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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Four Equal Spans » Wide Flange Steel I Beam » W21 × 68
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 = 1480 in4) for the W21 × 68 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 × 68 (Wide Flange 21 inch tall × 68 lbf/ft)
L = 3.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
68.0 1.33 × 10-6 5.61
70.0 1.37 × 10-6 5.78
80.0 1.56 × 10-6 6.61
90.0 1.76 × 10-6 7.43
100 1.96 × 10-6 8.26
200 3.91 × 10-6 16.5
300 5.87 × 10-6 24.8
400 7.82 × 10-6 33.0
500 9.78 × 10-6 41.3
600 1.17 × 10-5 49.5
700 1.37 × 10-5 57.8
800 1.56 × 10-5 66.1
900 1.76 × 10-5 74.3
1000 1.96 × 10-5 82.6
2000 3.91 × 10-5 165
3000 5.87 × 10-5 248
4000 7.82 × 10-5 330
5000 9.78 × 10-5 413
6000 1.17 × 10-4 495
7000 1.37 × 10-4 578
8000 1.56 × 10-4 661
9000 1.76 × 10-4 743
1.00 × 104 1.96 × 10-4 826
2.00 × 104 3.91 × 10-4 1650
3.00 × 104 5.87 × 10-4 2480
4.00 × 104 7.82 × 10-4 3300
5.00 × 104 9.78 × 10-4 4130
6.00 × 104 0.00117 4950
7.00 × 104 0.00137 5780
8.00 × 104 0.00156 6610
9.00 × 104 0.00176 7430
1.00 × 105 0.00196 8260
2.00 × 105 0.00391 1.65 × 104
3.00 × 105 0.00587 2.48 × 104
4.00 × 105 0.00782 3.30 × 104
5.00 × 105 0.00978 4.13 × 104
6.00 × 105 0.0117 4.95 × 104
7.00 × 105 0.0137 5.78 × 104
8.00 × 105 0.0156 6.61 × 104
9.00 × 105 0.0176 7.43 × 104
1.00 × 106 0.0196 8.26 × 104
2.00 × 106 0.0391 1.65 × 105
3.00 × 106 0.0587 2.48 × 105
3.60 × 106 0.0704 2.97 × 105
Steel I Beam: W21 × 68 (Wide Flange 21 inch tall × 68 lbf/ft)
L = 5.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
68.0 1.03 × 10-5 15.6
70.0 1.06 × 10-5 16.1
80.0 1.21 × 10-5 18.3
90.0 1.36 × 10-5 20.6
100 1.51 × 10-5 22.9
200 3.02 × 10-5 45.9
300 4.53 × 10-5 68.8
400 6.04 × 10-5 91.7
500 7.55 × 10-5 115
600 9.06 × 10-5 138
700 1.06 × 10-4 161
800 1.21 × 10-4 183
900 1.36 × 10-4 206
1000 1.51 × 10-4 229
2000 3.02 × 10-4 459
3000 4.53 × 10-4 688
4000 6.04 × 10-4 917
5000 7.55 × 10-4 1150
6000 9.06 × 10-4 1380
7000 0.00106 1610
8000 0.00121 1830
9000 0.00136 2060
1.00 × 104 0.00151 2290
2.00 × 104 0.00302 4590
3.00 × 104 0.00453 6880
4.00 × 104 0.00604 9170
5.00 × 104 0.00755 1.15 × 104
6.00 × 104 0.00906 1.38 × 104
7.00 × 104 0.0106 1.61 × 104
8.00 × 104 0.0121 1.83 × 104
9.00 × 104 0.0136 2.06 × 104
1.00 × 105 0.0151 2.29 × 104
2.00 × 105 0.0302 4.59 × 104
3.00 × 105 0.0453 6.88 × 104
4.00 × 105 0.0604 9.17 × 104
5.00 × 105 0.0755 1.15 × 105
6.00 × 105 0.0906 1.38 × 105
7.00 × 105 0.106 1.61 × 105
8.00 × 105 0.121 1.83 × 105
9.00 × 105 0.136 2.06 × 105
1.00 × 106 0.151 2.29 × 105
