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S Section Steel I Beam: S12 × 31.8
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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Two Equal Spans » S Section Steel I Beam » S12 × 31.8
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 = 218 in4) for the S12 × 31.8 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 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 3.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 3.49 × 10-6 11.8
40.0 4.39 × 10-6 14.9
50.0 5.49 × 10-6 18.6
60.0 6.59 × 10-6 22.3
70.0 7.69 × 10-6 26.0
80.0 8.78 × 10-6 29.7
90.0 9.88 × 10-6 33.4
100 1.10 × 10-5 37.2
200 2.20 × 10-5 74.3
300 3.29 × 10-5 111
400 4.39 × 10-5 149
500 5.49 × 10-5 186
600 6.59 × 10-5 223
700 7.69 × 10-5 260
800 8.78 × 10-5 297
900 9.88 × 10-5 334
1000 1.10 × 10-4 372
2000 2.20 × 10-4 743
3000 3.29 × 10-4 1110
4000 4.39 × 10-4 1490
5000 5.49 × 10-4 1860
6000 6.59 × 10-4 2230
7000 7.69 × 10-4 2600
8000 8.78 × 10-4 2970
9000 9.88 × 10-4 3340
1.00 × 104 0.00110 3720
2.00 × 104 0.00220 7430
3.00 × 104 0.00329 1.11 × 104
4.00 × 104 0.00439 1.49 × 104
5.00 × 104 0.00549 1.86 × 104
6.00 × 104 0.00659 2.23 × 104
7.00 × 104 0.00769 2.60 × 104
8.00 × 104 0.00878 2.97 × 104
9.00 × 104 0.00988 3.34 × 104
1.00 × 105 0.0110 3.72 × 104
2.00 × 105 0.0220 7.43 × 104
3.00 × 105 0.0329 1.11 × 105
4.00 × 105 0.0439 1.49 × 105
5.00 × 105 0.0549 1.86 × 105
6.00 × 105 0.0659 2.23 × 105
7.00 × 105 0.0769 2.60 × 105
7.99 × 105 0.0878 2.97 × 105
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 5.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 2.69 × 10-5 32.8
40.0 3.39 × 10-5 41.3
50.0 4.24 × 10-5 51.6
60.0 5.08 × 10-5 61.9
70.0 5.93 × 10-5 72.2
80.0 6.78 × 10-5 82.6
90.0 7.62 × 10-5 92.9
100 8.47 × 10-5 103
200 1.69 × 10-4 206
300 2.54 × 10-4 310
400 3.39 × 10-4 413
500 4.24 × 10-4 516
600 5.08 × 10-4 619
700 5.93 × 10-4 722
800 6.78 × 10-4 826
900 7.62 × 10-4 929
1000 8.47 × 10-4 1030
2000 0.00169 2060
3000 0.00254 3100
4000 0.00339 4130
5000 0.00424 5160
6000 0.00508 6190
7000 0.00593 7220
8000 0.00678 8260
9000 0.00762 9290
1.00 × 104 0.00847 1.03 × 104
2.00 × 104 0.0169 2.06 × 104
3.00 × 104 0.0254 3.10 × 104
4.00 × 104 0.0339 4.13 × 104
5.00 × 104 0.0424 5.16 × 104
6.00 × 104 0.0508 6.19 × 104
7.00 × 104 0.0593 7.22 × 104
8.00 × 104 0.0678 8.26 × 104
9.00 × 104 0.0762 9.29 × 104
1.00 × 105 0.0847 1.03 × 105
2.00 × 105 0.169 2.06 × 105
2.88 × 105 0.244 2.97 × 105
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 10.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 4.31 × 10-4 131
40.0 5.42 × 10-4 165
50.0 6.78 × 10-4 206
60.0 8.13 × 10-4 248
70.0 9.49 × 10-4 289
80.0 0.00108 330
90.0 0.00122 372
100 0.00136 413
200 0.00271 826
300 0.00407 1240
400 0.00542 1650
500 0.00678 2060
600 0.00813 2480
700 0.00949 2890
