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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Four 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 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 = 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 1.47 × 10-6 6.12
60.0 1.77 × 10-6 7.35
70.0 2.06 × 10-6 8.57
80.0 2.35 × 10-6 9.79
90.0 2.65 × 10-6 11.0
100 2.94 × 10-6 12.2
200 5.88 × 10-6 24.5
300 8.83 × 10-6 36.7
400 1.18 × 10-5 49.0
500 1.47 × 10-5 61.2
600 1.77 × 10-5 73.5
700 2.06 × 10-5 85.7
800 2.35 × 10-5 97.9
900 2.65 × 10-5 110
1000 2.94 × 10-5 122
2000 5.88 × 10-5 245
3000 8.83 × 10-5 367
4000 1.18 × 10-4 490
5000 1.47 × 10-4 612
6000 1.77 × 10-4 735
7000 2.06 × 10-4 857
8000 2.35 × 10-4 979
9000 2.65 × 10-4 1100
1.00 × 104 2.94 × 10-4 1220
2.00 × 104 5.88 × 10-4 2450
3.00 × 104 8.83 × 10-4 3670
4.00 × 104 0.00118 4900
5.00 × 104 0.00147 6120
6.00 × 104 0.00177 7350
7.00 × 104 0.00206 8570
8.00 × 104 0.00235 9790
9.00 × 104 0.00265 1.10 × 104
1.00 × 105 0.00294 1.22 × 104
2.00 × 105 0.00588 2.45 × 104
3.00 × 105 0.00883 3.67 × 104
4.00 × 105 0.0118 4.90 × 104
5.00 × 105 0.0147 6.12 × 104
6.00 × 105 0.0177 7.35 × 104
7.00 × 105 0.0206 8.57 × 104
8.00 × 105 0.0235 9.79 × 104
9.00 × 105 0.0265 1.10 × 105
1.00 × 106 0.0294 1.22 × 105
2.00 × 106 0.0588 2.45 × 105
2.43 × 106 0.0714 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 1.14 × 10-5 17.0
60.0 1.36 × 10-5 20.4
70.0 1.59 × 10-5 23.8
80.0 1.82 × 10-5 27.2
90.0 2.04 × 10-5 30.6
100 2.27 × 10-5 34.0
200 4.54 × 10-5 68.0
300 6.81 × 10-5 102
400 9.08 × 10-5 136
500 1.14 × 10-4 170
600 1.36 × 10-4 204
700 1.59 × 10-4 238
800 1.82 × 10-4 272
900 2.04 × 10-4 306
1000 2.27 × 10-4 340
2000 4.54 × 10-4 680
3000 6.81 × 10-4 1020
4000 9.08 × 10-4 1360
5000 0.00114 1700
6000 0.00136 2040
7000 0.00159 2380
8000 0.00182 2720
9000 0.00204 3060
1.00 × 104 0.00227 3400
2.00 × 104 0.00454 6800
3.00 × 104 0.00681 1.02 × 104
4.00 × 104 0.00908 1.36 × 104
5.00 × 104 0.0114 1.70 × 104
6.00 × 104 0.0136 2.04 × 104
7.00 × 104 0.0159 2.38 × 104
8.00 × 104 0.0182 2.72 × 104
9.00 × 104 0.0204 3.06 × 104
1.00 × 105 0.0227 3.40 × 104
2.00 × 105 0.0454 6.80 × 104
3.00 × 105 0.0681 1.02 × 105
4.00 × 105 0.0908 1.36 × 105
5.00 × 105 0.114 1.70 × 105
6.00 × 105 0.136 2.04 × 105
7.00 × 105 0.159 2.38 × 105
8.00 × 105 0.182 2.72 × 105
8.73 × 105 0.198 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 1.82 × 10-4 68.0
60.0 2.18 × 10-4 81.6
70.0 2.54 × 10-4 95.2
80.0 2.91 × 10-4 109
90.0 3.27 × 10-4 122
100 3.63 × 10-4 136
200 7.26 × 10-4 272
300 0.00109 408
400 0.00145 544
500 0.00182 680
600 0.00218 816
700 0.00254 952
800 0.00291 1090
900 0.00327 1220
1000 0.00363 1360
2000 0.00726 2720
3000 0.0109 4080
4000 0.0145 5440
5000 0.0182 6800
6000 0.0218 8160
7000 0.0254 9520
8000 0.0291 1.09 × 104
9000 0.0327 1.22 × 104
1.00 × 104 0.0363 1.36 × 104
2.00 × 104 0.0726 2.72 × 104
3.00 × 104 0.109 4.08 × 104