1.30 × 106 0.195 2.97 × 105
Steel I Beam: W21 × 68 (Wide Flange 21 inch tall × 68 lbf/ft)
L = 10.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
68.0 1.64 × 10-4 62.4
70.0 1.69 × 10-4 64.2
80.0 1.93 × 10-4 73.4
90.0 2.17 × 10-4 82.6
100 2.42 × 10-4 91.7
200 4.83 × 10-4 183
300 7.25 × 10-4 275
400 9.66 × 10-4 367
500 0.00121 459
600 0.00145 550
700 0.00169 642
800 0.00193 734
900 0.00217 826
1000 0.00242 917
2000 0.00483 1830
3000 0.00725 2750
4000 0.00966 3670
5000 0.0121 4590
6000 0.0145 5500
7000 0.0169 6420
8000 0.0193 7340
9000 0.0217 8260
1.00 × 104 0.0242 9170
2.00 × 104 0.0483 1.83 × 104
3.00 × 104 0.0725 2.75 × 104
4.00 × 104 0.0966 3.67 × 104
5.00 × 104 0.121 4.59 × 104
6.00 × 104 0.145 5.50 × 104
7.00 × 104 0.169 6.42 × 104
8.00 × 104 0.193 7.34 × 104
9.00 × 104 0.217 8.26 × 104
1.00 × 105 0.242 9.17 × 104
2.00 × 105 0.483 1.83 × 105
3.00 × 105 0.725 2.75 × 105
3.24 × 105 0.782 2.97 × 105
Steel I Beam: W21 × 68 (Wide Flange 21 inch tall × 68 lbf/ft)
L = 15.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
68.0 8.31 × 10-4 140
70.0 8.56 × 10-4 144
80.0 9.78 × 10-4 165
90.0 0.00110 186
100 0.00122 206
200 0.00245 413
300 0.00367 619
400 0.00489 826
500 0.00611 1030
600 0.00734 1240
700 0.00856 1440
800 0.00978 1650
900 0.0110 1860
1000 0.0122 2060
2000 0.0245 4130
3000 0.0367 6190
4000 0.0489 8260
5000 0.0611 1.03 × 104
6000 0.0734 1.24 × 104
7000 0.0856 1.44 × 104
8000 0.0978 1.65 × 104
9000 0.110 1.86 × 104
1.00 × 104 0.122 2.06 × 104
2.00 × 104 0.245 4.13 × 104
3.00 × 104 0.367 6.19 × 104
4.00 × 104 0.489 8.26 × 104
5.00 × 104 0.611 1.03 × 105
6.00 × 104 0.734 1.24 × 105
7.00 × 104 0.856 1.44 × 105
8.00 × 104 0.978 1.65 × 105
9.00 × 104 1.10 1.86 × 105
1.00 × 105 1.22 2.06 × 105
1.44 × 105 1.76 2.97 × 105
Steel I Beam: W21 × 68 (Wide Flange 21 inch tall × 68 lbf/ft)
L = 20.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
68.0 0.00263 250
70.0 0.00270 257
80.0 0.00309 294
90.0 0.00348 330
100 0.00386 367
200 0.00773 734
300 0.0116 1100
400 0.0155 1470
500 0.0193 1830
600 0.0232 2200
700 0.0270 2570
800 0.0309 2940
900 0.0348 3300
1000 0.0386 3670
2000 0.0773 7340
3000 0.116 1.10 × 104
4000 0.155 1.47 × 104
5000 0.193 1.83 × 104
6000 0.232 2.20 × 104
7000 0.270 2.57 × 104
8000 0.309 2.94 × 104
9000 0.348 3.30 × 104
1.00 × 104 0.386 3.67 × 104
2.00 × 104 0.773 7.34 × 104
3.00 × 104 1.16 1.10 × 105
4.00 × 104 1.55 1.47 × 105
5.00 × 104 1.93 1.83 × 105
6.00 × 104 2.32 2.20 × 105
7.00 × 104 2.70 2.57 × 105
8.00 × 104 3.09 2.94 × 105
8.09 × 104 3.13 2.97 × 105
Steel I Beam: W21 × 68 (Wide Flange 21 inch tall × 68 lbf/ft)
