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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Three Equal Spans » S Section Steel I Beam » S20 × 86
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 = 1580 in4) for the S20 × 86 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
L = 150 ft
   
Steel I Beam: S20 × 86 (S20 inch tall × 86 lbf/ft)
L = 3.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
86.0 1.70 × 10-6 5.97
90.0 1.78 × 10-6 6.24
100 1.98 × 10-6 6.94
200 3.96 × 10-6 13.9
300 5.93 × 10-6 20.8
400 7.91 × 10-6 27.8
500 9.89 × 10-6 34.7
600 1.19 × 10-5 41.6
700 1.38 × 10-5 48.6
800 1.58 × 10-5 55.5
900 1.78 × 10-5 62.4
1000 1.98 × 10-5 69.4
2000 3.96 × 10-5 139
3000 5.93 × 10-5 208
4000 7.91 × 10-5 278
5000 9.89 × 10-5 347
6000 1.19 × 10-4 416
7000 1.38 × 10-4 486
8000 1.58 × 10-4 555
9000 1.78 × 10-4 624
1.00 × 104 1.98 × 10-4 694
2.00 × 104 3.96 × 10-4 1390
3.00 × 104 5.93 × 10-4 2080
4.00 × 104 7.91 × 10-4 2780
5.00 × 104 9.89 × 10-4 3470
6.00 × 104 0.00119 4160
7.00 × 104 0.00138 4860
8.00 × 104 0.00158 5550
9.00 × 104 0.00178 6240
1.00 × 105 0.00198 6940
2.00 × 105 0.00396 1.39 × 104
3.00 × 105 0.00593 2.08 × 104
4.00 × 105 0.00791 2.78 × 104
5.00 × 105 0.00989 3.47 × 104
6.00 × 105 0.0119 4.16 × 104
7.00 × 105 0.0138 4.86 × 104
8.00 × 105 0.0158 5.55 × 104
9.00 × 105 0.0178 6.24 × 104
1.00 × 106 0.0198 6.94 × 104
2.00 × 106 0.0396 1.39 × 105
3.00 × 106 0.0593 2.08 × 105
4.00 × 106 0.0791 2.78 × 105
4.28 × 106 0.0847 2.97 × 105
Steel I Beam: S20 × 86 (S20 inch tall × 86 lbf/ft)
L = 5.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
86.0 1.31 × 10-5 16.6
90.0 1.37 × 10-5 17.3
100 1.53 × 10-5 19.3
200 3.05 × 10-5 38.5
300 4.58 × 10-5 57.8
400 6.10 × 10-5 77.1
500 7.63 × 10-5 96.4
600 9.16 × 10-5 116
700 1.07 × 10-4 135
800 1.22 × 10-4 154
900 1.37 × 10-4 173
1000 1.53 × 10-4 193
2000 3.05 × 10-4 385
3000 4.58 × 10-4 578
4000 6.10 × 10-4 771
5000 7.63 × 10-4 964
6000 9.16 × 10-4 1160
7000 0.00107 1350
8000 0.00122 1540
9000 0.00137 1730
1.00 × 104 0.00153 1930
2.00 × 104 0.00305 3850
3.00 × 104 0.00458 5780
4.00 × 104 0.00610 7710
5.00 × 104 0.00763 9640
6.00 × 104 0.00916 1.16 × 104
7.00 × 104 0.0107 1.35 × 104
8.00 × 104 0.0122 1.54 × 104
9.00 × 104 0.0137 1.73 × 104
1.00 × 105 0.0153 1.93 × 104
2.00 × 105 0.0305 3.85 × 104
3.00 × 105 0.0458 5.78 × 104
4.00 × 105 0.0610 7.71 × 104
5.00 × 105 0.0763 9.64 × 104
6.00 × 105 0.0916 1.16 × 105
7.00 × 105 0.107 1.35 × 105
8.00 × 105 0.122 1.54 × 105
9.00 × 105 0.137 1.73 × 105
1.00 × 106 0.153 1.93 × 105
1.54 × 106 0.235 2.97 × 105
Steel I Beam: S20 × 86 (S20 inch tall × 86 lbf/ft)
L = 10.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
86.0 2.10 × 10-4 66.3
90.0 2.20 × 10-4 69.4
100 2.44 × 10-4 77.1
200 4.88 × 10-4 154
300 7.33 × 10-4 231
400 9.77 × 10-4 308
500 0.00122 385
600 0.00147 463
700 0.00171 540
800 0.00195 617
900 0.00220 694
1000 0.00244 771
2000 0.00488 1540
3000 0.00733 2310
4000 0.00977 3080
5000 0.0122 3850
6000 0.0147 4630
7000 0.0171 5400
8000 0.0195 6170
9000 0.0220 6940
1.00 × 104 0.0244 7710
2.00 × 104 0.0488 1.54 × 104
3.00 × 104 0.0733 2.31 × 104
4.00 × 104 0.0977 3.08 × 104
5.00 × 104 0.122 3.85 × 104
6.00 × 104 0.147 4.63 × 104
7.00 × 104 0.171 5.40 × 104
