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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Four 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 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 = 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 4.22 × 10-6 10.1
40.0 5.31 × 10-6 12.7
50.0 6.64 × 10-6 15.9
60.0 7.97 × 10-6 19.1
70.0 9.30 × 10-6 22.3
80.0 1.06 × 10-5 25.5
90.0 1.20 × 10-5 28.7
100 1.33 × 10-5 31.8
200 2.66 × 10-5 63.7
300 3.98 × 10-5 95.5
400 5.31 × 10-5 127
500 6.64 × 10-5 159
600 7.97 × 10-5 191
700 9.30 × 10-5 223
800 1.06 × 10-4 255
900 1.20 × 10-4 287
1000 1.33 × 10-4 318
2000 2.66 × 10-4 637
3000 3.98 × 10-4 955
4000 5.31 × 10-4 1270
5000 6.64 × 10-4 1590
6000 7.97 × 10-4 1910
7000 9.30 × 10-4 2230
8000 0.00106 2550
9000 0.00120 2870
1.00 × 104 0.00133 3180
2.00 × 104 0.00266 6370
3.00 × 104 0.00398 9550
4.00 × 104 0.00531 1.27 × 104
5.00 × 104 0.00664 1.59 × 104
6.00 × 104 0.00797 1.91 × 104
7.00 × 104 0.00930 2.23 × 104
8.00 × 104 0.0106 2.55 × 104
9.00 × 104 0.0120 2.87 × 104
1.00 × 105 0.0133 3.18 × 104
2.00 × 105 0.0266 6.37 × 104
3.00 × 105 0.0398 9.55 × 104
4.00 × 105 0.0531 1.27 × 105
5.00 × 105 0.0664 1.59 × 105
6.00 × 105 0.0797 1.91 × 105
7.00 × 105 0.0930 2.23 × 105
8.00 × 105 0.106 2.55 × 105
9.00 × 105 0.120 2.87 × 105
9.33 × 105 0.124 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 3.26 × 10-5 28.1
40.0 4.10 × 10-5 35.4
50.0 5.12 × 10-5 44.2
60.0 6.15 × 10-5 53.1
70.0 7.17 × 10-5 61.9
80.0 8.20 × 10-5 70.7
90.0 9.22 × 10-5 79.6
100 1.02 × 10-4 88.4
200 2.05 × 10-4 177
300 3.07 × 10-4 265
400 4.10 × 10-4 354
500 5.12 × 10-4 442
600 6.15 × 10-4 531
700 7.17 × 10-4 619
800 8.20 × 10-4 707
900 9.22 × 10-4 796
1000 0.00102 884
2000 0.00205 1770
3000 0.00307 2650
4000 0.00410 3540
5000 0.00512 4420
6000 0.00615 5310
7000 0.00717 6190
8000 0.00820 7070
9000 0.00922 7960
1.00 × 104 0.0102 8840
2.00 × 104 0.0205 1.77 × 104
3.00 × 104 0.0307 2.65 × 104
4.00 × 104 0.0410 3.54 × 104
5.00 × 104 0.0512 4.42 × 104
6.00 × 104 0.0615 5.31 × 104
7.00 × 104 0.0717 6.19 × 104
8.00 × 104 0.0820 7.07 × 104
9.00 × 104 0.0922 7.96 × 104
1.00 × 105 0.102 8.84 × 104
2.00 × 105 0.205 1.77 × 105
3.00 × 105 0.307 2.65 × 105
3.36 × 105 0.344 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 5.21 × 10-4 112
40.0 6.56 × 10-4 141
50.0 8.20 × 10-4 177
60.0 9.84 × 10-4 212
70.0 0.00115 248
80.0 0.00131 283
90.0 0.00148 318
100 0.00164 354
200 0.00328 707
300 0.00492 1060
400 0.00656 1410
500 0.00820 1770
600 0.00984 2120
700 0.0115 2480
800 0.0131 2830
900 0.0148 3180
1000 0.0164 3540
2000 0.0328 7070
3000 0.0492 1.06 × 104
4000 0.0656 1.41 × 104
5000 0.0820 1.77 × 104
6000 0.0984 2.12 × 104
7000 0.115 2.48 × 104
8000 0.131 2.83 × 104
9000 0.148 3.18 × 104
1.00 × 104 0.164 3.54 × 104
2.00 × 104 0.328 7.07 × 104
3.00 × 104 0.492 1.06 × 105
4.00 × 104 0.656 1.41 × 105
5.00 × 104 0.820 1.77 × 105
6.00 × 104 0.984 2.12 × 105
7.00 × 104 1.15 2.48 × 105
8.00 × 104 1.31 2.83 × 105
8.40 × 104 1.38 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 0.00264 253
40.0 0.00332 318
50.0 0.00415 398
60.0 0.00498 478
70.0 0.00581 557
80.0 0.00664 637
90.0 0.00747 716
100 0.00830 796
200 0.0166 1590
300 0.0249 2390
400 0.0332 3180
500 0.0415 3980
600 0.0498 4780
700 0.0581 5570
800 0.0664 6370
900 0.0747 7160
1000 0.0830 7960
2000 0.166 1.59 × 104
3000 0.249 2.39 × 104
4000 0.332 3.18 × 104
5000 0.415 3.98 × 104
6000 0.498 4.78 × 104
7000 0.581 5.57 × 104
8000 0.664 6.37 × 104
9000 0.747 7.16 × 104
1.00 × 104 0.830 7.96 × 104
2.00 × 104 1.66 1.59 × 105
3.00 × 104 2.49 2.39 × 105
3.73 × 104 3.10 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 0.00834 450
