W40×167 Steel Beam
A W40×167 is a wide flange steel beam 38.6 inches deep with 11.8-inch flanges, weighing 167 pounds per foot. In ASTM A992 steel (Fy = 50 ksi) it has a design bending strength of 2,599 kip-ft (LRFD) when its compression flange is braced, and a design shear strength of 753 kips.
Design a W40×167 beam Opens a 59 ft span in the free beam designer.
W40×167 dimensions
| Dimension | Value |
|---|---|
| Depth, d | 38.6 in |
| Flange width, bf | 11.8 in |
| Flange thickness, tf | 1.03 in |
| Web thickness, tw | 0.650 in |
| Distance to web toe of fillet, kdes | 2.21 in |
| Distance between flange centroids, ho | 37.57 in |
| Cross-sectional area, A | 49.2 in2 |
| Weight | 167 lb/ft |
Dimensions are AISC design values. Detailing dimensions are rounded to the nearest 1/16 in.
W40×167 section properties
| Property | Strong axis (x) | Weak axis (y) |
|---|---|---|
| Moment of inertia, I | 11600 in4 | 283 in4 |
| Elastic section modulus, S | 600 in3 | 47.9 in3 |
| Plastic section modulus, Z | 693 in3 | 76.0 in3 |
| Radius of gyration, r | 15.3 in | 2.40 in |
| Torsion and slenderness | Value |
|---|---|
| Torsional constant, J | 14.0 in4 |
| Warping constant, Cw | 99700 in6 |
| Effective radius of gyration, rts | 2.98 in |
| Flange slenderness, bf/2tf | 5.76 |
| Web slenderness, h/tw | 52.6 |
W40×167 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 = 2,599 kip-ft | Mn/Ω = 1,729 kip-ft |
| Shear | φVn = 753 kips | Vn/Ω = 502 kips |
If the compression flange isn't braced, the beam can buckle sideways before it yields. Up to Lp = 8.5 ft between braces it keeps its full strength; past Lr = 24.8 ft it buckles elastically. With uniform moment between braces (Cb = 1.0):
| Unbraced length, Lb | φMn (LRFD) | Mn/Ω (ASD) |
|---|---|---|
| Braced | 2,599 kip-ft | 1,729 kip-ft |
| 5 ft | 2,599 kip-ft | 1,729 kip-ft |
| 8.5 ft (Lp) | 2,599 kip-ft | 1,729 kip-ft |
| 10 ft | 2,503 kip-ft | 1,665 kip-ft |
| 15 ft | 2,189 kip-ft | 1,456 kip-ft |
| 20 ft | 1,874 kip-ft | 1,247 kip-ft |
| 24.8 ft (Lr) | 1,575 kip-ft | 1,048 kip-ft |
| 25 ft | 1,548 kip-ft | 1,030 kip-ft |
| 30 ft | 1,150 kip-ft | 765 kip-ft |
| 35 ft | 906 kip-ft | 603 kip-ft |
| 40 ft | 744 kip-ft | 495 kip-ft |
| 45 ft | 630 kip-ft | 419 kip-ft |
| 50 ft | 546 kip-ft | 363 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.
W40×167 load table by span
The largest uniform load a simply supported W40×167 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 0.167 kips per foot.
| Span | Factored load (LRFD) | Allowable load (ASD) | Load at span/360 | Load at span/240 |
|---|---|---|---|---|
| 19 ft | 57.6 | 38.3 | 72.7 | 109.0 |
| 21 ft | 47.1 | 31.4 | 53.8 | 80.7 |
| 23 ft | 39.3 | 26.1 | 41.0 | 61.4 |
| 25 ft | 33.3 | 22.1 | 31.9 | 47.8 |
| 27 ft | 28.5 | 19.0 | 25.3 | 38.0 |
| 29 ft | 24.7 | 16.4 | 20.4 | 30.7 |
| 31 ft | 21.6 | 14.4 | 16.7 | 25.1 |
| 33 ft | 19.1 | 12.7 | 13.9 | 20.8 |
| 35 ft | 17.0 | 11.3 | 11.6 | 17.4 |
| 37 ft | 15.2 | 10.1 | 9.84 | 14.8 |
| 39 ft | 13.7 | 9.09 | 8.40 | 12.6 |
| 41 ft | 12.4 | 8.23 | 7.23 | 10.8 |
| 43 ft | 11.2 | 7.48 | 6.27 | 9.40 |
| 45 ft | 10.3 | 6.83 | 5.47 | 8.20 |
| 47 ft | 9.41 | 6.26 | 4.80 | 7.20 |
| 49 ft | 8.66 | 5.76 | 4.24 | 6.35 |
| 51 ft | 7.99 | 5.32 | 3.76 | 5.64 |
| 53 ft | 7.40 | 4.92 | 3.35 | 5.02 |
| 55 ft | 6.87 | 4.57 | 3.00 | 4.49 |
| 57 ft | 6.40 | 4.26 | 2.69 | 4.04 |
| 59 ft | 5.97 | 3.97 | 2.43 | 3.64 |
| 61 ft | 5.59 | 3.72 | 2.20 | 3.29 |
| 63 ft | 5.24 | 3.49 | 1.99 | 2.99 |
| 65 ft | 4.92 | 3.27 | 1.81 | 2.72 |
| 67 ft | 4.63 | 3.08 | 1.66 | 2.49 |
| 69 ft | 4.37 | 2.91 | 1.52 | 2.28 |
| 71 ft | 4.12 | 2.74 | 1.39 | 2.09 |
| 73 ft | 3.90 | 2.60 | 1.28 | 1.92 |
| 75 ft | 3.70 | 2.46 | 1.18 | 1.77 |
| 77 ft | 3.51 | 2.33 | 1.09 | 1.64 |
| 79 ft | 3.33 | 2.22 | 1.01 | 1.52 |
| 81 ft | 3.17 | 2.11 | 0.94 | 1.41 |
| 83 ft | 3.02 | 2.01 | 0.87 | 1.31 |
| 85 ft | 2.88 | 1.91 | 0.81 | 1.22 |
| 87 ft | 2.75 | 1.83 | 0.76 | 1.14 |
| 89 ft | 2.62 | 1.75 | 0.71 | 1.06 |
| 91 ft | 2.51 | 1.67 | 0.66 | 0.99 |
| 93 ft | 2.40 | 1.60 | 0.62 | 0.93 |
| 95 ft | 2.30 | 1.53 | 0.58 | 0.87 |
| 97 ft | 2.21 | 1.47 | 0.55 | 0.82 |
- 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 59 ft span, a W40×167 carries a factored load of 5.97 kips per foot (LRFD) or an allowable load of 3.97 kips per foot (ASD). A live load of 2.43 kips per foot would deflect it span/360, which is 1.97 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.
W40×167 questions
What does W40×167 mean?
W means a wide flange shape. 40 is its nominal depth in inches (the actual depth is 38.6 in) and 167 is its weight in pounds per foot.
How much does a W40×167 weigh?
167 pounds per foot, so a 20 ft W40×167 weighs about 3,340 pounds.
How far can a W40×167 span?
It depends on the load. Braced along its length, it carries 57.6 kips per foot of factored load at 19 ft and 2.21 kips per foot at 97 ft; the load table has the spans in between. Floor beams are often 58 to 77 ft for this depth (span-to-depth ratios of about 18 to 24), where deflection usually governs.
Is a W40×167 a compact section?
Yes. Its flanges (bf/2tf = 5.76) and web (h/tw = 52.6) are both compact for bending in 50 ksi steel.