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S Section Steel I Beam: S12 × 31.8
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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Three Equal Spans » S Section Steel I Beam » S12 × 31.8
S Section 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 = 218 in4) for the S12 × 31.8 S Section 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: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 3.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 4.56 × 10-6 9.45
40.0 5.73 × 10-6 11.9
50.0 7.17 × 10-6 14.9
60.0 8.60 × 10-6 17.8
70.0 1.00 × 10-5 20.8
80.0 1.15 × 10-5 23.8
90.0 1.29 × 10-5 26.8
100 1.43 × 10-5 29.7
200 2.87 × 10-5 59.4
300 4.30 × 10-5 89.2
400 5.73 × 10-5 119
500 7.17 × 10-5 149
600 8.60 × 10-5 178
700 1.00 × 10-4 208
800 1.15 × 10-4 238
900 1.29 × 10-4 268
1000 1.43 × 10-4 297
2000 2.87 × 10-4 594
3000 4.30 × 10-4 892
4000 5.73 × 10-4 1190
5000 7.17 × 10-4 1490
6000 8.60 × 10-4 1780
7000 0.00100 2080
8000 0.00115 2380
9000 0.00129 2680
1.00 × 104 0.00143 2970
2.00 × 104 0.00287 5940
3.00 × 104 0.00430 8920
4.00 × 104 0.00573 1.19 × 104
5.00 × 104 0.00717 1.49 × 104
6.00 × 104 0.00860 1.78 × 104
7.00 × 104 0.0100 2.08 × 104
8.00 × 104 0.0115 2.38 × 104
9.00 × 104 0.0129 2.68 × 104
1.00 × 105 0.0143 2.97 × 104
2.00 × 105 0.0287 5.94 × 104
3.00 × 105 0.0430 8.92 × 104
4.00 × 105 0.0573 1.19 × 105
5.00 × 105 0.0717 1.49 × 105
6.00 × 105 0.0860 1.78 × 105
7.00 × 105 0.100 2.08 × 105
8.00 × 105 0.115 2.38 × 105
9.00 × 105 0.129 2.68 × 105
9.99 × 105 0.143 2.97 × 105
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 5.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 3.52 × 10-5 26.3
40.0 4.42 × 10-5 33.0
50.0 5.53 × 10-5 41.3
60.0 6.64 × 10-5 49.5
70.0 7.74 × 10-5 57.8
80.0 8.85 × 10-5 66.1
90.0 9.95 × 10-5 74.3
100 1.11 × 10-4 82.6
200 2.21 × 10-4 165
300 3.32 × 10-4 248
400 4.42 × 10-4 330
500 5.53 × 10-4 413
600 6.64 × 10-4 495
700 7.74 × 10-4 578
800 8.85 × 10-4 661
900 9.95 × 10-4 743
1000 0.00111 826
2000 0.00221 1650
3000 0.00332 2480
4000 0.00442 3300
5000 0.00553 4130
6000 0.00664 4950
7000 0.00774 5780
8000 0.00885 6610
9000 0.00995 7430
1.00 × 104 0.0111 8260
2.00 × 104 0.0221 1.65 × 104
3.00 × 104 0.0332 2.48 × 104
4.00 × 104 0.0442 3.30 × 104
5.00 × 104 0.0553 4.13 × 104
6.00 × 104 0.0664 4.95 × 104
7.00 × 104 0.0774 5.78 × 104
8.00 × 104 0.0885 6.61 × 104
9.00 × 104 0.0995 7.43 × 104
1.00 × 105 0.111 8.26 × 104
2.00 × 105 0.221 1.65 × 105
3.00 × 105 0.332 2.48 × 105
3.60 × 105 0.398 2.97 × 105
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 10.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 5.63 × 10-4 105
40.0 7.08 × 10-4 132
50.0 8.85 × 10-4 165
60.0 0.00106 198
70.0 0.00124 231
80.0 0.00142 264
90.0 0.00159 297
100 0.00177 330
200 0.00354 661
300 0.00531 991
400 0.00708 1320
500 0.00885 1650
600 0.0106 1980
700 0.0124 2310
800 0.0142 2640
900 0.0159 2970
1000 0.0177 3300
2000 0.0354 6610
3000 0.0531 9910
4000 0.0708 1.32 × 104
5000 0.0885 1.65 × 104
6000 0.106 1.98 × 104
7000 0.124 2.31 × 104
8000 0.142 2.64 × 104
9000 0.159 2.97 × 104
1.00 × 104 0.177 3.30 × 104
2.00 × 104 0.354 6.61 × 104
3.00 × 104 0.531 9.91 × 104
4.00 × 104 0.708 1.32 × 105
5.00 × 104 0.885 1.65 × 105
6.00 × 104 1.06 1.98 × 105
7.00 × 104 1.24 2.31 × 105
8.00 × 104 1.42 2.64 × 105
8.99 × 104 1.59 2.97 × 105
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 15.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 0.00285 236
40.0 0.00358 297
50.0 0.00448 372
60.0 0.00538 446
70.0 0.00627 520
80.0 0.00717 594
90.0 0.00806 669
100 0.00896 743
200 0.0179 1490
300 0.0269 2230
400 0.0358 2970
500 0.0448 3720
600 0.0538 4460
700 0.0627 5200
800 0.0717 5940
900 0.0806 6690
1000 0.0896 7430
2000 0.179 1.49 × 104
3000 0.269 2.23 × 104
4000 0.358 2.97 × 104
5000 0.448 3.72 × 104
6000 0.538 4.46 × 104
7000 0.627 5.20 × 104
8000 0.717 5.94 × 104
9000 0.806 6.69 × 104
1.00 × 104 0.896 7.43 × 104
2.00 × 104 1.79 1.49 × 105
3.00 × 104 2.69 2.23 × 105
4.00 × 104 3.58 2.97 × 105
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 20.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 0.00900 420
