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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Four 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 four equal spans, we compute the displacement at the middle of the first and fourth spans, and the maximum normal stress stress_max occuring at the second and fourth 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
L = 80 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 1.37 × 10-5 19.1
30.0 2.05 × 10-5 28.6
40.0 2.73 × 10-5 38.2
50.0 3.41 × 10-5 47.7
60.0 4.10 × 10-5 57.3
70.0 4.78 × 10-5 66.8
80.0 5.46 × 10-5 76.4
90.0 6.15 × 10-5 85.9
100 6.83 × 10-5 95.5
200 1.37 × 10-4 191
300 2.05 × 10-4 286
400 2.73 × 10-4 382
500 3.41 × 10-4 477
600 4.10 × 10-4 573
700 4.78 × 10-4 668
800 5.46 × 10-4 764
900 6.15 × 10-4 859
1000 6.83 × 10-4 955
2000 0.00137 1910
3000 0.00205 2860
4000 0.00273 3820
5000 0.00341 4770
6000 0.00410 5730
7000 0.00478 6680
8000 0.00546 7640
9000 0.00615 8590
1.00 × 104 0.00683 9550
2.00 × 104 0.0137 1.91 × 104
3.00 × 104 0.0205 2.86 × 104
4.00 × 104 0.0273 3.82 × 104
5.00 × 104 0.0341 4.77 × 104
6.00 × 104 0.0410 5.73 × 104
7.00 × 104 0.0478 6.68 × 104
8.00 × 104 0.0546 7.64 × 104
9.00 × 104 0.0615 8.59 × 104
1.00 × 105 0.0683 9.55 × 104
2.00 × 105 0.137 1.91 × 105
3.00 × 105 0.205 2.86 × 105
3.11 × 105 0.212 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 1.05 × 10-4 53.0
30.0 1.58 × 10-4 79.6
40.0 2.11 × 10-4 106
50.0 2.63 × 10-4 133
60.0 3.16 × 10-4 159
70.0 3.69 × 10-4 186
80.0 4.21 × 10-4 212
90.0 4.74 × 10-4 239
100 5.27 × 10-4 265
200 0.00105 530
300 0.00158 796
400 0.00211 1060
500 0.00263 1330
600 0.00316 1590
700 0.00369 1860
800 0.00421 2120
900 0.00474 2390
1000 0.00527 2650
2000 0.0105 5300
3000 0.0158 7960
4000 0.0211 1.06 × 104
5000 0.0263 1.33 × 104
6000 0.0316 1.59 × 104
7000 0.0369 1.86 × 104
8000 0.0421 2.12 × 104
9000 0.0474 2.39 × 104
1.00 × 104 0.0527 2.65 × 104
2.00 × 104 0.105 5.30 × 104
3.00 × 104 0.158 7.96 × 104
4.00 × 104 0.211 1.06 × 105
5.00 × 104 0.263 1.33 × 105
6.00 × 104 0.316 1.59 × 105
7.00 × 104 0.369 1.86 × 105
8.00 × 104 0.421 2.12 × 105
9.00 × 104 0.474 2.39 × 105
1.00 × 105 0.527 2.65 × 105
1.12 × 105 0.590 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 0.00169 212
30.0 0.00253 318
40.0 0.00337 424
50.0 0.00421 530
60.0 0.00506 637
70.0 0.00590 743
80.0 0.00674 849
90.0 0.00759 955
100 0.00843 1060
200 0.0169 2120
300 0.0253 3180
400 0.0337 4240
500 0.0421 5300
600 0.0506 6370
700 0.0590 7430
800 0.0674 8490
900 0.0759 9550
1000 0.0843 1.06 × 104
2000 0.169 2.12 × 104
3000 0.253 3.18 × 104
4000 0.337 4.24 × 104
5000 0.421 5.30 × 104
6000 0.506 6.37 × 104
7000 0.590 7.43 × 104
8000 0.674 8.49 × 104
9000 0.759 9.55 × 104
1.00 × 104 0.843 1.06 × 105
2.00 × 104 1.69 2.12 × 105
2.80 × 104 2.36 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 0.00854 477
30.0 0.0128 716
40.0 0.0171 955
50.0 0.0213 1190
60.0 0.0256 1430
70.0 0.0299 1670
80.0 0.0341 1910
90.0 0.0384 2150
100 0.0427 2390
200 0.0854 4770
300 0.128 7160
400 0.171 9550
500 0.213 1.19 × 104
