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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Four Equal Spans » Wide Flange Steel I Beam » W21 × 57
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 = 1170 in4) for the W21 × 57 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 × 57 (Wide Flange 21 inch tall × 57 lbf/ft)
L = 3.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
57.0 1.41 × 10-6 5.93
60.0 1.48 × 10-6 6.25
70.0 1.73 × 10-6 7.29
80.0 1.98 × 10-6 8.33
90.0 2.23 × 10-6 9.37
100 2.47 × 10-6 10.4
200 4.95 × 10-6 20.8
300 7.42 × 10-6 31.2
400 9.90 × 10-6 41.6
500 1.24 × 10-5 52.1
600 1.48 × 10-5 62.5
700 1.73 × 10-5 72.9
800 1.98 × 10-5 83.3
900 2.23 × 10-5 93.7
1000 2.47 × 10-5 104
2000 4.95 × 10-5 208
3000 7.42 × 10-5 312
4000 9.90 × 10-5 416
5000 1.24 × 10-4 521
6000 1.48 × 10-4 625
7000 1.73 × 10-4 729
8000 1.98 × 10-4 833
9000 2.23 × 10-4 937
1.00 × 104 2.47 × 10-4 1040
2.00 × 104 4.95 × 10-4 2080
3.00 × 104 7.42 × 10-4 3120
4.00 × 104 9.90 × 10-4 4160
5.00 × 104 0.00124 5210
6.00 × 104 0.00148 6250
7.00 × 104 0.00173 7290
8.00 × 104 0.00198 8330
9.00 × 104 0.00223 9370
1.00 × 105 0.00247 1.04 × 104
2.00 × 105 0.00495 2.08 × 104
3.00 × 105 0.00742 3.12 × 104
4.00 × 105 0.00990 4.16 × 104
5.00 × 105 0.0124 5.21 × 104
6.00 × 105 0.0148 6.25 × 104
7.00 × 105 0.0173 7.29 × 104
8.00 × 105 0.0198 8.33 × 104
9.00 × 105 0.0223 9.37 × 104
1.00 × 106 0.0247 1.04 × 105
2.00 × 106 0.0495 2.08 × 105
2.85 × 106 0.0706 2.97 × 105
Steel I Beam: W21 × 57 (Wide Flange 21 inch tall × 57 lbf/ft)
L = 5.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
57.0 1.09 × 10-5 16.5
60.0 1.15 × 10-5 17.4
70.0 1.34 × 10-5 20.2
80.0 1.53 × 10-5 23.1
90.0 1.72 × 10-5 26.0
100 1.91 × 10-5 28.9
200 3.82 × 10-5 57.8
300 5.73 × 10-5 86.8
400 7.64 × 10-5 116
500 9.55 × 10-5 145
600 1.15 × 10-4 174
700 1.34 × 10-4 202
800 1.53 × 10-4 231
900 1.72 × 10-4 260
1000 1.91 × 10-4 289
2000 3.82 × 10-4 578
3000 5.73 × 10-4 868
4000 7.64 × 10-4 1160
5000 9.55 × 10-4 1450
6000 0.00115 1740
7000 0.00134 2020
8000 0.00153 2310
9000 0.00172 2600
1.00 × 104 0.00191 2890
2.00 × 104 0.00382 5780
3.00 × 104 0.00573 8680
4.00 × 104 0.00764 1.16 × 104
5.00 × 104 0.00955 1.45 × 104
6.00 × 104 0.0115 1.74 × 104
7.00 × 104 0.0134 2.02 × 104
8.00 × 104 0.0153 2.31 × 104
9.00 × 104 0.0172 2.60 × 104
1.00 × 105 0.0191 2.89 × 104
2.00 × 105 0.0382 5.78 × 104
3.00 × 105 0.0573 8.68 × 104
4.00 × 105 0.0764 1.16 × 105
5.00 × 105 0.0955 1.45 × 105
6.00 × 105 0.115 1.74 × 105
7.00 × 105 0.134 2.02 × 105
8.00 × 105 0.153 2.31 × 105
9.00 × 105 0.172 2.60 × 105