800 0.0108 3300
900 0.0122 3720
1000 0.0136 4130
2000 0.0271 8260
3000 0.0407 1.24 × 104
4000 0.0542 1.65 × 104
5000 0.0678 2.06 × 104
6000 0.0813 2.48 × 104
7000 0.0949 2.89 × 104
8000 0.108 3.30 × 104
9000 0.122 3.72 × 104
1.00 × 104 0.136 4.13 × 104
2.00 × 104 0.271 8.26 × 104
3.00 × 104 0.407 1.24 × 105
4.00 × 104 0.542 1.65 × 105
5.00 × 104 0.678 2.06 × 105
6.00 × 104 0.813 2.48 × 105
7.00 × 104 0.949 2.89 × 105
7.19 × 104 0.975 2.97 × 105
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 15.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 0.00218 295
40.0 0.00274 372
50.0 0.00343 464
60.0 0.00412 557
70.0 0.00480 650
80.0 0.00549 743
90.0 0.00618 836
100 0.00686 929
200 0.0137 1860
300 0.0206 2790
400 0.0274 3720
500 0.0343 4640
600 0.0412 5570
700 0.0480 6500
800 0.0549 7430
900 0.0618 8360
1000 0.0686 9290
2000 0.137 1.86 × 104
3000 0.206 2.79 × 104
4000 0.274 3.72 × 104
5000 0.343 4.64 × 104
6000 0.412 5.57 × 104
7000 0.480 6.50 × 104
8000 0.549 7.43 × 104
9000 0.618 8.36 × 104
1.00 × 104 0.686 9.29 × 104
2.00 × 104 1.37 1.86 × 105
3.00 × 104 2.06 2.79 × 105
3.20 × 104 2.19 2.97 × 105
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 20.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 0.00690 525
40.0 0.00867 661
50.0 0.0108 826
60.0 0.0130 991
70.0 0.0152 1160
80.0 0.0173 1320
90.0 0.0195 1490
100 0.0217 1650
200 0.0434 3300
300 0.0651 4950
400 0.0867 6610
500 0.108 8260
600 0.130 9910
700 0.152 1.16 × 104
800 0.173 1.32 × 104
900 0.195 1.49 × 104
1000 0.217 1.65 × 104
2000 0.434 3.30 × 104
3000 0.651 4.95 × 104
4000 0.867 6.61 × 104
5000 1.08 8.26 × 104
6000 1.30 9.91 × 104
7000 1.52 1.16 × 105
8000 1.73 1.32 × 105
9000 1.95 1.49 × 105
1.00 × 104 2.17 1.65 × 105
1.80 × 104 3.90 2.97 × 105
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 25.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 0.0168 821
40.0 0.0212 1030
50.0 0.0265 1290
60.0 0.0318 1550
70.0 0.0371 1810
80.0 0.0424 2060
90.0 0.0477 2320
100 0.0529 2580
200 0.106 5160
300 0.159 7740
400 0.212 1.03 × 104
500 0.265 1.29 × 104
600 0.318 1.55 × 104
700 0.371 1.81 × 104
800 0.424 2.06 × 104
900 0.477 2.32 × 104
1000 0.529 2.58 × 104
2000 1.06 5.16 × 104
3000 1.59 7.74 × 104
4000 2.12 1.03 × 105
5000 2.65 1.29 × 105
6000 3.18 1.55 × 105
7000 3.71 1.81 × 105
8000 4.24 2.06 × 105
9000 4.77 2.32 × 105
1.00 × 104 5.29 2.58 × 105
1.15 × 104 6.10 2.97 × 105
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 30.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 0.0349 1180
40.0 0.0439 1490
50.0 0.0549 1860
60.0 0.0659 2230
70.0 0.0769 2600
80.0 0.0878 2970
90.0 0.0988 3340
100 0.110 3720
200 0.220 7430
300 0.329 1.11 × 104
400 0.439 1.49 × 104
500 0.549 1.86 × 104
600 0.659 2.23 × 104
700 0.769 2.60 × 104
800 0.878 2.97 × 104
900 0.988 3.34 × 104
1000 1.10 3.72 × 104
