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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Four Equal Spans » S Section Steel I Beam » S20 × 75
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 = 1280 in4) for the S20 × 75 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 × 75 (S20 inch tall × 75 lbf/ft)
L = 3.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
75.0 1.70 × 10-6 6.78
80.0 1.81 × 10-6 7.23
90.0 2.04 × 10-6 8.13
100 2.26 × 10-6 9.04
200 4.52 × 10-6 18.1
300 6.79 × 10-6 27.1
400 9.05 × 10-6 36.1
500 1.13 × 10-5 45.2
600 1.36 × 10-5 54.2
700 1.58 × 10-5 63.3
800 1.81 × 10-5 72.3
900 2.04 × 10-5 81.3
1000 2.26 × 10-5 90.4
2000 4.52 × 10-5 181
3000 6.79 × 10-5 271
4000 9.05 × 10-5 361
5000 1.13 × 10-4 452
6000 1.36 × 10-4 542
7000 1.58 × 10-4 633
8000 1.81 × 10-4 723
9000 2.04 × 10-4 813
1.00 × 104 2.26 × 10-4 904
2.00 × 104 4.52 × 10-4 1810
3.00 × 104 6.79 × 10-4 2710
4.00 × 104 9.05 × 10-4 3610
5.00 × 104 0.00113 4520
6.00 × 104 0.00136 5420
7.00 × 104 0.00158 6330
8.00 × 104 0.00181 7230
9.00 × 104 0.00204 8130
1.00 × 105 0.00226 9040
2.00 × 105 0.00452 1.81 × 104
3.00 × 105 0.00679 2.71 × 104
4.00 × 105 0.00905 3.61 × 104
5.00 × 105 0.0113 4.52 × 104
6.00 × 105 0.0136 5.42 × 104
7.00 × 105 0.0158 6.33 × 104
8.00 × 105 0.0181 7.23 × 104
9.00 × 105 0.0204 8.13 × 104
1.00 × 106 0.0226 9.04 × 104
2.00 × 106 0.0452 1.81 × 105
3.00 × 106 0.0679 2.71 × 105
3.29 × 106 0.0743 2.97 × 105
Steel I Beam: S20 × 75 (S20 inch tall × 75 lbf/ft)
L = 5.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
75.0 1.31 × 10-5 18.8
80.0 1.40 × 10-5 20.1
90.0 1.57 × 10-5 22.6
100 1.75 × 10-5 25.1
200 3.49 × 10-5 50.2
300 5.24 × 10-5 75.3
400 6.98 × 10-5 100
500 8.73 × 10-5 126
600 1.05 × 10-4 151
700 1.22 × 10-4 176
800 1.40 × 10-4 201
900 1.57 × 10-4 226
1000 1.75 × 10-4 251
2000 3.49 × 10-4 502
3000 5.24 × 10-4 753
4000 6.98 × 10-4 1000
5000 8.73 × 10-4 1260
6000 0.00105 1510
7000 0.00122 1760
8000 0.00140 2010
9000 0.00157 2260
1.00 × 104 0.00175 2510
2.00 × 104 0.00349 5020
3.00 × 104 0.00524 7530
4.00 × 104 0.00698 1.00 × 104
5.00 × 104 0.00873 1.26 × 104
6.00 × 104 0.0105 1.51 × 104
7.00 × 104 0.0122 1.76 × 104
8.00 × 104 0.0140 2.01 × 104
9.00 × 104 0.0157 2.26 × 104
1.00 × 105 0.0175 2.51 × 104
2.00 × 105 0.0349 5.02 × 104
3.00 × 105 0.0524 7.53 × 104
4.00 × 105 0.0698 1.00 × 105
5.00 × 105 0.0873 1.26 × 105
6.00 × 105 0.105 1.51 × 105
7.00 × 105 0.122 1.76 × 105
8.00 × 105 0.140 2.01 × 105
9.00 × 105 0.157 2.26 × 105
1.00 × 106 0.175 2.51 × 105
1.18 × 106 0.207 2.97 × 105
Steel I Beam: S20 × 75 (S20 inch tall × 75 lbf/ft)
L = 10.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
75.0 2.09 × 10-4 75.3
80.0 2.23 × 10-4 80.3
90.0 2.51 × 10-4 90.4
100 2.79 × 10-4 100
200 5.58 × 10-4 201
300 8.38 × 10-4 301
400 0.00112 402
500 0.00140 502
600 0.00168 602
700 0.00195 703
800 0.00223 803
900 0.00251 904
1000 0.00279 1000
2000 0.00558 2010
3000 0.00838 3010
4000 0.0112 4020
5000 0.0140 5020
6000 0.0168 6020
7000 0.0195 7030
8000 0.0223 8030
9000 0.0251 9040
1.00 × 104 0.0279 1.00 × 104
2.00 × 104 0.0558 2.01 × 104
3.00 × 104 0.0838 3.01 × 104
4.00 × 104 0.112 4.02 × 104
5.00 × 104 0.140 5.02 × 104
6.00 × 104 0.168 6.02 × 104
