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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Single Span » 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 a single span, the maximum displacement w_max and the maximum normal stress stress_max occur at the center 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 3.04 × 10-6 7.14
60.0 3.65 × 10-6 8.57
70.0 4.26 × 10-6 10.0
80.0 4.86 × 10-6 11.4
90.0 5.47 × 10-6 12.9
100 6.08 × 10-6 14.3
200 1.22 × 10-5 28.6
300 1.82 × 10-5 42.9
400 2.43 × 10-5 57.2
500 3.04 × 10-5 71.4
600 3.65 × 10-5 85.7
700 4.26 × 10-5 100
800 4.86 × 10-5 114
900 5.47 × 10-5 129
1000 6.08 × 10-5 143
2000 1.22 × 10-4 286
3000 1.82 × 10-4 429
4000 2.43 × 10-4 572
5000 3.04 × 10-4 714
6000 3.65 × 10-4 857
7000 4.26 × 10-4 1000
8000 4.86 × 10-4 1140
9000 5.47 × 10-4 1290
1.00 × 104 6.08 × 10-4 1430
2.00 × 104 0.00122 2860
3.00 × 104 0.00182 4290
4.00 × 104 0.00243 5720
5.00 × 104 0.00304 7140
6.00 × 104 0.00365 8570
7.00 × 104 0.00426 1.00 × 104
8.00 × 104 0.00486 1.14 × 104
9.00 × 104 0.00547 1.29 × 104
1.00 × 105 0.00608 1.43 × 104
2.00 × 105 0.0122 2.86 × 104
3.00 × 105 0.0182 4.29 × 104
4.00 × 105 0.0243 5.72 × 104
5.00 × 105 0.0304 7.14 × 104
6.00 × 105 0.0365 8.57 × 104
7.00 × 105 0.0426 1.00 × 105
8.00 × 105 0.0486 1.14 × 105
9.00 × 105 0.0547 1.29 × 105
1.00 × 106 0.0608 1.43 × 105
2.00 × 106 0.122 2.86 × 105
2.08 × 106 0.126 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 2.35 × 10-5 19.8
60.0 2.82 × 10-5 23.8
70.0 3.28 × 10-5 27.8
80.0 3.75 × 10-5 31.8
90.0 4.22 × 10-5 35.7
100 4.69 × 10-5 39.7
200 9.38 × 10-5 79.4
300 1.41 × 10-4 119
400 1.88 × 10-4 159
500 2.35 × 10-4 198
600 2.82 × 10-4 238
700 3.28 × 10-4 278
800 3.75 × 10-4 318
900 4.22 × 10-4 357
1000 4.69 × 10-4 397
2000 9.38 × 10-4 794
3000 0.00141 1190
4000 0.00188 1590
5000 0.00235 1980
6000 0.00282 2380
7000 0.00328 2780
8000 0.00375 3180
9000 0.00422 3570
1.00 × 104 0.00469 3970
2.00 × 104 0.00938 7940
3.00 × 104 0.0141 1.19 × 104
4.00 × 104 0.0188 1.59 × 104
5.00 × 104 0.0235 1.98 × 104
6.00 × 104 0.0282 2.38 × 104
7.00 × 104 0.0328 2.78 × 104
8.00 × 104 0.0375 3.18 × 104
9.00 × 104 0.0422 3.57 × 104
1.00 × 105 0.0469 3.97 × 104
2.00 × 105 0.0938 7.94 × 104
3.00 × 105 0.141 1.19 × 105
4.00 × 105 0.188 1.59 × 105
5.00 × 105 0.235 1.98 × 105
6.00 × 105 0.282 2.38 × 105
7.00 × 105 0.328 2.78 × 105
7.48 × 105 0.351 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 3.75 × 10-4 79.4
60.0 4.50 × 10-4 95.3
70.0 5.26 × 10-4 111
80.0 6.01 × 10-4 127
90.0 6.76 × 10-4 143
100 7.51 × 10-4 159
200 0.00150 318
300 0.00225 476
400 0.00300 635
500 0.00375 794
600 0.00450 953
700 0.00526 1110
800 0.00601 1270
900 0.00676 1430
1000 0.00751 1590
2000 0.0150 3180
3000 0.0225 4760
4000 0.0300 6350
5000 0.0375 7940
6000 0.0450 9530
7000 0.0526 1.11 × 104
