CNC Machining Design Guide

Optimize your designs, reduce machining time, and lower your costs.

Salary Expectation

8 things to know about the interview question "What's your salary expectation"?

STEM Career Outlook

Wages, employment opportunities, and growth projections for STEM jobs.

Selecting the Right 3D Printer

Discover how to choose the right 3D printer for your needs and the key performance attributes to consider.

more free publications

Materials

Design

Processes

Units

Formulas

Math
Glossary » Beams » Simply Supported » Uniformly Distributed Load » Four Equal Spans » Wide Flange Steel I Beam » W10 × 77
Wide Flange Steel I Beam | Single Span | Two Equal Spans | Three Equal Spans | Four Equal Spans

For a simply supported beam in four equal spans, we compute the displacement at the middle of the first and fourth spans, and the maximum normal stress stress_max occuring at the second and fourth supports of the beam.
The tabulated data listed in this page are calculated based on the area moment of inertia (Ixx = 455 in4) for the W10 × 77 Wide Flange Steel I Beam and the typical Young's modulus (E = 3.046 × 107 psi) of steels. Note that the typical yielding stress Yield of steels can range from 1.015 × 104 to 2.970 × 105 psi. The purpose of this page is to give a rough estimation of the load-bearing capacity of this particular beam, rather than a guideline for designing actual building structures. Please check your local building codes for regulatory requirements.
Note: The weight of the beam itself is not included in the calculation.
L = 3 ft
L = 5 ft
L = 10 ft
L = 15 ft
L = 20 ft
L = 25 ft
L = 30 ft
L = 40 ft
L = 50 ft
L = 60 ft
L = 70 ft
L = 80 ft
L = 90 ft
L = 100 ft
   