600 0.256 1.43 × 104
700 0.299 1.67 × 104
800 0.341 1.91 × 104
900 0.384 2.15 × 104
1000 0.427 2.39 × 104
2000 0.854 4.77 × 104
3000 1.28 7.16 × 104
4000 1.71 9.55 × 104
5000 2.13 1.19 × 105
6000 2.56 1.43 × 105
7000 2.99 1.67 × 105
8000 3.41 1.91 × 105
9000 3.84 2.15 × 105
1.00 × 104 4.27 2.39 × 105
1.24 × 104 5.31 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 0.0270 849
30.0 0.0405 1270
40.0 0.0540 1700
50.0 0.0674 2120
60.0 0.0809 2550
70.0 0.0944 2970
80.0 0.108 3390
90.0 0.121 3820
100 0.135 4240
200 0.270 8490
300 0.405 1.27 × 104
400 0.540 1.70 × 104
500 0.674 2.12 × 104
600 0.809 2.55 × 104
700 0.944 2.97 × 104
800 1.08 3.39 × 104
900 1.21 3.82 × 104
1000 1.35 4.24 × 104
2000 2.70 8.49 × 104
3000 4.05 1.27 × 105
4000 5.40 1.70 × 105
5000 6.74 2.12 × 105
5190 7.00 2.20 × 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 0.0659 1330
30.0 0.0988 1990
40.0 0.132 2650
50.0 0.165 3320
60.0 0.198 3980
70.0 0.231 4640
80.0 0.263 5300
90.0 0.296 5970
100 0.329 6630
200 0.659 1.33 × 104
300 0.988 1.99 × 104
400 1.32 2.65 × 104
500 1.65 3.32 × 104
600 1.98 3.98 × 104
700 2.31 4.64 × 104
800 2.63 5.30 × 104
900 2.96 5.97 × 104
1000 3.29 6.63 × 104
2000 6.59 1.33 × 105
2130 7.00 1.41 × 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 0.137 1910
30.0 0.205 2860
40.0 0.273 3820
50.0 0.341 4770
60.0 0.410 5730
70.0 0.478 6680
80.0 0.546 7640
90.0 0.615 8590
100 0.683 9550
200 1.37 1.91 × 104
300 2.05 2.86 × 104
400 2.73 3.82 × 104
500 3.41 4.77 × 104
600 4.10 5.73 × 104
700 4.78 6.68 × 104
800 5.46 7.64 × 104
900 6.15 8.59 × 104
1000 6.83 9.55 × 104
1030 7.00 9.79 × 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 0.432 3390
30.0 0.647 5090
40.0 0.863 6790
50.0 1.08 8490
60.0 1.29 1.02 × 104
70.0 1.51 1.19 × 104
80.0 1.73 1.36 × 104
90.0 1.94 1.53 × 104
100 2.16 1.70 × 104
200 4.32 3.39 × 104
300 6.47 5.09 × 104
324 7.00 5.51 × 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 1.05 5300
30.0 1.58 7960
40.0 2.11 1.06 × 104
50.0 2.63 1.33 × 104
60.0 3.16 1.59 × 104
70.0 3.69 1.86 × 104
80.0 4.21 2.12 × 104
90.0 4.74 2.39 × 104
100 5.27 2.65 × 104
133 7.00 3.52 × 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 2.19 7640
30.0 3.28 1.15 × 104
40.0 4.37 1.53 × 104
50.0 5.46 1.91 × 104
60.0 6.56 2.29 × 104
64.1 7.00 2.45 × 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 4.05 1.04 × 104
30.0 6.07 1.56 × 104
34.6 7.00 1.80 × 104
Steel I Beam: S7 × 20 (S7 inch tall × 20 lbf/ft)
L = 80.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
20.0 6.91 1.36 × 104
20.3 7.00 1.38 × 104
Additional Information
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FREE Publications
Mechanical Engineers Outlook

Guide for those interested in becoming a mechanical engineer. Includes qualifications, pay, and job duties.

STEM Career Outlook

Wages, employment opportunities, and growth projections for STEM jobs.

3D Scanners

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

Metal 3D Printing Design Guide

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

more publications