1.00 × 106 0.191 2.89 × 105
1.03 × 106 0.196 2.97 × 105
Steel I Beam: W21 × 57 (Wide Flange 21 inch tall × 57 lbf/ft)
L = 10.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
57.0 1.74 × 10-4 65.9
60.0 1.83 × 10-4 69.4
70.0 2.14 × 10-4 81.0
80.0 2.44 × 10-4 92.5
90.0 2.75 × 10-4 104
100 3.05 × 10-4 116
200 6.11 × 10-4 231
300 9.16 × 10-4 347
400 0.00122 463
500 0.00153 578
600 0.00183 694
700 0.00214 810
800 0.00244 925
900 0.00275 1040
1000 0.00305 1160
2000 0.00611 2310
3000 0.00916 3470
4000 0.0122 4630
5000 0.0153 5780
6000 0.0183 6940
7000 0.0214 8100
8000 0.0244 9250
9000 0.0275 1.04 × 104
1.00 × 104 0.0305 1.16 × 104
2.00 × 104 0.0611 2.31 × 104
3.00 × 104 0.0916 3.47 × 104
4.00 × 104 0.122 4.63 × 104
5.00 × 104 0.153 5.78 × 104
6.00 × 104 0.183 6.94 × 104
7.00 × 104 0.214 8.10 × 104
8.00 × 104 0.244 9.25 × 104
9.00 × 104 0.275 1.04 × 105
1.00 × 105 0.305 1.16 × 105
2.00 × 105 0.611 2.31 × 105
2.57 × 105 0.785 2.97 × 105
Steel I Beam: W21 × 57 (Wide Flange 21 inch tall × 57 lbf/ft)
L = 15.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
57.0 8.82 × 10-4 148
60.0 9.28 × 10-4 156
70.0 0.00108 182
80.0 0.00124 208
90.0 0.00139 234
100 0.00155 260
200 0.00309 521
300 0.00464 781
400 0.00619 1040
500 0.00773 1300
600 0.00928 1560
700 0.0108 1820
800 0.0124 2080
900 0.0139 2340
1000 0.0155 2600
2000 0.0309 5210
3000 0.0464 7810
4000 0.0619 1.04 × 104
5000 0.0773 1.30 × 104
6000 0.0928 1.56 × 104
7000 0.108 1.82 × 104
8000 0.124 2.08 × 104
9000 0.139 2.34 × 104
1.00 × 104 0.155 2.60 × 104
2.00 × 104 0.309 5.21 × 104
3.00 × 104 0.464 7.81 × 104
4.00 × 104 0.619 1.04 × 105
5.00 × 104 0.773 1.30 × 105
6.00 × 104 0.928 1.56 × 105
7.00 × 104 1.08 1.82 × 105
8.00 × 104 1.24 2.08 × 105
9.00 × 104 1.39 2.34 × 105
1.00 × 105 1.55 2.60 × 105
1.14 × 105 1.77 2.97 × 105
Steel I Beam: W21 × 57 (Wide Flange 21 inch tall × 57 lbf/ft)
L = 20.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
57.0 0.00279 264
60.0 0.00293 278
70.0 0.00342 324
80.0 0.00391 370
90.0 0.00440 416
100 0.00489 463
200 0.00978 925
300 0.0147 1390
400 0.0196 1850
500 0.0244 2310
600 0.0293 2780
700 0.0342 3240
800 0.0391 3700
900 0.0440 4160
1000 0.0489 4630
2000 0.0978 9250
3000 0.147 1.39 × 104
4000 0.196 1.85 × 104
5000 0.244 2.31 × 104
6000 0.293 2.78 × 104
7000 0.342 3.24 × 104
8000 0.391 3.70 × 104
9000 0.440 4.16 × 104
1.00 × 104 0.489 4.63 × 104
2.00 × 104 0.978 9.25 × 104
3.00 × 104 1.47 1.39 × 105
4.00 × 104 1.96 1.85 × 105
5.00 × 104 2.44 2.31 × 105
6.00 × 104 2.93 2.78 × 105
6.42 × 104 3.14 2.97 × 105
Steel I Beam: W21 × 57 (Wide Flange 21 inch tall × 57 lbf/ft)