8000 0.0601 1.27 × 104
9000 0.0676 1.43 × 104
1.00 × 104 0.0751 1.59 × 104
2.00 × 104 0.150 3.18 × 104
3.00 × 104 0.225 4.76 × 104
4.00 × 104 0.300 6.35 × 104
5.00 × 104 0.375 7.94 × 104
6.00 × 104 0.450 9.53 × 104
7.00 × 104 0.526 1.11 × 105
8.00 × 104 0.601 1.27 × 105
9.00 × 104 0.676 1.43 × 105
1.00 × 105 0.751 1.59 × 105
1.87 × 105 1.40 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 0.00190 179
60.0 0.00228 214
70.0 0.00266 250
80.0 0.00304 286
90.0 0.00342 321
100 0.00380 357
200 0.00760 714
300 0.0114 1070
400 0.0152 1430
500 0.0190 1790
600 0.0228 2140
700 0.0266 2500
800 0.0304 2860
900 0.0342 3210
1000 0.0380 3570
2000 0.0760 7140
3000 0.114 1.07 × 104
4000 0.152 1.43 × 104
5000 0.190 1.79 × 104
6000 0.228 2.14 × 104
7000 0.266 2.50 × 104
8000 0.304 2.86 × 104
9000 0.342 3.21 × 104
1.00 × 104 0.380 3.57 × 104
2.00 × 104 0.760 7.14 × 104
3.00 × 104 1.14 1.07 × 105
4.00 × 104 1.52 1.43 × 105
5.00 × 104 1.90 1.79 × 105
6.00 × 104 2.28 2.14 × 105
7.00 × 104 2.66 2.50 × 105
8.00 × 104 3.04 2.86 × 105
8.32 × 104 3.16 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 0.00601 318
60.0 0.00721 381
70.0 0.00841 445
80.0 0.00961 508
90.0 0.0108 572
100 0.0120 635
200 0.0240 1270
300 0.0360 1910
400 0.0480 2540
500 0.0601 3180
600 0.0721 3810
700 0.0841 4450
800 0.0961 5080
900 0.108 5720
1000 0.120 6350
2000 0.240 1.27 × 104
3000 0.360 1.91 × 104
4000 0.480 2.54 × 104
5000 0.601 3.18 × 104
6000 0.721 3.81 × 104
7000 0.841 4.45 × 104
8000 0.961 5.08 × 104
9000 1.08 5.72 × 104
1.00 × 104 1.20 6.35 × 104
2.00 × 104 2.40 1.27 × 105
3.00 × 104 3.60 1.91 × 105
4.00 × 104 4.80 2.54 × 105
4.68 × 104 5.62 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 0.0147 496
60.0 0.0176 595
70.0 0.0205 695
80.0 0.0235 794
90.0 0.0264 893
100 0.0293 992
200 0.0587 1980
300 0.0880 2980
400 0.117 3970
500 0.147 4960
600 0.176 5950
700 0.205 6950
800 0.235 7940
900 0.264 8930
1000 0.293 9920
2000 0.587 1.98 × 104
3000 0.880 2.98 × 104
4000 1.17 3.97 × 104
5000 1.47 4.96 × 104
6000 1.76 5.95 × 104
7000 2.05 6.95 × 104
8000 2.35 7.94 × 104
9000 2.64 8.93 × 104
1.00 × 104 2.93 9.92 × 104
2.00 × 104 5.87 1.98 × 105
2.99 × 104 8.78 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 0.0304 714
60.0 0.0365 857
70.0 0.0426 1000
80.0 0.0486 1140
90.0 0.0547 1290
100 0.0608 1430
200 0.122 2860
300 0.182 4290
400 0.243 5720
500 0.304 7140
600 0.365 8570
700 0.426 1.00 × 104
800 0.486 1.14 × 104
900 0.547 1.29 × 104
1000 0.608 1.43 × 104
2000 1.22 2.86 × 104
3000 1.82 4.29 × 104
4000 2.43 5.72 × 104
5000 3.04 7.14 × 104
6000 3.65 8.57 × 104
7000 4.26 1.00 × 105
8000 4.86 1.14 × 105
9000 5.47 1.29 × 105
1.00 × 104 6.08 1.43 × 105
2.00 × 104 12.2 2.86 × 105
2.08 × 104 12.6 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 0.0961 1270
60.0 0.115 1520
70.0 0.135 1780
