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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Three 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 three equal spans, we compute the displacement at the middle of the first and the third spans, and the maximum normal stress stress_max occuring at the second and third 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
  
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 4.03 × 10-6 8.32
50.0 5.04 × 10-6 10.4
60.0 6.05 × 10-6 12.5
70.0 7.06 × 10-6 14.6
80.0 8.06 × 10-6 16.6
90.0 9.07 × 10-6 18.7
100 1.01 × 10-5 20.8
200 2.02 × 10-5 41.6
300 3.02 × 10-5 62.4
400 4.03 × 10-5 83.2
500 5.04 × 10-5 104
600 6.05 × 10-5 125
700 7.06 × 10-5 146
800 8.06 × 10-5 166
900 9.07 × 10-5 187
1000 1.01 × 10-4 208
2000 2.02 × 10-4 416
3000 3.02 × 10-4 624
4000 4.03 × 10-4 832
5000 5.04 × 10-4 1040
6000 6.05 × 10-4 1250
7000 7.06 × 10-4 1460
8000 8.06 × 10-4 1660
9000 9.07 × 10-4 1870
1.00 × 104 0.00101 2080
2.00 × 104 0.00202 4160
3.00 × 104 0.00302 6240
4.00 × 104 0.00403 8320
5.00 × 104 0.00504 1.04 × 104
6.00 × 104 0.00605 1.25 × 104
7.00 × 104 0.00706 1.46 × 104
8.00 × 104 0.00806 1.66 × 104
9.00 × 104 0.00907 1.87 × 104
1.00 × 105 0.0101 2.08 × 104
2.00 × 105 0.0202 4.16 × 104
3.00 × 105 0.0302 6.24 × 104
4.00 × 105 0.0403 8.32 × 104
5.00 × 105 0.0504 1.04 × 105
6.00 × 105 0.0605 1.25 × 105
7.00 × 105 0.0706 1.46 × 105
8.00 × 105 0.0806 1.66 × 105
9.00 × 105 0.0907 1.87 × 105
1.00 × 106 0.101 2.08 × 105
1.43 × 106 0.144 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 3.11 × 10-5 23.1
50.0 3.89 × 10-5 28.9
60.0 4.67 × 10-5 34.7
70.0 5.44 × 10-5 40.4
80.0 6.22 × 10-5 46.2
90.0 7.00 × 10-5 52.0
100 7.78 × 10-5 57.8
200 1.56 × 10-4 116
300 2.33 × 10-4 173
400 3.11 × 10-4 231
500 3.89 × 10-4 289
600 4.67 × 10-4 347
700 5.44 × 10-4 404
800 6.22 × 10-4 462
900 7.00 × 10-4 520
1000 7.78 × 10-4 578
2000 0.00156 1160
3000 0.00233 1730
4000 0.00311 2310
5000 0.00389 2890
6000 0.00467 3470
7000 0.00544 4040
8000 0.00622 4620
9000 0.00700 5200
1.00 × 104 0.00778 5780
2.00 × 104 0.0156 1.16 × 104
3.00 × 104 0.0233 1.73 × 104
4.00 × 104 0.0311 2.31 × 104
5.00 × 104 0.0389 2.89 × 104
6.00 × 104 0.0467 3.47 × 104
7.00 × 104 0.0544 4.04 × 104
8.00 × 104 0.0622 4.62 × 104
9.00 × 104 0.0700 5.20 × 104
1.00 × 105 0.0778 5.78 × 104
2.00 × 105 0.156 1.16 × 105
3.00 × 105 0.233 1.73 × 105
4.00 × 105 0.311 2.31 × 105
5.00 × 105 0.389 2.89 × 105
5.14 × 105 0.400 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 4.98 × 10-4 92.4
50.0 6.22 × 10-4 116
60.0 7.47 × 10-4 139
70.0 8.71 × 10-4 162
80.0 9.96 × 10-4 185
90.0 0.00112 208
100 0.00124 231
200 0.00249 462
300 0.00373 693
400 0.00498 924
500 0.00622 1160
600 0.00747 1390
700 0.00871 1620
800 0.00996 1850
900 0.0112 2080
1000 0.0124 2310
2000 0.0249 4620
3000 0.0373 6930
4000 0.0498 9240
5000 0.0622 1.16 × 104
6000 0.0747 1.39 × 104
7000 0.0871 1.62 × 104
8000 0.0996 1.85 × 104
9000 0.112 2.08 × 104
1.00 × 104 0.124 2.31 × 104
2.00 × 104 0.249 4.62 × 104
3.00 × 104 0.373 6.93 × 104
4.00 × 104 0.498 9.24 × 104
5.00 × 104 0.622 1.16 × 105
6.00 × 104 0.747 1.39 × 105
7.00 × 104 0.871 1.62 × 105
8.00 × 104 0.996 1.85 × 105
9.00 × 104 1.12 2.08 × 105
1.00 × 105 1.24 2.31 × 105
1.29 × 105 1.60 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 0.00252 208
50.0 0.00315 260
60.0 0.00378 312
70.0 0.00441 364
80.0 0.00504 416
90.0 0.00567 468
100 0.00630 520
200 0.0126 1040
300 0.0189 1560
400 0.0252 2080
500 0.0315 2600
600 0.0378 3120
700 0.0441 3640
800 0.0504 4160
900 0.0567 4680
1000 0.0630 5200
2000 0.126 1.04 × 104
3000 0.189 1.56 × 104
4000 0.252 2.08 × 104
5000 0.315 2.60 × 104
6000 0.378 3.12 × 104
7000 0.441 3.64 × 104
8000 0.504 4.16 × 104
9000 0.567 4.68 × 104
1.00 × 104 0.630 5.20 × 104