L = 25.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
68.0 0.00641 390
70.0 0.00660 401
80.0 0.00755 459
90.0 0.00849 516
100 0.00943 573
200 0.0189 1150
300 0.0283 1720
400 0.0377 2290
500 0.0472 2870
600 0.0566 3440
700 0.0660 4010
800 0.0755 4590
900 0.0849 5160
1000 0.0943 5730
2000 0.189 1.15 × 104
3000 0.283 1.72 × 104
4000 0.377 2.29 × 104
5000 0.472 2.87 × 104
6000 0.566 3.44 × 104
7000 0.660 4.01 × 104
8000 0.755 4.59 × 104
9000 0.849 5.16 × 104
1.00 × 104 0.943 5.73 × 104
2.00 × 104 1.89 1.15 × 105
3.00 × 104 2.83 1.72 × 105
4.00 × 104 3.77 2.29 × 105
5.00 × 104 4.72 2.87 × 105
5.18 × 104 4.89 2.97 × 105
Steel I Beam: W21 × 68 (Wide Flange 21 inch tall × 68 lbf/ft)
L = 30.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
68.0 0.0133 561
70.0 0.0137 578
80.0 0.0156 661
90.0 0.0176 743
100 0.0196 826
200 0.0391 1650
300 0.0587 2480
400 0.0782 3300
500 0.0978 4130
600 0.117 4950
700 0.137 5780
800 0.156 6610
900 0.176 7430
1000 0.196 8260
2000 0.391 1.65 × 104
3000 0.587 2.48 × 104
4000 0.782 3.30 × 104
5000 0.978 4.13 × 104
6000 1.17 4.95 × 104
7000 1.37 5.78 × 104
8000 1.56 6.61 × 104
9000 1.76 7.43 × 104
1.00 × 104 1.96 8.26 × 104
2.00 × 104 3.91 1.65 × 105
3.00 × 104 5.87 2.48 × 105
3.60 × 104 7.04 2.97 × 105
Steel I Beam: W21 × 68 (Wide Flange 21 inch tall × 68 lbf/ft)
L = 40.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
68.0 0.0420 998
70.0 0.0433 1030
80.0 0.0495 1170
90.0 0.0556 1320
100 0.0618 1470
200 0.124 2940
300 0.185 4400
400 0.247 5870
500 0.309 7340
600 0.371 8810
700 0.433 1.03 × 104
800 0.495 1.17 × 104
900 0.556 1.32 × 104
1000 0.618 1.47 × 104
2000 1.24 2.94 × 104
3000 1.85 4.40 × 104
4000 2.47 5.87 × 104
5000 3.09 7.34 × 104
6000 3.71 8.81 × 104
7000 4.33 1.03 × 105
8000 4.95 1.17 × 105
9000 5.56 1.32 × 105
1.00 × 104 6.18 1.47 × 105
2.00 × 104 12.4 2.94 × 105
2.02 × 104 12.5 2.97 × 105
Steel I Beam: W21 × 68 (Wide Flange 21 inch tall × 68 lbf/ft)
L = 50.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
68.0 0.103 1560
70.0 0.106 1610
80.0 0.121 1830
90.0 0.136 2060
100 0.151 2290
200 0.302 4590
300 0.453 6880
400 0.604 9170
500 0.755 1.15 × 104
600 0.906 1.38 × 104
700 1.06 1.61 × 104
800 1.21 1.83 × 104
900 1.36 2.06 × 104
1000 1.51 2.29 × 104
2000 3.02 4.59 × 104
3000 4.53 6.88 × 104
4000 6.04 9.17 × 104
5000 7.55 1.15 × 105
6000 9.06 1.38 × 105
7000 10.6 1.61 × 105
8000 12.1 1.83 × 105
9000 13.6 2.06 × 105
1.00 × 104 15.1 2.29 × 105
1.30 × 104 19.5 2.97 × 105
Steel I Beam: W21 × 68 (Wide Flange 21 inch tall × 68 lbf/ft)
L = 60.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
