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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Three Equal Spans » Wide Flange Steel I Beam » W21 × 83
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 = 1830 in4) for the W21 × 83 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 × 83 (Wide Flange 21 inch tall × 83 lbf/ft)
L = 3.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
83.0 1.42 × 10-6 5.25
90.0 1.54 × 10-6 5.69
100 1.71 × 10-6 6.32
200 3.42 × 10-6 12.6
300 5.12 × 10-6 19.0
400 6.83 × 10-6 25.3
500 8.54 × 10-6 31.6
600 1.02 × 10-5 37.9
700 1.20 × 10-5 44.3
800 1.37 × 10-5 50.6
900 1.54 × 10-5 56.9
1000 1.71 × 10-5 63.2
2000 3.42 × 10-5 126
3000 5.12 × 10-5 190
4000 6.83 × 10-5 253
5000 8.54 × 10-5 316
6000 1.02 × 10-4 379
7000 1.20 × 10-4 443
8000 1.37 × 10-4 506
9000 1.54 × 10-4 569
1.00 × 104 1.71 × 10-4 632
2.00 × 104 3.42 × 10-4 1260
3.00 × 104 5.12 × 10-4 1900
4.00 × 104 6.83 × 10-4 2530
5.00 × 104 8.54 × 10-4 3160
6.00 × 104 0.00102 3790
7.00 × 104 0.00120 4430
8.00 × 104 0.00137 5060
9.00 × 104 0.00154 5690
1.00 × 105 0.00171 6320
2.00 × 105 0.00342 1.26 × 104
3.00 × 105 0.00512 1.90 × 104
4.00 × 105 0.00683 2.53 × 104
5.00 × 105 0.00854 3.16 × 104
6.00 × 105 0.0102 3.79 × 104
7.00 × 105 0.0120 4.43 × 104
8.00 × 105 0.0137 5.06 × 104
9.00 × 105 0.0154 5.69 × 104
1.00 × 106 0.0171 6.32 × 104
2.00 × 106 0.0342 1.26 × 105
3.00 × 106 0.0512 1.90 × 105
4.00 × 106 0.0683 2.53 × 105
4.70 × 106 0.0802 2.97 × 105
Steel I Beam: W21 × 83 (Wide Flange 21 inch tall × 83 lbf/ft)
L = 5.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
83.0 1.09 × 10-5 14.6
90.0 1.19 × 10-5 15.8
100 1.32 × 10-5 17.6
200 2.64 × 10-5 35.1
300 3.95 × 10-5 52.7
400 5.27 × 10-5 70.3
500 6.59 × 10-5 87.8
600 7.91 × 10-5 105
700 9.22 × 10-5 123
800 1.05 × 10-4 141
900 1.19 × 10-4 158
1000 1.32 × 10-4 176
2000 2.64 × 10-4 351
3000 3.95 × 10-4 527
4000 5.27 × 10-4 703
5000 6.59 × 10-4 878
6000 7.91 × 10-4 1050
7000 9.22 × 10-4 1230
8000 0.00105 1410
9000 0.00119 1580
1.00 × 104 0.00132 1760
2.00 × 104 0.00264 3510
3.00 × 104 0.00395 5270
4.00 × 104 0.00527 7030
5.00 × 104 0.00659 8780
6.00 × 104 0.00791 1.05 × 104
7.00 × 104 0.00922 1.23 × 104
8.00 × 104 0.0105 1.41 × 104
9.00 × 104 0.0119 1.58 × 104
1.00 × 105 0.0132 1.76 × 104
2.00 × 105 0.0264 3.51 × 104
3.00 × 105 0.0395 5.27 × 104
4.00 × 105 0.0527 7.03 × 104
5.00 × 105 0.0659 8.78 × 104
6.00 × 105 0.0791 1.05 × 105
7.00 × 105 0.0922 1.23 × 105
8.00 × 105 0.105 1.41 × 105
9.00 × 105 0.119 1.58 × 105
1.00 × 106 0.132 1.76 × 105
1.69 × 106 0.223 2.97 × 105
