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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Four Equal Spans » Wide Flange Steel I Beam » W16 × 40
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 = 518 in4) for the W16 × 40 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
L = 125 ft
L = 150 ft
   
Steel I Beam: W16 × 40 (Wide Flange 16 inch tall × 40 lbf/ft)
L = 3.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 2.24 × 10-6 7.15
50.0 2.79 × 10-6 8.94
60.0 3.35 × 10-6 10.7
70.0 3.91 × 10-6 12.5
80.0 4.47 × 10-6 14.3
90.0 5.03 × 10-6 16.1
100 5.59 × 10-6 17.9
200 1.12 × 10-5 35.7
300 1.68 × 10-5 53.6
400 2.24 × 10-5 71.5
500 2.79 × 10-5 89.4
600 3.35 × 10-5 107
700 3.91 × 10-5 125
800 4.47 × 10-5 143
900 5.03 × 10-5 161
1000 5.59 × 10-5 179
2000 1.12 × 10-4 357
3000 1.68 × 10-4 536
4000 2.24 × 10-4 715
5000 2.79 × 10-4 894
6000 3.35 × 10-4 1070
7000 3.91 × 10-4 1250
8000 4.47 × 10-4 1430
9000 5.03 × 10-4 1610
1.00 × 104 5.59 × 10-4 1790
2.00 × 104 0.00112 3570
3.00 × 104 0.00168 5360
4.00 × 104 0.00224 7150
5.00 × 104 0.00279 8940
6.00 × 104 0.00335 1.07 × 104
7.00 × 104 0.00391 1.25 × 104
8.00 × 104 0.00447 1.43 × 104
9.00 × 104 0.00503 1.61 × 104
1.00 × 105 0.00559 1.79 × 104
2.00 × 105 0.0112 3.57 × 104
3.00 × 105 0.0168 5.36 × 104
4.00 × 105 0.0224 7.15 × 104
5.00 × 105 0.0279 8.94 × 104
6.00 × 105 0.0335 1.07 × 105
7.00 × 105 0.0391 1.25 × 105
8.00 × 105 0.0447 1.43 × 105
9.00 × 105 0.0503 1.61 × 105
1.00 × 106 0.0559 1.79 × 105
1.66 × 106 0.0929 2.97 × 105
Steel I Beam: W16 × 40 (Wide Flange 16 inch tall × 40 lbf/ft)
L = 5.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 1.73 × 10-5 19.9
50.0 2.16 × 10-5 24.8
60.0 2.59 × 10-5 29.8
70.0 3.02 × 10-5 34.8
80.0 3.45 × 10-5 39.7
90.0 3.88 × 10-5 44.7
100 4.31 × 10-5 49.7
200 8.63 × 10-5 99.3
300 1.29 × 10-4 149
400 1.73 × 10-4 199
500 2.16 × 10-4 248
600 2.59 × 10-4 298
700 3.02 × 10-4 348
800 3.45 × 10-4 397
900 3.88 × 10-4 447
1000 4.31 × 10-4 497
2000 8.63 × 10-4 993
3000 0.00129 1490
4000 0.00173 1990
5000 0.00216 2480
6000 0.00259 2980
7000 0.00302 3480
8000 0.00345 3970
9000 0.00388 4470
1.00 × 104 0.00431 4970
2.00 × 104 0.00863 9930
3.00 × 104 0.0129 1.49 × 104
4.00 × 104 0.0173 1.99 × 104
5.00 × 104 0.0216 2.48 × 104
6.00 × 104 0.0259 2.98 × 104
7.00 × 104 0.0302 3.48 × 104
8.00 × 104 0.0345 3.97 × 104
9.00 × 104 0.0388 4.47 × 104
1.00 × 105 0.0431 4.97 × 104
2.00 × 105 0.0863 9.93 × 104
3.00 × 105 0.129 1.49 × 105
4.00 × 105 0.173 1.99 × 105
5.00 × 105 0.216 2.48 × 105
5.98 × 105 0.258 2.97 × 105
Steel I Beam: W16 × 40 (Wide Flange 16 inch tall × 40 lbf/ft)
L = 10.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 2.76 × 10-4 79.4
50.0 3.45 × 10-4 99.3
60.0 4.14 × 10-4 119
70.0 4.83 × 10-4 139
80.0 5.52 × 10-4 159
90.0 6.21 × 10-4 179
100 6.90 × 10-4 199
200 0.00138 397
300 0.00207 596
400 0.00276 794
500 0.00345 993
600 0.00414 1190
700 0.00483 1390
800 0.00552 1590
900 0.00621 1790
1000 0.00690 1990
2000 0.0138 3970
3000 0.0207 5960
4000 0.0276 7940
5000 0.0345 9930
6000 0.0414 1.19 × 104
7000 0.0483 1.39 × 104
8000 0.0552 1.59 × 104
9000 0.0621 1.79 × 104
1.00 × 104 0.0690 1.99 × 104
2.00 × 104 0.138 3.97 × 104
3.00 × 104 0.207 5.96 × 104
4.00 × 104 0.276 7.94 × 104
5.00 × 104 0.345 9.93 × 104