4.00 × 104 0.145 5.44 × 104
5.00 × 104 0.182 6.80 × 104
6.00 × 104 0.218 8.16 × 104
7.00 × 104 0.254 9.52 × 104
8.00 × 104 0.291 1.09 × 105
9.00 × 104 0.327 1.22 × 105
1.00 × 105 0.363 1.36 × 105
2.00 × 105 0.726 2.72 × 105
2.18 × 105 0.793 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 9.19 × 10-4 153
60.0 0.00110 184
70.0 0.00129 214
80.0 0.00147 245
90.0 0.00165 275
100 0.00184 306
200 0.00368 612
300 0.00552 918
400 0.00736 1220
500 0.00919 1530
600 0.0110 1840
700 0.0129 2140
800 0.0147 2450
900 0.0165 2750
1000 0.0184 3060
2000 0.0368 6120
3000 0.0552 9180
4000 0.0736 1.22 × 104
5000 0.0919 1.53 × 104
6000 0.110 1.84 × 104
7000 0.129 2.14 × 104
8000 0.147 2.45 × 104
9000 0.165 2.75 × 104
1.00 × 104 0.184 3.06 × 104
2.00 × 104 0.368 6.12 × 104
3.00 × 104 0.552 9.18 × 104
4.00 × 104 0.736 1.22 × 105
5.00 × 104 0.919 1.53 × 105
6.00 × 104 1.10 1.84 × 105
7.00 × 104 1.29 2.14 × 105
8.00 × 104 1.47 2.45 × 105
9.00 × 104 1.65 2.75 × 105
9.70 × 104 1.78 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 0.00291 272
60.0 0.00349 326
70.0 0.00407 381
80.0 0.00465 435
90.0 0.00523 490
100 0.00581 544
200 0.0116 1090
300 0.0174 1630
400 0.0232 2180
500 0.0291 2720
600 0.0349 3260
700 0.0407 3810
800 0.0465 4350
900 0.0523 4900
1000 0.0581 5440
2000 0.116 1.09 × 104
3000 0.174 1.63 × 104
4000 0.232 2.18 × 104
5000 0.291 2.72 × 104
6000 0.349 3.26 × 104
7000 0.407 3.81 × 104
8000 0.465 4.35 × 104
9000 0.523 4.90 × 104
1.00 × 104 0.581 5.44 × 104
2.00 × 104 1.16 1.09 × 105
3.00 × 104 1.74 1.63 × 105
4.00 × 104 2.32 2.18 × 105
5.00 × 104 2.91 2.72 × 105
5.46 × 104 3.17 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 0.00709 425
60.0 0.00851 510
70.0 0.00993 595
80.0 0.0114 680
90.0 0.0128 765
100 0.0142 850
200 0.0284 1700
300 0.0426 2550
400 0.0568 3400
500 0.0709 4250
600 0.0851 5100
700 0.0993 5950
800 0.114 6800
900 0.128 7650
1000 0.142 8500
2000 0.284 1.70 × 104
3000 0.426 2.55 × 104
4000 0.568 3.40 × 104
5000 0.709 4.25 × 104
6000 0.851 5.10 × 104
7000 0.993 5.95 × 104
8000 1.14 6.80 × 104
9000 1.28 7.65 × 104
1.00 × 104 1.42 8.50 × 104
2.00 × 104 2.84 1.70 × 105
3.00 × 104 4.26 2.55 × 105
3.49 × 104 4.96 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 0.0147 612
60.0 0.0177 735
70.0 0.0206 857
80.0 0.0235 979
90.0 0.0265 1100
100 0.0294 1220
200 0.0588 2450
300 0.0883 3670
400 0.118 4900
500 0.147 6120
600 0.177 7350
700 0.206 8570
800 0.235 9790
900 0.265 1.10 × 104
1000 0.294 1.22 × 104
2000 0.588 2.45 × 104
3000 0.883 3.67 × 104
4000 1.18 4.90 × 104
5000 1.47 6.12 × 104
6000 1.77 7.35 × 104
7000 2.06 8.57 × 104
8000 2.35 9.79 × 104
9000 2.65 1.10 × 105
1.00 × 104 2.94 1.22 × 105
2.00 × 104 5.88 2.45 × 105
2.43 × 104 7.14 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 0.0465 1090
60.0 0.0558 1310
70.0 0.0651 1520
80.0 0.0744 1740
90.0 0.0837 1960
100 0.0930 2180
200 0.186 4350
300 0.279 6530
400 0.372 8710
500 0.465 1.09 × 104