8.00 × 104 0.195 6.17 × 104
9.00 × 104 0.220 6.94 × 104
1.00 × 105 0.244 7.71 × 104
2.00 × 105 0.488 1.54 × 105
3.00 × 105 0.733 2.31 × 105
3.85 × 105 0.941 2.97 × 105
Steel I Beam: S20 × 86 (S20 inch tall × 86 lbf/ft)
L = 15.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
86.0 0.00106 149
90.0 0.00111 156
100 0.00124 173
200 0.00247 347
300 0.00371 520
400 0.00494 694
500 0.00618 867
600 0.00742 1040
700 0.00865 1210
800 0.00989 1390
900 0.0111 1560
1000 0.0124 1730
2000 0.0247 3470
3000 0.0371 5200
4000 0.0494 6940
5000 0.0618 8670
6000 0.0742 1.04 × 104
7000 0.0865 1.21 × 104
8000 0.0989 1.39 × 104
9000 0.111 1.56 × 104
1.00 × 104 0.124 1.73 × 104
2.00 × 104 0.247 3.47 × 104
3.00 × 104 0.371 5.20 × 104
4.00 × 104 0.494 6.94 × 104
5.00 × 104 0.618 8.67 × 104
6.00 × 104 0.742 1.04 × 105
7.00 × 104 0.865 1.21 × 105
8.00 × 104 0.989 1.39 × 105
9.00 × 104 1.11 1.56 × 105
1.00 × 105 1.24 1.73 × 105
1.71 × 105 2.12 2.97 × 105
Steel I Beam: S20 × 86 (S20 inch tall × 86 lbf/ft)
L = 20.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
86.0 0.00336 265
90.0 0.00352 278
100 0.00391 308
200 0.00781 617
300 0.0117 925
400 0.0156 1230
500 0.0195 1540
600 0.0234 1850
700 0.0273 2160
800 0.0313 2470
900 0.0352 2780
1000 0.0391 3080
2000 0.0781 6170
3000 0.117 9250
4000 0.156 1.23 × 104
5000 0.195 1.54 × 104
6000 0.234 1.85 × 104
7000 0.273 2.16 × 104
8000 0.313 2.47 × 104
9000 0.352 2.78 × 104
1.00 × 104 0.391 3.08 × 104
2.00 × 104 0.781 6.17 × 104
3.00 × 104 1.17 9.25 × 104
4.00 × 104 1.56 1.23 × 105
5.00 × 104 1.95 1.54 × 105
6.00 × 104 2.34 1.85 × 105
7.00 × 104 2.73 2.16 × 105
8.00 × 104 3.13 2.47 × 105
9.00 × 104 3.52 2.78 × 105
9.63 × 104 3.76 2.97 × 105
Steel I Beam: S20 × 86 (S20 inch tall × 86 lbf/ft)
L = 25.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
86.0 0.00820 414
90.0 0.00858 434
100 0.00954 482
200 0.0191 964
300 0.0286 1450
400 0.0382 1930
500 0.0477 2410
600 0.0572 2890
700 0.0668 3370
800 0.0763 3850
900 0.0858 4340
1000 0.0954 4820
2000 0.191 9640
3000 0.286 1.45 × 104
4000 0.382 1.93 × 104
5000 0.477 2.41 × 104
6000 0.572 2.89 × 104
7000 0.668 3.37 × 104
8000 0.763 3.85 × 104
9000 0.858 4.34 × 104
1.00 × 104 0.954 4.82 × 104
2.00 × 104 1.91 9.64 × 104
3.00 × 104 2.86 1.45 × 105
4.00 × 104 3.82 1.93 × 105
5.00 × 104 4.77 2.41 × 105
6.00 × 104 5.72 2.89 × 105
6.17 × 104 5.88 2.97 × 105
Steel I Beam: S20 × 86 (S20 inch tall × 86 lbf/ft)
L = 30.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
86.0 0.0170 597
90.0 0.0178 624
100 0.0198 694
200 0.0396 1390
300 0.0593 2080
400 0.0791 2780
500 0.0989 3470
600 0.119 4160
700 0.138 4860
800 0.158 5550
900 0.178 6240
1000 0.198 6940
2000 0.396 1.39 × 104
3000 0.593 2.08 × 104
4000 0.791 2.78 × 104
5000 0.989 3.47 × 104
6000 1.19 4.16 × 104
7000 1.38 4.86 × 104
8000 1.58 5.55 × 104
9000 1.78 6.24 × 104
1.00 × 104 1.98 6.94 × 104
2.00 × 104 3.96 1.39 × 105
3.00 × 104 5.93 2.08 × 105
4.00 × 104 7.91 2.78 × 105
4.28 × 104 8.47 2.97 × 105
Steel I Beam: S20 × 86 (S20 inch tall × 86 lbf/ft)
L = 40.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
86.0 0.0538 1060
90.0 0.0563 1110
100 0.0625 1230
200 0.125 2470
300 0.188 3700
400 0.250 4930
500 0.313 6170
600 0.375 7400
700 0.438 8630
