 kips per foot (ASD). A live load of 2.18 kips per foot would deflect it span/360, which is 1.20 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.
W24×84 questions
What does W24×84 mean?
W means a wide flange shape. 24 is its nominal depth in inches (the actual depth is 24.1 in) and 84 is its weight in pounds per foot.
How much does a W24×84 weigh?
84 pounds per foot, so a 20 ft W24×84 weighs about 1,680 pounds.
How far can a W24×84 span?
It depends on the load. Braced along its length, it carries 46.7 kips per foot of factored load at 12 ft and 1.87 kips per foot at 60 ft; the load table has the spans in between. Floor beams are often 36 to 48 ft for this depth (span-to-depth ratios of about 18 to 24), where deflection usually governs.
Is a W24×84 a compact section?
Yes. Its flanges (bf/2tf = 5.86) and web (h/tw = 45.9) are both compact for bending in 50 ksi steel.