6.00 × 104 0.414 1.19 × 105
7.00 × 104 0.483 1.39 × 105
8.00 × 104 0.552 1.59 × 105
9.00 × 104 0.621 1.79 × 105
1.00 × 105 0.690 1.99 × 105
1.50 × 105 1.03 2.97 × 105
Steel I Beam: W16 × 40 (Wide Flange 16 inch tall × 40 lbf/ft)
L = 15.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 0.00140 179
50.0 0.00175 223
60.0 0.00210 268
70.0 0.00245 313
80.0 0.00279 357
90.0 0.00314 402
100 0.00349 447
200 0.00699 894
300 0.0105 1340
400 0.0140 1790
500 0.0175 2230
600 0.0210 2680
700 0.0245 3130
800 0.0279 3570
900 0.0314 4020
1000 0.0349 4470
2000 0.0699 8940
3000 0.105 1.34 × 104
4000 0.140 1.79 × 104
5000 0.175 2.23 × 104
6000 0.210 2.68 × 104
7000 0.245 3.13 × 104
8000 0.279 3.57 × 104
9000 0.314 4.02 × 104
1.00 × 104 0.349 4.47 × 104
2.00 × 104 0.699 8.94 × 104
3.00 × 104 1.05 1.34 × 105
4.00 × 104 1.40 1.79 × 105
5.00 × 104 1.75 2.23 × 105
6.00 × 104 2.10 2.68 × 105
6.65 × 104 2.32 2.97 × 105
Steel I Beam: W16 × 40 (Wide Flange 16 inch tall × 40 lbf/ft)
L = 20.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 0.00442 318
50.0 0.00552 397
60.0 0.00662 477
70.0 0.00773 556
80.0 0.00883 636
90.0 0.00994 715
100 0.0110 794
200 0.0221 1590
300 0.0331 2380
400 0.0442 3180
500 0.0552 3970
600 0.0662 4770
700 0.0773 5560
800 0.0883 6360
900 0.0994 7150
1000 0.110 7940
2000 0.221 1.59 × 104
3000 0.331 2.38 × 104
4000 0.442 3.18 × 104
5000 0.552 3.97 × 104
6000 0.662 4.77 × 104
7000 0.773 5.56 × 104
8000 0.883 6.36 × 104
9000 0.994 7.15 × 104
1.00 × 104 1.10 7.94 × 104
2.00 × 104 2.21 1.59 × 105
3.00 × 104 3.31 2.38 × 105
3.74 × 104 4.13 2.97 × 105
Steel I Beam: W16 × 40 (Wide Flange 16 inch tall × 40 lbf/ft)
L = 25.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 0.0108 497
50.0 0.0135 621
60.0 0.0162 745
70.0 0.0189 869
80.0 0.0216 993
90.0 0.0243 1120
100 0.0270 1240
200 0.0539 2480
300 0.0809 3720
400 0.108 4970
500 0.135 6210
600 0.162 7450
700 0.189 8690
800 0.216 9930
900 0.243 1.12 × 104
1000 0.270 1.24 × 104
2000 0.539 2.48 × 104
3000 0.809 3.72 × 104
4000 1.08 4.97 × 104
5000 1.35 6.21 × 104
6000 1.62 7.45 × 104
7000 1.89 8.69 × 104
8000 2.16 9.93 × 104
9000 2.43 1.12 × 105
1.00 × 104 2.70 1.24 × 105
2.00 × 104 5.39 2.48 × 105
2.39 × 104 6.45 2.97 × 105
Steel I Beam: W16 × 40 (Wide Flange 16 inch tall × 40 lbf/ft)
L = 30.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 0.0224 715
50.0 0.0279 894
60.0 0.0335 1070
70.0 0.0391 1250
80.0 0.0447 1430
90.0 0.0503 1610
100 0.0559 1790
200 0.112 3570
300 0.168 5360
400 0.224 7150
500 0.279 8940
600 0.335 1.07 × 104
700 0.391 1.25 × 104
800 0.447 1.43 × 104
900 0.503 1.61 × 104
1000 0.559 1.79 × 104
2000 1.12 3.57 × 104
3000 1.68 5.36 × 104
4000 2.24 7.15 × 104
5000 2.79 8.94 × 104
6000 3.35 1.07 × 105
7000 3.91 1.25 × 105
8000 4.47 1.43 × 105
9000 5.03 1.61 × 105
1.00 × 104 5.59 1.79 × 105
1.66 × 104 9.29 2.97 × 105
Steel I Beam: W16 × 40 (Wide Flange 16 inch tall × 40 lbf/ft)
L = 40.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 0.0707 1270
50.0 0.0883 1590
60.0 0.106 1910
70.0 0.124 2220
80.0 0.141 2540
90.0 0.159 2860
100 0.177 3180
200 0.353 6360
300 0.530 9530
400 0.707 1.27 × 104
500 0.883 1.59 × 104
600 1.06 1.91 × 104
700 1.24 2.22 × 104
800 1.41 2.54 × 104
900 1.59 2.86 × 104
1000 1.77 3.18 × 104
2000 3.53 6.36 × 104
3000 5.30 9.53 × 104
