engineering fundamentals
Wide Flange Steel I Beam: W8 × 31
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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Two 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 two equal spans, we compute the displacement at the middle of each span w_mid and the maximum normal stress stress_max occuring at the center support 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 6.75 × 10-6 15.2
40.0 8.70 × 10-6 19.6
50.0 1.09 × 10-5 24.5
60.0 1.31 × 10-5 29.5
70.0 1.52 × 10-5 34.4
80.0 1.74 × 10-5 39.3
90.0 1.96 × 10-5 44.2
100 2.18 × 10-5 49.1
200 4.35 × 10-5 98.2
300 6.53 × 10-5 147
400 8.70 × 10-5 196
500 1.09 × 10-4 245
600 1.31 × 10-4 295
700 1.52 × 10-4 344
800 1.74 × 10-4 393
900 1.96 × 10-4 442
1000 2.18 × 10-4 491
2000 4.35 × 10-4 982
3000 6.53 × 10-4 1470
4000 8.70 × 10-4 1960
5000 0.00109 2450
6000 0.00131 2950
7000 0.00152 3440
8000 0.00174 3930
9000 0.00196 4420
1.00 × 104 0.00218 4910
2.00 × 104 0.00435 9820
3.00 × 104 0.00653 1.47 × 104
4.00 × 104 0.00870 1.96 × 104
5.00 × 104 0.0109 2.45 × 104
6.00 × 104 0.0131 2.95 × 104
7.00 × 104 0.0152 3.44 × 104
8.00 × 104 0.0174 3.93 × 104
9.00 × 104 0.0196 4.42 × 104
1.00 × 105 0.0218 4.91 × 104
2.00 × 105 0.0435 9.82 × 104
3.00 × 105 0.0653 1.47 × 105
4.00 × 105 0.0870 1.96 × 105
5.00 × 105 0.109 2.45 × 105
6.00 × 105 0.131 2.95 × 105
6.05 × 105 0.132 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 5.20 × 10-5 42.3
40.0 6.72 × 10-5 54.5
50.0 8.39 × 10-5 68.2
60.0 1.01 × 10-4 81.8
70.0 1.18 × 10-4 95.5
80.0 1.34 × 10-4 109
90.0 1.51 × 10-4 123
100 1.68 × 10-4 136
200 3.36 × 10-4 273
300 5.04 × 10-4 409
400 6.72 × 10-4 545
500 8.39 × 10-4 682
600 0.00101 818
700 0.00118 955
800 0.00134 1090
900 0.00151 1230
1000 0.00168 1360
2000 0.00336 2730
3000 0.00504 4090
4000 0.00672 5450
5000 0.00839 6820
6000 0.0101 8180
7000 0.0118 9550
8000 0.0134 1.09 × 104
9000 0.0151 1.23 × 104
1.00 × 104 0.0168 1.36 × 104
2.00 × 104 0.0336 2.73 × 104
3.00 × 104 0.0504 4.09 × 104
4.00 × 104 0.0672 5.45 × 104
5.00 × 104 0.0839 6.82 × 104
6.00 × 104 0.101 8.18 × 104
7.00 × 104 0.118 9.55 × 104
8.00 × 104 0.134 1.09 × 105
9.00 × 104 0.151 1.23 × 105
1.00 × 105 0.168 1.36 × 105
2.00 × 105 0.336 2.73 × 105
2.18 × 105 0.366 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 8.33 × 10-4 169
40.0 0.00107 218
50.0 0.00134 273
60.0 0.00161 327
70.0 0.00188 382
80.0 0.00215 436
90.0 0.00242 491
100 0.00269 545
200 0.00537 1090
300 0.00806 1640
400 0.0107 2180
500 0.0134 2730
600 0.0161 3270
700 0.0188 3820
800 0.0215 4360
900 0.0242 4910
1000 0.0269 5450
2000 0.0537 1.09 × 104
3000 0.0806 1.64 × 104
4000 0.107 2.18 × 104
5000 0.134 2.73 × 104
6000 0.161 3.27 × 104
7000 0.188 3.82 × 104
8000 0.215 4.36 × 104
9000 0.242 4.91 × 104
1.00 × 104 0.269 5.45 × 104
2.00 × 104 0.537 1.09 × 105
3.00 × 104 0.806 1.64 × 105
4.00 × 104 1.07 2.18 × 105
5.00 × 104 1.34 2.73 × 105
5.45 × 104 1.46 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 0.00422 380
40.0 0.00544 491
50.0 0.00680 614
60.0 0.00816 736
70.0 0.00952 859
80.0 0.0109 982
90.0 0.0122 1100
100 0.0136 1230
200 0.0272 2450
300 0.0408 3680
400 0.0544 4910
500 0.0680 6140
600 0.0816 7360
700 0.0952 8590
800 0.109 9820