68.0 0.213 2250
70.0 0.219 2310
80.0 0.250 2640
90.0 0.282 2970
100 0.313 3300
200 0.626 6610
300 0.939 9910
400 1.25 1.32 × 104
500 1.56 1.65 × 104
600 1.88 1.98 × 104
700 2.19 2.31 × 104
800 2.50 2.64 × 104
900 2.82 2.97 × 104
1000 3.13 3.30 × 104
2000 6.26 6.61 × 104
3000 9.39 9.91 × 104
4000 12.5 1.32 × 105
5000 15.6 1.65 × 105
6000 18.8 1.98 × 105
6750 21.1 2.23 × 105
Steel I Beam: W21 × 68 (Wide Flange 21 inch tall × 68 lbf/ft)
L = 70.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
68.0 0.394 3060
70.0 0.406 3150
80.0 0.464 3600
90.0 0.522 4050
100 0.580 4500
200 1.16 8990
300 1.74 1.35 × 104
400 2.32 1.80 × 104
500 2.90 2.25 × 104
600 3.48 2.70 × 104
700 4.06 3.15 × 104
800 4.64 3.60 × 104
900 5.22 4.05 × 104
1000 5.80 4.50 × 104
2000 11.6 8.99 × 104
3000 17.4 1.35 × 105
3640 21.1 1.64 × 105
Steel I Beam: W21 × 68 (Wide Flange 21 inch tall × 68 lbf/ft)
L = 80.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
68.0 0.673 3990
70.0 0.692 4110
80.0 0.791 4700
90.0 0.890 5280
100 0.989 5870
200 1.98 1.17 × 104
300 2.97 1.76 × 104
400 3.96 2.35 × 104
500 4.95 2.94 × 104
600 5.94 3.52 × 104
700 6.92 4.11 × 104
800 7.91 4.70 × 104
900 8.90 5.28 × 104
1000 9.89 5.87 × 104
2000 19.8 1.17 × 105
2140 21.1 1.25 × 105
Steel I Beam: W21 × 68 (Wide Flange 21 inch tall × 68 lbf/ft)
L = 90.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
68.0 1.08 5050
70.0 1.11 5200
80.0 1.27 5950
90.0 1.43 6690
100 1.58 7430
200 3.17 1.49 × 104
300 4.75 2.23 × 104
400 6.34 2.97 × 104
500 7.92 3.72 × 104
600 9.51 4.46 × 104
700 11.1 5.20 × 104
800 12.7 5.95 × 104
900 14.3 6.69 × 104
1000 15.8 7.43 × 104
1330 21.1 9.91 × 104
Steel I Beam: W21 × 68 (Wide Flange 21 inch tall × 68 lbf/ft)
L = 100 ft
P (lbf/ft) w_max (in) stress_max (psi)
68.0 1.64 6240
70.0 1.69 6420
80.0 1.93 7340
90.0 2.17 8260
100 2.42 9170
200 4.83 1.83 × 104
300 7.25 2.75 × 104
400 9.66 3.67 × 104
500 12.1 4.59 × 104
600 14.5 5.50 × 104
700 16.9 6.42 × 104
800 19.3 7.34 × 104
875 21.1 8.03 × 104
Steel I Beam: W21 × 68 (Wide Flange 21 inch tall × 68 lbf/ft)
L = 125 ft
P (lbf/ft) w_max (in) stress_max (psi)
68.0 4.01 9750
70.0 4.13 1.00 × 104
80.0 4.72 1.15 × 104
90.0 5.31 1.29 × 104
100 5.90 1.43 × 104
200 11.8 2.87 × 104
300 17.7 4.30 × 104
358 21.1 5.14 × 104
Steel I Beam: W21 × 68 (Wide Flange 21 inch tall × 68 lbf/ft)
L = 150 ft
P (lbf/ft) w_max (in) stress_max (psi)
68.0 8.31 1.40 × 104
70.0 8.56 1.44 × 104
80.0 9.78 1.65 × 104
90.0 11.0 1.86 × 104
100 12.2 2.06 × 104
173 21.1 3.57 × 104
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