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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Two 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 two equal spans, we compute the displacement at the middle of each span w_mid and the maximum normal stress stress_max occuring at the center support 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 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
L = 125 ft
   
Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft)
L = 3.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 3.59 × 10-6 12.1
50.0 4.40 × 10-6 14.9
60.0 5.28 × 10-6 17.9
70.0 6.16 × 10-6 20.8
80.0 7.04 × 10-6 23.8
90.0 7.92 × 10-6 26.8
100 8.80 × 10-6 29.8
200 1.76 × 10-5 59.6
300 2.64 × 10-5 89.3
400 3.52 × 10-5 119
500 4.40 × 10-5 149
600 5.28 × 10-5 179
700 6.16 × 10-5 208
800 7.04 × 10-5 238
900 7.92 × 10-5 268
1000 8.80 × 10-5 298
2000 1.76 × 10-4 596
3000 2.64 × 10-4 893
4000 3.52 × 10-4 1190
5000 4.40 × 10-4 1490
6000 5.28 × 10-4 1790
7000 6.16 × 10-4 2080
8000 7.04 × 10-4 2380
9000 7.92 × 10-4 2680
1.00 × 104 8.80 × 10-4 2980
2.00 × 104 0.00176 5960
3.00 × 104 0.00264 8930
4.00 × 104 0.00352 1.19 × 104
5.00 × 104 0.00440 1.49 × 104
6.00 × 104 0.00528 1.79 × 104
7.00 × 104 0.00616 2.08 × 104
8.00 × 104 0.00704 2.38 × 104
9.00 × 104 0.00792 2.68 × 104
1.00 × 105 0.00880 2.98 × 104
2.00 × 105 0.0176 5.96 × 104
3.00 × 105 0.0264 8.93 × 104
4.00 × 105 0.0352 1.19 × 105
5.00 × 105 0.0440 1.49 × 105
6.00 × 105 0.0528 1.79 × 105
7.00 × 105 0.0616 2.08 × 105
8.00 × 105 0.0704 2.38 × 105
9.00 × 105 0.0792 2.68 × 105
9.97 × 105 0.0878 2.97 × 105
Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft)
L = 5.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 2.77 × 10-5 33.8
50.0 3.39 × 10-5 41.4
60.0 4.07 × 10-5 49.6
70.0 4.75 × 10-5 57.9
80.0 5.43 × 10-5 66.2
90.0 6.11 × 10-5 74.4
100 6.79 × 10-5 82.7
200 1.36 × 10-4 165
300 2.04 × 10-4 248
400 2.72 × 10-4 331
500 3.39 × 10-4 414
600 4.07 × 10-4 496
700 4.75 × 10-4 579
800 5.43 × 10-4 662
900 6.11 × 10-4 744
1000 6.79 × 10-4 827
2000 0.00136 1650
3000 0.00204 2480
4000 0.00272 3310
5000 0.00339 4140
6000 0.00407 4960
7000 0.00475 5790
8000 0.00543 6620
9000 0.00611 7440
1.00 × 104 0.00679 8270
2.00 × 104 0.0136 1.65 × 104
3.00 × 104 0.0204 2.48 × 104
4.00 × 104 0.0272 3.31 × 104
5.00 × 104 0.0339 4.14 × 104
6.00 × 104 0.0407 4.96 × 104
7.00 × 104 0.0475 5.79 × 104
8.00 × 104 0.0543 6.62 × 104
9.00 × 104 0.0611 7.44 × 104
1.00 × 105 0.0679 8.27 × 104
2.00 × 105 0.136 1.65 × 105
3.00 × 105 0.204 2.48 × 105
3.59 × 105 0.244 2.97 × 105
Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft)
L = 10.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 4.43 × 10-4 135
50.0 5.43 × 10-4 165
60.0 6.52 × 10-4 199
70.0 7.60 × 10-4 232
80.0 8.69 × 10-4 265
90.0 9.78 × 10-4 298
100 0.00109 331
200 0.00217 662
300 0.00326 993
400 0.00435 1320
500 0.00543 1650
600 0.00652 1990
700 0.00760 2320
800 0.00869 2650
900 0.00978 2980
1000 0.0109 3310
2000 0.0217 6620
3000 0.0326 9930
4000 0.0435 1.32 × 104