Steel I Beam: W21 × 83 (Wide Flange 21 inch tall × 83 lbf/ft)
L = 10.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
83.0 1.75 × 10-4 58.3
90.0 1.90 × 10-4 63.2
100 2.11 × 10-4 70.3
200 4.22 × 10-4 141
300 6.32 × 10-4 211
400 8.43 × 10-4 281
500 0.00105 351
600 0.00126 422
700 0.00148 492
800 0.00169 562
900 0.00190 632
1000 0.00211 703
2000 0.00422 1410
3000 0.00632 2110
4000 0.00843 2810
5000 0.0105 3510
6000 0.0126 4220
7000 0.0148 4920
8000 0.0169 5620
9000 0.0190 6320
1.00 × 104 0.0211 7030
2.00 × 104 0.0422 1.41 × 104
3.00 × 104 0.0632 2.11 × 104
4.00 × 104 0.0843 2.81 × 104
5.00 × 104 0.105 3.51 × 104
6.00 × 104 0.126 4.22 × 104
7.00 × 104 0.148 4.92 × 104
8.00 × 104 0.169 5.62 × 104
9.00 × 104 0.190 6.32 × 104
1.00 × 105 0.211 7.03 × 104
2.00 × 105 0.422 1.41 × 105
3.00 × 105 0.632 2.11 × 105
4.00 × 105 0.843 2.81 × 105
4.23 × 105 0.891 2.97 × 105
Steel I Beam: W21 × 83 (Wide Flange 21 inch tall × 83 lbf/ft)
L = 15.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
83.0 8.86 × 10-4 131
90.0 9.61 × 10-4 142
100 0.00107 158
200 0.00213 316
300 0.00320 474
400 0.00427 632
500 0.00534 790
600 0.00640 949
700 0.00747 1110
800 0.00854 1260
900 0.00961 1420
1000 0.0107 1580
2000 0.0213 3160
3000 0.0320 4740
4000 0.0427 6320
5000 0.0534 7900
6000 0.0640 9490
7000 0.0747 1.11 × 104
8000 0.0854 1.26 × 104
9000 0.0961 1.42 × 104
1.00 × 104 0.107 1.58 × 104
2.00 × 104 0.213 3.16 × 104
3.00 × 104 0.320 4.74 × 104
4.00 × 104 0.427 6.32 × 104
5.00 × 104 0.534 7.90 × 104
6.00 × 104 0.640 9.49 × 104
7.00 × 104 0.747 1.11 × 105
8.00 × 104 0.854 1.26 × 105
9.00 × 104 0.961 1.42 × 105
1.00 × 105 1.07 1.58 × 105
1.88 × 105 2.01 2.97 × 105
Steel I Beam: W21 × 83 (Wide Flange 21 inch tall × 83 lbf/ft)
L = 20.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
83.0 0.00280 233
90.0 0.00304 253
100 0.00337 281
200 0.00675 562
300 0.0101 843
400 0.0135 1120
500 0.0169 1410
600 0.0202 1690
700 0.0236 1970
800 0.0270 2250
900 0.0304 2530
1000 0.0337 2810
2000 0.0675 5620
3000 0.101 8430
4000 0.135 1.12 × 104
5000 0.169 1.41 × 104
6000 0.202 1.69 × 104
7000 0.236 1.97 × 104
8000 0.270 2.25 × 104
9000 0.304 2.53 × 104
1.00 × 104 0.337 2.81 × 104
2.00 × 104 0.675 5.62 × 104
3.00 × 104 1.01 8.43 × 104
4.00 × 104 1.35 1.12 × 105
5.00 × 104 1.69 1.41 × 105
6.00 × 104 2.02 1.69 × 105
7.00 × 104 2.36 1.97 × 105
8.00 × 104 2.70 2.25 × 105
9.00 × 104 3.04 2.53 × 105
1.00 × 105 3.37 2.81 × 105
1.06 × 105 3.56 2.97 × 105
Steel I Beam: W21 × 83 (Wide Flange 21 inch tall × 83 lbf/ft)
L = 25.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
83.0 0.00684 364
90.0 0.00741 395
