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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Three Equal Spans » S Section Steel I Beam » S4 × 7.7
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 = 6.08 in4) for the S4 × 7.7 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
   
Steel I Beam: S4 × 7.7 (S4 inch tall × 7.7 lbf/ft)
L = 3.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
7.70 3.96 × 10-5 27.4
8.00 4.11 × 10-5 28.4
9.00 4.63 × 10-5 32.0
10.0 5.14 × 10-5 35.5
20.0 1.03 × 10-4 71.1
30.0 1.54 × 10-4 107
40.0 2.06 × 10-4 142
50.0 2.57 × 10-4 178
60.0 3.08 × 10-4 213
70.0 3.60 × 10-4 249
80.0 4.11 × 10-4 284
90.0 4.63 × 10-4 320
100 5.14 × 10-4 355
200 0.00103 711
300 0.00154 1070
400 0.00206 1420
500 0.00257 1780
600 0.00308 2130
700 0.00360 2490
800 0.00411 2840
900 0.00463 3200
1000 0.00514 3550
2000 0.0103 7110
3000 0.0154 1.07 × 104
4000 0.0206 1.42 × 104
5000 0.0257 1.78 × 104
6000 0.0308 2.13 × 104
7000 0.0360 2.49 × 104
8000 0.0411 2.84 × 104
9000 0.0463 3.20 × 104
1.00 × 104 0.0514 3.55 × 104
2.00 × 104 0.103 7.11 × 104
3.00 × 104 0.154 1.07 × 105
4.00 × 104 0.206 1.42 × 105
5.00 × 104 0.257 1.78 × 105
6.00 × 104 0.308 2.13 × 105
7.00 × 104 0.360 2.49 × 105
8.00 × 104 0.411 2.84 × 105
8.36 × 104 0.430 2.97 × 105
Steel I Beam: S4 × 7.7 (S4 inch tall × 7.7 lbf/ft)
L = 5.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
7.70 3.05 × 10-4 76.0
8.00 3.17 × 10-4 78.9
9.00 3.57 × 10-4 88.8
10.0 3.97 × 10-4 98.7
20.0 7.93 × 10-4 197
30.0 0.00119 296
40.0 0.00159 395
50.0 0.00198 493
60.0 0.00238 592
70.0 0.00278 691
80.0 0.00317 789
90.0 0.00357 888
100 0.00397 987
200 0.00793 1970
300 0.0119 2960
400 0.0159 3950
500 0.0198 4930
600 0.0238 5920
700 0.0278 6910
800 0.0317 7890
900 0.0357 8880
1000 0.0397 9870
2000 0.0793 1.97 × 104
3000 0.119 2.96 × 104
4000 0.159 3.95 × 104
5000 0.198 4.93 × 104
6000 0.238 5.92 × 104
7000 0.278 6.91 × 104
8000 0.317 7.89 × 104
9000 0.357 8.88 × 104
1.00 × 104 0.397 9.87 × 104
2.00 × 104 0.793 1.97 × 105
3.00 × 104 1.19 2.96 × 105
3.01 × 104 1.19 2.97 × 105
Steel I Beam: S4 × 7.7 (S4 inch tall × 7.7 lbf/ft)
L = 10.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
7.70 0.00489 304
8.00 0.00508 316
9.00 0.00571 355
10.0 0.00635 395
20.0 0.0127 789
30.0 0.0190 1180
40.0 0.0254 1580
50.0 0.0317 1970
60.0 0.0381 2370
70.0 0.0444 2760
80.0 0.0508 3160
90.0 0.0571 3550
100 0.0635 3950
200 0.127 7890
300 0.190 1.18 × 104
400 0.254 1.58 × 104
500 0.317 1.97 × 104
600 0.381 2.37 × 104
700 0.444 2.76 × 104
800 0.508 3.16 × 104
900 0.571 3.55 × 104
1000 0.635 3.95 × 104
2000 1.27 7.89 × 104
3000 1.90 1.18 × 105
4000 2.54 1.58 × 105
5000 3.17 1.97 × 105
6000 3.81 2.37 × 105
6300 4.00 2.49 × 105
Steel I Beam: S4 × 7.7 (S4 inch tall × 7.7 lbf/ft)
L = 15.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
7.70 0.0247 684
8.00 0.0257 711
9.00 0.0289 799
10.0 0.0321 888
20.0 0.0642 1780
30.0 0.0964 2660
40.0 0.128 3550
50.0 0.161 4440
60.0 0.193 5330
70.0 0.225 6220
80.0 0.257 7110
90.0 0.289 7990
100 0.321 8880
200 0.642 1.78 × 104
300 0.964 2.66 × 104
400 1.28 3.55 × 104
500 1.61 4.44 × 104
600 1.93 5.33 × 104
700 2.25 6.22 × 104
800 2.57 7.11 × 104
900 2.89 7.99 × 104
1000 3.21 8.88 × 104
1250 4.00 1.11 × 105
Steel I Beam: S4 × 7.7 (S4 inch tall × 7.7 lbf/ft)
L = 20.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
7.70 0.0782 1220
8.00 0.0812 1260
9.00 0.0914 1420
10.0 0.102 1580
20.0 0.203 3160
30.0 0.305 4740
40.0 0.406 6320
50.0 0.508 7890
60.0 0.609 9470
70.0 0.711 1.11 × 104
80.0 0.812 1.26 × 104
90.0 0.914 1.42 × 104
100 1.02 1.58 × 104
200 2.03 3.16 × 104
300 3.05 4.74 × 104
394 4.00 6.22 × 104
Steel I Beam: S4 × 7.7 (S4 inch tall × 7.7 lbf/ft)
L = 25.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
7.70 0.191 1900
8.00 0.198 1970
9.00 0.223 2220
10.0 0.248 2470
20.0 0.496 4930
30.0 0.744 7400
40.0 0.991 9870
50.0 1.24 1.23 × 104
60.0 1.49 1.48 × 104
70.0 1.74 1.73 × 104
80.0 1.98 1.97 × 104
90.0 2.23 2.22 × 104
100 2.48 2.47 × 104
161 4.00 3.98 × 104
Steel I Beam: S4 × 7.7 (S4 inch tall × 7.7 lbf/ft)
L = 30.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
7.70 0.396 2740
8.00 0.411 2840
9.00 0.463 3200
10.0 0.514 3550
20.0 1.03 7110
30.0 1.54 1.07 × 104
40.0 2.06 1.42 × 104
50.0 2.57 1.78 × 104
60.0 3.08 2.13 × 104
70.0 3.60 2.49 × 104
77.8 4.00 2.76 × 104
Steel I Beam: S4 × 7.7 (S4 inch tall × 7.7 lbf/ft)
L = 40.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
7.70 1.25 4860
8.00 1.30 5050
9.00 1.46 5680
10.0 1.62 6320
20.0 3.25 1.26 × 104
24.6 4.00 1.56 × 104
Steel I Beam: S4 × 7.7 (S4 inch tall × 7.7 lbf/ft)
L = 50.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
7.70 3.05 7600
8.00 3.17 7890
9.00 3.57 8880
10.0 3.97 9870
10.1 4.00 9950
Additional Information
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Mechanical Engineers Outlook

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

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

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Optimize your designs, reduce machining time, and lower your costs.

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

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