5000 0.0543 1.65 × 104
6000 0.0652 1.99 × 104
7000 0.0760 2.32 × 104
8000 0.0869 2.65 × 104
9000 0.0978 2.98 × 104
1.00 × 104 0.109 3.31 × 104
2.00 × 104 0.217 6.62 × 104
3.00 × 104 0.326 9.93 × 104
4.00 × 104 0.435 1.32 × 105
5.00 × 104 0.543 1.65 × 105
6.00 × 104 0.652 1.99 × 105
7.00 × 104 0.760 2.32 × 105
8.00 × 104 0.869 2.65 × 105
8.98 × 104 0.975 2.97 × 105
Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft)
L = 15.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 0.00224 304
50.0 0.00275 372
60.0 0.00330 447
70.0 0.00385 521
80.0 0.00440 596
90.0 0.00495 670
100 0.00550 744
200 0.0110 1490
300 0.0165 2230
400 0.0220 2980
500 0.0275 3720
600 0.0330 4470
700 0.0385 5210
800 0.0440 5960
900 0.0495 6700
1000 0.0550 7440
2000 0.110 1.49 × 104
3000 0.165 2.23 × 104
4000 0.220 2.98 × 104
5000 0.275 3.72 × 104
6000 0.330 4.47 × 104
7000 0.385 5.21 × 104
8000 0.440 5.96 × 104
9000 0.495 6.70 × 104
1.00 × 104 0.550 7.44 × 104
2.00 × 104 1.10 1.49 × 105
3.00 × 104 1.65 2.23 × 105
3.99 × 104 2.19 2.97 × 105
Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft)
L = 20.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 0.00709 540
50.0 0.00869 662
60.0 0.0104 794
70.0 0.0122 926
80.0 0.0139 1060
90.0 0.0156 1190
100 0.0174 1320
200 0.0348 2650
300 0.0521 3970
400 0.0695 5290
500 0.0869 6620
600 0.104 7940
700 0.122 9260
800 0.139 1.06 × 104
900 0.156 1.19 × 104
1000 0.174 1.32 × 104
2000 0.348 2.65 × 104
3000 0.521 3.97 × 104
4000 0.695 5.29 × 104
5000 0.869 6.62 × 104
6000 1.04 7.94 × 104
7000 1.22 9.26 × 104
8000 1.39 1.06 × 105
9000 1.56 1.19 × 105
1.00 × 104 1.74 1.32 × 105
2.00 × 104 3.48 2.65 × 105
2.24 × 104 3.90 2.97 × 105
Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft)
L = 25.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 0.0173 844
50.0 0.0212 1030
60.0 0.0255 1240
70.0 0.0297 1450
80.0 0.0339 1650
90.0 0.0382 1860
100 0.0424 2070
200 0.0849 4140
300 0.127 6200
400 0.170 8270
500 0.212 1.03 × 104
600 0.255 1.24 × 104
700 0.297 1.45 × 104
800 0.339 1.65 × 104
900 0.382 1.86 × 104
1000 0.424 2.07 × 104
2000 0.849 4.14 × 104
3000 1.27 6.20 × 104
4000 1.70 8.27 × 104
5000 2.12 1.03 × 105
6000 2.55 1.24 × 105
7000 2.97 1.45 × 105
8000 3.39 1.65 × 105
9000 3.82 1.86 × 105
1.00 × 104 4.24 2.07 × 105
1.44 × 104 6.10 2.97 × 105
Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft)
L = 30.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 0.0359 1220
50.0 0.0440 1490
60.0 0.0528 1790
70.0 0.0616 2080
80.0 0.0704 2380
90.0 0.0792 2680
100 0.0880 2980
200 0.176 5960
300 0.264 8930
400 0.352 1.19 × 104
500 0.440 1.49 × 104
600 0.528 1.79 × 104
700 0.616 2.08 × 104
800 0.704 2.38 × 104
900 0.792 2.68 × 104
1000 0.880 2.98 × 104
2000 1.76 5.96 × 104
3000 2.64 8.93 × 104
4000 3.52 1.19 × 105
5000 4.40 1.49 × 105
6000 5.28 1.79 × 105
7000 6.16 2.08 × 105
8000 7.04 2.38 × 105
9000 7.92 2.68 × 105
9970 8.78 2.97 × 105
Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft)
L = 40.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 0.113 2160
