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S Section Steel I Beam: S12 × 40.8
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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Four 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 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 = 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 4.34 × 10-6 10.4
50.0 5.32 × 10-6 12.8
60.0 6.39 × 10-6 15.3
70.0 7.45 × 10-6 17.9
80.0 8.52 × 10-6 20.4
90.0 9.58 × 10-6 23.0
100 1.06 × 10-5 25.5
200 2.13 × 10-5 51.0
300 3.19 × 10-5 76.5
400 4.26 × 10-5 102
500 5.32 × 10-5 128
600 6.39 × 10-5 153
700 7.45 × 10-5 179
800 8.52 × 10-5 204
900 9.58 × 10-5 230
1000 1.06 × 10-4 255
2000 2.13 × 10-4 510
3000 3.19 × 10-4 765
4000 4.26 × 10-4 1020
5000 5.32 × 10-4 1280
6000 6.39 × 10-4 1530
7000 7.45 × 10-4 1790
8000 8.52 × 10-4 2040
9000 9.58 × 10-4 2300
1.00 × 104 0.00106 2550
2.00 × 104 0.00213 5100
3.00 × 104 0.00319 7650
4.00 × 104 0.00426 1.02 × 104
5.00 × 104 0.00532 1.28 × 104
6.00 × 104 0.00639 1.53 × 104
7.00 × 104 0.00745 1.79 × 104
8.00 × 104 0.00852 2.04 × 104
9.00 × 104 0.00958 2.30 × 104
1.00 × 105 0.0106 2.55 × 104
2.00 × 105 0.0213 5.10 × 104
3.00 × 105 0.0319 7.65 × 104
4.00 × 105 0.0426 1.02 × 105
5.00 × 105 0.0532 1.28 × 105
6.00 × 105 0.0639 1.53 × 105
7.00 × 105 0.0745 1.79 × 105
8.00 × 105 0.0852 2.04 × 105
9.00 × 105 0.0958 2.30 × 105
1.00 × 106 0.106 2.55 × 105
1.16 × 106 0.124 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 3.35 × 10-5 28.9
50.0 4.11 × 10-5 35.4
60.0 4.93 × 10-5 42.5
70.0 5.75 × 10-5 49.6
80.0 6.57 × 10-5 56.7
90.0 7.39 × 10-5 63.8
100 8.21 × 10-5 70.9
200 1.64 × 10-4 142
300 2.46 × 10-4 213
400 3.29 × 10-4 284
500 4.11 × 10-4 354
600 4.93 × 10-4 425
700 5.75 × 10-4 496
800 6.57 × 10-4 567
900 7.39 × 10-4 638
1000 8.21 × 10-4 709
2000 0.00164 1420
3000 0.00246 2130
4000 0.00329 2830
5000 0.00411 3540
6000 0.00493 4250
7000 0.00575 4960
8000 0.00657 5670
9000 0.00739 6380
1.00 × 104 0.00821 7090
2.00 × 104 0.0164 1.42 × 104
3.00 × 104 0.0246 2.13 × 104
4.00 × 104 0.0329 2.84 × 104
5.00 × 104 0.0411 3.54 × 104
6.00 × 104 0.0493 4.25 × 104
7.00 × 104 0.0575 4.96 × 104
8.00 × 104 0.0657 5.67 × 104
9.00 × 104 0.0739 6.38 × 104
1.00 × 105 0.0821 7.09 × 104
2.00 × 105 0.164 1.42 × 105
3.00 × 105 0.246 2.13 × 105
4.00 × 105 0.329 2.84 × 105
4.19 × 105 0.344 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 5.36 × 10-4 116
50.0 6.57 × 10-4 142
60.0 7.88 × 10-4 170
70.0 9.20 × 10-4 198
80.0 0.00105 227
90.0 0.00118 255
100 0.00131 284
200 0.00263 567
300 0.00394 851
400 0.00526 1130
500 0.00657 1420
600 0.00788 1700
700 0.00920 1980
800 0.0105 2270
900 0.0118 2550
1000 0.0131 2830
2000 0.0263 5670
3000 0.0394 8510
4000 0.0526 1.13 × 104
5000 0.0657 1.42 × 104
6000 0.0788 1.70 × 104
7000 0.0920 1.98 × 104
8000 0.105 2.27 × 104
9000 0.118 2.55 × 104
1.00 × 104 0.131 2.84 × 104
2.00 × 104 0.263 5.67 × 104
3.00 × 104 0.394 8.51 × 104
4.00 × 104 0.526 1.13 × 105
5.00 × 104 0.657 1.42 × 105
6.00 × 104 0.788 1.70 × 105
7.00 × 104 0.920 1.98 × 105
8.00 × 104 1.05 2.27 × 105
9.00 × 104 1.18 2.55 × 105
1.00 × 105 1.31 2.84 × 105
1.05 × 105 1.38 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 0.00271 260
50.0 0.00333 319
60.0 0.00399 383
70.0 0.00466 447
80.0 0.00532 510
90.0 0.00599 574
100 0.00665 638
200 0.0133 1280
300 0.0200 1910
400 0.0266 2550
500 0.0333 3190
600 0.0399 3830
700 0.0466 4470
800 0.0532 5100
900 0.0599 5740
1000 0.0665 6380
2000 0.133 1.28 × 104
3000 0.200 1.91 × 104
4000 0.266 2.55 × 104
5000 0.333 3.19 × 104
6000 0.399 3.83 × 104
7000 0.466 4.47 × 104
8000 0.532 5.10 × 104
9000 0.599 5.74 × 104
1.00 × 104 0.665 6.38 × 104
2.00 × 104 1.33 1.28 × 105