80.0 0.154 2030
90.0 0.173 2290
100 0.192 2540
200 0.384 5080
300 0.577 7620
400 0.769 1.02 × 104
500 0.961 1.27 × 104
600 1.15 1.52 × 104
700 1.35 1.78 × 104
800 1.54 2.03 × 104
900 1.73 2.29 × 104
1000 1.92 2.54 × 104
2000 3.84 5.08 × 104
3000 5.77 7.62 × 104
4000 7.69 1.02 × 105
5000 9.61 1.27 × 105
6000 11.5 1.52 × 105
7000 13.5 1.78 × 105
8000 15.4 2.03 × 105
9000 17.3 2.29 × 105
1.00 × 104 19.2 2.54 × 105
1.17 × 104 22.5 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 0.235 1980
60.0 0.282 2380
70.0 0.328 2780
80.0 0.375 3180
90.0 0.422 3570
100 0.469 3970
200 0.938 7940
300 1.41 1.19 × 104
400 1.88 1.59 × 104
500 2.35 1.98 × 104
600 2.82 2.38 × 104
700 3.28 2.78 × 104
800 3.75 3.18 × 104
900 4.22 3.57 × 104
1000 4.69 3.97 × 104
2000 9.38 7.94 × 104
3000 14.1 1.19 × 105
4000 18.8 1.59 × 105
4440 20.8 1.76 × 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 0.486 2860
60.0 0.584 3430
70.0 0.681 4000
80.0 0.778 4570
90.0 0.876 5140
100 0.973 5720
200 1.95 1.14 × 104
300 2.92 1.71 × 104
400 3.89 2.29 × 104
500 4.86 2.86 × 104
600 5.84 3.43 × 104
700 6.81 4.00 × 104
800 7.78 4.57 × 104
900 8.76 5.14 × 104
1000 9.73 5.72 × 104
2000 19.5 1.14 × 105
2140 20.8 1.22 × 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 0.901 3890
60.0 1.08 4670
70.0 1.26 5450
80.0 1.44 6220
90.0 1.62 7000
100 1.80 7780
200 3.61 1.56 × 104
300 5.41 2.33 × 104
400 7.21 3.11 × 104
500 9.01 3.89 × 104
600 10.8 4.67 × 104
700 12.6 5.45 × 104
800 14.4 6.22 × 104
900 16.2 7.00 × 104
1000 18.0 7.78 × 104
1160 20.8 8.99 × 104
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 1.54 5080
60.0 1.85 6100
70.0 2.15 7110
80.0 2.46 8130
90.0 2.77 9140
100 3.08 1.02 × 104
200 6.15 2.03 × 104
300 9.23 3.05 × 104
400 12.3 4.06 × 104
500 15.4 5.08 × 104
600 18.5 6.10 × 104
677 20.8 6.88 × 104
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 2.46 6430
60.0 2.96 7720
70.0 3.45 9000
80.0 3.94 1.03 × 104
90.0 4.43 1.16 × 104
100 4.93 1.29 × 104
200 9.85 2.57 × 104
300 14.8 3.86 × 104
400 19.7 5.14 × 104
423 20.8 5.44 × 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 3.75 7940
60.0 4.50 9530
70.0 5.26 1.11 × 104
80.0 6.01 1.27 × 104
90.0 6.76 1.43 × 104
100 7.51 1.59 × 104
200 15.0 3.18 × 104
277 20.8 4.41 × 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 9.16 1.24 × 104
60.0 11.0 1.49 × 104
70.0 12.8 1.74 × 104
80.0 14.7 1.98 × 104
90.0 16.5 2.23 × 104
100 18.3 2.48 × 104
114 20.8 2.82 × 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 19.0 1.79 × 104
54.8 20.8 1.96 × 104
Additional Information
Related Pages
Glossary
FREE Publications
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.

CNC Machining Design Guide

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

3D Scanners

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

more publications