L = 25.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
57.0 0.00680 412
60.0 0.00716 434
70.0 0.00835 506
80.0 0.00955 578
90.0 0.0107 651
100 0.0119 723
200 0.0239 1450
300 0.0358 2170
400 0.0477 2890
500 0.0597 3610
600 0.0716 4340
700 0.0835 5060
800 0.0955 5780
900 0.107 6510
1000 0.119 7230
2000 0.239 1.45 × 104
3000 0.358 2.17 × 104
4000 0.477 2.89 × 104
5000 0.597 3.61 × 104
6000 0.716 4.34 × 104
7000 0.835 5.06 × 104
8000 0.955 5.78 × 104
9000 1.07 6.51 × 104
1.00 × 104 1.19 7.23 × 104
2.00 × 104 2.39 1.45 × 105
3.00 × 104 3.58 2.17 × 105
4.00 × 104 4.77 2.89 × 105
4.11 × 104 4.90 2.97 × 105
Steel I Beam: W21 × 57 (Wide Flange 21 inch tall × 57 lbf/ft)
L = 30.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
57.0 0.0141 593
60.0 0.0148 625
70.0 0.0173 729
80.0 0.0198 833
90.0 0.0223 937
100 0.0247 1040
200 0.0495 2080
300 0.0742 3120
400 0.0990 4160
500 0.124 5210
600 0.148 6250
700 0.173 7290
800 0.198 8330
900 0.223 9370
1000 0.247 1.04 × 104
2000 0.495 2.08 × 104
3000 0.742 3.12 × 104
4000 0.990 4.16 × 104
5000 1.24 5.21 × 104
6000 1.48 6.25 × 104
7000 1.73 7.29 × 104
8000 1.98 8.33 × 104
9000 2.23 9.37 × 104
1.00 × 104 2.47 1.04 × 105
2.00 × 104 4.95 2.08 × 105
2.85 × 104 7.06 2.97 × 105
Steel I Beam: W21 × 57 (Wide Flange 21 inch tall × 57 lbf/ft)
L = 40.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
57.0 0.0446 1050
60.0 0.0469 1110
70.0 0.0547 1300
80.0 0.0626 1480
90.0 0.0704 1670
100 0.0782 1850
200 0.156 3700
300 0.235 5550
400 0.313 7400
500 0.391 9250
600 0.469 1.11 × 104
700 0.547 1.30 × 104
800 0.626 1.48 × 104
900 0.704 1.67 × 104
1000 0.782 1.85 × 104
2000 1.56 3.70 × 104
3000 2.35 5.55 × 104
4000 3.13 7.40 × 104
5000 3.91 9.25 × 104
6000 4.69 1.11 × 105
7000 5.47 1.30 × 105
8000 6.26 1.48 × 105
9000 7.04 1.67 × 105
1.00 × 104 7.82 1.85 × 105
1.61 × 104 12.6 2.97 × 105
Steel I Beam: W21 × 57 (Wide Flange 21 inch tall × 57 lbf/ft)
L = 50.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
57.0 0.109 1650
60.0 0.115 1740
70.0 0.134 2020
80.0 0.153 2310
90.0 0.172 2600
100 0.191 2890
200 0.382 5780
300 0.573 8680
400 0.764 1.16 × 104
500 0.955 1.45 × 104
600 1.15 1.74 × 104
700 1.34 2.02 × 104
800 1.53 2.31 × 104
900 1.72 2.60 × 104
1000 1.91 2.89 × 104
2000 3.82 5.78 × 104
3000 5.73 8.68 × 104
4000 7.64 1.16 × 105
5000 9.55 1.45 × 105
6000 11.5 1.74 × 105
7000 13.4 2.02 × 105
8000 15.3 2.31 × 105
9000 17.2 2.60 × 105
1.00 × 104 19.1 2.89 × 105
1.03 × 104 19.6 2.97 × 105
Steel I Beam: W21 × 57 (Wide Flange 21 inch tall × 57 lbf/ft)
L = 60.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
