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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Four Equal Spans » Wide Flange Steel I Beam » W12 × 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 = 310 in4) for the W12 × 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
   
Steel I Beam: W12 × 40 (Wide Flange 12 inch tall × 40 lbf/ft)
L = 3.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 3.74 × 10-6 8.91
50.0 4.67 × 10-6 11.1
60.0 5.60 × 10-6 13.4
70.0 6.54 × 10-6 15.6
80.0 7.47 × 10-6 17.8
90.0 8.41 × 10-6 20.0
100 9.34 × 10-6 22.3
200 1.87 × 10-5 44.6
300 2.80 × 10-5 66.8
400 3.74 × 10-5 89.1
500 4.67 × 10-5 111
600 5.60 × 10-5 134
700 6.54 × 10-5 156
800 7.47 × 10-5 178
900 8.41 × 10-5 200
1000 9.34 × 10-5 223
2000 1.87 × 10-4 446
3000 2.80 × 10-4 668
4000 3.74 × 10-4 891
5000 4.67 × 10-4 1110
6000 5.60 × 10-4 1340
7000 6.54 × 10-4 1560
8000 7.47 × 10-4 1780
9000 8.41 × 10-4 2000
1.00 × 104 9.34 × 10-4 2230
2.00 × 104 0.00187 4460
3.00 × 104 0.00280 6680
4.00 × 104 0.00374 8910
5.00 × 104 0.00467 1.11 × 104
6.00 × 104 0.00560 1.34 × 104
7.00 × 104 0.00654 1.56 × 104
8.00 × 104 0.00747 1.78 × 104
9.00 × 104 0.00841 2.00 × 104
1.00 × 105 0.00934 2.23 × 104
2.00 × 105 0.0187 4.46 × 104
3.00 × 105 0.0280 6.68 × 104
4.00 × 105 0.0374 8.91 × 104
5.00 × 105 0.0467 1.11 × 105
6.00 × 105 0.0560 1.34 × 105
7.00 × 105 0.0654 1.56 × 105
8.00 × 105 0.0747 1.78 × 105
9.00 × 105 0.0841 2.00 × 105
1.00 × 106 0.0934 2.23 × 105
1.33 × 106 0.125 2.97 × 105
Steel I Beam: W12 × 40 (Wide Flange 12 inch tall × 40 lbf/ft)
L = 5.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 2.88 × 10-5 24.8
50.0 3.60 × 10-5 30.9
60.0 4.32 × 10-5 37.1
70.0 5.04 × 10-5 43.3
80.0 5.76 × 10-5 49.5
90.0 6.49 × 10-5 55.7
100 7.21 × 10-5 61.9
200 1.44 × 10-4 124
300 2.16 × 10-4 186
400 2.88 × 10-4 248
500 3.60 × 10-4 309
600 4.32 × 10-4 371
700 5.04 × 10-4 433
800 5.76 × 10-4 495
900 6.49 × 10-4 557
1000 7.21 × 10-4 619
2000 0.00144 1240
3000 0.00216 1860
4000 0.00288 2480
5000 0.00360 3090
6000 0.00432 3710
7000 0.00504 4330
8000 0.00576 4950
9000 0.00649 5570
1.00 × 104 0.00721 6190
2.00 × 104 0.0144 1.24 × 104
3.00 × 104 0.0216 1.86 × 104
4.00 × 104 0.0288 2.48 × 104
5.00 × 104 0.0360 3.09 × 104
6.00 × 104 0.0432 3.71 × 104
7.00 × 104 0.0504 4.33 × 104
8.00 × 104 0.0576 4.95 × 104
9.00 × 104 0.0649 5.57 × 104
1.00 × 105 0.0721 6.19 × 104
2.00 × 105 0.144 1.24 × 105
3.00 × 105 0.216 1.86 × 105
4.00 × 105 0.288 2.48 × 105
4.80 × 105 0.346 2.97 × 105
Steel I Beam: W12 × 40 (Wide Flange 12 inch tall × 40 lbf/ft)
L = 10.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 4.61 × 10-4 99.0
50.0 5.76 × 10-4 124
60.0 6.92 × 10-4 149
70.0 8.07 × 10-4 173
80.0 9.22 × 10-4 198
90.0 0.00104 223
100 0.00115 248
200 0.00231 495
300 0.00346 743
400 0.00461 990
500 0.00576 1240
600 0.00692 1490
700 0.00807 1730
800 0.00922 1980
900 0.0104 2230
1000 0.0115 2480