Steel I Beam: W10 × 77 (Wide Flange 10 inch tall × 77 lbf/ft)
L = 3.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
77.0 4.90 × 10-6 10.4
80.0 5.09 × 10-6 10.8
90.0 5.73 × 10-6 12.1
100 6.36 × 10-6 13.5
200 1.27 × 10-5 26.9
300 1.91 × 10-5 40.4
400 2.55 × 10-5 53.9
500 3.18 × 10-5 67.4
600 3.82 × 10-5 80.8
700 4.45 × 10-5 94.3
800 5.09 × 10-5 108
900 5.73 × 10-5 121
1000 6.36 × 10-5 135
2000 1.27 × 10-4 269
3000 1.91 × 10-4 404
4000 2.55 × 10-4 539
5000 3.18 × 10-4 674
6000 3.82 × 10-4 808
7000 4.45 × 10-4 943
8000 5.09 × 10-4 1080
9000 5.73 × 10-4 1210
1.00 × 104 6.36 × 10-4 1350
2.00 × 104 0.00127 2690
3.00 × 104 0.00191 4040
4.00 × 104 0.00255 5390
5.00 × 104 0.00318 6740
6.00 × 104 0.00382 8080
7.00 × 104 0.00445 9430
8.00 × 104 0.00509 1.08 × 104
9.00 × 104 0.00573 1.21 × 104
1.00 × 105 0.00636 1.35 × 104
2.00 × 105 0.0127 2.69 × 104
3.00 × 105 0.0191 4.04 × 104
4.00 × 105 0.0255 5.39 × 104
5.00 × 105 0.0318 6.74 × 104
6.00 × 105 0.0382 8.08 × 104
7.00 × 105 0.0445 9.43 × 104
8.00 × 105 0.0509 1.08 × 105
9.00 × 105 0.0573 1.21 × 105
1.00 × 106 0.0636 1.35 × 105
2.00 × 106 0.127 2.69 × 105
2.20 × 106 0.140 2.97 × 105
Steel I Beam: W10 × 77 (Wide Flange 10 inch tall × 77 lbf/ft)
L = 5.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
77.0 3.78 × 10-5 28.8
80.0 3.93 × 10-5 29.9
90.0 4.42 × 10-5 33.7
100 4.91 × 10-5 37.4
200 9.82 × 10-5 74.9
300 1.47 × 10-4 112
400 1.96 × 10-4 150
500 2.45 × 10-4 187
600 2.95 × 10-4 225
700 3.44 × 10-4 262
800 3.93 × 10-4 299
900 4.42 × 10-4 337
1000 4.91 × 10-4 374
2000 9.82 × 10-4 749
3000 0.00147 1120
4000 0.00196 1500
5000 0.00245 1870
6000 0.00295 2250
7000 0.00344 2620
8000 0.00393 2990
9000 0.00442 3370
1.00 × 104 0.00491 3740
2.00 × 104 0.00982 7490
3.00 × 104 0.0147 1.12 × 104
4.00 × 104 0.0196 1.50 × 104
5.00 × 104 0.0245 1.87 × 104
6.00 × 104 0.0295 2.25 × 104
7.00 × 104 0.0344 2.62 × 104
8.00 × 104 0.0393 2.99 × 104
9.00 × 104 0.0442 3.37 × 104
1.00 × 105 0.0491 3.74 × 104
2.00 × 105 0.0982 7.49 × 104
3.00 × 105 0.147 1.12 × 105
4.00 × 105 0.196 1.50 × 105
5.00 × 105 0.245 1.87 × 105
6.00 × 105 0.295 2.25 × 105
7.00 × 105 0.344 2.62 × 105
7.94 × 105 0.390 2.97 × 105
Steel I Beam: W10 × 77 (Wide Flange 10 inch tall × 77 lbf/ft)
L = 10.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
77.0 6.05 × 10-4 115
80.0 6.28 × 10-4 120
90.0 7.07 × 10-4 135
100 7.86 × 10-4 150
200 0.00157 299
300 0.00236 449
400 0.00314 599
500 0.00393 749
600 0.00471 898
700 0.00550 1050
800 0.00628 1200
900 0.00707 1350
1000 0.00786 1500
2000 0.0157 2990
3000 0.0236 4490
4000 0.0314 5990
5000 0.0393 7490
6000 0.0471 8980
7000 0.0550 1.05 × 104
8000 0.0628 1.20 × 104
9000 0.0707 1.35 × 104
1.00 × 104 0.0786 1.50 × 104
2.00 × 104 0.157 2.99 × 104
3.00 × 104 0.236 4.49 × 104
4.00 × 104 0.314 5.99 × 104
5.00 × 104 0.393 7.49 × 104
6.00 × 104 0.471 8.98 × 104
7.00 × 104 0.550 1.05 × 105
8.00 × 104 0.628 1.20 × 105
9.00 × 104 0.707 1.35 × 105
1.00 × 105 0.786 1.50 × 105
1.98 × 105 1.56 2.97 × 105
Steel I Beam: W10 × 77 (Wide Flange 10 inch tall × 77 lbf/ft)
L = 15.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
77.0 0.00306 259
80.0 0.00318 269
90.0 0.00358 303
100 0.00398 337
200 0.00795 674
300 0.0119 1010
400 0.0159 1350
500 0.0199 1680
600 0.0239 2020
700 0.0278 2360
800 0.0318 2690
900 0.0358 3030
1000 0.0398 3370
2000 0.0795 6740
3000 0.119 1.01 × 104
4000 0.159 1.35 × 104
5000 0.199 1.68 × 104
6000 0.239 2.02 × 104
7000 0.278 2.36 × 104
8000 0.318 2.69 × 104
9000 0.358 3.03 × 104
1.00 × 104 0.398 3.37 × 104
2.00 × 104 0.795 6.74 × 104
3.00 × 104 1.19 1.01 × 105
4.00 × 104 1.59 1.35 × 105
5.00 × 104 1.99 1.68 × 105
6.00 × 104 2.39 2.02 × 105
7.00 × 104 2.78 2.36 × 105
8.00 × 104 3.18 2.69 × 105
8.82 × 104 3.51 2.97 × 105
Steel I Beam: W10 × 77 (Wide Flange 10 inch tall × 77 lbf/ft)
L = 20.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
77.0 0.00968 461
80.0 0.0101 479
90.0 0.0113 539
100 0.0126 599
200 0.0251 1200
300 0.0377 1800
400 0.0503 2400
500 0.0628 2990
600 0.0754 3590
700 0.0880 4190
800 0.101 4790
900 0.113 5390
1000 0.126 5990
2000 0.251 1.20 × 104
3000 0.377 1.80 × 104
4000 0.503 2.40 × 104
