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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Three Equal Spans » S Section Steel I Beam » S7 × 20
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 = 42.4 in4) for the S7 × 20 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
   
Steel I Beam: S7 × 20 (S7 inch tall × 20 lbf/ft)
L = 3.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
20.0 1.47 × 10-5 17.8
30.0 2.21 × 10-5 26.7
40.0 2.95 × 10-5 35.7
50.0 3.69 × 10-5 44.6
60.0 4.42 × 10-5 53.5
70.0 5.16 × 10-5 62.4
80.0 5.90 × 10-5 71.3
90.0 6.63 × 10-5 80.2
100 7.37 × 10-5 89.2
200 1.47 × 10-4 178
300 2.21 × 10-4 267
400 2.95 × 10-4 357
500 3.69 × 10-4 446
600 4.42 × 10-4 535
700 5.16 × 10-4 624
800 5.90 × 10-4 713
900 6.63 × 10-4 802
1000 7.37 × 10-4 892
2000 0.00147 1780
3000 0.00221 2670
4000 0.00295 3570
5000 0.00369 4460
6000 0.00442 5350
7000 0.00516 6240
8000 0.00590 7130
9000 0.00663 8020
1.00 × 104 0.00737 8920
2.00 × 104 0.0147 1.78 × 104
3.00 × 104 0.0221 2.67 × 104
4.00 × 104 0.0295 3.57 × 104
5.00 × 104 0.0369 4.46 × 104
6.00 × 104 0.0442 5.35 × 104
7.00 × 104 0.0516 6.24 × 104
8.00 × 104 0.0590 7.13 × 104
9.00 × 104 0.0663 8.02 × 104
1.00 × 105 0.0737 8.92 × 104
2.00 × 105 0.147 1.78 × 105
3.00 × 105 0.221 2.67 × 105
3.33 × 105 0.246 2.97 × 105
Steel I Beam: S7 × 20 (S7 inch tall × 20 lbf/ft)
L = 5.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
20.0 1.14 × 10-4 49.5
30.0 1.71 × 10-4 74.3
40.0 2.27 × 10-4 99.1
50.0 2.84 × 10-4 124
60.0 3.41 × 10-4 149
70.0 3.98 × 10-4 173
80.0 4.55 × 10-4 198
90.0 5.12 × 10-4 223
100 5.69 × 10-4 248
200 0.00114 495
300 0.00171 743
400 0.00227 991
500 0.00284 1240
600 0.00341 1490
700 0.00398 1730
800 0.00455 1980
900 0.00512 2230
1000 0.00569 2480
2000 0.0114 4950
3000 0.0171 7430
4000 0.0227 9910
5000 0.0284 1.24 × 104
6000 0.0341 1.49 × 104
7000 0.0398 1.73 × 104
8000 0.0455 1.98 × 104
9000 0.0512 2.23 × 104
1.00 × 104 0.0569 2.48 × 104
2.00 × 104 0.114 4.95 × 104
3.00 × 104 0.171 7.43 × 104
4.00 × 104 0.227 9.91 × 104
5.00 × 104 0.284 1.24 × 105
6.00 × 104 0.341 1.49 × 105
7.00 × 104 0.398 1.73 × 105
8.00 × 104 0.455 1.98 × 105
9.00 × 104 0.512 2.23 × 105
1.00 × 105 0.569 2.48 × 105
1.20 × 105 0.682 2.97 × 105
Steel I Beam: S7 × 20 (S7 inch tall × 20 lbf/ft)
L = 10.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
20.0 0.00182 198
30.0 0.00273 297
40.0 0.00364 396
50.0 0.00455 495
60.0 0.00546 594
70.0 0.00637 693
80.0 0.00728 792
90.0 0.00819 892
100 0.00910 991
200 0.0182 1980
300 0.0273 2970
400 0.0364 3960
500 0.0455 4950
600 0.0546 5940
700 0.0637 6930
800 0.0728 7920
900 0.0819 8920
1000 0.0910 9910
2000 0.182 1.98 × 104
3000 0.273 2.97 × 104
4000 0.364 3.96 × 104
5000 0.455 4.95 × 104
6000 0.546 5.94 × 104
7000 0.637 6.93 × 104
8000 0.728 7.92 × 104
9000 0.819 8.92 × 104
1.00 × 104 0.910 9.91 × 104
2.00 × 104 1.82 1.98 × 105
3.00 × 104 2.73 2.97 × 105
Steel I Beam: S7 × 20 (S7 inch tall × 20 lbf/ft)
L = 15.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
20.0 0.00921 446
30.0 0.0138 669
40.0 0.0184 892
50.0 0.0230 1110
60.0 0.0276 1340
70.0 0.0322 1560
80.0 0.0369 1780
90.0 0.0415 2010
100 0.0461 2230
200 0.0921 4460
300 0.138 6690
400 0.184 8920
500 0.230 1.11 × 104
600 0.276 1.34 × 104
700 0.322 1.56 × 104
