W10×77 Steel Beam
A W10×77 is a wide flange steel beam 10.6 inches deep with 10.2-inch flanges, weighing 77 pounds per foot. In ASTM A992 steel (Fy = 50 ksi) it has a design bending strength of 366 kip-ft (LRFD) when its compression flange is braced, and a design shear strength of 169 kips.
Design a W10×77 beam Opens a 16 ft span in the free beam designer.
W10×77 dimensions
| Dimension | Value |
|---|---|
| Depth, d | 10.6 in |
| Flange width, bf | 10.2 in |
| Flange thickness, tf | 0.870 in |
| Web thickness, tw | 0.530 in |
| Distance to web toe of fillet, kdes | 1.37 in |
| Distance between flange centroids, ho | 9.73 in |
| Cross-sectional area, A | 22.6 in2 |
| Weight | 77 lb/ft |
Dimensions are AISC design values. Detailing dimensions are rounded to the nearest 1/16 in.
W10×77 section properties
| Property | Strong axis (x) | Weak axis (y) |
|---|---|---|
| Moment of inertia, I | 455 in4 | 154 in4 |
| Elastic section modulus, S | 85.9 in3 | 30.1 in3 |
| Plastic section modulus, Z | 97.6 in3 | 45.9 in3 |
| Radius of gyration, r | 4.49 in | 2.60 in |
| Torsion and slenderness | Value |
|---|---|
| Torsional constant, J | 5.11 in4 |
| Warping constant, Cw | 3630 in6 |
| Effective radius of gyration, rts | 2.95 in |
| Flange slenderness, bf/2tf | 5.86 |
| Web slenderness, h/tw | 14.8 |
W10×77 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 = 366 kip-ft | Mn/Ω = 244 kip-ft |
| Shear | φVn = 169 kips | Vn/Ω = 112 kips |
If the compression flange isn't braced, the beam can buckle sideways before it yields. Up to Lp = 9.2 ft between braces it keeps its full strength; past Lr = 45.3 ft it buckles elastically. With uniform moment between braces (Cb = 1.0):
| Unbraced length, Lb | φMn (LRFD) | Mn/Ω (ASD) |
|---|---|---|
| Braced | 366 kip-ft | 244 kip-ft |
| 9.2 ft (Lp) | 366 kip-ft | 244 kip-ft |
| 10 ft | 363 kip-ft | 241 kip-ft |
| 20 ft | 324 kip-ft | 215 kip-ft |
| 30 ft | 285 kip-ft | 190 kip-ft |
| 40 ft | 246 kip-ft | 164 kip-ft |
| 45.3 ft (Lr) | 225 kip-ft | 150 kip-ft |
| 50 ft | 203 kip-ft | 135 kip-ft |
| 60 ft | 168 kip-ft | 112 kip-ft |
| 70 ft | 143 kip-ft | 95.3 kip-ft |
| 80 ft | 125 kip-ft | 83.1 kip-ft |
| 90 ft | 111 kip-ft | 73.8 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.
W10×77 load table by span
The largest uniform load a simply supported W10×77 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 0.077 kips per foot.
| Span | Factored load (LRFD) | Allowable load (ASD) | Load at span/360 | Load at span/240 |
|---|---|---|---|---|
| 5 ft | 67.4* | 44.9* | 156.4 | 234.6 |
| 6 ft | 56.2* | 37.5* | 90.5 | 135.8 |
| 7 ft | 48.2* | 32.1* | 57.0 | 85.5 |
| 8 ft | 42.1* | 28.1* | 38.2 | 57.3 |
| 9 ft | 36.1 | 24.1 | 26.8 | 40.2 |
| 10 ft | 29.3 | 19.5 | 19.5 | 29.3 |
| 11 ft | 24.2 | 16.1 | 14.7 | 22.0 |
| 12 ft | 20.3 | 13.5 | 11.3 | 17.0 |
| 13 ft | 17.3 | 11.5 | 8.90 | 13.3 |
| 14 ft | 14.9 | 9.94 | 7.12 | 10.7 |
| 15 ft | 13.0 | 8.66 | 5.79 | 8.69 |
| 16 ft | 11.4 | 7.61 | 4.77 | 7.16 |
| 17 ft | 10.1 | 6.74 | 3.98 | 5.97 |
| 18 ft | 9.04 | 6.01 | 3.35 | 5.03 |
| 19 ft | 8.11 | 5.40 | 2.85 | 4.27 |
| 20 ft | 7.32 | 4.87 | 2.44 | 3.67 |
| 21 ft | 6.64 | 4.42 | 2.11 | 3.17 |
| 22 ft | 6.05 | 4.03 | 1.84 | 2.75 |
| 23 ft | 5.53 | 3.68 | 1.61 | 2.41 |
| 24 ft | 5.08 | 3.38 | 1.41 | 2.12 |
| 25 ft | 4.68 | 3.12 | 1.25 | 1.88 |
| 26 ft | 4.33 | 2.88 | 1.11 | 1.67 |
| 27 ft | 4.02 | 2.67 | 0.99 | 1.49 |
- 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 16 ft span, a W10×77 carries a factored load of 11.4 kips per foot (LRFD) or an allowable load of 7.61 kips per foot (ASD). A live load of 4.77 kips per foot would deflect it span/360, which is 0.53 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.
W10×77 questions
What does W10×77 mean?
W means a wide flange shape. 10 is its nominal depth in inches (the actual depth is 10.6 in) and 77 is its weight in pounds per foot.
How much does a W10×77 weigh?
77 pounds per foot, so a 20 ft W10×77 weighs about 1,540 pounds.
How far can a W10×77 span?
It depends on the load. Braced along its length, it carries 67.4 kips per foot of factored load at 5 ft and 4.02 kips per foot at 27 ft; the load table has the spans in between. Floor beams are often 16 to 21 ft for this depth (span-to-depth ratios of about 18 to 24), where deflection usually governs.
Is a W10×77 a compact section?
Yes. Its flanges (bf/2tf = 5.86) and web (h/tw = 14.8) are both compact for bending in 50 ksi steel.