40.0 0.0105 566
50.0 0.0131 707
60.0 0.0157 849
70.0 0.0184 990
80.0 0.0210 1130
90.0 0.0236 1270
100 0.0262 1410
200 0.0525 2830
300 0.0787 4240
400 0.105 5660
500 0.131 7070
600 0.157 8490
700 0.184 9900
800 0.210 1.13 × 104
900 0.236 1.27 × 104
1000 0.262 1.41 × 104
2000 0.525 2.83 × 104
3000 0.787 4.24 × 104
4000 1.05 5.66 × 104
5000 1.31 7.07 × 104
6000 1.57 8.49 × 104
7000 1.84 9.90 × 104
8000 2.10 1.13 × 105
9000 2.36 1.27 × 105
1.00 × 104 2.62 1.41 × 105
2.00 × 104 5.25 2.83 × 105
2.10 × 104 5.51 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 0.0204 703
40.0 0.0256 884
50.0 0.0320 1110
60.0 0.0384 1330
70.0 0.0448 1550
80.0 0.0512 1770
90.0 0.0576 1990
100 0.0640 2210
200 0.128 4420
300 0.192 6630
400 0.256 8840
500 0.320 1.11 × 104
600 0.384 1.33 × 104
700 0.448 1.55 × 104
800 0.512 1.77 × 104
900 0.576 1.99 × 104
1000 0.640 2.21 × 104
2000 1.28 4.42 × 104
3000 1.92 6.63 × 104
4000 2.56 8.84 × 104
5000 3.20 1.11 × 105
6000 3.84 1.33 × 105
7000 4.48 1.55 × 105
8000 5.12 1.77 × 105
9000 5.76 1.99 × 105
1.00 × 104 6.40 2.21 × 105
1.34 × 104 8.61 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 0.0422 1010
40.0 0.0531 1270
50.0 0.0664 1590
60.0 0.0797 1910
70.0 0.0930 2230
80.0 0.106 2550
90.0 0.120 2870
100 0.133 3180
200 0.266 6370
300 0.398 9550
400 0.531 1.27 × 104
500 0.664 1.59 × 104
600 0.797 1.91 × 104
700 0.930 2.23 × 104
800 1.06 2.55 × 104
900 1.20 2.87 × 104
1000 1.33 3.18 × 104
2000 2.66 6.37 × 104
3000 3.98 9.55 × 104
4000 5.31 1.27 × 105
5000 6.64 1.59 × 105
6000 7.97 1.91 × 105
7000 9.30 2.23 × 105
8000 10.6 2.55 × 105
9000 12.0 2.87 × 105
9330 12.4 2.97 × 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 0.133 1800
40.0 0.168 2260
50.0 0.210 2830
60.0 0.252 3400
70.0 0.294 3960
80.0 0.336 4530
90.0 0.378 5090
100 0.420 5660
200 0.839 1.13 × 104
300 1.26 1.70 × 104
400 1.68 2.26 × 104
500 2.10 2.83 × 104
600 2.52 3.40 × 104
700 2.94 3.96 × 104
800 3.36 4.53 × 104
900 3.78 5.09 × 104
1000 4.20 5.66 × 104
2000 8.39 1.13 × 105
2860 12.0 1.62 × 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 0.326 2810
40.0 0.410 3540
50.0 0.512 4420
60.0 0.615 5310
70.0 0.717 6190
80.0 0.820 7070
90.0 0.922 7960
100 1.02 8840
200 2.05 1.77 × 104
300 3.07 2.65 × 104
400 4.10 3.54 × 104
500 5.12 4.42 × 104
600 6.15 5.31 × 104
700 7.17 6.19 × 104
800 8.20 7.07 × 104
900 9.22 7.96 × 104
1000 10.2 8.84 × 104
1170 12.0 1.04 × 105
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 0.676 4050
40.0 0.850 5090
50.0 1.06 6370
60.0 1.27 7640
70.0 1.49 8910
80.0 1.70 1.02 × 104
90.0 1.91 1.15 × 104
100 2.12 1.27 × 104
200 4.25 2.55 × 104
300 6.37 3.82 × 104
400 8.50 5.09 × 104
500 10.6 6.37 × 104
565 12.0 7.19 × 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 1.25 5510
40.0 1.57 6930
50.0 1.97 8670
60.0 2.36 1.04 × 104
70.0 2.76 1.21 × 104
80.0 3.15 1.39 × 104
90.0 3.54 1.56 × 104
100 3.94 1.73 × 104
200 7.87 3.47 × 104
300 11.8 5.20 × 104
305 12.0 5.28 × 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 2.14 7200
40.0 2.69 9060
50.0 3.36 1.13 × 104
60.0 4.03 1.36 × 104
70.0 4.70 1.58 × 104
80.0 5.37 1.81 × 104
90.0 6.04 2.04 × 104
100 6.72 2.26 × 104
179 12.0 4.05 × 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 3.42 9110
40.0 4.30 1.15 × 104
50.0 5.38 1.43 × 104
60.0 6.45 1.72 × 104
70.0 7.53 2.01 × 104
80.0 8.61 2.29 × 104
90.0 9.68 2.58 × 104
100 10.8 2.87 × 104
112 12.0 3.20 × 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 5.21 1.12 × 104
40.0 6.56 1.41 × 104
50.0 8.20 1.77 × 104
60.0 9.84 2.12 × 104
70.0 11.5 2.48 × 104
73.2 12.0 2.59 × 104
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