800 0.500 9870
900 0.563 1.11 × 104
1000 0.625 1.23 × 104
2000 1.25 2.47 × 104
3000 1.88 3.70 × 104
4000 2.50 4.93 × 104
5000 3.13 6.17 × 104
6000 3.75 7.40 × 104
7000 4.38 8.63 × 104
8000 5.00 9.87 × 104
9000 5.63 1.11 × 105
1.00 × 104 6.25 1.23 × 105
2.00 × 104 12.5 2.47 × 105
2.41 × 104 15.1 2.97 × 105
Steel I Beam: S20 × 86 (S20 inch tall × 86 lbf/ft)
L = 50.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
86.0 0.131 1660
90.0 0.137 1730
100 0.153 1930
200 0.305 3850
300 0.458 5780
400 0.610 7710
500 0.763 9640
600 0.916 1.16 × 104
700 1.07 1.35 × 104
800 1.22 1.54 × 104
900 1.37 1.73 × 104
1000 1.53 1.93 × 104
2000 3.05 3.85 × 104
3000 4.58 5.78 × 104
4000 6.10 7.71 × 104
5000 7.63 9.64 × 104
6000 9.16 1.16 × 105
7000 10.7 1.35 × 105
8000 12.2 1.54 × 105
9000 13.7 1.73 × 105
1.00 × 104 15.3 1.93 × 105
1.54 × 104 23.5 2.97 × 105
Steel I Beam: S20 × 86 (S20 inch tall × 86 lbf/ft)
L = 60.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
86.0 0.272 2390
90.0 0.285 2500
100 0.316 2780
200 0.633 5550
300 0.949 8330
400 1.27 1.11 × 104
500 1.58 1.39 × 104
600 1.90 1.67 × 104
700 2.22 1.94 × 104
800 2.53 2.22 × 104
900 2.85 2.50 × 104
1000 3.16 2.78 × 104
2000 6.33 5.55 × 104
3000 9.49 8.33 × 104
4000 12.7 1.11 × 105
5000 15.8 1.39 × 105
6000 19.0 1.67 × 105
6410 20.3 1.78 × 105
Steel I Beam: S20 × 86 (S20 inch tall × 86 lbf/ft)
L = 70.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
86.0 0.504 3250
90.0 0.528 3400
100 0.586 3780
200 1.17 7550
300 1.76 1.13 × 104
400 2.35 1.51 × 104
500 2.93 1.89 × 104
600 3.52 2.27 × 104
700 4.10 2.64 × 104
800 4.69 3.02 × 104
900 5.28 3.40 × 104
1000 5.86 3.78 × 104
2000 11.7 7.55 × 104
3000 17.6 1.13 × 105
3460 20.3 1.31 × 105
Steel I Beam: S20 × 86 (S20 inch tall × 86 lbf/ft)
L = 80.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
86.0 0.860 4240
90.0 0.900 4440
100 1.00 4930
200 2.00 9870
300 3.00 1.48 × 104
400 4.00 1.97 × 104
500 5.00 2.47 × 104
600 6.00 2.96 × 104
700 7.00 3.45 × 104
800 8.00 3.95 × 104
900 9.00 4.44 × 104
1000 10.0 4.93 × 104
2000 20.0 9.87 × 104
2030 20.3 1.00 × 105
Steel I Beam: S20 × 86 (S20 inch tall × 86 lbf/ft)
L = 90.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
86.0 1.38 5370
90.0 1.44 5620
100 1.60 6240
200 3.20 1.25 × 104
300 4.81 1.87 × 104
400 6.41 2.50 × 104
500 8.01 3.12 × 104
600 9.61 3.75 × 104
700 11.2 4.37 × 104
800 12.8 5.00 × 104
900 14.4 5.62 × 104
1000 16.0 6.24 × 104
1270 20.3 7.91 × 104
Steel I Beam: S20 × 86 (S20 inch tall × 86 lbf/ft)
L = 100 ft
P (lbf/ft) w_max (in) stress_max (psi)
86.0 2.10 6630
90.0 2.20 6940
100 2.44 7710
200 4.88 1.54 × 104
300 7.33 2.31 × 104
400 9.77 3.08 × 104
500 12.2 3.85 × 104
600 14.7 4.63 × 104
700 17.1 5.40 × 104
800 19.5 6.17 × 104
831 20.3 6.41 × 104
Steel I Beam: S20 × 86 (S20 inch tall × 86 lbf/ft)
L = 125 ft
P (lbf/ft) w_max (in) stress_max (psi)
86.0 5.13 1.04 × 104
90.0 5.37 1.08 × 104
100 5.96 1.20 × 104
200 11.9 2.41 × 104
300 17.9 3.61 × 104
341 20.3 4.10 × 104
Steel I Beam: S20 × 86 (S20 inch tall × 86 lbf/ft)
L = 150 ft
P (lbf/ft) w_max (in) stress_max (psi)
86.0 10.6 1.49 × 104
90.0 11.1 1.56 × 104
100 12.4 1.73 × 104
164 20.3 2.85 × 104
Additional Information
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