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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Three Equal Spans » S Section Steel I Beam » S12 × 40.8
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 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 = 272 in4) for the S12 × 40.8 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 × 40.8 (S12 inch tall × 40.8 lbf/ft) L = 3.00 ft (lbf/ft) (in) (psi) 40.8 4.69 × 10-6 9.72 50.0 5.74 × 10-6 11.9 60.0 6.89 × 10-6 14.3 70.0 8.04 × 10-6 16.7 80.0 9.19 × 10-6 19.1 90.0 1.03 × 10-5 21.4 100 1.15 × 10-5 23.8 200 2.30 × 10-5 47.6 300 3.45 × 10-5 71.5 400 4.60 × 10-5 95.3 500 5.74 × 10-5 119 600 6.89 × 10-5 143 700 8.04 × 10-5 167 800 9.19 × 10-5 191 900 1.03 × 10-4 214 1000 1.15 × 10-4 238 2000 2.30 × 10-4 476 3000 3.45 × 10-4 715 4000 4.60 × 10-4 953 5000 5.74 × 10-4 1190 6000 6.89 × 10-4 1430 7000 8.04 × 10-4 1670 8000 9.19 × 10-4 1910 9000 0.00103 2140 1.00 × 104 0.00115 2380 2.00 × 104 0.00230 4760 3.00 × 104 0.00345 7150 4.00 × 104 0.00460 9530 5.00 × 104 0.00574 1.19 × 104 6.00 × 104 0.00689 1.43 × 104 7.00 × 104 0.00804 1.67 × 104 8.00 × 104 0.00919 1.91 × 104 9.00 × 104 0.0103 2.14 × 104 1.00 × 105 0.0115 2.38 × 104 2.00 × 105 0.0230 4.76 × 104 3.00 × 105 0.0345 7.15 × 104 4.00 × 105 0.0460 9.53 × 104 5.00 × 105 0.0574 1.19 × 105 6.00 × 105 0.0689 1.43 × 105 7.00 × 105 0.0804 1.67 × 105 8.00 × 105 0.0919 1.91 × 105 9.00 × 105 0.103 2.14 × 105 1.00 × 106 0.115 2.38 × 105 1.25 × 106 0.143 2.97 × 105
 Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft) L = 5.00 ft (lbf/ft) (in) (psi) 40.8 3.62 × 10-5 27.0 50.0 4.43 × 10-5 33.1 60.0 5.32 × 10-5 39.7 70.0 6.21 × 10-5 46.3 80.0 7.09 × 10-5 52.9 90.0 7.98 × 10-5 59.6 100 8.86 × 10-5 66.2 200 1.77 × 10-4 132 300 2.66 × 10-4 199 400 3.55 × 10-4 265 500 4.43 × 10-4 331 600 5.32 × 10-4 397 700 6.21 × 10-4 463 800 7.09 × 10-4 529 900 7.98 × 10-4 596 1000 8.86 × 10-4 662 2000 0.00177 1320 3000 0.00266 1990 4000 0.00355 2650 5000 0.00443 3310 6000 0.00532 3970 7000 0.00621 4630 8000 0.00709 5290 9000 0.00798 5960 1.00 × 104 0.00886 6620 2.00 × 104 0.0177 1.32 × 104 3.00 × 104 0.0266 1.99 × 104 4.00 × 104 0.0355 2.65 × 104 5.00 × 104 0.0443 3.31 × 104 6.00 × 104 0.0532 3.97 × 104 7.00 × 104 0.0621 4.63 × 104 8.00 × 104 0.0709 5.29 × 104 9.00 × 104 0.0798 5.96 × 104 1.00 × 105 0.0886 6.62 × 104 2.00 × 105 0.177 1.32 × 105 3.00 × 105 0.266 1.99 × 105 4.00 × 105 0.355 2.65 × 105 4.49 × 105 0.398 2.97 × 105
 Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft) L = 10.0 ft (lbf/ft) (in) (psi) 40.8 5.79 × 10-4 108 50.0 7.09 × 10-4 132 60.0 8.51 × 10-4 159 70.0 9.93 × 10-4 185 80.0 0.00113 212 90.0 0.00128 238 100 0.00142 265 200 0.00284 529 300 0.00426 794 400 0.00567 1060 500 0.00709 1320 600 0.00851 1590 700 0.00993 1850 800 0.0113 2120 900 0.0128 2380 1000 0.0142 2650 2000 0.0284 5290 3000 0.0426 7940 4000 0.0567 1.06 × 104 5000 0.0709 1.32 × 104 6000 0.0851 1.59 × 104 7000 0.0993 1.85 × 104 8000 0.113 2.12 × 104 9000 0.128 2.38 × 104 1.00 × 104 0.142 2.65 × 104 2.00 × 104 0.284 5.29 × 104 3.00 × 104 0.426 7.94 × 104 4.00 × 104 0.567 1.06 × 105 5.00 × 104 0.709 1.32 × 105 6.00 × 104 0.851 1.59 × 105 7.00 × 104 0.993 1.85 × 105 8.00 × 104 1.13 2.12 × 105 9.00 × 104 1.28 2.38 × 105 1.00 × 105 1.42 2.65 × 105 1.12 × 105 1.59 2.97 × 105
 Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft) L = 15.0 ft (lbf/ft) (in) (psi) 40.8 0.00293 243 50.0 0.00359 298 60.0 0.00431 357 70.0 0.00503 417 80.0 0.00574 476 90.0 0.00646 536 100 0.00718 596 200 0.0144 1190 300 0.0215 1790 400 0.0287 2380 500 0.0359 2980 600 0.0431 3570 700 0.0503 4170 800 0.0574 4760 900 0.0646 5360 1000 0.0718 5960 2000 0.144 1.19 × 104 3000 0.215 1.79 × 104 4000 0.287 2.38 × 104 5000 0.359 2.98 × 104 6000 0.431 3.57 × 104 7000 0.503 4.17 × 104 8000 0.574 4.76 × 104 9000 0.646 5.36 × 104 1.00 × 104 0.718 5.96 × 104 2.00 × 104 1.44 1.19 × 105 3.00 × 104 2.15 1.79 × 105 4.00 × 104 2.87 2.38 × 105 4.99 × 104 3.58 2.97 × 105
 Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft) L = 20.0 ft (lbf/ft) (in) (psi) 40.8 0.00926 432 50.0 0.0113 529 60.0 0.0136 635 70.0 0.0159 741 80.0 0.0182 847 90.0 0.0204 953 100 0.0227 1060 200 0.0454 2120 300 0.0681 3180 400 0.0908 4240 500 0.113 5290 600 0.136 6350 700 0.159 7410 800 0.182 8470 900 0.204 9530 1000 0.227 1.06 × 104 2000 0.454 2.12 × 104 3000 0.681 3.18 × 104 4000 0.908 4.24 × 104 5000 1.13 5.29 × 104 6000 1.36 6.35 × 104 7000 1.59 7.41 × 104 8000 1.82 8.47 × 104 9000 2.04 9.53 × 104 1.00 × 104 2.27 1.06 × 105 2.00 × 104 4.54 2.12 × 105 2.81 × 104 6.37 2.97 × 105
 Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft) L = 25.0 ft (lbf/ft) (in) (psi) 40.8 0.0226 675 50.0 0.0277 827 60.0 0.0332 993 70.0 0.0388 1160 80.0 0.0443 1320 90.0 0.0499 1490 100 0.0554 1650 200 0.111 3310 300 0.166 4960 400 0.222 6620 500 0.277 8270 600 0.332 9930 700 0.388 1.16 × 104 800 0.443 1.32 × 104 900 0.499 1.49 × 104 1000 0.554 1.65 × 104 2000 1.11 3.31 × 104 3000 1.66 4.96 × 104 4000 2.22 6.62 × 104 5000 2.77 8.27 × 104 6000 3.32 9.93 × 104 7000 3.88 1.16 × 105 8000 4.43 1.32 × 105 9000 4.99 1.49 × 105 1.00 × 104 5.54 1.65 × 105 1.80 × 104 9.95 2.97 × 105
 Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft) L = 30.0 ft (lbf/ft) (in) (psi) 40.8 0.0469 972 50.0 0.0574 1190 60.0 0.0689 1430 70.0 0.0804 1670 80.0 0.0919 1910 90.0 0.103 2140 100 0.115 2380 200 0.230 4760 300 0.345 7150 400 0.460 9530 500 0.574 1.19 × 104 600 0.689 1.43 × 104 700 0.804 1.67 × 104 800 0.919 1.91 × 104 900 1.03 2.14 × 104 1000 1.15 2.38 × 104 2000 2.30 4.76 × 104 3000 3.45 7.15 × 104 4000 4.60 9.53 × 104 5000 5.74 1.19 × 105 6000 6.89 1.43 × 105 7000 8.04 1.67 × 105 8000 9.19 1.91 × 105 9000 10.3 2.14 × 105 1.00 × 104 11.5 2.38 × 105 1.25 × 104 14.3 2.97 × 105
 Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft) L = 40.0 ft (lbf/ft) (in) (psi) 40.8 0.148 1730 50.0 0.182 2120 60.0 0.218 2540 70.0 0.254 2960 80.0 0.290 3390 90.0 0.327 3810 100 0.363 4240 200 0.726 8470 300 1.09 1.27 × 104 400 1.45 1.69 × 104 500 1.82 2.12 × 104 600 2.18 2.54 × 104 700 2.54 2.96 × 104 800 2.90 3.39 × 104 900 3.27 3.81 × 104 1000 3.63 4.24 × 104 2000 7.26 8.47 × 104 3000 10.9 1.27 × 105 3300 12.0 1.40 × 105
 Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft) L = 50.0 ft (lbf/ft) (in) (psi) 40.8 0.362 2700 50.0 0.443 3310 60.0 0.532 3970 70.0 0.621 4630 80.0 0.709 5290 90.0 0.798 5960 100 0.886 6620 200 1.77 1.32 × 104 300 2.66 1.99 × 104 400 3.55 2.65 × 104 500 4.43 3.31 × 104 600 5.32 3.97 × 104 700 6.21 4.63 × 104 800 7.09 5.29 × 104 900 7.98 5.96 × 104 1000 8.86 6.62 × 104 1350 12.0 8.96 × 104
 Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft) L = 60.0 ft (lbf/ft) (in) (psi) 40.8 0.750 3890 50.0 0.919 4760 60.0 1.10 5720 70.0 1.29 6670 80.0 1.47 7620 90.0 1.65 8580 100 1.84 9530 200 3.68 1.91 × 104 300 5.51 2.86 × 104 400 7.35 3.81 × 104 500 9.19 4.76 × 104 600 11.0 5.72 × 104 653 12.0 6.22 × 104
 Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft) L = 70.0 ft (lbf/ft) (in) (psi) 40.8 1.39 5290 50.0 1.70 6490 60.0 2.04 7780 70.0 2.38 9080 80.0 2.72 1.04 × 104 90.0 3.06 1.17 × 104 100 3.41 1.30 × 104 200 6.81 2.59 × 104 300 10.2 3.89 × 104 352 12.0 4.57 × 104
 Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft) L = 80.0 ft (lbf/ft) (in) (psi) 40.8 2.37 6910 50.0 2.90 8470 60.0 3.49 1.02 × 104 70.0 4.07 1.19 × 104 80.0 4.65 1.36 × 104 90.0 5.23 1.52 × 104 100 5.81 1.69 × 104 200 11.6 3.39 × 104 207 12.0 3.50 × 104
 Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft) L = 90.0 ft (lbf/ft) (in) (psi) 40.8 3.80 8750 50.0 4.65 1.07 × 104 60.0 5.58 1.29 × 104 70.0 6.51 1.50 × 104 80.0 7.44 1.72 × 104 90.0 8.38 1.93 × 104 100 9.31 2.14 × 104 129 12.0 2.76 × 104
 Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft) L = 100 ft (lbf/ft) (in) (psi) 40.8 5.79 1.08 × 104 50.0 7.09 1.32 × 104 60.0 8.51 1.59 × 104 70.0 9.93 1.85 × 104 80.0 11.3 2.12 × 104 84.6 12.0 2.24 × 104