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Wide Flange Steel I Beam: W21 × 50
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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Three Equal Spans » Wide Flange Steel I Beam » W21 × 50
Wide Flange 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 = 984 in4) for the W21 × 50 Wide Flange 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: W21 × 50 (Wide Flange 21 inch tall × 50 lbf/ft)
L = 3.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
50.0 1.59 × 10-6 5.72
60.0 1.91 × 10-6 6.86
70.0 2.22 × 10-6 8.00
80.0 2.54 × 10-6 9.14
90.0 2.86 × 10-6 10.3
100 3.18 × 10-6 11.4
200 6.35 × 10-6 22.9
300 9.53 × 10-6 34.3
400 1.27 × 10-5 45.7
500 1.59 × 10-5 57.2
600 1.91 × 10-5 68.6
700 2.22 × 10-5 80.0
800 2.54 × 10-5 91.4
900 2.86 × 10-5 103
1000 3.18 × 10-5 114
2000 6.35 × 10-5 229
3000 9.53 × 10-5 343
4000 1.27 × 10-4 457
5000 1.59 × 10-4 572
6000 1.91 × 10-4 686
7000 2.22 × 10-4 800
8000 2.54 × 10-4 914
9000 2.86 × 10-4 1030
1.00 × 104 3.18 × 10-4 1140
2.00 × 104 6.35 × 10-4 2290
3.00 × 104 9.53 × 10-4 3430
4.00 × 104 0.00127 4570
5.00 × 104 0.00159 5720
6.00 × 104 0.00191 6860
7.00 × 104 0.00222 8000
8.00 × 104 0.00254 9140
9.00 × 104 0.00286 1.03 × 104
1.00 × 105 0.00318 1.14 × 104
2.00 × 105 0.00635 2.29 × 104
3.00 × 105 0.00953 3.43 × 104
4.00 × 105 0.0127 4.57 × 104
5.00 × 105 0.0159 5.72 × 104
6.00 × 105 0.0191 6.86 × 104
7.00 × 105 0.0222 8.00 × 104
8.00 × 105 0.0254 9.14 × 104
9.00 × 105 0.0286 1.03 × 105
1.00 × 106 0.0318 1.14 × 105
2.00 × 106 0.0635 2.29 × 105
2.60 × 106 0.0825 2.97 × 105
Steel I Beam: W21 × 50 (Wide Flange 21 inch tall × 50 lbf/ft)
L = 5.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
50.0 1.23 × 10-5 15.9
60.0 1.47 × 10-5 19.1
70.0 1.72 × 10-5 22.2
80.0 1.96 × 10-5 25.4
90.0 2.21 × 10-5 28.6
100 2.45 × 10-5 31.8
200 4.90 × 10-5 63.5
300 7.35 × 10-5 95.3
400 9.80 × 10-5 127
500 1.23 × 10-4 159
600 1.47 × 10-4 191
700 1.72 × 10-4 222
800 1.96 × 10-4 254
900 2.21 × 10-4 286
1000 2.45 × 10-4 318
2000 4.90 × 10-4 635
3000 7.35 × 10-4 953
4000 9.80 × 10-4 1270
5000 0.00123 1590
6000 0.00147 1910
7000 0.00172 2220
8000 0.00196 2540
9000 0.00221 2860
1.00 × 104 0.00245 3180
2.00 × 104 0.00490 6350
3.00 × 104 0.00735 9530
4.00 × 104 0.00980 1.27 × 104
5.00 × 104 0.0123 1.59 × 104
6.00 × 104 0.0147 1.91 × 104
7.00 × 104 0.0172 2.22 × 104
8.00 × 104 0.0196 2.54 × 104
9.00 × 104 0.0221 2.86 × 104
1.00 × 105 0.0245 3.18 × 104
2.00 × 105 0.0490 6.35 × 104
3.00 × 105 0.0735 9.53 × 104
4.00 × 105 0.0980 1.27 × 105