100 0.00823 439
200 0.0165 878
300 0.0247 1320
400 0.0329 1760
500 0.0412 2200
600 0.0494 2630
700 0.0576 3070
800 0.0659 3510
900 0.0741 3950
1000 0.0823 4390
2000 0.165 8780
3000 0.247 1.32 × 104
4000 0.329 1.76 × 104
5000 0.412 2.20 × 104
6000 0.494 2.63 × 104
7000 0.576 3.07 × 104
8000 0.659 3.51 × 104
9000 0.741 3.95 × 104
1.00 × 104 0.823 4.39 × 104
2.00 × 104 1.65 8.78 × 104
3.00 × 104 2.47 1.32 × 105
4.00 × 104 3.29 1.76 × 105
5.00 × 104 4.12 2.20 × 105
6.00 × 104 4.94 2.63 × 105
6.76 × 104 5.57 2.97 × 105
Steel I Beam: W21 × 83 (Wide Flange 21 inch tall × 83 lbf/ft)
L = 30.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
83.0 0.0142 525
90.0 0.0154 569
100 0.0171 632
200 0.0342 1260
300 0.0512 1900
400 0.0683 2530
500 0.0854 3160
600 0.102 3790
700 0.120 4430
800 0.137 5060
900 0.154 5690
1000 0.171 6320
2000 0.342 1.26 × 104
3000 0.512 1.90 × 104
4000 0.683 2.53 × 104
5000 0.854 3.16 × 104
6000 1.02 3.79 × 104
7000 1.20 4.43 × 104
8000 1.37 5.06 × 104
9000 1.54 5.69 × 104
1.00 × 104 1.71 6.32 × 104
2.00 × 104 3.42 1.26 × 105
3.00 × 104 5.12 1.90 × 105
4.00 × 104 6.83 2.53 × 105
4.70 × 104 8.02 2.97 × 105
Steel I Beam: W21 × 83 (Wide Flange 21 inch tall × 83 lbf/ft)
L = 40.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
83.0 0.0448 933
90.0 0.0486 1010
100 0.0540 1120
200 0.108 2250
300 0.162 3370
400 0.216 4500
500 0.270 5620
600 0.324 6750
700 0.378 7870
800 0.432 8990
900 0.486 1.01 × 104
1000 0.540 1.12 × 104
2000 1.08 2.25 × 104
3000 1.62 3.37 × 104
4000 2.16 4.50 × 104
5000 2.70 5.62 × 104
6000 3.24 6.75 × 104
7000 3.78 7.87 × 104
8000 4.32 8.99 × 104
9000 4.86 1.01 × 105
1.00 × 104 5.40 1.12 × 105
2.00 × 104 10.8 2.25 × 105
2.64 × 104 14.3 2.97 × 105
Steel I Beam: W21 × 83 (Wide Flange 21 inch tall × 83 lbf/ft)
L = 50.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
83.0 0.109 1460
90.0 0.119 1580
100 0.132 1760
200 0.264 3510
300 0.395 5270
400 0.527 7030
500 0.659 8780
600 0.791 1.05 × 104
700 0.922 1.23 × 104
800 1.05 1.41 × 104
900 1.19 1.58 × 104
1000 1.32 1.76 × 104
2000 2.64 3.51 × 104
3000 3.95 5.27 × 104
4000 5.27 7.03 × 104
5000 6.59 8.78 × 104
6000 7.91 1.05 × 105
7000 9.22 1.23 × 105
8000 10.5 1.41 × 105
9000 11.9 1.58 × 105
1.00 × 104 13.2 1.76 × 105
1.69 × 104 22.3 2.97 × 105
Steel I Beam: W21 × 83 (Wide Flange 21 inch tall × 83 lbf/ft)
L = 60.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
83.0 0.227 2100
90.0 0.246 2280
100 0.273 2530
200 0.546 5060
300 0.820 7590
400 1.09 1.01 × 104
500 1.37 1.26 × 104
600 1.64 1.52 × 104
700 1.91 1.77 × 104
800 2.19 2.02 × 104