7.00 × 104 0.195 7.03 × 104
8.00 × 104 0.223 8.03 × 104
9.00 × 104 0.251 9.04 × 104
1.00 × 105 0.279 1.00 × 105
2.00 × 105 0.558 2.01 × 105
2.96 × 105 0.826 2.97 × 105
Steel I Beam: S20 × 75 (S20 inch tall × 75 lbf/ft)
L = 15.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
75.0 0.00106 169
80.0 0.00113 181
90.0 0.00127 203
100 0.00141 226
200 0.00283 452
300 0.00424 678
400 0.00565 904
500 0.00707 1130
600 0.00848 1360
700 0.00990 1580
800 0.0113 1810
900 0.0127 2030
1000 0.0141 2260
2000 0.0283 4520
3000 0.0424 6780
4000 0.0565 9040
5000 0.0707 1.13 × 104
6000 0.0848 1.36 × 104
7000 0.0990 1.58 × 104
8000 0.113 1.81 × 104
9000 0.127 2.03 × 104
1.00 × 104 0.141 2.26 × 104
2.00 × 104 0.283 4.52 × 104
3.00 × 104 0.424 6.78 × 104
4.00 × 104 0.565 9.04 × 104
5.00 × 104 0.707 1.13 × 105
6.00 × 104 0.848 1.36 × 105
7.00 × 104 0.990 1.58 × 105
8.00 × 104 1.13 1.81 × 105
9.00 × 104 1.27 2.03 × 105
1.00 × 105 1.41 2.26 × 105
1.31 × 105 1.86 2.97 × 105
Steel I Beam: S20 × 75 (S20 inch tall × 75 lbf/ft)
L = 20.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
75.0 0.00335 301
80.0 0.00357 321
90.0 0.00402 361
100 0.00447 402
200 0.00894 803
300 0.0134 1200
400 0.0179 1610
500 0.0223 2010
600 0.0268 2410
700 0.0313 2810
800 0.0357 3210
900 0.0402 3610
1000 0.0447 4020
2000 0.0894 8030
3000 0.134 1.20 × 104
4000 0.179 1.61 × 104
5000 0.223 2.01 × 104
6000 0.268 2.41 × 104
7000 0.313 2.81 × 104
8000 0.357 3.21 × 104
9000 0.402 3.61 × 104
1.00 × 104 0.447 4.02 × 104
2.00 × 104 0.894 8.03 × 104
3.00 × 104 1.34 1.20 × 105
4.00 × 104 1.79 1.61 × 105
5.00 × 104 2.23 2.01 × 105
6.00 × 104 2.68 2.41 × 105
7.00 × 104 3.13 2.81 × 105
7.40 × 104 3.30 2.97 × 105
Steel I Beam: S20 × 75 (S20 inch tall × 75 lbf/ft)
L = 25.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
75.0 0.00818 471
80.0 0.00873 502
90.0 0.00982 565
100 0.0109 628
200 0.0218 1260
300 0.0327 1880
400 0.0436 2510
500 0.0545 3140
600 0.0654 3770
700 0.0764 4390
800 0.0873 5020
900 0.0982 5650
1000 0.109 6280
2000 0.218 1.26 × 104
3000 0.327 1.88 × 104
4000 0.436 2.51 × 104
5000 0.545 3.14 × 104
6000 0.654 3.77 × 104
7000 0.764 4.39 × 104
8000 0.873 5.02 × 104
9000 0.982 5.65 × 104
1.00 × 104 1.09 6.28 × 104
2.00 × 104 2.18 1.26 × 105
3.00 × 104 3.27 1.88 × 105
4.00 × 104 4.36 2.51 × 105
4.73 × 104 5.16 2.97 × 105
Steel I Beam: S20 × 75 (S20 inch tall × 75 lbf/ft)
L = 30.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
75.0 0.0170 678
80.0 0.0181 723
90.0 0.0204 813
100 0.0226 904
200 0.0452 1810
300 0.0679 2710
400 0.0905 3610
500 0.113 4520
600 0.136 5420
700 0.158 6330
800 0.181 7230
900 0.204 8130
1000 0.226 9040
2000 0.452 1.81 × 104
3000 0.679 2.71 × 104
4000 0.905 3.61 × 104
5000 1.13 4.52 × 104
6000 1.36 5.42 × 104
7000 1.58 6.33 × 104
8000 1.81 7.23 × 104
9000 2.04 8.13 × 104
1.00 × 104 2.26 9.04 × 104
2.00 × 104 4.52 1.81 × 105
3.00 × 104 6.79 2.71 × 105
3.29 × 104 7.43 2.97 × 105
Steel I Beam: S20 × 75 (S20 inch tall × 75 lbf/ft)
L = 40.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
75.0 0.0536 1200
80.0 0.0572 1290
90.0 0.0643 1450
100 0.0715 1610
200 0.143 3210
300 0.214 4820
400 0.286 6430
500 0.357 8030
600 0.429 9640
700 0.500 1.12 × 104
800 0.572 1.29 × 104
900 0.643 1.45 × 104
