Metal 3D Printing Design Guide

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

Injection Molding Design Guide

Guide for high quality and cost-effective plastic injection molding.

Mechanical Engineers Outlook

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

CNC Machining Design Guide

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

more free publications

Materials

Design

Processes

Units

Formulas

Math
Glossary » Beams » Simply Supported » Uniformly Distributed Load » Four 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 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 = 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 3.67 × 10-5 29.3
8.00 3.81 × 10-5 30.4
9.00 4.29 × 10-5 34.2
10.0 4.76 × 10-5 38.0
20.0 9.52 × 10-5 76.1
30.0 1.43 × 10-4 114
40.0 1.90 × 10-4 152
50.0 2.38 × 10-4 190
60.0 2.86 × 10-4 228
70.0 3.33 × 10-4 266
80.0 3.81 × 10-4 304
90.0 4.29 × 10-4 342
100 4.76 × 10-4 380
200 9.52 × 10-4 761
300 0.00143 1140
400 0.00190 1520
500 0.00238 1900
600 0.00286 2280
700 0.00333 2660
800 0.00381 3040
900 0.00429 3420
1000 0.00476 3800
2000 0.00952 7610
3000 0.0143 1.14 × 104
4000 0.0190 1.52 × 104
5000 0.0238 1.90 × 104
6000 0.0286 2.28 × 104
7000 0.0333 2.66 × 104
8000 0.0381 3.04 × 104
9000 0.0429 3.42 × 104
1.00 × 104 0.0476 3.80 × 104
2.00 × 104 0.0952 7.61 × 104
3.00 × 104 0.143 1.14 × 105
4.00 × 104 0.190 1.52 × 105
5.00 × 104 0.238 1.90 × 105
6.00 × 104 0.286 2.28 × 105
7.00 × 104 0.333 2.66 × 105
7.81 × 104 0.372 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 2.83 × 10-4 81.4
8.00 2.94 × 10-4 84.6
9.00 3.31 × 10-4 95.1
10.0 3.67 × 10-4 106
20.0 7.35 × 10-4 211
30.0 0.00110 317
40.0 0.00147 423
50.0 0.00184 528
60.0 0.00220 634
70.0 0.00257 740
80.0 0.00294 846
90.0 0.00331 951
100 0.00367 1060
200 0.00735 2110
300 0.0110 3170
400 0.0147 4230
500 0.0184 5280
600 0.0220 6340
700 0.0257 7400
800 0.0294 8460
900 0.0331 9510
1000 0.0367 1.06 × 104
2000 0.0735 2.11 × 104
3000 0.110 3.17 × 104
4000 0.147 4.23 × 104
5000 0.184 5.28 × 104
6000 0.220 6.34 × 104
7000 0.257 7.40 × 104
8000 0.294 8.46 × 104
9000 0.331 9.51 × 104
1.00 × 104 0.367 1.06 × 105
2.00 × 104 0.735 2.11 × 105
2.81 × 104 1.03 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 0.00453 326
8.00 0.00470 338
9.00 0.00529 380
10.0 0.00588 423
20.0 0.0118 846
30.0 0.0176 1270
40.0 0.0235 1690
50.0 0.0294 2110
60.0 0.0353 2540
70.0 0.0412 2960
80.0 0.0470 3380
90.0 0.0529 3800
100 0.0588 4230
200 0.118 8460
300 0.176 1.27 × 104
400 0.235 1.69 × 104
500 0.294 2.11 × 104
600 0.353 2.54 × 104
700 0.412 2.96 × 104
800 0.470 3.38 × 104
900 0.529 3.80 × 104
1000 0.588 4.23 × 104
2000 1.18 8.46 × 104
3000 1.76 1.27 × 105
4000 2.35 1.69 × 105
5000 2.94 2.11 × 105
6000 3.53 2.54 × 105
6800 4.00 2.88 × 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 0.0229 732
8.00 0.0238 761
9.00 0.0268 856
10.0 0.0298 951
20.0 0.0595 1900
30.0 0.0893 2850
40.0 0.119 3800
50.0 0.149 4760
60.0 0.179 5710
70.0 0.208 6660
80.0 0.238 7610
90.0 0.268 8560
100 0.298 9510
200 0.595 1.90 × 104
300 0.893 2.85 × 104
400 1.19 3.80 × 104
500 1.49 4.76 × 104
600 1.79 5.71 × 104
700 2.08 6.66 × 104
800 2.38 7.61 × 104
900 2.68 8.56 × 104
1000 2.98 9.51 × 104
1340 4.00 1.28 × 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 0.0724 1300
8.00 0.0752 1350
9.00 0.0847 1520
10.0 0.0941 1690
20.0 0.188 3380
30.0 0.282 5070
40.0 0.376 6760
50.0 0.470 8460
60.0 0.564 1.01 × 104
70.0 0.658 1.18 × 104
80.0 0.752 1.35 × 104
90.0 0.847 1.52 × 104
100 0.941 1.69 × 104
200 1.88 3.38 × 104
300 2.82 5.07 × 104
400 3.76 6.76 × 104
425 4.00 7.19 × 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 0.177 2030
8.00 0.184 2110
9.00 0.207 2380
10.0 0.230 2640
20.0 0.459 5280
30.0 0.689 7930
40.0 0.919 1.06 × 104
50.0 1.15 1.32 × 104
60.0 1.38 1.59 × 104
70.0 1.61 1.85 × 104
80.0 1.84 2.11 × 104
90.0 2.07 2.38 × 104
100 2.30 2.64 × 104
174 4.00 4.60 × 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 0.367 2930
8.00 0.381 3040
9.00 0.429 3420
10.0 0.476 3800
20.0 0.952 7610
30.0 1.43 1.14 × 104
40.0 1.90 1.52 × 104
50.0 2.38 1.90 × 104
60.0 2.86 2.28 × 104
70.0 3.33 2.66 × 104
80.0 3.81 3.04 × 104
84.0 4.00 3.20 × 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 1.16 5210
8.00 1.20 5410
9.00 1.35 6090
10.0 1.50 6760
20.0 3.01 1.35 × 104
26.6 4.00 1.80 × 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 2.83 8140
8.00 2.94 8460
9.00 3.31 9510
10.0 3.67 1.06 × 104
10.9 4.00 1.15 × 104
Additional Information
Related Pages
FREE Publications
Metal 3D Printing Design Guide

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

Injection Molding Design Guide

Guide for high quality and cost-effective plastic injection molding.

Mechanical Engineers Outlook

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

CNC Machining Design Guide

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

more publications