900 2.46 2.28 × 104
1000 2.73 2.53 × 104
2000 5.46 5.06 × 104
3000 8.20 7.59 × 104
4000 10.9 1.01 × 105
5000 13.7 1.26 × 105
6000 16.4 1.52 × 105
7000 19.1 1.77 × 105
7840 21.4 1.98 × 105
Steel I Beam: W21 × 83 (Wide Flange 21 inch tall × 83 lbf/ft)
L = 70.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
83.0 0.420 2860
90.0 0.456 3100
100 0.506 3440
200 1.01 6890
300 1.52 1.03 × 104
400 2.02 1.38 × 104
500 2.53 1.72 × 104
600 3.04 2.07 × 104
700 3.54 2.41 × 104
800 4.05 2.75 × 104
900 4.56 3.10 × 104
1000 5.06 3.44 × 104
2000 10.1 6.89 × 104
3000 15.2 1.03 × 105
4000 20.2 1.38 × 105
4230 21.4 1.46 × 105
Steel I Beam: W21 × 83 (Wide Flange 21 inch tall × 83 lbf/ft)
L = 80.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
83.0 0.717 3730
90.0 0.777 4050
100 0.863 4500
200 1.73 8990
300 2.59 1.35 × 104
400 3.45 1.80 × 104
500 4.32 2.25 × 104
600 5.18 2.70 × 104
700 6.04 3.15 × 104
800 6.91 3.60 × 104
900 7.77 4.05 × 104
1000 8.63 4.50 × 104
2000 17.3 8.99 × 104
2480 21.4 1.12 × 105
Steel I Beam: W21 × 83 (Wide Flange 21 inch tall × 83 lbf/ft)
L = 90.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
83.0 1.15 4720
90.0 1.24 5120
100 1.38 5690
200 2.77 1.14 × 104
300 4.15 1.71 × 104
400 5.53 2.28 × 104
500 6.92 2.85 × 104
600 8.30 3.41 × 104
700 9.68 3.98 × 104
800 11.1 4.55 × 104
900 12.4 5.12 × 104
1000 13.8 5.69 × 104
1550 21.4 8.82 × 104
Steel I Beam: W21 × 83 (Wide Flange 21 inch tall × 83 lbf/ft)
L = 100 ft
P (lbf/ft) w_max (in) stress_max (psi)
83.0 1.75 5830
90.0 1.90 6320
100 2.11 7030
200 4.22 1.41 × 104
300 6.32 2.11 × 104
400 8.43 2.81 × 104
500 10.5 3.51 × 104
600 12.6 4.22 × 104
700 14.8 4.92 × 104
800 16.9 5.62 × 104
900 19.0 6.32 × 104
1000 21.1 7.03 × 104
1020 21.4 7.14 × 104
Steel I Beam: W21 × 83 (Wide Flange 21 inch tall × 83 lbf/ft)
L = 125 ft
P (lbf/ft) w_max (in) stress_max (psi)
83.0 4.27 9110
90.0 4.63 9880
100 5.15 1.10 × 104
200 10.3 2.20 × 104
300 15.4 3.29 × 104
400 20.6 4.39 × 104
416 21.4 4.57 × 104
Steel I Beam: W21 × 83 (Wide Flange 21 inch tall × 83 lbf/ft)
L = 150 ft
P (lbf/ft) w_max (in) stress_max (psi)
83.0 8.86 1.31 × 104
90.0 9.61 1.42 × 104
100 10.7 1.58 × 104
200 21.3 3.16 × 104
201 21.4 3.17 × 104
Additional Information
Related Pages
FREE Publications
3D Scanners

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

CNC Machining Design Guide

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

Mechanical Engineers Outlook

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

Metal 3D Printing Design Guide

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

more publications