2.00 × 104 1.26 1.04 × 105
3.00 × 104 1.89 1.56 × 105
4.00 × 104 2.52 2.08 × 105
5.00 × 104 3.15 2.60 × 105
5.71 × 104 3.60 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 0.00796 370
50.0 0.00996 462
60.0 0.0119 555
70.0 0.0139 647
80.0 0.0159 740
90.0 0.0179 832
100 0.0199 924
200 0.0398 1850
300 0.0597 2770
400 0.0796 3700
500 0.0996 4620
600 0.119 5550
700 0.139 6470
800 0.159 7400
900 0.179 8320
1000 0.199 9240
2000 0.398 1.85 × 104
3000 0.597 2.77 × 104
4000 0.796 3.70 × 104
5000 0.996 4.62 × 104
6000 1.19 5.55 × 104
7000 1.39 6.47 × 104
8000 1.59 7.40 × 104
9000 1.79 8.32 × 104
1.00 × 104 1.99 9.24 × 104
2.00 × 104 3.98 1.85 × 105
3.00 × 104 5.97 2.77 × 105
3.21 × 104 6.40 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 0.0194 578
50.0 0.0243 722
60.0 0.0292 867
70.0 0.0340 1010
80.0 0.0389 1160
90.0 0.0438 1300
100 0.0486 1440
200 0.0972 2890
300 0.146 4330
400 0.194 5780
500 0.243 7220
600 0.292 8670
700 0.340 1.01 × 104
800 0.389 1.16 × 104
900 0.438 1.30 × 104
1000 0.486 1.44 × 104
2000 0.972 2.89 × 104
3000 1.46 4.33 × 104
4000 1.94 5.78 × 104
5000 2.43 7.22 × 104
6000 2.92 8.67 × 104
7000 3.40 1.01 × 105
8000 3.89 1.16 × 105
9000 4.38 1.30 × 105
1.00 × 104 4.86 1.44 × 105
2.00 × 104 9.72 2.89 × 105
2.06 × 104 10.0 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 0.0403 832
50.0 0.0504 1040
60.0 0.0605 1250
70.0 0.0706 1460
80.0 0.0806 1660
90.0 0.0907 1870
100 0.101 2080
200 0.202 4160
300 0.302 6240
400 0.403 8320
500 0.504 1.04 × 104
600 0.605 1.25 × 104
700 0.706 1.46 × 104
800 0.806 1.66 × 104
900 0.907 1.87 × 104
1000 1.01 2.08 × 104
2000 2.02 4.16 × 104
3000 3.02 6.24 × 104
4000 4.03 8.32 × 104
5000 5.04 1.04 × 105
6000 6.05 1.25 × 105
7000 7.06 1.46 × 105
8000 8.06 1.66 × 105
9000 9.07 1.87 × 105
1.00 × 104 10.1 2.08 × 105
1.43 × 104 14.4 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 0.127 1480
50.0 0.159 1850
60.0 0.191 2220
70.0 0.223 2590
80.0 0.255 2960
90.0 0.287 3330
100 0.319 3700
200 0.637 7400
300 0.956 1.11 × 104
400 1.27 1.48 × 104
500 1.59 1.85 × 104
600 1.91 2.22 × 104
700 2.23 2.59 × 104
800 2.55 2.96 × 104
900 2.87 3.33 × 104
1000 3.19 3.70 × 104
2000 6.37 7.40 × 104
3000 9.56 1.11 × 105
3750 11.9 1.39 × 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 0.311 2310
50.0 0.389 2890
60.0 0.467 3470
70.0 0.544 4040
80.0 0.622 4620
90.0 0.700 5200
100 0.778 5780
200 1.56 1.16 × 104
300 2.33 1.73 × 104
400 3.11 2.31 × 104
500 3.89 2.89 × 104
600 4.67 3.47 × 104
700 5.44 4.04 × 104
800 6.22 4.62 × 104
900 7.00 5.20 × 104
1000 7.78 5.78 × 104
1540 11.9 8.87 × 104
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 0.645 3330
50.0 0.806 4160
60.0 0.968 4990
70.0 1.13 5820
80.0 1.29 6660
90.0 1.45 7490
100 1.61 8320
200 3.23 1.66 × 104
300 4.84 2.50 × 104
400 6.45 3.33 × 104
500 8.06 4.16 × 104
600 9.68 4.99 × 104
700 11.3 5.82 × 104
740 11.9 6.16 × 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 1.20 4530
50.0 1.49 5660
60.0 1.79 6790
70.0 2.09 7930
80.0 2.39 9060
90.0 2.69 1.02 × 104
100 2.99 1.13 × 104
200 5.98 2.26 × 104
300 8.96 3.40 × 104
400 11.9 4.52 × 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 2.04 5920
50.0 2.55 7400
60.0 3.06 8870
70.0 3.57 1.04 × 104
80.0 4.08 1.18 × 104
90.0 4.59 1.33 × 104
100 5.10 1.48 × 104
200 10.2 2.96 × 104
234 11.9 3.46 × 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 3.27 7490
50.0 4.08 9360
60.0 4.90 1.12 × 104
70.0 5.72 1.31 × 104
80.0 6.53 1.50 × 104
90.0 7.35 1.68 × 104
100 8.17 1.87 × 104
146 11.9 2.74 × 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 4.98 9240
50.0 6.22 1.16 × 104
60.0 7.47 1.39 × 104
70.0 8.71 1.62 × 104
80.0 9.96 1.85 × 104
90.0 11.2 2.08 × 104
95.9 11.9 2.22 × 104
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