50.0 0.139 2650
60.0 0.167 3180
70.0 0.195 3710
80.0 0.222 4240
90.0 0.250 4760
100 0.278 5290
200 0.556 1.06 × 104
300 0.834 1.59 × 104
400 1.11 2.12 × 104
500 1.39 2.65 × 104
600 1.67 3.18 × 104
700 1.95 3.71 × 104
800 2.22 4.24 × 104
900 2.50 4.76 × 104
1000 2.78 5.29 × 104
2000 5.56 1.06 × 105
3000 8.34 1.59 × 105
4000 11.1 2.12 × 105
4310 12.0 2.28 × 105
Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft)
L = 50.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 0.277 3380
50.0 0.339 4140
60.0 0.407 4960
70.0 0.475 5790
80.0 0.543 6620
90.0 0.611 7440
100 0.679 8270
200 1.36 1.65 × 104
300 2.04 2.48 × 104
400 2.72 3.31 × 104
500 3.39 4.14 × 104
600 4.07 4.96 × 104
700 4.75 5.79 × 104
800 5.43 6.62 × 104
900 6.11 7.44 × 104
1000 6.79 8.27 × 104
1770 12.0 1.46 × 105
Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft)
L = 60.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 0.574 4860
50.0 0.704 5960
60.0 0.845 7150
70.0 0.986 8340
80.0 1.13 9530
90.0 1.27 1.07 × 104
100 1.41 1.19 × 104
200 2.82 2.38 × 104
300 4.22 3.57 × 104
400 5.63 4.76 × 104
500 7.04 5.96 × 104
600 8.45 7.15 × 104
700 9.86 8.34 × 104
800 11.3 9.53 × 104
852 12.0 1.02 × 105
Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft)
L = 70.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 1.06 6620
50.0 1.30 8110
60.0 1.57 9730
70.0 1.83 1.13 × 104
80.0 2.09 1.30 × 104
90.0 2.35 1.46 × 104
100 2.61 1.62 × 104
200 5.22 3.24 × 104
300 7.83 4.86 × 104
400 10.4 6.49 × 104
460 12.0 7.46 × 104
Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft)
L = 80.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 1.82 8640
50.0 2.22 1.06 × 104
60.0 2.67 1.27 × 104
70.0 3.11 1.48 × 104
80.0 3.56 1.69 × 104
90.0 4.00 1.91 × 104
100 4.45 2.12 × 104
200 8.90 4.24 × 104
270 12.0 5.71 × 104
Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft)
L = 90.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 2.91 1.09 × 104
50.0 3.56 1.34 × 104
60.0 4.28 1.61 × 104
70.0 4.99 1.88 × 104
80.0 5.70 2.14 × 104
90.0 6.41 2.41 × 104
100 7.13 2.68 × 104
168 12.0 4.51 × 104
Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft)
L = 100 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 4.43 1.35 × 104
50.0 5.43 1.65 × 104
60.0 6.52 1.99 × 104
70.0 7.60 2.32 × 104
80.0 8.69 2.65 × 104
90.0 9.78 2.98 × 104
100 10.9 3.31 × 104
110 12.0 3.65 × 104
Steel I Beam: S12 × 40.8 (S12 inch tall × 40.8 lbf/ft)
L = 125 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 10.8 2.11 × 104
45.2 12.0 2.34 × 104
Additional Information
Related Pages
FREE Publications
Essentials of Manufacturing

Information, coverage of important developments and expert commentary in manufacturing.

Injection Molding Design Guide

Guide for high quality and cost-effective plastic injection molding.

STEM Career Outlook

Wages, employment opportunities, and growth projections for STEM jobs.

Metal 3D Printing Design Guide

Direct Metal Laser Sintering (DMLS) 3D printing for parts with reduced cost and little waste.

more publications