40.0 0.0113 528
50.0 0.0142 661
60.0 0.0170 793
70.0 0.0198 925
80.0 0.0227 1060
90.0 0.0255 1190
100 0.0283 1320
200 0.0566 2640
300 0.0849 3960
400 0.113 5280
500 0.142 6610
600 0.170 7930
700 0.198 9250
800 0.227 1.06 × 104
900 0.255 1.19 × 104
1000 0.283 1.32 × 104
2000 0.566 2.64 × 104
3000 0.849 3.96 × 104
4000 1.13 5.28 × 104
5000 1.42 6.61 × 104
6000 1.70 7.93 × 104
7000 1.98 9.25 × 104
8000 2.27 1.06 × 105
9000 2.55 1.19 × 105
1.00 × 104 2.83 1.32 × 105
2.00 × 104 5.66 2.64 × 105
2.25 × 104 6.37 2.97 × 105
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 25.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 0.0220 656
40.0 0.0277 826
50.0 0.0346 1030
60.0 0.0415 1240
70.0 0.0484 1440
80.0 0.0553 1650
90.0 0.0622 1860
100 0.0691 2060
200 0.138 4130
300 0.207 6190
400 0.277 8260
500 0.346 1.03 × 104
600 0.415 1.24 × 104
700 0.484 1.44 × 104
800 0.553 1.65 × 104
900 0.622 1.86 × 104
1000 0.691 2.06 × 104
2000 1.38 4.13 × 104
3000 2.07 6.19 × 104
4000 2.77 8.26 × 104
5000 3.46 1.03 × 105
6000 4.15 1.24 × 105
7000 4.84 1.44 × 105
8000 5.53 1.65 × 105
9000 6.22 1.86 × 105
1.00 × 104 6.91 2.06 × 105
1.44 × 104 9.95 2.97 × 105
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 30.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 0.0456 945
40.0 0.0573 1190
50.0 0.0717 1490
60.0 0.0860 1780
70.0 0.100 2080
80.0 0.115 2380
90.0 0.129 2680
100 0.143 2970
200 0.287 5940
300 0.430 8920
400 0.573 1.19 × 104
500 0.717 1.49 × 104
600 0.860 1.78 × 104
700 1.00 2.08 × 104
800 1.15 2.38 × 104
900 1.29 2.68 × 104
1000 1.43 2.97 × 104
2000 2.87 5.94 × 104
3000 4.30 8.92 × 104
4000 5.73 1.19 × 105
5000 7.17 1.49 × 105
6000 8.60 1.78 × 105
7000 10.0 2.08 × 105
8000 11.5 2.38 × 105
8370 12.0 2.49 × 105
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 40.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 0.144 1680
40.0 0.181 2110
50.0 0.227 2640
60.0 0.272 3170
70.0 0.317 3700
80.0 0.362 4230
90.0 0.408 4760
100 0.453 5280
200 0.906 1.06 × 104
300 1.36 1.59 × 104
400 1.81 2.11 × 104
500 2.27 2.64 × 104
600 2.72 3.17 × 104
700 3.17 3.70 × 104
800 3.62 4.23 × 104
900 4.08 4.76 × 104
1000 4.53 5.28 × 104
2000 9.06 1.06 × 105
2650 12.0 1.40 × 105
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 50.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 0.352 2630
40.0 0.442 3300
50.0 0.553 4130
60.0 0.664 4950
70.0 0.774 5780
80.0 0.885 6610
90.0 0.995 7430
100 1.11 8260
200 2.21 1.65 × 104
300 3.32 2.48 × 104
400 4.42 3.30 × 104
500 5.53 4.13 × 104
600 6.64 4.95 × 104
700 7.74 5.78 × 104
800 8.85 6.61 × 104
900 9.95 7.43 × 104
1000 11.1 8.26 × 104
1080 12.0 8.96 × 104
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 60.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 0.729 3780
40.0 0.917 4760
50.0 1.15 5940
60.0 1.38 7130
70.0 1.61 8320
80.0 1.83 9510
90.0 2.06 1.07 × 104
100 2.29 1.19 × 104
200 4.59 2.38 × 104
300 6.88 3.57 × 104
400 9.17 4.76 × 104
500 11.5 5.94 × 104
523 12.0 6.22 × 104
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 70.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 1.35 5150
40.0 1.70 6470
50.0 2.12 8090
60.0 2.55 9710
70.0 2.97 1.13 × 104
80.0 3.40 1.29 × 104
90.0 3.82 1.46 × 104
100 4.25 1.62 × 104
200 8.50 3.24 × 104
282 12.0 4.57 × 104
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 80.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 2.31 6720
40.0 2.90 8460
50.0 3.62 1.06 × 104
60.0 4.35 1.27 × 104
70.0 5.07 1.48 × 104
80.0 5.80 1.69 × 104
90.0 6.52 1.90 × 104
100 7.25 2.11 × 104
166 12.0 3.50 × 104
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 90.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 3.69 8510
40.0 4.64 1.07 × 104
50.0 5.81 1.34 × 104
60.0 6.97 1.61 × 104
70.0 8.13 1.87 × 104
80.0 9.29 2.14 × 104
90.0 10.4 2.41 × 104
100 11.6 2.68 × 104
103 12.0 2.76 × 104
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 100 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 5.63 1.05 × 104
40.0 7.08 1.32 × 104
50.0 8.85 1.65 × 104
60.0 10.6 1.98 × 104
67.8 12.0 2.24 × 104
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