2000 0.0231 4950
3000 0.0346 7430
4000 0.0461 9900
5000 0.0576 1.24 × 104
6000 0.0692 1.49 × 104
7000 0.0807 1.73 × 104
8000 0.0922 1.98 × 104
9000 0.104 2.23 × 104
1.00 × 104 0.115 2.48 × 104
2.00 × 104 0.231 4.95 × 104
3.00 × 104 0.346 7.43 × 104
4.00 × 104 0.461 9.90 × 104
5.00 × 104 0.576 1.24 × 105
6.00 × 104 0.692 1.49 × 105
7.00 × 104 0.807 1.73 × 105
8.00 × 104 0.922 1.98 × 105
9.00 × 104 1.04 2.23 × 105
1.00 × 105 1.15 2.48 × 105
1.20 × 105 1.38 2.97 × 105
Steel I Beam: W12 × 40 (Wide Flange 12 inch tall × 40 lbf/ft)
L = 15.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 0.00233 223
50.0 0.00292 278
60.0 0.00350 334
70.0 0.00409 390
80.0 0.00467 446
90.0 0.00525 501
100 0.00584 557
200 0.0117 1110
300 0.0175 1670
400 0.0233 2230
500 0.0292 2780
600 0.0350 3340
700 0.0409 3900
800 0.0467 4460
900 0.0525 5010
1000 0.0584 5570
2000 0.117 1.11 × 104
3000 0.175 1.67 × 104
4000 0.233 2.23 × 104
5000 0.292 2.78 × 104
6000 0.350 3.34 × 104
7000 0.409 3.90 × 104
8000 0.467 4.46 × 104
9000 0.525 5.01 × 104
1.00 × 104 0.584 5.57 × 104
2.00 × 104 1.17 1.11 × 105
3.00 × 104 1.75 1.67 × 105
4.00 × 104 2.33 2.23 × 105
5.00 × 104 2.92 2.78 × 105
5.33 × 104 3.11 2.97 × 105
Steel I Beam: W12 × 40 (Wide Flange 12 inch tall × 40 lbf/ft)
L = 20.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 0.00738 396
50.0 0.00922 495
60.0 0.0111 594
70.0 0.0129 693
80.0 0.0148 792
90.0 0.0166 891
100 0.0184 990
200 0.0369 1980
300 0.0553 2970
400 0.0738 3960
500 0.0922 4950
600 0.111 5940
700 0.129 6930
800 0.148 7920
900 0.166 8910
1000 0.184 9900
2000 0.369 1.98 × 104
3000 0.553 2.97 × 104
4000 0.738 3.96 × 104
5000 0.922 4.95 × 104
6000 1.11 5.94 × 104
7000 1.29 6.93 × 104
8000 1.48 7.92 × 104
9000 1.66 8.91 × 104
1.00 × 104 1.84 9.90 × 104
2.00 × 104 3.69 1.98 × 105
3.00 × 104 5.53 2.97 × 105
3.00 × 104 5.53 2.97 × 105
Steel I Beam: W12 × 40 (Wide Flange 12 inch tall × 40 lbf/ft)
L = 25.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 0.0180 619
50.0 0.0225 773
60.0 0.0270 928
70.0 0.0315 1080
80.0 0.0360 1240
90.0 0.0405 1390
100 0.0450 1550
200 0.0901 3090
300 0.135 4640
400 0.180 6190
500 0.225 7730
600 0.270 9280
700 0.315 1.08 × 104
800 0.360 1.24 × 104
900 0.405 1.39 × 104
1000 0.450 1.55 × 104
2000 0.901 3.09 × 104
3000 1.35 4.64 × 104
4000 1.80 6.19 × 104
5000 2.25 7.73 × 104
6000 2.70 9.28 × 104
7000 3.15 1.08 × 105
8000 3.60 1.24 × 105
9000 4.05 1.39 × 105
1.00 × 104 4.50 1.55 × 105
1.92 × 104 8.65 2.97 × 105
Steel I Beam: W12 × 40 (Wide Flange 12 inch tall × 40 lbf/ft)
L = 30.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 0.0374 891
50.0 0.0467 1110
60.0 0.0560 1340
70.0 0.0654 1560
80.0 0.0747 1780
90.0 0.0841 2000
100 0.0934 2230
200 0.187 4460
300 0.280 6680
400 0.374 8910
500 0.467 1.11 × 104
600 0.560 1.34 × 104
700 0.654 1.56 × 104
800 0.747 1.78 × 104
900 0.841 2.00 × 104
1000 0.934 2.23 × 104
2000 1.87 4.46 × 104
