engineering fundamentals
S Section Steel I Beam: S12 × 31.8
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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Single Span » 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 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 = 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
   
Steel I Beam: S12 × 31.8 (S Section 12 inch tall × 31.8 lbf/ft)
L = 3.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 8.73 × 10-6 11.8
40.0 1.10 × 10-5 14.9
50.0 1.37 × 10-5 18.6
60.0 1.65 × 10-5 22.3
70.0 1.92 × 10-5 26.0
80.0 2.20 × 10-5 29.7
90.0 2.47 × 10-5 33.4
100 2.74 × 10-5 37.2
200 5.49 × 10-5 74.3
300 8.23 × 10-5 111
400 1.10 × 10-4 149
500 1.37 × 10-4 186
600 1.65 × 10-4 223
700 1.92 × 10-4 260
800 2.20 × 10-4 297
900 2.47 × 10-4 334
1000 2.74 × 10-4 372
2000 5.49 × 10-4 743
3000 8.23 × 10-4 1110
4000 0.00110 1490
5000 0.00137 1860
6000 0.00165 2230
7000 0.00192 2600
8000 0.00220 2970
9000 0.00247 3340
1.00 × 104 0.00274 3720
2.00 × 104 0.00549 7430
3.00 × 104 0.00823 1.11 × 104
4.00 × 104 0.0110 1.49 × 104
5.00 × 104 0.0137 1.86 × 104
6.00 × 104 0.0165 2.23 × 104
7.00 × 104 0.0192 2.60 × 104
8.00 × 104 0.0220 2.97 × 104
9.00 × 104 0.0247 3.34 × 104
1.00 × 105 0.0274 3.72 × 104
2.00 × 105 0.0549 7.43 × 104
3.00 × 105 0.0823 1.11 × 105
4.00 × 105 0.110 1.49 × 105
5.00 × 105 0.137 1.86 × 105
6.00 × 105 0.165 2.23 × 105
7.00 × 105 0.192 2.60 × 105
7.99 × 105 0.219 2.97 × 105
Steel I Beam: S12 × 31.8 (S Section 12 inch tall × 31.8 lbf/ft)
L = 5.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 6.73 × 10-5 32.8
40.0 8.47 × 10-5 41.3
50.0 1.06 × 10-4 51.6
60.0 1.27 × 10-4 61.9
70.0 1.48 × 10-4 72.2
80.0 1.69 × 10-4 82.6
90.0 1.91 × 10-4 92.9
100 2.12 × 10-4 103
200 4.24 × 10-4 206
300 6.35 × 10-4 310
400 8.47 × 10-4 413
500 0.00106 516
600 0.00127 619
700 0.00148 722
800 0.00169 826
900 0.00191 929
1000 0.00212 1030
2000 0.00424 2060
3000 0.00635 3100
4000 0.00847 4130
5000 0.0106 5160
6000 0.0127 6190
7000 0.0148 7220
8000 0.0169 8260
9000 0.0191 9290
1.00 × 104 0.0212 1.03 × 104
2.00 × 104 0.0424 2.06 × 104
3.00 × 104 0.0635 3.10 × 104
4.00 × 104 0.0847 4.13 × 104
5.00 × 104 0.106 5.16 × 104
6.00 × 104 0.127 6.19 × 104
7.00 × 104 0.148 7.22 × 104
8.00 × 104 0.169 8.26 × 104
9.00 × 104 0.191 9.29 × 104
1.00 × 105 0.212 1.03 × 105
2.00 × 105 0.424 2.06 × 105
2.88 × 105 0.610 2.97 × 105
Steel I Beam: S12 × 31.8 (S Section 12 inch tall × 31.8 lbf/ft)
L = 10.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 0.00108 131
40.0 0.00136 165
50.0 0.00169 206
60.0 0.00203 248
70.0 0.00237 289
80.0 0.00271 330
90.0 0.00305 372
100 0.00339 413
200 0.00678 826
300 0.0102 1240
400 0.0136 1650
500 0.0169 2060
600 0.0203 2480
700 0.0237 2890
800 0.0271 3300
900 0.0305 3720
1000 0.0339 4130
2000 0.0678 8260
3000 0.102 1.24 × 104
4000 0.136 1.65 × 104
5000 0.169 2.06 × 104
6000 0.203 2.48 × 104
7000 0.237 2.89 × 104
8000 0.271 3.30 × 104
9000 0.305 3.72 × 104
1.00 × 104 0.339 4.13 × 104
2.00 × 104 0.678 8.26 × 104
3.00 × 104 1.02 1.24 × 105
4.00 × 104 1.36 1.65 × 105
5.00 × 104 1.69 2.06 × 105
6.00 × 104 2.03 2.48 × 105
7.00 × 104 2.37 2.89 × 105
7.19 × 104 2.44 2.97 × 105
Steel I Beam: S12 × 31.8 (S Section 12 inch tall × 31.8 lbf/ft)
L = 15.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 0.00546 295
40.0 0.00686 372
50.0 0.00858 464
60.0 0.0103 557
70.0 0.0120 650
80.0 0.0137 743
90.0 0.0154 836
100 0.0172 929
200 0.0343 1860
300 0.0515 2790
400 0.0686 3720
500 0.0858 4640
600 0.103 5570
700 0.120 6500
800 0.137 7430
900 0.154 8360
1000 0.172 9290
2000 0.343 1.86 × 104
3000 0.515 2.79 × 104
4000 0.686 3.72 × 104
5000 0.858 4.64 × 104
6000 1.03 5.57 × 104
7000 1.20 6.50 × 104
8000 1.37 7.43 × 104
9000 1.54 8.36 × 104
1.00 × 104 1.72 9.29 × 104
2.00 × 104 3.43 1.86 × 105
3.00 × 104 5.15 2.79 × 105
3.20 × 104 5.49 2.97 × 105