57.0 0.226 2370
60.0 0.238 2500
70.0 0.277 2910
80.0 0.317 3330
90.0 0.356 3750
100 0.396 4160
200 0.792 8330
300 1.19 1.25 × 104
400 1.58 1.67 × 104
500 1.98 2.08 × 104
600 2.38 2.50 × 104
700 2.77 2.91 × 104
800 3.17 3.33 × 104
900 3.56 3.75 × 104
1000 3.96 4.16 × 104
2000 7.92 8.33 × 104
3000 11.9 1.25 × 105
4000 15.8 1.67 × 105
5000 19.8 2.08 × 105
5320 21.1 2.21 × 105
Steel I Beam: W21 × 57 (Wide Flange 21 inch tall × 57 lbf/ft)
L = 70.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
57.0 0.418 3230
60.0 0.440 3400
70.0 0.513 3970
80.0 0.587 4530
90.0 0.660 5100
100 0.733 5670
200 1.47 1.13 × 104
300 2.20 1.70 × 104
400 2.93 2.27 × 104
500 3.67 2.83 × 104
600 4.40 3.40 × 104
700 5.13 3.97 × 104
800 5.87 4.53 × 104
900 6.60 5.10 × 104
1000 7.33 5.67 × 104
2000 14.7 1.13 × 105
2870 21.1 1.63 × 105
Steel I Beam: W21 × 57 (Wide Flange 21 inch tall × 57 lbf/ft)
L = 80.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
57.0 0.713 4220
60.0 0.751 4440
70.0 0.876 5180
80.0 1.00 5920
90.0 1.13 6660
100 1.25 7400
200 2.50 1.48 × 104
300 3.75 2.22 × 104
400 5.01 2.96 × 104
500 6.26 3.70 × 104
600 7.51 4.44 × 104
700 8.76 5.18 × 104
800 10.0 5.92 × 104
900 11.3 6.66 × 104
1000 12.5 7.40 × 104
1680 21.1 1.25 × 105
Steel I Beam: W21 × 57 (Wide Flange 21 inch tall × 57 lbf/ft)
L = 90.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
57.0 1.14 5340
60.0 1.20 5620
70.0 1.40 6560
80.0 1.60 7500
90.0 1.80 8430
100 2.00 9370
200 4.01 1.87 × 104
300 6.01 2.81 × 104
400 8.02 3.75 × 104
500 10.0 4.68 × 104
600 12.0 5.62 × 104
700 14.0 6.56 × 104
800 16.0 7.50 × 104
900 18.0 8.43 × 104
1000 20.0 9.37 × 104
1050 21.1 9.84 × 104
Steel I Beam: W21 × 57 (Wide Flange 21 inch tall × 57 lbf/ft)
L = 100 ft
P (lbf/ft) w_max (in) stress_max (psi)
57.0 1.74 6590
60.0 1.83 6940
70.0 2.14 8100
80.0 2.44 9250
90.0 2.75 1.04 × 104
100 3.05 1.16 × 104
200 6.11 2.31 × 104
300 9.16 3.47 × 104
400 12.2 4.63 × 104
500 15.3 5.78 × 104
600 18.3 6.94 × 104
689 21.1 7.97 × 104
Steel I Beam: W21 × 57 (Wide Flange 21 inch tall × 57 lbf/ft)
L = 125 ft
P (lbf/ft) w_max (in) stress_max (psi)
57.0 4.25 1.03 × 104
60.0 4.47 1.08 × 104
70.0 5.22 1.27 × 104
80.0 5.97 1.45 × 104
90.0 6.71 1.63 × 104
100 7.46 1.81 × 104
200 14.9 3.61 × 104
282 21.1 5.10 × 104
Steel I Beam: W21 × 57 (Wide Flange 21 inch tall × 57 lbf/ft)
L = 150 ft
P (lbf/ft) w_max (in) stress_max (psi)
57.0 8.82 1.48 × 104
60.0 9.28 1.56 × 104
70.0 10.8 1.82 × 104
80.0 12.4 2.08 × 104
90.0 13.9 2.34 × 104
100 15.5 2.60 × 104
136 21.1 3.54 × 104
Additional Information
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