2000 2.20 7.43 × 104
3000 3.29 1.11 × 105
4000 4.39 1.49 × 105
5000 5.49 1.86 × 105
6000 6.59 2.23 × 105
7000 7.69 2.60 × 105
7990 8.78 2.97 × 105
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 40.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 0.110 2100
40.0 0.139 2640
50.0 0.173 3300
60.0 0.208 3960
70.0 0.243 4620
80.0 0.278 5280
90.0 0.312 5940
100 0.347 6610
200 0.694 1.32 × 104
300 1.04 1.98 × 104
400 1.39 2.64 × 104
500 1.73 3.30 × 104
600 2.08 3.96 × 104
700 2.43 4.62 × 104
800 2.78 5.28 × 104
900 3.12 5.94 × 104
1000 3.47 6.61 × 104
2000 6.94 1.32 × 105
3000 10.4 1.98 × 105
3460 12.0 2.28 × 105
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 50.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 0.269 3280
40.0 0.339 4130
50.0 0.424 5160
60.0 0.508 6190
70.0 0.593 7220
80.0 0.678 8260
90.0 0.762 9290
100 0.847 1.03 × 104
200 1.69 2.06 × 104
300 2.54 3.10 × 104
400 3.39 4.13 × 104
500 4.24 5.16 × 104
600 5.08 6.19 × 104
700 5.93 7.22 × 104
800 6.78 8.26 × 104
900 7.62 9.29 × 104
1000 8.47 1.03 × 105
1420 12.0 1.46 × 105
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 60.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 0.559 4730
40.0 0.703 5940
50.0 0.878 7430
60.0 1.05 8920
70.0 1.23 1.04 × 104
80.0 1.41 1.19 × 104
90.0 1.58 1.34 × 104
100 1.76 1.49 × 104
200 3.51 2.97 × 104
300 5.27 4.46 × 104
400 7.03 5.94 × 104
500 8.78 7.43 × 104
600 10.5 8.92 × 104
683 12.0 1.02 × 105
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 70.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 1.03 6430
40.0 1.30 8090
50.0 1.63 1.01 × 104
60.0 1.95 1.21 × 104
70.0 2.28 1.42 × 104
80.0 2.60 1.62 × 104
90.0 2.93 1.82 × 104
100 3.25 2.02 × 104
200 6.51 4.05 × 104
300 9.76 6.07 × 104
369 12.0 7.46 × 104
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 80.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 1.77 8400
40.0 2.22 1.06 × 104
50.0 2.78 1.32 × 104
60.0 3.33 1.59 × 104
70.0 3.89 1.85 × 104
80.0 4.44 2.11 × 104
90.0 5.00 2.38 × 104
100 5.55 2.64 × 104
200 11.1 5.28 × 104
216 12.0 5.71 × 104
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 90.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 2.83 1.06 × 104
40.0 3.56 1.34 × 104
50.0 4.45 1.67 × 104
60.0 5.34 2.01 × 104
70.0 6.23 2.34 × 104
80.0 7.11 2.68 × 104
90.0 8.00 3.01 × 104
100 8.89 3.34 × 104
135 12.0 4.51 × 104
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 100 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 4.31 1.31 × 104
40.0 5.42 1.65 × 104
50.0 6.78 2.06 × 104
60.0 8.13 2.48 × 104
70.0 9.49 2.89 × 104
80.0 10.8 3.30 × 104
88.5 12.0 3.65 × 104
Steel I Beam: S12 × 31.8 (S12 inch tall × 31.8 lbf/ft)
L = 125 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 10.5 2.05 × 104
36.3 12.0 2.34 × 104
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