5.00 × 105 0.123 1.59 × 105
6.00 × 105 0.147 1.91 × 105
7.00 × 105 0.172 2.22 × 105
8.00 × 105 0.196 2.54 × 105
9.00 × 105 0.221 2.86 × 105
9.35 × 105 0.229 2.97 × 105
Steel I Beam: W21 × 50 (Wide Flange 21 inch tall × 50 lbf/ft)
L = 10.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
50.0 1.96 × 10-4 63.5
60.0 2.35 × 10-4 76.2
70.0 2.74 × 10-4 88.9
80.0 3.14 × 10-4 102
90.0 3.53 × 10-4 114
100 3.92 × 10-4 127
200 7.84 × 10-4 254
300 0.00118 381
400 0.00157 508
500 0.00196 635
600 0.00235 762
700 0.00274 889
800 0.00314 1020
900 0.00353 1140
1000 0.00392 1270
2000 0.00784 2540
3000 0.0118 3810
4000 0.0157 5080
5000 0.0196 6350
6000 0.0235 7620
7000 0.0274 8890
8000 0.0314 1.02 × 104
9000 0.0353 1.14 × 104
1.00 × 104 0.0392 1.27 × 104
2.00 × 104 0.0784 2.54 × 104
3.00 × 104 0.118 3.81 × 104
4.00 × 104 0.157 5.08 × 104
5.00 × 104 0.196 6.35 × 104
6.00 × 104 0.235 7.62 × 104
7.00 × 104 0.274 8.89 × 104
8.00 × 104 0.314 1.02 × 105
9.00 × 104 0.353 1.14 × 105
1.00 × 105 0.392 1.27 × 105
2.00 × 105 0.784 2.54 × 105
2.34 × 105 0.917 2.97 × 105
Steel I Beam: W21 × 50 (Wide Flange 21 inch tall × 50 lbf/ft)
L = 15.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
50.0 9.92 × 10-4 143
60.0 0.00119 171
70.0 0.00139 200
80.0 0.00159 229
90.0 0.00179 257
100 0.00198 286
200 0.00397 572
300 0.00595 857
400 0.00794 1140
500 0.00992 1430
600 0.0119 1710
700 0.0139 2000
800 0.0159 2290
900 0.0179 2570
1000 0.0198 2860
2000 0.0397 5720
3000 0.0595 8570
4000 0.0794 1.14 × 104
5000 0.0992 1.43 × 104
6000 0.119 1.71 × 104
7000 0.139 2.00 × 104
8000 0.159 2.29 × 104
9000 0.179 2.57 × 104
1.00 × 104 0.198 2.86 × 104
2.00 × 104 0.397 5.72 × 104
3.00 × 104 0.595 8.57 × 104
4.00 × 104 0.794 1.14 × 105
5.00 × 104 0.992 1.43 × 105
6.00 × 104 1.19 1.71 × 105
7.00 × 104 1.39 2.00 × 105
8.00 × 104 1.59 2.29 × 105
9.00 × 104 1.79 2.57 × 105
1.00 × 105 1.98 2.86 × 105
1.04 × 105 2.06 2.97 × 105
Steel I Beam: W21 × 50 (Wide Flange 21 inch tall × 50 lbf/ft)
L = 20.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
50.0 0.00314 254
60.0 0.00376 305
70.0 0.00439 356
80.0 0.00502 406
90.0 0.00565 457
100 0.00627 508
200 0.0125 1020
300 0.0188 1520
400 0.0251 2030
500 0.0314 2540
600 0.0376 3050
700 0.0439 3560
800 0.0502 4060
900 0.0565 4570
1000 0.0627 5080
2000 0.125 1.02 × 104
3000 0.188 1.52 × 104
4000 0.251 2.03 × 104
5000 0.314 2.54 × 104
6000 0.376 3.05 × 104
7000 0.439 3.56 × 104
8000 0.502 4.06 × 104
9000 0.565 4.57 × 104
1.00 × 104 0.627 5.08 × 104
2.00 × 104 1.25 1.02 × 105
3.00 × 104 1.88 1.52 × 105
4.00 × 104 2.51 2.03 × 105
