engineering fundamentals
S Section Steel I Beam: S12 × 40.8
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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Single Span » 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 a single span, the maximum displacement w_max and the maximum normal stress stress_max occur at the center 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 (S Section 12 inch tall × 40.8 lbf/ft)
L = 3.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 8.98 × 10-6 12.1
50.0 1.10 × 10-5 14.9
60.0 1.32 × 10-5 17.9
70.0 1.54 × 10-5 20.8
80.0 1.76 × 10-5 23.8
90.0 1.98 × 10-5 26.8
100 2.20 × 10-5 29.8
200 4.40 × 10-5 59.6
300 6.60 × 10-5 89.3
400 8.80 × 10-5 119
500 1.10 × 10-4 149
600 1.32 × 10-4 179
700 1.54 × 10-4 208
800 1.76 × 10-4 238
900 1.98 × 10-4 268
1000 2.20 × 10-4 298
2000 4.40 × 10-4 596
3000 6.60 × 10-4 893
4000 8.80 × 10-4 1190
5000 0.00110 1490
6000 0.00132 1790
7000 0.00154 2080
8000 0.00176 2380
9000 0.00198 2680
1.00 × 104 0.00220 2980
2.00 × 104 0.00440 5960
3.00 × 104 0.00660 8930
4.00 × 104 0.00880 1.19 × 104
5.00 × 104 0.0110 1.49 × 104
6.00 × 104 0.0132 1.79 × 104
7.00 × 104 0.0154 2.08 × 104
8.00 × 104 0.0176 2.38 × 104
9.00 × 104 0.0198 2.68 × 104
1.00 × 105 0.0220 2.98 × 104
2.00 × 105 0.0440 5.96 × 104
3.00 × 105 0.0660 8.93 × 104
4.00 × 105 0.0880 1.19 × 105
5.00 × 105 0.110 1.49 × 105
6.00 × 105 0.132 1.79 × 105
7.00 × 105 0.154 2.08 × 105
8.00 × 105 0.176 2.38 × 105
9.00 × 105 0.198 2.68 × 105
9.97 × 105 0.219 2.97 × 105
Steel I Beam: S12 × 40.8 (S Section 12 inch tall × 40.8 lbf/ft)
L = 5.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 6.93 × 10-5 33.8
50.0 8.49 × 10-5 41.4
60.0 1.02 × 10-4 49.6
70.0 1.19 × 10-4 57.9
80.0 1.36 × 10-4 66.2
90.0 1.53 × 10-4 74.4
100 1.70 × 10-4 82.7
200 3.39 × 10-4 165
300 5.09 × 10-4 248
400 6.79 × 10-4 331
500 8.49 × 10-4 414
600 0.00102 496
700 0.00119 579
800 0.00136 662
900 0.00153 744
1000 0.00170 827
2000 0.00339 1650
3000 0.00509 2480
4000 0.00679 3310
5000 0.00849 4140
6000 0.0102 4960
7000 0.0119 5790
8000 0.0136 6620
9000 0.0153 7440
1.00 × 104 0.0170 8270
2.00 × 104 0.0339 1.65 × 104
3.00 × 104 0.0509 2.48 × 104
4.00 × 104 0.0679 3.31 × 104
5.00 × 104 0.0849 4.14 × 104
6.00 × 104 0.102 4.96 × 104
7.00 × 104 0.119 5.79 × 104
8.00 × 104 0.136 6.62 × 104
9.00 × 104 0.153 7.44 × 104
1.00 × 105 0.170 8.27 × 104
2.00 × 105 0.339 1.65 × 105
3.00 × 105 0.509 2.48 × 105
3.59 × 105 0.610 2.97 × 105
Steel I Beam: S12 × 40.8 (S Section 12 inch tall × 40.8 lbf/ft)
L = 10.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 0.00111 135