1000 0.715 1.61 × 104
2000 1.43 3.21 × 104
3000 2.14 4.82 × 104
4000 2.86 6.43 × 104
5000 3.57 8.03 × 104
6000 4.29 9.64 × 104
7000 5.00 1.12 × 105
8000 5.72 1.29 × 105
9000 6.43 1.45 × 105
1.00 × 104 7.15 1.61 × 105
1.85 × 104 13.2 2.97 × 105
Steel I Beam: S20 × 75 (S20 inch tall × 75 lbf/ft)
L = 50.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
75.0 0.131 1880
80.0 0.140 2010
90.0 0.157 2260
100 0.175 2510
200 0.349 5020
300 0.524 7530
400 0.698 1.00 × 104
500 0.873 1.26 × 104
600 1.05 1.51 × 104
700 1.22 1.76 × 104
800 1.40 2.01 × 104
900 1.57 2.26 × 104
1000 1.75 2.51 × 104
2000 3.49 5.02 × 104
3000 5.24 7.53 × 104
4000 6.98 1.00 × 105
5000 8.73 1.26 × 105
6000 10.5 1.51 × 105
7000 12.2 1.76 × 105
8000 14.0 2.01 × 105
9000 15.7 2.26 × 105
1.00 × 104 17.5 2.51 × 105
1.18 × 104 20.7 2.97 × 105
Steel I Beam: S20 × 75 (S20 inch tall × 75 lbf/ft)
L = 60.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
75.0 0.271 2710
80.0 0.290 2890
90.0 0.326 3250
100 0.362 3610
200 0.724 7230
300 1.09 1.08 × 104
400 1.45 1.45 × 104
500 1.81 1.81 × 104
600 2.17 2.17 × 104
700 2.53 2.53 × 104
800 2.90 2.89 × 104
900 3.26 3.25 × 104
1000 3.62 3.61 × 104
2000 7.24 7.23 × 104
3000 10.9 1.08 × 105
4000 14.5 1.45 × 105
5000 18.1 1.81 × 105
5530 20.0 2.00 × 105
Steel I Beam: S20 × 75 (S20 inch tall × 75 lbf/ft)
L = 70.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
75.0 0.503 3690
80.0 0.536 3940
90.0 0.603 4430
100 0.670 4920
200 1.34 9840
300 2.01 1.48 × 104
400 2.68 1.97 × 104
500 3.35 2.46 × 104
600 4.02 2.95 × 104
700 4.69 3.44 × 104
800 5.36 3.94 × 104
900 6.03 4.43 × 104
1000 6.70 4.92 × 104
2000 13.4 9.84 × 104
2980 20.0 1.47 × 105
Steel I Beam: S20 × 75 (S20 inch tall × 75 lbf/ft)
L = 80.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
75.0 0.858 4820
80.0 0.915 5140
90.0 1.03 5780
100 1.14 6430
200 2.29 1.29 × 104
300 3.43 1.93 × 104
400 4.58 2.57 × 104
500 5.72 3.21 × 104
600 6.86 3.86 × 104
700 8.01 4.50 × 104
800 9.15 5.14 × 104
900 10.3 5.78 × 104
1000 11.4 6.43 × 104
1750 20.0 1.12 × 105
Steel I Beam: S20 × 75 (S20 inch tall × 75 lbf/ft)
L = 90.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
75.0 1.37 6100
80.0 1.47 6510
90.0 1.65 7320
100 1.83 8130
200 3.66 1.63 × 104
300 5.50 2.44 × 104
400 7.33 3.25 × 104
500 9.16 4.07 × 104
600 11.0 4.88 × 104
700 12.8 5.69 × 104
800 14.7 6.51 × 104
900 16.5 7.32 × 104
1000 18.3 8.13 × 104
1090 20.0 8.88 × 104
Steel I Beam: S20 × 75 (S20 inch tall × 75 lbf/ft)
L = 100 ft
P (lbf/ft) w_max (in) stress_max (psi)
75.0 2.09 7530
80.0 2.23 8030
90.0 2.51 9040
100 2.79 1.00 × 104
200 5.58 2.01 × 104
300 8.38 3.01 × 104
400 11.2 4.02 × 104
500 14.0 5.02 × 104
600 16.8 6.02 × 104
700 19.5 7.03 × 104
716 20.0 7.19 × 104
Steel I Beam: S20 × 75 (S20 inch tall × 75 lbf/ft)
L = 125 ft
P (lbf/ft) w_max (in) stress_max (psi)
75.0 5.11 1.18 × 104
80.0 5.45 1.26 × 104
90.0 6.14 1.41 × 104
100 6.82 1.57 × 104
200 13.6 3.14 × 104
293 20.0 4.60 × 104
Steel I Beam: S20 × 75 (S20 inch tall × 75 lbf/ft)
L = 150 ft
P (lbf/ft) w_max (in) stress_max (psi)
75.0 10.6 1.69 × 104
80.0 11.3 1.81 × 104
90.0 12.7 2.03 × 104
100 14.1 2.26 × 104
141 20.0 3.20 × 104
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