Steel I Beam: S12 × 31.8 (S Section 12 inch tall × 31.8 lbf/ft)
L = 20.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 0.0172 525
40.0 0.0217 661
50.0 0.0271 826
60.0 0.0325 991
70.0 0.0380 1160
80.0 0.0434 1320
90.0 0.0488 1490
100 0.0542 1650
200 0.108 3300
300 0.163 4950
400 0.217 6610
500 0.271 8260
600 0.325 9910
700 0.380 1.16 × 104
800 0.434 1.32 × 104
900 0.488 1.49 × 104
1000 0.542 1.65 × 104
2000 1.08 3.30 × 104
3000 1.63 4.95 × 104
4000 2.17 6.61 × 104
5000 2.71 8.26 × 104
6000 3.25 9.91 × 104
7000 3.80 1.16 × 105
8000 4.34 1.32 × 105
9000 4.88 1.49 × 105
1.00 × 104 5.42 1.65 × 105
1.80 × 104 9.75 2.97 × 105
Steel I Beam: S12 × 31.8 (S Section 12 inch tall × 31.8 lbf/ft)
L = 25.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 0.0421 821
40.0 0.0529 1030
50.0 0.0662 1290
60.0 0.0794 1550
70.0 0.0927 1810
80.0 0.106 2060
90.0 0.119 2320
100 0.132 2580
200 0.265 5160
300 0.397 7740
400 0.529 1.03 × 104
500 0.662 1.29 × 104
600 0.794 1.55 × 104
700 0.927 1.81 × 104
800 1.06 2.06 × 104
900 1.19 2.32 × 104
1000 1.32 2.58 × 104
2000 2.65 5.16 × 104
3000 3.97 7.74 × 104
4000 5.29 1.03 × 105
5000 6.62 1.29 × 105
6000 7.94 1.55 × 105
7000 9.27 1.81 × 105
8000 10.6 2.06 × 105
9000 11.9 2.32 × 105
9070 12.0 2.34 × 105
Steel I Beam: S12 × 31.8 (S Section 12 inch tall × 31.8 lbf/ft)
L = 30.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 0.0873 1180
40.0 0.110 1490
50.0 0.137 1860
60.0 0.165 2230
70.0 0.192 2600
80.0 0.220 2970
90.0 0.247 3340
100 0.274 3720
200 0.549 7430
300 0.823 1.11 × 104
400 1.10 1.49 × 104
500 1.37 1.86 × 104
600 1.65 2.23 × 104
700 1.92 2.60 × 104
800 2.20 2.97 × 104
900 2.47 3.34 × 104
1000 2.74 3.72 × 104
2000 5.49 7.43 × 104
3000 8.23 1.11 × 105
4000 11.0 1.49 × 105
4370 12.0 1.62 × 105
Steel I Beam: S12 × 31.8 (S Section 12 inch tall × 31.8 lbf/ft)
L = 40.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 0.276 2100
40.0 0.347 2640
50.0 0.434 3300
60.0 0.520 3960
70.0 0.607 4620
80.0 0.694 5280
90.0 0.781 5940
100 0.867 6610
200 1.73 1.32 × 104
300 2.60 1.98 × 104
400 3.47 2.64 × 104
500 4.34 3.30 × 104
600 5.20 3.96 × 104
700 6.07 4.62 × 104
800 6.94 5.28 × 104
900 7.81 5.94 × 104
1000 8.67 6.61 × 104
1380 12.0 9.14 × 104
Steel I Beam: S12 × 31.8 (S Section 12 inch tall × 31.8 lbf/ft)
L = 50.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 0.673 3280
40.0 0.847 4130
50.0 1.06 5160
60.0 1.27 6190
70.0 1.48 7220
80.0 1.69 8260
90.0 1.91 9290
100 2.12 1.03 × 104
200 4.24 2.06 × 104
300 6.35 3.10 × 104
400 8.47 4.13 × 104
500 10.6 5.16 × 104
567 12.0 5.85 × 104
Steel I Beam: S12 × 31.8 (S Section 12 inch tall × 31.8 lbf/ft)
L = 60.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 1.40 4730
40.0 1.76 5940
50.0 2.20 7430
60.0 2.64 8920
70.0 3.07 1.04 × 104
80.0 3.51 1.19 × 104
90.0 3.95 1.34 × 104
100 4.39 1.49 × 104
200 8.78 2.97 × 104
273 12.0 4.06 × 104
Steel I Beam: S12 × 31.8 (S Section 12 inch tall × 31.8 lbf/ft)
L = 70.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 2.59 6430
40.0 3.25 8090
50.0 4.07 1.01 × 104
60.0 4.88 1.21 × 104
70.0 5.70 1.42 × 104
80.0 6.51 1.62 × 104
90.0 7.32 1.82 × 104
100 8.14 2.02 × 104
147 12.0 2.98 × 104
Steel I Beam: S12 × 31.8 (S Section 12 inch tall × 31.8 lbf/ft)
L = 80.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 4.41 8400
40.0 5.55 1.06 × 104
50.0 6.94 1.32 × 104
60.0 8.33 1.59 × 104
70.0 9.72 1.85 × 104
80.0 11.1 2.11 × 104
86.5 12.0 2.28 × 104
Steel I Beam: S12 × 31.8 (S Section 12 inch tall × 31.8 lbf/ft)
L = 90.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 7.07 1.06 × 104
40.0 8.89 1.34 × 104
50.0 11.1 1.67 × 104
54.0 12.0 1.80 × 104
Steel I Beam: S12 × 31.8 (S Section 12 inch tall × 31.8 lbf/ft)
L = 100 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.8 10.8 1.31 × 104
35.4 12.0 1.46 × 104
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