800 0.369 1.78 × 104
900 0.415 2.01 × 104
1000 0.461 2.23 × 104
2000 0.921 4.46 × 104
3000 1.38 6.69 × 104
4000 1.84 8.92 × 104
5000 2.30 1.11 × 105
6000 2.76 1.34 × 105
7000 3.22 1.56 × 105
8000 3.69 1.78 × 105
9000 4.15 2.01 × 105
1.00 × 104 4.61 2.23 × 105
1.33 × 104 6.14 2.97 × 105
Steel I Beam: S7 × 20 (S7 inch tall × 20 lbf/ft)
L = 20.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
20.0 0.0291 792
30.0 0.0437 1190
40.0 0.0582 1580
50.0 0.0728 1980
60.0 0.0873 2380
70.0 0.102 2770
80.0 0.116 3170
90.0 0.131 3570
100 0.146 3960
200 0.291 7920
300 0.437 1.19 × 104
400 0.582 1.58 × 104
500 0.728 1.98 × 104
600 0.873 2.38 × 104
700 1.02 2.77 × 104
800 1.16 3.17 × 104
900 1.31 3.57 × 104
1000 1.46 3.96 × 104
2000 2.91 7.92 × 104
3000 4.37 1.19 × 105
4000 5.82 1.58 × 105
4810 7.00 1.91 × 105
Steel I Beam: S7 × 20 (S7 inch tall × 20 lbf/ft)
L = 25.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
20.0 0.0711 1240
30.0 0.107 1860
40.0 0.142 2480
50.0 0.178 3100
60.0 0.213 3710
70.0 0.249 4330
80.0 0.284 4950
90.0 0.320 5570
100 0.355 6190
200 0.711 1.24 × 104
300 1.07 1.86 × 104
400 1.42 2.48 × 104
500 1.78 3.10 × 104
600 2.13 3.71 × 104
700 2.49 4.33 × 104
800 2.84 4.95 × 104
900 3.20 5.57 × 104
1000 3.55 6.19 × 104
1970 7.00 1.22 × 105
Steel I Beam: S7 × 20 (S7 inch tall × 20 lbf/ft)
L = 30.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
20.0 0.147 1780
30.0 0.221 2670
40.0 0.295 3570
50.0 0.369 4460
60.0 0.442 5350
70.0 0.516 6240
80.0 0.590 7130
90.0 0.663 8020
100 0.737 8920
200 1.47 1.78 × 104
300 2.21 2.67 × 104
400 2.95 3.57 × 104
500 3.69 4.46 × 104
600 4.42 5.35 × 104
700 5.16 6.24 × 104
800 5.90 7.13 × 104
900 6.63 8.02 × 104
950 7.00 8.47 × 104
Steel I Beam: S7 × 20 (S7 inch tall × 20 lbf/ft)
L = 40.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
20.0 0.466 3170
30.0 0.699 4750
40.0 0.932 6340
50.0 1.16 7920
60.0 1.40 9510
70.0 1.63 1.11 × 104
80.0 1.86 1.27 × 104
90.0 2.10 1.43 × 104
100 2.33 1.58 × 104
200 4.66 3.17 × 104
300 6.99 4.75 × 104
301 7.00 4.76 × 104
Steel I Beam: S7 × 20 (S7 inch tall × 20 lbf/ft)
L = 50.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
20.0 1.14 4950
30.0 1.71 7430
40.0 2.27 9910
50.0 2.84 1.24 × 104
60.0 3.41 1.49 × 104
70.0 3.98 1.73 × 104
80.0 4.55 1.98 × 104
90.0 5.12 2.23 × 104
100 5.69 2.48 × 104
123 7.00 3.05 × 104
Steel I Beam: S7 × 20 (S7 inch tall × 20 lbf/ft)
L = 60.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
20.0 2.36 7130
30.0 3.54 1.07 × 104
40.0 4.72 1.43 × 104
50.0 5.90 1.78 × 104
59.4 7.00 2.12 × 104
Steel I Beam: S7 × 20 (S7 inch tall × 20 lbf/ft)
L = 70.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
20.0 4.37 9710
30.0 6.55 1.46 × 104
32.0 7.00 1.56 × 104
Additional Information
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FREE Publications
Metal 3D Printing Design Guide

Direct Metal Laser Sintering (DMLS) 3D printing for parts with reduced cost and little waste.

Negotiate Your Salary

Learn the best principles to negotiate the salary you deserve!

3D Scanners

A white paper to assist in the evaluation of 3D scanning hardware solutions.

Essentials of Manufacturing

Information, coverage of important developments and expert commentary in manufacturing.

more publications