900 0.122 1.10 × 104
1000 0.136 1.23 × 104
2000 0.272 2.45 × 104
3000 0.408 3.68 × 104
4000 0.544 4.91 × 104
5000 0.680 6.14 × 104
6000 0.816 7.36 × 104
7000 0.952 8.59 × 104
8000 1.09 9.82 × 104
9000 1.22 1.10 × 105
1.00 × 104 1.36 1.23 × 105
2.00 × 104 2.72 2.45 × 105
2.42 × 104 3.29 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 0.0133 676
40.0 0.0172 873
50.0 0.0215 1090
60.0 0.0258 1310
70.0 0.0301 1530
80.0 0.0344 1750
90.0 0.0387 1960
100 0.0430 2180
200 0.0860 4360
300 0.129 6550
400 0.172 8730
500 0.215 1.09 × 104
600 0.258 1.31 × 104
700 0.301 1.53 × 104
800 0.344 1.75 × 104
900 0.387 1.96 × 104
1000 0.430 2.18 × 104
2000 0.860 4.36 × 104
3000 1.29 6.55 × 104
4000 1.72 8.73 × 104
5000 2.15 1.09 × 105
6000 2.58 1.31 × 105
7000 3.01 1.53 × 105
8000 3.44 1.75 × 105
9000 3.87 1.96 × 105
1.00 × 104 4.30 2.18 × 105
1.36 × 104 5.85 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 0.0325 1060
40.0 0.0420 1360
50.0 0.0525 1700
60.0 0.0630 2050
70.0 0.0735 2390
80.0 0.0839 2730
90.0 0.0944 3070
100 0.105 3410
200 0.210 6820
300 0.315 1.02 × 104
400 0.420 1.36 × 104
500 0.525 1.70 × 104
600 0.630 2.05 × 104
700 0.735 2.39 × 104
800 0.839 2.73 × 104
900 0.944 3.07 × 104
1000 1.05 3.41 × 104
2000 2.10 6.82 × 104
3000 3.15 1.02 × 105
4000 4.20 1.36 × 105
5000 5.25 1.70 × 105
6000 6.30 2.05 × 105
7000 7.35 2.39 × 105
7620 8.00 2.60 × 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 0.0675 1520
40.0 0.0870 1960
50.0 0.109 2450
60.0 0.131 2950
70.0 0.152 3440
80.0 0.174 3930
90.0 0.196 4420
100 0.218 4910
200 0.435 9820
300 0.653 1.47 × 104
400 0.870 1.96 × 104
500 1.09 2.45 × 104
600 1.31 2.95 × 104
700 1.52 3.44 × 104
800 1.74 3.93 × 104
900 1.96 4.42 × 104
1000 2.18 4.91 × 104
2000 4.35 9.82 × 104
3000 6.53 1.47 × 105
3680 8.00 1.80 × 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 0.213 2710
40.0 0.275 3490
50.0 0.344 4360
60.0 0.413 5240
70.0 0.481 6110
80.0 0.550 6980
90.0 0.619 7850
100 0.688 8730
200 1.38 1.75 × 104
300 2.06 2.62 × 104
400 2.75 3.49 × 104
500 3.44 4.36 × 104
600 4.13 5.24 × 104
700 4.81 6.11 × 104
800 5.50 6.98 × 104
900 6.19 7.85 × 104
1000 6.88 8.73 × 104
1160 8.00 1.02 × 105
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 0.520 4230
40.0 0.672 5450
50.0 0.839 6820
60.0 1.01 8180
70.0 1.18 9550
80.0 1.34 1.09 × 104
90.0 1.51 1.23 × 104
100 1.68 1.36 × 104
200 3.36 2.73 × 104
300 5.04 4.09 × 104
400 6.72 5.45 × 104
476 8.00 6.50 × 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 1.08 6090
40.0 1.39 7850
50.0 1.74 9820
60.0 2.09 1.18 × 104
70.0 2.44 1.37 × 104
80.0 2.79 1.57 × 104
90.0 3.13 1.77 × 104
100 3.48 1.96 × 104
200 6.96 3.93 × 104
230 8.00 4.51 × 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 2.00 8290
40.0 2.58 1.07 × 104
50.0 3.22 1.34 × 104
60.0 3.87 1.60 × 104
70.0 4.51 1.87 × 104
80.0 5.16 2.14 × 104
90.0 5.80 2.41 × 104
100 6.45 2.67 × 104
124 8.00 3.32 × 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 3.41 1.08 × 104
40.0 4.40 1.40 × 104
50.0 5.50 1.75 × 104
60.0 6.60 2.09 × 104
70.0 7.70 2.44 × 104
72.7 8.00 2.54 × 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 5.46 1.37 × 104
40.0 7.05 1.77 × 104
45.4 8.00 2.01 × 104
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