3000 2.80 6.68 × 104
4000 3.74 8.91 × 104
5000 4.67 1.11 × 105
6000 5.60 1.34 × 105
7000 6.54 1.56 × 105
8000 7.47 1.78 × 105
9000 8.41 2.00 × 105
1.00 × 104 9.34 2.23 × 105
1.33 × 104 12.5 2.97 × 105
Steel I Beam: W12 × 40 (Wide Flange 12 inch tall × 40 lbf/ft)
L = 40.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 0.118 1580
50.0 0.148 1980
60.0 0.177 2380
70.0 0.207 2770
80.0 0.236 3170
90.0 0.266 3560
100 0.295 3960
200 0.590 7920
300 0.885 1.19 × 104
400 1.18 1.58 × 104
500 1.48 1.98 × 104
600 1.77 2.38 × 104
700 2.07 2.77 × 104
800 2.36 3.17 × 104
900 2.66 3.56 × 104
1000 2.95 3.96 × 104
2000 5.90 7.92 × 104
3000 8.85 1.19 × 105
4000 11.8 1.58 × 105
4050 11.9 1.60 × 105
Steel I Beam: W12 × 40 (Wide Flange 12 inch tall × 40 lbf/ft)
L = 50.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 0.288 2480
50.0 0.360 3090
60.0 0.432 3710
70.0 0.504 4330
80.0 0.576 4950
90.0 0.649 5570
100 0.721 6190
200 1.44 1.24 × 104
300 2.16 1.86 × 104
400 2.88 2.48 × 104
500 3.60 3.09 × 104
600 4.32 3.71 × 104
700 5.04 4.33 × 104
800 5.76 4.95 × 104
900 6.49 5.57 × 104
1000 7.21 6.19 × 104
1660 11.9 1.03 × 105
Steel I Beam: W12 × 40 (Wide Flange 12 inch tall × 40 lbf/ft)
L = 60.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 0.598 3560
50.0 0.747 4460
60.0 0.897 5350
70.0 1.05 6240
80.0 1.20 7130
90.0 1.34 8020
100 1.49 8910
200 2.99 1.78 × 104
300 4.48 2.67 × 104
400 5.98 3.56 × 104
500 7.47 4.46 × 104
600 8.97 5.35 × 104
700 10.5 6.24 × 104
799 11.9 7.12 × 104
Steel I Beam: W12 × 40 (Wide Flange 12 inch tall × 40 lbf/ft)
L = 70.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 1.11 4850
50.0 1.38 6060
60.0 1.66 7280
70.0 1.94 8490
80.0 2.21 9700
90.0 2.49 1.09 × 104
100 2.77 1.21 × 104
200 5.54 2.43 × 104
300 8.30 3.64 × 104
400 11.1 4.85 × 104
431 11.9 5.23 × 104
Steel I Beam: W12 × 40 (Wide Flange 12 inch tall × 40 lbf/ft)
L = 80.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 1.89 6340
50.0 2.36 7920
60.0 2.83 9500
70.0 3.31 1.11 × 104
80.0 3.78 1.27 × 104
90.0 4.25 1.43 × 104
100 4.72 1.58 × 104
200 9.45 3.17 × 104
253 11.9 4.00 × 104
Steel I Beam: W12 × 40 (Wide Flange 12 inch tall × 40 lbf/ft)
L = 90.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 3.03 8020
50.0 3.78 1.00 × 104
60.0 4.54 1.20 × 104
70.0 5.30 1.40 × 104
80.0 6.05 1.60 × 104
90.0 6.81 1.80 × 104
100 7.56 2.00 × 104
158 11.9 3.16 × 104
Steel I Beam: W12 × 40 (Wide Flange 12 inch tall × 40 lbf/ft)
L = 100 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 4.61 9900
50.0 5.76 1.24 × 104
60.0 6.92 1.49 × 104
70.0 8.07 1.73 × 104
80.0 9.22 1.98 × 104
90.0 10.4 2.23 × 104
100 11.5 2.48 × 104
104 11.9 2.56 × 104
Steel I Beam: W12 × 40 (Wide Flange 12 inch tall × 40 lbf/ft)
L = 125 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.0 11.3 1.55 × 104
42.4 11.9 1.64 × 104
Additional Information
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