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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 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 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.

 Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft) L = 3.00 ft (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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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