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Wide Flange Steel I Beam: W8 × 31
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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Four Equal Spans » Wide Flange Steel I Beam » W8 × 31
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 = 110 in4) for the W8 × 31 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
   
Steel I Beam: W8 × 31 (Wide Flange 8 inch tall × 31 lbf/ft)
L = 3.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 8.16 × 10-6 13.0
40.0 1.05 × 10-5 16.8
50.0 1.32 × 10-5 21.0
60.0 1.58 × 10-5 25.2
70.0 1.84 × 10-5 29.4
80.0 2.11 × 10-5 33.6
90.0 2.37 × 10-5 37.9
100 2.63 × 10-5 42.1
200 5.26 × 10-5 84.1
300 7.90 × 10-5 126
400 1.05 × 10-4 168
500 1.32 × 10-4 210
600 1.58 × 10-4 252
700 1.84 × 10-4 294
800 2.11 × 10-4 336
900 2.37 × 10-4 379
1000 2.63 × 10-4 421
2000 5.26 × 10-4 841
3000 7.90 × 10-4 1260
4000 0.00105 1680
5000 0.00132 2100
6000 0.00158 2520
7000 0.00184 2940
8000 0.00211 3360
9000 0.00237 3790
1.00 × 104 0.00263 4210
2.00 × 104 0.00526 8410
3.00 × 104 0.00790 1.26 × 104
4.00 × 104 0.0105 1.68 × 104
5.00 × 104 0.0132 2.10 × 104
6.00 × 104 0.0158 2.52 × 104
7.00 × 104 0.0184 2.94 × 104
8.00 × 104 0.0211 3.36 × 104
9.00 × 104 0.0237 3.79 × 104
1.00 × 105 0.0263 4.21 × 104
2.00 × 105 0.0526 8.41 × 104
3.00 × 105 0.0790 1.26 × 105
4.00 × 105 0.105 1.68 × 105
5.00 × 105 0.132 2.10 × 105
6.00 × 105 0.158 2.52 × 105
7.00 × 105 0.184 2.94 × 105
7.06 × 105 0.186 2.97 × 105
Steel I Beam: W8 × 31 (Wide Flange 8 inch tall × 31 lbf/ft)
L = 5.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 6.30 × 10-5 36.2
40.0 8.12 × 10-5 46.7
50.0 1.02 × 10-4 58.4
60.0 1.22 × 10-4 70.1
70.0 1.42 × 10-4 81.8
80.0 1.62 × 10-4 93.5
90.0 1.83 × 10-4 105
100 2.03 × 10-4 117
200 4.06 × 10-4 234
300 6.09 × 10-4 351
400 8.12 × 10-4 467
500 0.00102 584
600 0.00122 701
700 0.00142 818
800 0.00162 935
900 0.00183 1050
1000 0.00203 1170
2000 0.00406 2340
3000 0.00609 3510
4000 0.00812 4670
5000 0.0102 5840
6000 0.0122 7010
7000 0.0142 8180
8000 0.0162 9350
9000 0.0183 1.05 × 104
1.00 × 104 0.0203 1.17 × 104
2.00 × 104 0.0406 2.34 × 104
3.00 × 104 0.0609 3.51 × 104
4.00 × 104 0.0812 4.67 × 104
5.00 × 104 0.102 5.84 × 104
6.00 × 104 0.122 7.01 × 104
7.00 × 104 0.142 8.18 × 104
8.00 × 104 0.162 9.35 × 104
9.00 × 104 0.183 1.05 × 105
1.00 × 105 0.203 1.17 × 105
2.00 × 105 0.406 2.34 × 105
2.54 × 105 0.516 2.97 × 105
Steel I Beam: W8 × 31 (Wide Flange 8 inch tall × 31 lbf/ft)
L = 10.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 0.00101 145
40.0 0.00130 187
50.0 0.00162 234
60.0 0.00195 280
70.0 0.00227 327
80.0 0.00260 374
90.0 0.00292 421
100 0.00325 467
200 0.00650 935
300 0.00975 1400
400 0.0130 1870
500 0.0162 2340
600 0.0195 2800
700 0.0227 3270
800 0.0260 3740
900 0.0292 4210
1000 0.0325 4670
2000 0.0650 9350
3000 0.0975 1.40 × 104
4000 0.130 1.87 × 104
5000 0.162 2.34 × 104
6000 0.195 2.80 × 104
7000 0.227 3.27 × 104
8000 0.260 3.74 × 104
9000 0.292 4.21 × 104
1.00 × 104 0.325 4.67 × 104
2.00 × 104 0.650 9.35 × 104
3.00 × 104 0.975 1.40 × 105
4.00 × 104 1.30 1.87 × 105
5.00 × 104 1.62 2.34 × 105
6.00 × 104 1.95 2.80 × 105
6.36 × 104 2.07 2.97 × 105
Steel I Beam: W8 × 31 (Wide Flange 8 inch tall × 31 lbf/ft)
L = 15.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 0.00510 326
40.0 0.00658 421
50.0 0.00822 526
60.0 0.00987 631
70.0 0.0115 736
80.0 0.0132 841
90.0 0.0148 946
100 0.0164 1050
200 0.0329 2100
300 0.0493 3150
400 0.0658 4210
500 0.0822 5260
600 0.0987 6310
700 0.115 7360
800 0.132 8410
900 0.148 9460
1000 0.164 1.05 × 104
2000 0.329 2.10 × 104
3000 0.493 3.15 × 104
