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S Section Steel I Beam: S12 × 40.8
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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 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 = 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
  
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 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
P (lbf/ft) w_max (in) stress_max (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
P (lbf/ft) w_max (in) stress_max (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
P (lbf/ft) w_max (in) stress_max (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
P (lbf/ft) w_max (in) stress_max (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
P (lbf/ft) w_max (in) stress_max (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
P (lbf/ft) w_max (in) stress_max (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
P (lbf/ft) w_max (in) stress_max (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
P (lbf/ft) w_max (in) stress_max (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
P (lbf/ft) w_max (in) stress_max (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
P (lbf/ft) w_max (in) stress_max (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
P (lbf/ft) w_max (in) stress_max (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
P (lbf/ft) w_max (in) stress_max (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
P (lbf/ft) w_max (in) stress_max (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
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