600 0.558 1.31 × 104
700 0.651 1.52 × 104
800 0.744 1.74 × 104
900 0.837 1.96 × 104
1000 0.930 2.18 × 104
2000 1.86 4.35 × 104
3000 2.79 6.53 × 104
4000 3.72 8.71 × 104
5000 4.65 1.09 × 105
6000 5.58 1.31 × 105
7000 6.51 1.52 × 105
8000 7.44 1.74 × 105
9000 8.37 1.96 × 105
1.00 × 104 9.30 2.18 × 105
1.36 × 104 12.7 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 0.114 1700
60.0 0.136 2040
70.0 0.159 2380
80.0 0.182 2720
90.0 0.204 3060
100 0.227 3400
200 0.454 6800
300 0.681 1.02 × 104
400 0.908 1.36 × 104
500 1.14 1.70 × 104
600 1.36 2.04 × 104
700 1.59 2.38 × 104
800 1.82 2.72 × 104
900 2.04 3.06 × 104
1000 2.27 3.40 × 104
2000 4.54 6.80 × 104
3000 6.81 1.02 × 105
4000 9.08 1.36 × 105
5000 11.4 1.70 × 105
6000 13.6 2.04 × 105
7000 15.9 2.38 × 105
8000 18.2 2.72 × 105
8730 19.8 2.97 × 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 0.235 2450
60.0 0.282 2940
70.0 0.330 3430
80.0 0.377 3920
90.0 0.424 4410
100 0.471 4900
200 0.942 9790
300 1.41 1.47 × 104
400 1.88 1.96 × 104
500 2.35 2.45 × 104
600 2.82 2.94 × 104
700 3.30 3.43 × 104
800 3.77 3.92 × 104
900 4.24 4.41 × 104
1000 4.71 4.90 × 104
2000 9.42 9.79 × 104
3000 14.1 1.47 × 105
4000 18.8 1.96 × 105
4420 20.8 2.17 × 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 0.436 3330
60.0 0.523 4000
70.0 0.610 4670
80.0 0.698 5330
90.0 0.785 6000
100 0.872 6670
200 1.74 1.33 × 104
300 2.62 2.00 × 104
400 3.49 2.67 × 104
500 4.36 3.33 × 104
600 5.23 4.00 × 104
700 6.10 4.67 × 104
800 6.98 5.33 × 104
900 7.85 6.00 × 104
1000 8.72 6.67 × 104
2000 17.4 1.33 × 105
2390 20.8 1.59 × 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 0.744 4350
60.0 0.893 5220
70.0 1.04 6090
80.0 1.19 6960
90.0 1.34 7840
100 1.49 8710
200 2.98 1.74 × 104
300 4.46 2.61 × 104
400 5.95 3.48 × 104
500 7.44 4.35 × 104
600 8.93 5.22 × 104
700 10.4 6.09 × 104
800 11.9 6.96 × 104
900 13.4 7.84 × 104
1000 14.9 8.71 × 104
1400 20.8 1.22 × 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 1.19 5510
60.0 1.43 6610
70.0 1.67 7710
80.0 1.91 8810
90.0 2.14 9920
100 2.38 1.10 × 104
200 4.77 2.20 × 104
300 7.15 3.31 × 104
400 9.53 4.41 × 104
500 11.9 5.51 × 104
600 14.3 6.61 × 104
700 16.7 7.71 × 104
800 19.1 8.81 × 104
874 20.8 9.63 × 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 1.82 6800
60.0 2.18 8160
70.0 2.54 9520
80.0 2.91 1.09 × 104
90.0 3.27 1.22 × 104
100 3.63 1.36 × 104
200 7.26 2.72 × 104
300 10.9 4.08 × 104
400 14.5 5.44 × 104
500 18.2 6.80 × 104
573 20.8 7.80 × 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 4.43 1.06 × 104
60.0 5.32 1.28 × 104
70.0 6.21 1.49 × 104
80.0 7.09 1.70 × 104
90.0 7.98 1.91 × 104
100 8.87 2.13 × 104
200 17.7 4.25 × 104
235 20.8 4.99 × 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 9.19 1.53 × 104
60.0 11.0 1.84 × 104
70.0 12.9 2.14 × 104
80.0 14.7 2.45 × 104
90.0 16.5 2.75 × 104
100 18.4 3.06 × 104
113 20.8 3.47 × 104
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