5.00 × 104 3.14 2.54 × 105
5.85 × 104 3.67 2.97 × 105
Steel I Beam: W21 × 50 (Wide Flange 21 inch tall × 50 lbf/ft)
L = 25.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
50.0 0.00766 397
60.0 0.00919 476
70.0 0.0107 556
80.0 0.0123 635
90.0 0.0138 714
100 0.0153 794
200 0.0306 1590
300 0.0459 2380
400 0.0613 3180
500 0.0766 3970
600 0.0919 4760
700 0.107 5560
800 0.123 6350
900 0.138 7140
1000 0.153 7940
2000 0.306 1.59 × 104
3000 0.459 2.38 × 104
4000 0.613 3.18 × 104
5000 0.766 3.97 × 104
6000 0.919 4.76 × 104
7000 1.07 5.56 × 104
8000 1.23 6.35 × 104
9000 1.38 7.14 × 104
1.00 × 104 1.53 7.94 × 104
2.00 × 104 3.06 1.59 × 105
3.00 × 104 4.59 2.38 × 105
3.74 × 104 5.73 2.97 × 105
Steel I Beam: W21 × 50 (Wide Flange 21 inch tall × 50 lbf/ft)
L = 30.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
50.0 0.0159 572
60.0 0.0191 686
70.0 0.0222 800
80.0 0.0254 914
90.0 0.0286 1030
100 0.0318 1140
200 0.0635 2290
300 0.0953 3430
400 0.127 4570
500 0.159 5720
600 0.191 6860
700 0.222 8000
800 0.254 9140
900 0.286 1.03 × 104
1000 0.318 1.14 × 104
2000 0.635 2.29 × 104
3000 0.953 3.43 × 104
4000 1.27 4.57 × 104
5000 1.59 5.72 × 104
6000 1.91 6.86 × 104
7000 2.22 8.00 × 104
8000 2.54 9.14 × 104
9000 2.86 1.03 × 105
1.00 × 104 3.18 1.14 × 105
2.00 × 104 6.35 2.29 × 105
2.60 × 104 8.25 2.97 × 105
Steel I Beam: W21 × 50 (Wide Flange 21 inch tall × 50 lbf/ft)
L = 40.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
50.0 0.0502 1020
60.0 0.0602 1220
70.0 0.0703 1420
80.0 0.0803 1630
90.0 0.0903 1830
100 0.100 2030
200 0.201 4060
300 0.301 6100
400 0.401 8130
500 0.502 1.02 × 104
600 0.602 1.22 × 104
700 0.703 1.42 × 104
800 0.803 1.63 × 104
900 0.903 1.83 × 104
1000 1.00 2.03 × 104
2000 2.01 4.06 × 104
3000 3.01 6.10 × 104
4000 4.01 8.13 × 104
5000 5.02 1.02 × 105
6000 6.02 1.22 × 105
7000 7.03 1.42 × 105
8000 8.03 1.63 × 105
9000 9.03 1.83 × 105
1.00 × 104 10.0 2.03 × 105
1.46 × 104 14.7 2.97 × 105
Steel I Beam: W21 × 50 (Wide Flange 21 inch tall × 50 lbf/ft)
L = 50.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
50.0 0.123 1590
60.0 0.147 1910
70.0 0.172 2220
80.0 0.196 2540
90.0 0.221 2860
100 0.245 3180
200 0.490 6350
300 0.735 9530
400 0.980 1.27 × 104
500 1.23 1.59 × 104
600 1.47 1.91 × 104
700 1.72 2.22 × 104
800 1.96 2.54 × 104
900 2.21 2.86 × 104
1000 2.45 3.18 × 104
2000 4.90 6.35 × 104
3000 7.35 9.53 × 104
4000 9.80 1.27 × 105
5000 12.3 1.59 × 105
6000 14.7 1.91 × 105
7000 17.2 2.22 × 105
8000 19.6 2.54 × 105
8500 20.8 2.70 × 105
Steel I Beam: W21 × 50 (Wide Flange 21 inch tall × 50 lbf/ft)