5000 0.628 2.99 × 104
6000 0.754 3.59 × 104
7000 0.880 4.19 × 104
8000 1.01 4.79 × 104
9000 1.13 5.39 × 104
1.00 × 104 1.26 5.99 × 104
2.00 × 104 2.51 1.20 × 105
3.00 × 104 3.77 1.80 × 105
4.00 × 104 5.03 2.40 × 105
4.96 × 104 6.23 2.97 × 105
Steel I Beam: W10 × 77 (Wide Flange 10 inch tall × 77 lbf/ft)
L = 25.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
77.0 0.0236 720
80.0 0.0245 749
90.0 0.0276 842
100 0.0307 936
200 0.0614 1870
300 0.0921 2810
400 0.123 3740
500 0.153 4680
600 0.184 5610
700 0.215 6550
800 0.245 7490
900 0.276 8420
1000 0.307 9360
2000 0.614 1.87 × 104
3000 0.921 2.81 × 104
4000 1.23 3.74 × 104
5000 1.53 4.68 × 104
6000 1.84 5.61 × 104
7000 2.15 6.55 × 104
8000 2.45 7.49 × 104
9000 2.76 8.42 × 104
1.00 × 104 3.07 9.36 × 104
2.00 × 104 6.14 1.87 × 105
3.00 × 104 9.21 2.81 × 105
3.17 × 104 9.74 2.97 × 105
Steel I Beam: W10 × 77 (Wide Flange 10 inch tall × 77 lbf/ft)
L = 30.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
77.0 0.0490 1040
80.0 0.0509 1080
90.0 0.0573 1210
100 0.0636 1350
200 0.127 2690
300 0.191 4040
400 0.255 5390
500 0.318 6740
600 0.382 8080
700 0.445 9430
800 0.509 1.08 × 104
900 0.573 1.21 × 104
1000 0.636 1.35 × 104
2000 1.27 2.69 × 104
3000 1.91 4.04 × 104
4000 2.55 5.39 × 104
5000 3.18 6.74 × 104
6000 3.82 8.08 × 104
7000 4.45 9.43 × 104
8000 5.09 1.08 × 105
9000 5.73 1.21 × 105
1.00 × 104 6.36 1.35 × 105
1.67 × 104 10.6 2.24 × 105
Steel I Beam: W10 × 77 (Wide Flange 10 inch tall × 77 lbf/ft)
L = 40.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
77.0 0.155 1840
80.0 0.161 1920
90.0 0.181 2160
100 0.201 2400
200 0.402 4790
300 0.603 7190
400 0.804 9580
500 1.01 1.20 × 104
600 1.21 1.44 × 104
700 1.41 1.68 × 104
800 1.61 1.92 × 104
900 1.81 2.16 × 104
1000 2.01 2.40 × 104
2000 4.02 4.79 × 104
3000 6.03 7.19 × 104
4000 8.04 9.58 × 104
5000 10.1 1.20 × 105
5270 10.6 1.26 × 105
Steel I Beam: W10 × 77 (Wide Flange 10 inch tall × 77 lbf/ft)
L = 50.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
77.0 0.378 2880
80.0 0.393 2990
90.0 0.442 3370
100 0.491 3740
200 0.982 7490
300 1.47 1.12 × 104
400 1.96 1.50 × 104
500 2.45 1.87 × 104
600 2.95 2.25 × 104
700 3.44 2.62 × 104
800 3.93 2.99 × 104
900 4.42 3.37 × 104
1000 4.91 3.74 × 104
2000 9.82 7.49 × 104
2160 10.6 8.08 × 104
Steel I Beam: W10 × 77 (Wide Flange 10 inch tall × 77 lbf/ft)
L = 60.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
77.0 0.784 4150
80.0 0.814 4310
90.0 0.916 4850
100 1.02 5390
200 2.04 1.08 × 104
300 3.05 1.62 × 104
400 4.07 2.16 × 104
500 5.09 2.69 × 104
600 6.11 3.23 × 104
700 7.13 3.77 × 104
800 8.14 4.31 × 104
900 9.16 4.85 × 104
1000 10.2 5.39 × 104
1040 10.6 5.61 × 104
Steel I Beam: W10 × 77 (Wide Flange 10 inch tall × 77 lbf/ft)
L = 70.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
77.0 1.45 5650
80.0 1.51 5870
90.0 1.70 6600
100 1.89 7340
200 3.77 1.47 × 104
300 5.66 2.20 × 104
400 7.54 2.93 × 104
500 9.43 3.67 × 104
562 10.6 4.12 × 104
Steel I Beam: W10 × 77 (Wide Flange 10 inch tall × 77 lbf/ft)
L = 80.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
77.0 2.48 7380
80.0 2.57 7660
90.0 2.90 8620
100 3.22 9580
200 6.44 1.92 × 104
300 9.65 2.87 × 104
329 10.6 3.16 × 104
Steel I Beam: W10 × 77 (Wide Flange 10 inch tall × 77 lbf/ft)
L = 90.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
77.0 3.97 9340
80.0 4.12 9700
90.0 4.64 1.09 × 104
100 5.15 1.21 × 104
200 10.3 2.43 × 104
206 10.6 2.49 × 104
Steel I Beam: W10 × 77 (Wide Flange 10 inch tall × 77 lbf/ft)
L = 100 ft
P (lbf/ft) w_max (in) stress_max (psi)
77.0 6.05 1.15 × 104
80.0 6.28 1.20 × 104
90.0 7.07 1.35 × 104
100 7.86 1.50 × 104
135 10.6 2.02 × 104
Additional Information
Related Pages
FREE Publications
CNC Machining Design Guide

Optimize your designs, reduce machining time, and lower your costs.

Salary Expectation

8 things to know about the interview question "What's your salary expectation"?

STEM Career Outlook

Wages, employment opportunities, and growth projections for STEM jobs.

Selecting the Right 3D Printer

Discover how to choose the right 3D printer for your needs and the key performance attributes to consider.

more publications