4000 7.07 1.27 × 105
5000 8.83 1.59 × 105
6000 10.6 1.91 × 105
7000 12.4 2.22 × 105
8000 14.1 2.54 × 105
9000 15.9 2.86 × 105
9350 16.5 2.97 × 105
Steel I Beam: W16 × 40 (Wide Flange 16 inch tall × 40 lbf/ft)
L = 50.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 0.173 1990
50.0 0.216 2480
60.0 0.259 2980
70.0 0.302 3480
80.0 0.345 3970
90.0 0.388 4470
100 0.431 4970
200 0.863 9930
300 1.29 1.49 × 104
400 1.73 1.99 × 104
500 2.16 2.48 × 104
600 2.59 2.98 × 104
700 3.02 3.48 × 104
800 3.45 3.97 × 104
900 3.88 4.47 × 104
1000 4.31 4.97 × 104
2000 8.63 9.93 × 104
3000 12.9 1.49 × 105
3710 16.0 1.84 × 105
Steel I Beam: W16 × 40 (Wide Flange 16 inch tall × 40 lbf/ft)
L = 60.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 0.358 2860
50.0 0.447 3570
60.0 0.537 4290
70.0 0.626 5000
80.0 0.715 5720
90.0 0.805 6430
100 0.894 7150
200 1.79 1.43 × 104
300 2.68 2.14 × 104
400 3.58 2.86 × 104
500 4.47 3.57 × 104
600 5.37 4.29 × 104
700 6.26 5.00 × 104
800 7.15 5.72 × 104
900 8.05 6.43 × 104
1000 8.94 7.15 × 104
1790 16.0 1.28 × 105
Steel I Beam: W16 × 40 (Wide Flange 16 inch tall × 40 lbf/ft)
L = 70.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 0.663 3890
50.0 0.828 4870
60.0 0.994 5840
70.0 1.16 6810
80.0 1.33 7790
90.0 1.49 8760
100 1.66 9730
200 3.31 1.95 × 104
300 4.97 2.92 × 104
400 6.63 3.89 × 104
500 8.28 4.87 × 104
600 9.94 5.84 × 104
700 11.6 6.81 × 104
800 13.3 7.79 × 104
900 14.9 8.76 × 104
966 16.0 9.40 × 104
Steel I Beam: W16 × 40 (Wide Flange 16 inch tall × 40 lbf/ft)
L = 80.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 1.13 5080
50.0 1.41 6360
60.0 1.70 7630
70.0 1.98 8900
80.0 2.26 1.02 × 104
90.0 2.54 1.14 × 104
100 2.83 1.27 × 104
200 5.65 2.54 × 104
300 8.48 3.81 × 104
400 11.3 5.08 × 104
500 14.1 6.36 × 104
566 16.0 7.20 × 104
Steel I Beam: W16 × 40 (Wide Flange 16 inch tall × 40 lbf/ft)
L = 90.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 1.81 6430
50.0 2.26 8040
60.0 2.72 9650
70.0 3.17 1.13 × 104
80.0 3.62 1.29 × 104
90.0 4.07 1.45 × 104
100 4.53 1.61 × 104
200 9.05 3.22 × 104
300 13.6 4.83 × 104
354 16.0 5.69 × 104
Steel I Beam: W16 × 40 (Wide Flange 16 inch tall × 40 lbf/ft)
L = 100 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 2.76 7940
50.0 3.45 9930
60.0 4.14 1.19 × 104
70.0 4.83 1.39 × 104
80.0 5.52 1.59 × 104
90.0 6.21 1.79 × 104
100 6.90 1.99 × 104
200 13.8 3.97 × 104
232 16.0 4.61 × 104
Steel I Beam: W16 × 40 (Wide Flange 16 inch tall × 40 lbf/ft)
L = 125 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 6.74 1.24 × 104
50.0 8.42 1.55 × 104
60.0 10.1 1.86 × 104
70.0 11.8 2.17 × 104
80.0 13.5 2.48 × 104
90.0 15.2 2.79 × 104
95.0 16.0 2.95 × 104
Steel I Beam: W16 × 40 (Wide Flange 16 inch tall × 40 lbf/ft)
L = 150 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 14.0 1.79 × 104
45.8 16.0 2.05 × 104
Additional Information
Related Pages
FREE Publications
Metal 3D Printing Design Guide

Direct Metal Laser Sintering (DMLS) 3D printing for parts with reduced cost and little waste.

STEM Career Outlook

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

Negotiate Your Salary

Learn the best principles to negotiate the salary you deserve!

CNC Machining Design Guide

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

more publications