L = 60.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
50.0 0.254 2290
60.0 0.305 2740
70.0 0.356 3200
80.0 0.406 3660
90.0 0.457 4120
100 0.508 4570
200 1.02 9140
300 1.52 1.37 × 104
400 2.03 1.83 × 104
500 2.54 2.29 × 104
600 3.05 2.74 × 104
700 3.56 3.20 × 104
800 4.06 3.66 × 104
900 4.57 4.12 × 104
1000 5.08 4.57 × 104
2000 10.2 9.14 × 104
3000 15.2 1.37 × 105
4000 20.3 1.83 × 105
4100 20.8 1.87 × 105
Steel I Beam: W21 × 50 (Wide Flange 21 inch tall × 50 lbf/ft)
L = 70.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
50.0 0.471 3110
60.0 0.565 3730
70.0 0.659 4360
80.0 0.753 4980
90.0 0.847 5600
100 0.941 6220
200 1.88 1.24 × 104
300 2.82 1.87 × 104
400 3.77 2.49 × 104
500 4.71 3.11 × 104
600 5.65 3.73 × 104
700 6.59 4.36 × 104
800 7.53 4.98 × 104
900 8.47 5.60 × 104
1000 9.41 6.22 × 104
2000 18.8 1.24 × 105
2210 20.8 1.38 × 105
Steel I Beam: W21 × 50 (Wide Flange 21 inch tall × 50 lbf/ft)
L = 80.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
50.0 0.803 4060
60.0 0.964 4880
70.0 1.12 5690
80.0 1.28 6500
90.0 1.45 7320
100 1.61 8130
200 3.21 1.63 × 104
300 4.82 2.44 × 104
400 6.42 3.25 × 104
500 8.03 4.06 × 104
600 9.64 4.88 × 104
700 11.2 5.69 × 104
800 12.8 6.50 × 104
900 14.5 7.32 × 104
1000 16.1 8.13 × 104
1300 20.8 1.05 × 105
Steel I Beam: W21 × 50 (Wide Flange 21 inch tall × 50 lbf/ft)
L = 90.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
50.0 1.29 5140
60.0 1.54 6170
70.0 1.80 7200
80.0 2.06 8230
90.0 2.32 9260
100 2.57 1.03 × 104
200 5.14 2.06 × 104
300 7.72 3.09 × 104
400 10.3 4.12 × 104
500 12.9 5.14 × 104
600 15.4 6.17 × 104
700 18.0 7.20 × 104
800 20.6 8.23 × 104
810 20.8 8.33 × 104
Steel I Beam: W21 × 50 (Wide Flange 21 inch tall × 50 lbf/ft)
L = 100 ft
P (lbf/ft) w_max (in) stress_max (psi)
50.0 1.96 6350
60.0 2.35 7620
70.0 2.74 8890
80.0 3.14 1.02 × 104
90.0 3.53 1.14 × 104
100 3.92 1.27 × 104
200 7.84 2.54 × 104
300 11.8 3.81 × 104
400 15.7 5.08 × 104
500 19.6 6.35 × 104
531 20.8 6.75 × 104
Steel I Beam: W21 × 50 (Wide Flange 21 inch tall × 50 lbf/ft)
L = 125 ft
P (lbf/ft) w_max (in) stress_max (psi)
50.0 4.79 9920
60.0 5.74 1.19 × 104
70.0 6.70 1.39 × 104
80.0 7.66 1.59 × 104
90.0 8.61 1.79 × 104
100 9.57 1.98 × 104
200 19.1 3.97 × 104
218 20.8 4.32 × 104
Steel I Beam: W21 × 50 (Wide Flange 21 inch tall × 50 lbf/ft)
L = 150 ft
P (lbf/ft) w_max (in) stress_max (psi)
50.0 9.92 1.43 × 104
60.0 11.9 1.71 × 104
70.0 13.9 2.00 × 104
80.0 15.9 2.29 × 104
90.0 17.9 2.57 × 104
100 19.8 2.86 × 104
105 20.8 3.00 × 104
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