50.0 0.00136 165
60.0 0.00163 199
70.0 0.00190 232
80.0 0.00217 265
90.0 0.00244 298
100 0.00272 331
200 0.00543 662
300 0.00815 993
400 0.0109 1320
500 0.0136 1650
600 0.0163 1990
700 0.0190 2320
800 0.0217 2650
900 0.0244 2980
1000 0.0272 3310
2000 0.0543 6620
3000 0.0815 9930
4000 0.109 1.32 × 104
5000 0.136 1.65 × 104
6000 0.163 1.99 × 104
7000 0.190 2.32 × 104
8000 0.217 2.65 × 104
9000 0.244 2.98 × 104
1.00 × 104 0.272 3.31 × 104
2.00 × 104 0.543 6.62 × 104
3.00 × 104 0.815 9.93 × 104
4.00 × 104 1.09 1.32 × 105
5.00 × 104 1.36 1.65 × 105
6.00 × 104 1.63 1.99 × 105
7.00 × 104 1.90 2.32 × 105
8.00 × 104 2.17 2.65 × 105
8.98 × 104 2.44 2.97 × 105
Steel I Beam: S12 × 40.8 (S Section 12 inch tall × 40.8 lbf/ft)
L = 15.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 0.00561 304
50.0 0.00687 372
60.0 0.00825 447
70.0 0.00962 521
80.0 0.0110 596
90.0 0.0124 670
100 0.0137 744
200 0.0275 1490
300 0.0412 2230
400 0.0550 2980
500 0.0687 3720
600 0.0825 4470
700 0.0962 5210
800 0.110 5960
900 0.124 6700
1000 0.137 7440
2000 0.275 1.49 × 104
3000 0.412 2.23 × 104
4000 0.550 2.98 × 104
5000 0.687 3.72 × 104
6000 0.825 4.47 × 104
7000 0.962 5.21 × 104
8000 1.10 5.96 × 104
9000 1.24 6.70 × 104
1.00 × 104 1.37 7.44 × 104
2.00 × 104 2.75 1.49 × 105
3.00 × 104 4.12 2.23 × 105
3.99 × 104 5.49 2.97 × 105
Steel I Beam: S12 × 40.8 (S Section 12 inch tall × 40.8 lbf/ft)
L = 20.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 0.0177 540
50.0 0.0217 662
60.0 0.0261 794
70.0 0.0304 926
80.0 0.0348 1060
90.0 0.0391 1190
100 0.0435 1320
200 0.0869 2650
300 0.130 3970
400 0.174 5290
500 0.217 6620
600 0.261 7940
700 0.304 9260
800 0.348 1.06 × 104
900 0.391 1.19 × 104
1000 0.435 1.32 × 104
2000 0.869 2.65 × 104
3000 1.30 3.97 × 104
4000 1.74 5.29 × 104
5000 2.17 6.62 × 104
6000 2.61 7.94 × 104
7000 3.04 9.26 × 104
8000 3.48 1.06 × 105
9000 3.91 1.19 × 105
1.00 × 104 4.35 1.32 × 105
2.00 × 104 8.69 2.65 × 105
2.24 × 104 9.75 2.97 × 105
Steel I Beam: S12 × 40.8 (S Section 12 inch tall × 40.8 lbf/ft)
L = 25.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 0.0433 844
50.0 0.0530 1030
60.0 0.0637 1240
70.0 0.0743 1450
80.0 0.0849 1650
90.0 0.0955 1860
100 0.106 2070
200 0.212 4140
300 0.318 6200
400 0.424 8270
500 0.530 1.03 × 104
600 0.637 1.24 × 104
700 0.743 1.45 × 104
800 0.849 1.65 × 104
900 0.955 1.86 × 104
1000 1.06 2.07 × 104
2000 2.12 4.14 × 104
3000 3.18 6.20 × 104
4000 4.24 8.27 × 104
5000 5.30 1.03 × 105
6000 6.37 1.24 × 105
7000 7.43 1.45 × 105
8000 8.49 1.65 × 105
9000 9.55 1.86 × 105
1.00 × 104 10.6 2.07 × 105
1.44 × 104 15.2 2.97 × 105