4000 0.658 4.21 × 104
5000 0.822 5.26 × 104
6000 0.987 6.31 × 104
7000 1.15 7.36 × 104
8000 1.32 8.41 × 104
9000 1.48 9.46 × 104
1.00 × 104 1.64 1.05 × 105
2.00 × 104 3.29 2.10 × 105
2.82 × 104 4.65 2.97 × 105
Steel I Beam: W8 × 31 (Wide Flange 8 inch tall × 31 lbf/ft)
L = 20.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 0.0161 580
40.0 0.0208 748
50.0 0.0260 935
60.0 0.0312 1120
70.0 0.0364 1310
80.0 0.0416 1500
90.0 0.0468 1680
100 0.0520 1870
200 0.104 3740
300 0.156 5610
400 0.208 7480
500 0.260 9350
600 0.312 1.12 × 104
700 0.364 1.31 × 104
800 0.416 1.50 × 104
900 0.468 1.68 × 104
1000 0.520 1.87 × 104
2000 1.04 3.74 × 104
3000 1.56 5.61 × 104
4000 2.08 7.48 × 104
5000 2.60 9.35 × 104
6000 3.12 1.12 × 105
7000 3.64 1.31 × 105
8000 4.16 1.50 × 105
9000 4.68 1.68 × 105
1.00 × 104 5.20 1.87 × 105
1.59 × 104 8.26 2.97 × 105
Steel I Beam: W8 × 31 (Wide Flange 8 inch tall × 31 lbf/ft)
L = 25.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 0.0393 905
40.0 0.0508 1170
50.0 0.0635 1460
60.0 0.0762 1750
70.0 0.0888 2040
80.0 0.102 2340
90.0 0.114 2630
100 0.127 2920
200 0.254 5840
300 0.381 8760
400 0.508 1.17 × 104
500 0.635 1.46 × 104
600 0.762 1.75 × 104
700 0.888 2.04 × 104
800 1.02 2.34 × 104
900 1.14 2.63 × 104
1000 1.27 2.92 × 104
2000 2.54 5.84 × 104
3000 3.81 8.76 × 104
4000 5.08 1.17 × 105
5000 6.35 1.46 × 105
6000 7.62 1.75 × 105
6300 8.00 1.84 × 105
Steel I Beam: W8 × 31 (Wide Flange 8 inch tall × 31 lbf/ft)
L = 30.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 0.0816 1300
40.0 0.105 1680
50.0 0.132 2100
60.0 0.158 2520
70.0 0.184 2940
80.0 0.211 3360
90.0 0.237 3790
100 0.263 4210
200 0.526 8410
300 0.790 1.26 × 104
400 1.05 1.68 × 104
500 1.32 2.10 × 104
600 1.58 2.52 × 104
700 1.84 2.94 × 104
800 2.11 3.36 × 104
900 2.37 3.79 × 104
1000 2.63 4.21 × 104
2000 5.26 8.41 × 104
3000 7.90 1.26 × 105
3040 8.00 1.28 × 105
Steel I Beam: W8 × 31 (Wide Flange 8 inch tall × 31 lbf/ft)
L = 40.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 0.258 2320
40.0 0.333 2990
50.0 0.416 3740
60.0 0.499 4490
70.0 0.582 5230
80.0 0.665 5980
90.0 0.749 6730
100 0.832 7480
200 1.66 1.50 × 104
300 2.50 2.24 × 104
400 3.33 2.99 × 104
500 4.16 3.74 × 104
600 4.99 4.49 × 104
700 5.82 5.23 × 104
800 6.65 5.98 × 104
900 7.49 6.73 × 104
962 8.00 7.19 × 104
Steel I Beam: W8 × 31 (Wide Flange 8 inch tall × 31 lbf/ft)
L = 50.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 0.630 3620
40.0 0.812 4670
50.0 1.02 5840
60.0 1.22 7010
70.0 1.42 8180
80.0 1.62 9350
90.0 1.83 1.05 × 104
100 2.03 1.17 × 104
200 4.06 2.34 × 104
300 6.09 3.51 × 104
394 8.00 4.60 × 104
Steel I Beam: W8 × 31 (Wide Flange 8 inch tall × 31 lbf/ft)
L = 60.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 1.31 5220
40.0 1.68 6730
50.0 2.11 8410
60.0 2.53 1.01 × 104
70.0 2.95 1.18 × 104
80.0 3.37 1.35 × 104
90.0 3.79 1.51 × 104
100 4.21 1.68 × 104
190 8.00 3.20 × 104
Steel I Beam: W8 × 31 (Wide Flange 8 inch tall × 31 lbf/ft)
L = 70.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 2.42 7100
40.0 3.12 9160
50.0 3.90 1.14 × 104
60.0 4.68 1.37 × 104
70.0 5.46 1.60 × 104
80.0 6.24 1.83 × 104
90.0 7.02 2.06 × 104
100 7.80 2.29 × 104
103 8.00 2.35 × 104
Steel I Beam: W8 × 31 (Wide Flange 8 inch tall × 31 lbf/ft)
L = 80.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 4.13 9270
40.0 5.32 1.20 × 104
50.0 6.65 1.50 × 104
60.0 7.99 1.79 × 104
60.1 8.00 1.80 × 104
Steel I Beam: W8 × 31 (Wide Flange 8 inch tall × 31 lbf/ft)
L = 90.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 6.61 1.17 × 104
37.5 8.00 1.42 × 104
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