3.00 × 104 2.00 1.91 × 105
4.00 × 104 2.66 2.55 × 105
4.66 × 104 3.10 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 0.00858 463
50.0 0.0105 567
60.0 0.0126 680
70.0 0.0147 794
80.0 0.0168 907
90.0 0.0189 1020
100 0.0210 1130
200 0.0420 2270
300 0.0631 3400
400 0.0841 4540
500 0.105 5670
600 0.126 6800
700 0.147 7940
800 0.168 9070
900 0.189 1.02 × 104
1000 0.210 1.13 × 104
2000 0.420 2.27 × 104
3000 0.631 3.40 × 104
4000 0.841 4.54 × 104
5000 1.05 5.67 × 104
6000 1.26 6.80 × 104
7000 1.47 7.94 × 104
8000 1.68 9.07 × 104
9000 1.89 1.02 × 105
1.00 × 104 2.10 1.13 × 105
2.00 × 104 4.20 2.27 × 105
2.62 × 104 5.51 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 0.0209 723
50.0 0.0257 886
60.0 0.0308 1060
70.0 0.0359 1240
80.0 0.0411 1420
90.0 0.0462 1590
100 0.0513 1770
200 0.103 3540
300 0.154 5320
400 0.205 7090
500 0.257 8860
600 0.308 1.06 × 104
700 0.359 1.24 × 104
800 0.411 1.42 × 104
900 0.462 1.59 × 104
1000 0.513 1.77 × 104
2000 1.03 3.54 × 104
3000 1.54 5.32 × 104
4000 2.05 7.09 × 104
5000 2.57 8.86 × 104
6000 3.08 1.06 × 105
7000 3.59 1.24 × 105
8000 4.11 1.42 × 105
9000 4.62 1.59 × 105
1.00 × 104 5.13 1.77 × 105
1.68 × 104 8.61 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 0.0434 1040
50.0 0.0532 1280
60.0 0.0639 1530
70.0 0.0745 1790
80.0 0.0852 2040
90.0 0.0958 2300
100 0.106 2550
200 0.213 5100
300 0.319 7650
400 0.426 1.02 × 104
500 0.532 1.28 × 104
600 0.639 1.53 × 104
700 0.745 1.79 × 104
800 0.852 2.04 × 104
900 0.958 2.30 × 104
1000 1.06 2.55 × 104
2000 2.13 5.10 × 104
3000 3.19 7.65 × 104
4000 4.26 1.02 × 105
5000 5.32 1.28 × 105
6000 6.39 1.53 × 105
7000 7.45 1.79 × 105
8000 8.52 2.04 × 105
9000 9.58 2.30 × 105
1.00 × 104 10.6 2.55 × 105
1.16 × 104 12.4 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 0.137 1850
50.0 0.168 2270
60.0 0.202 2720
70.0 0.235 3180
80.0 0.269 3630
90.0 0.303 4080
100 0.336 4540
200 0.673 9070
300 1.01 1.36 × 104
400 1.35 1.81 × 104
500 1.68 2.27 × 104
600 2.02 2.72 × 104
700 2.35 3.18 × 104
800 2.69 3.63 × 104
900 3.03 4.08 × 104
1000 3.36 4.54 × 104
2000 6.73 9.07 × 104
3000 10.1 1.36 × 105
3570 12.0 1.62 × 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 0.335 2890
50.0 0.411 3540
60.0 0.493 4250
70.0 0.575 4960
80.0 0.657 5670
90.0 0.739 6380
100 0.821 7090
200 1.64 1.42 × 104
300 2.46 2.13 × 104
400 3.29 2.84 × 104
500 4.11 3.54 × 104
600 4.93 4.25 × 104
700 5.75 4.96 × 104
800 6.57 5.67 × 104
900 7.39 6.38 × 104
1000 8.21 7.09 × 104
1460 12.0 1.04 × 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 0.695 4160
50.0 0.852 5100
60.0 1.02 6120
70.0 1.19 7140
80.0 1.36 8160
90.0 1.53 9190
100 1.70 1.02 × 104
200 3.41 2.04 × 104
300 5.11 3.06 × 104
400 6.81 4.08 × 104
500 8.52 5.10 × 104
600 10.2 6.12 × 104
700 11.9 7.14 × 104
705 12.0 7.19 × 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 1.29 5670
50.0 1.58 6950
60.0 1.89 8330
70.0 2.21 9720
80.0 2.52 1.11 × 104
90.0 2.84 1.25 × 104
100 3.16 1.39 × 104
200 6.31 2.78 × 104
300 9.47 4.17 × 104
380 12.0 5.28 × 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 2.20 7400
50.0 2.69 9070
60.0 3.23 1.09 × 104
70.0 3.77 1.27 × 104
80.0 4.31 1.45 × 104
90.0 4.84 1.63 × 104
100 5.38 1.81 × 104
200 10.8 3.63 × 104
223 12.0 4.05 × 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 3.52 9370
50.0 4.31 1.15 × 104
60.0 5.17 1.38 × 104
70.0 6.04 1.61 × 104
80.0 6.90 1.84 × 104
90.0 7.76 2.07 × 104
100 8.62 2.30 × 104
139 12.0 3.20 × 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 5.36 1.16 × 104
50.0 6.57 1.42 × 104
60.0 7.88 1.70 × 104
70.0 9.20 1.98 × 104
80.0 10.5 2.27 × 104
90.0 11.8 2.55 × 104
91.3 12.0 2.59 × 104
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