Steel I Beam: S12 × 40.8 (S Section 12 inch tall × 40.8 lbf/ft)
L = 30.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 0.0898 1220
50.0 0.110 1490
60.0 0.132 1790
70.0 0.154 2080
80.0 0.176 2380
90.0 0.198 2680
100 0.220 2980
200 0.440 5960
300 0.660 8930
400 0.880 1.19 × 104
500 1.10 1.49 × 104
600 1.32 1.79 × 104
700 1.54 2.08 × 104
800 1.76 2.38 × 104
900 1.98 2.68 × 104
1000 2.20 2.98 × 104
2000 4.40 5.96 × 104
3000 6.60 8.93 × 104
4000 8.80 1.19 × 105
5000 11.0 1.49 × 105
5450 12.0 1.62 × 105
Steel I Beam: S12 × 40.8 (S Section 12 inch tall × 40.8 lbf/ft)
L = 40.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 0.284 2160
50.0 0.348 2650
60.0 0.417 3180
70.0 0.487 3710
80.0 0.556 4240
90.0 0.626 4760
100 0.695 5290
200 1.39 1.06 × 104
300 2.09 1.59 × 104
400 2.78 2.12 × 104
500 3.48 2.65 × 104
600 4.17 3.18 × 104
700 4.87 3.71 × 104
800 5.56 4.24 × 104
900 6.26 4.76 × 104
1000 6.95 5.29 × 104
1730 12.0 9.14 × 104
Steel I Beam: S12 × 40.8 (S Section 12 inch tall × 40.8 lbf/ft)
L = 50.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 0.693 3380
50.0 0.849 4140
60.0 1.02 4960
70.0 1.19 5790
80.0 1.36 6620
90.0 1.53 7440
100 1.70 8270
200 3.39 1.65 × 104
300 5.09 2.48 × 104
400 6.79 3.31 × 104
500 8.49 4.14 × 104
600 10.2 4.96 × 104
700 11.9 5.79 × 104
707 12.0 5.85 × 104
Steel I Beam: S12 × 40.8 (S Section 12 inch tall × 40.8 lbf/ft)
L = 60.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 1.44 4860
50.0 1.76 5960
60.0 2.11 7150
70.0 2.46 8340
80.0 2.82 9530
90.0 3.17 1.07 × 104
100 3.52 1.19 × 104
200 7.04 2.38 × 104
300 10.6 3.57 × 104
341 12.0 4.06 × 104
Steel I Beam: S12 × 40.8 (S Section 12 inch tall × 40.8 lbf/ft)
L = 70.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 2.66 6620
50.0 3.26 8110
60.0 3.91 9730
70.0 4.56 1.13 × 104
80.0 5.22 1.30 × 104
90.0 5.87 1.46 × 104
100 6.52 1.62 × 104
184 12.0 2.98 × 104
Steel I Beam: S12 × 40.8 (S Section 12 inch tall × 40.8 lbf/ft)
L = 80.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 4.54 8640
50.0 5.56 1.06 × 104
60.0 6.67 1.27 × 104
70.0 7.79 1.48 × 104
80.0 8.90 1.69 × 104
90.0 10.0 1.91 × 104
100 11.1 2.12 × 104
108 12.0 2.28 × 104
Steel I Beam: S12 × 40.8 (S Section 12 inch tall × 40.8 lbf/ft)
L = 90.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 7.27 1.09 × 104
50.0 8.91 1.34 × 104
60.0 10.7 1.61 × 104
67.3 12.0 1.80 × 104
Steel I Beam: S12 × 40.8 (S Section 12 inch tall × 40.8 lbf/ft)
L = 100 ft
P (lbf/ft) w_max (in) stress_max (psi)
40.8 11.1 1.35 × 104
44.2 12.0 1.46 × 104
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