W40×324 Steel Beam
A W40×324 is a wide flange steel beam 40.2 inches deep with 15.9-inch flanges, weighing 324 pounds per foot. In ASTM A992 steel (Fy = 50 ksi) it has a design bending strength of 5,475 kip-ft (LRFD) when its compression flange is braced, and a design shear strength of 1,206 kips.
Design a W40×324 beam Opens a 60 ft span in the free beam designer.
W40×324 dimensions
| Dimension | Value |
|---|---|
| Depth, d | 40.2 in |
| Flange width, bf | 15.9 in |
| Flange thickness, tf | 1.81 in |
| Web thickness, tw | 1.00 in |
| Distance to web toe of fillet, kdes | 2.99 in |
| Distance between flange centroids, ho | 38.39 in |
| Cross-sectional area, A | 95.3 in2 |
| Weight | 324 lb/ft |
Dimensions are AISC design values. Detailing dimensions are rounded to the nearest 1/16 in.
W40×324 section properties
| Property | Strong axis (x) | Weak axis (y) |
|---|---|---|
| Moment of inertia, I | 25600 in4 | 1220 in4 |
| Elastic section modulus, S | 1280 in3 | 153 in3 |
| Plastic section modulus, Z | 1460 in3 | 239 in3 |
| Radius of gyration, r | 16.4 in | 3.58 in |
| Torsion and slenderness | Value |
|---|---|
| Torsional constant, J | 79.4 in4 |
| Warping constant, Cw | 448000 in6 |
| Effective radius of gyration, rts | 4.27 in |
| Flange slenderness, bf/2tf | 4.40 |
| Web slenderness, h/tw | 34.2 |
W40×324 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 = 5,475 kip-ft | Mn/Ω = 3,643 kip-ft |
| Shear | φVn = 1,206 kips | Vn/Ω = 804 kips |
If the compression flange isn't braced, the beam can buckle sideways before it yields. Up to Lp = 12.6 ft between braces it keeps its full strength; past Lr = 41.3 ft it buckles elastically. With uniform moment between braces (Cb = 1.0):
| Unbraced length, Lb | φMn (LRFD) | Mn/Ω (ASD) |
|---|---|---|
| Braced | 5,475 kip-ft | 3,643 kip-ft |
| 10 ft | 5,475 kip-ft | 3,643 kip-ft |
| 12.7 ft (Lp) | 5,475 kip-ft | 3,642 kip-ft |
| 20 ft | 4,932 kip-ft | 3,281 kip-ft |
| 30 ft | 4,193 kip-ft | 2,790 kip-ft |
| 40 ft | 3,454 kip-ft | 2,298 kip-ft |
| 41.3 ft (Lr) | 3,356 kip-ft | 2,233 kip-ft |
| 50 ft | 2,602 kip-ft | 1,731 kip-ft |
| 60 ft | 2,071 kip-ft | 1,378 kip-ft |
| 70 ft | 1,723 kip-ft | 1,146 kip-ft |
| 80 ft | 1,477 kip-ft | 983 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.
W40×324 load table by span
The largest uniform load a simply supported W40×324 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 0.324 kips per foot.
| Span | Factored load (LRFD) | Allowable load (ASD) | Load at span/360 | Load at span/240 |
|---|---|---|---|---|
| 20 ft | 109.5 | 72.9 | 137.5 | 206.2 |
| 22 ft | 90.5 | 60.2 | 103.3 | 154.9 |
| 24 ft | 76.0 | 50.6 | 79.6 | 119.3 |
| 26 ft | 64.8 | 43.1 | 62.6 | 93.9 |
| 28 ft | 55.9 | 37.2 | 50.1 | 75.2 |
| 30 ft | 48.7 | 32.4 | 40.7 | 61.1 |
| 32 ft | 42.8 | 28.5 | 33.6 | 50.3 |
| 34 ft | 37.9 | 25.2 | 28.0 | 42.0 |
| 36 ft | 33.8 | 22.5 | 23.6 | 35.4 |
| 38 ft | 30.3 | 20.2 | 20.0 | 30.1 |
| 40 ft | 27.4 | 18.2 | 17.2 | 25.8 |
| 42 ft | 24.8 | 16.5 | 14.8 | 22.3 |
| 44 ft | 22.6 | 15.1 | 12.9 | 19.4 |
| 46 ft | 20.7 | 13.8 | 11.3 | 16.9 |
| 48 ft | 19.0 | 12.6 | 9.95 | 14.9 |
| 50 ft | 17.5 | 11.7 | 8.80 | 13.2 |
| 52 ft | 16.2 | 10.8 | 7.82 | 11.7 |
| 54 ft | 15.0 | 9.99 | 6.98 | 10.5 |
| 56 ft | 14.0 | 9.29 | 6.26 | 9.39 |
| 58 ft | 13.0 | 8.66 | 5.64 | 8.46 |
| 60 ft | 12.2 | 8.09 | 5.09 | 7.64 |
| 62 ft | 11.4 | 7.58 | 4.61 | 6.92 |
| 64 ft | 10.7 | 7.11 | 4.20 | 6.29 |
| 66 ft | 10.1 | 6.69 | 3.83 | 5.74 |
| 68 ft | 9.47 | 6.30 | 3.50 | 5.25 |
| 70 ft | 8.94 | 5.95 | 3.21 | 4.81 |
| 72 ft | 8.45 | 5.62 | 2.95 | 4.42 |
| 74 ft | 8.00 | 5.32 | 2.71 | 4.07 |
| 76 ft | 7.58 | 5.05 | 2.51 | 3.76 |
| 78 ft | 7.20 | 4.79 | 2.32 | 3.48 |
| 80 ft | 6.84 | 4.55 | 2.15 | 3.22 |
| 82 ft | 6.51 | 4.33 | 1.99 | 2.99 |
| 84 ft | 6.21 | 4.13 | 1.86 | 2.78 |
| 86 ft | 5.92 | 3.94 | 1.73 | 2.59 |
| 88 ft | 5.66 | 3.76 | 1.61 | 2.42 |
| 90 ft | 5.41 | 3.60 | 1.51 | 2.26 |
| 92 ft | 5.17 | 3.44 | 1.41 | 2.12 |
| 94 ft | 4.96 | 3.30 | 1.32 | 1.99 |
| 96 ft | 4.75 | 3.16 | 1.24 | 1.86 |
| 98 ft | 4.56 | 3.03 | 1.17 | 1.75 |
| 100 ft | 4.38 | 2.91 | 1.10 | 1.65 |
- 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 60 ft span, a W40×324 carries a factored load of 12.2 kips per foot (LRFD) or an allowable load of 8.09 kips per foot (ASD). A live load of 5.09 kips per foot would deflect it span/360, which is 2.00 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.
W40×324 questions
What does W40×324 mean?
W means a wide flange shape. 40 is its nominal depth in inches (the actual depth is 40.2 in) and 324 is its weight in pounds per foot.
How much does a W40×324 weigh?
324 pounds per foot, so a 20 ft W40×324 weighs about 6,480 pounds.
How far can a W40×324 span?
It depends on the load. Braced along its length, it carries 109.5 kips per foot of factored load at 20 ft and 4.38 kips per foot at 100 ft; the load table has the spans in between. Floor beams are often 60 to 80 ft for this depth (span-to-depth ratios of about 18 to 24), where deflection usually governs.
Is a W40×324 a compact section?
Yes. Its flanges (bf/2tf = 4.40) and web (h/tw = 34.2) are both compact for bending in 50 ksi steel.