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Wide Flange Steel I Beam: W8 × 31
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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Three 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 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 = 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 8.81 × 10-6 12.2
40.0 1.14 × 10-5 15.7
50.0 1.42 × 10-5 19.6
60.0 1.70 × 10-5 23.6
70.0 1.99 × 10-5 27.5
80.0 2.27 × 10-5 31.4
90.0 2.56 × 10-5 35.3
100 2.84 × 10-5 39.3
200 5.68 × 10-5 78.5
300 8.52 × 10-5 118
400 1.14 × 10-4 157
500 1.42 × 10-4 196
600 1.70 × 10-4 236
700 1.99 × 10-4 275
800 2.27 × 10-4 314
900 2.56 × 10-4 353
1000 2.84 × 10-4 393
2000 5.68 × 10-4 785
3000 8.52 × 10-4 1180
4000 0.00114 1570
5000 0.00142 1960
6000 0.00170 2360
7000 0.00199 2750
8000 0.00227 3140
9000 0.00256 3530
1.00 × 104 0.00284 3930
2.00 × 104 0.00568 7850
3.00 × 104 0.00852 1.18 × 104
4.00 × 104 0.0114 1.57 × 104
5.00 × 104 0.0142 1.96 × 104
6.00 × 104 0.0170 2.36 × 104
7.00 × 104 0.0199 2.75 × 104
8.00 × 104 0.0227 3.14 × 104
9.00 × 104 0.0256 3.53 × 104
1.00 × 105 0.0284 3.93 × 104
2.00 × 105 0.0568 7.85 × 104
3.00 × 105 0.0852 1.18 × 105
4.00 × 105 0.114 1.57 × 105
5.00 × 105 0.142 1.96 × 105
6.00 × 105 0.170 2.36 × 105
7.00 × 105 0.199 2.75 × 105
7.56 × 105 0.215 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 6.80 × 10-5 33.8
40.0 8.77 × 10-5 43.6
50.0 1.10 × 10-4 54.5
60.0 1.32 × 10-4 65.5
70.0 1.53 × 10-4 76.4
80.0 1.75 × 10-4 87.3
90.0 1.97 × 10-4 98.2
100 2.19 × 10-4 109
200 4.38 × 10-4 218
300 6.58 × 10-4 327
400 8.77 × 10-4 436
500 0.00110 545
600 0.00132 655
700 0.00153 764
800 0.00175 873
900 0.00197 982
1000 0.00219 1090
2000 0.00438 2180
3000 0.00658 3270
4000 0.00877 4360
5000 0.0110 5450
6000 0.0132 6550
7000 0.0153 7640
8000 0.0175 8730
9000 0.0197 9820
1.00 × 104 0.0219 1.09 × 104
2.00 × 104 0.0438 2.18 × 104
3.00 × 104 0.0658 3.27 × 104
4.00 × 104 0.0877 4.36 × 104
5.00 × 104 0.110 5.45 × 104
6.00 × 104 0.132 6.55 × 104
7.00 × 104 0.153 7.64 × 104
8.00 × 104 0.175 8.73 × 104
9.00 × 104 0.197 9.82 × 104
1.00 × 105 0.219 1.09 × 105
2.00 × 105 0.438 2.18 × 105
2.72 × 105 0.597 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 0.00109 135
40.0 0.00140 175
50.0 0.00175 218
60.0 0.00210 262
70.0 0.00246 305
80.0 0.00281 349
90.0 0.00316 393
100 0.00351 436
200 0.00701 873
300 0.0105 1310
400 0.0140 1750
500 0.0175 2180
600 0.0210 2620
700 0.0246 3050
800 0.0281 3490
900 0.0316 3930
1000 0.0351 4360
2000 0.0701 8730
3000 0.105 1.31 × 104
4000 0.140 1.75 × 104
5000 0.175 2.18 × 104
6000 0.210 2.62 × 104
7000 0.246 3.05 × 104
8000 0.281 3.49 × 104
9000 0.316 3.93 × 104
1.00 × 104 0.351 4.36 × 104
2.00 × 104 0.701 8.73 × 104
3.00 × 104 1.05 1.31 × 105
4.00 × 104 1.40 1.75 × 105
5.00 × 104 1.75 2.18 × 105
6.00 × 104 2.10 2.62 × 105
6.81 × 104 2.39 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 0.00550 304
40.0 0.00710 393
50.0 0.00888 491
60.0 0.0107 589
70.0 0.0124 687
80.0 0.0142 785
90.0 0.0160 884
100 0.0178 982
200 0.0355 1960
300 0.0533 2950
400 0.0710 3930
500 0.0888 4910
600 0.107 5890
700 0.124 6870
800 0.142 7850
900 0.160 8840
1000 0.178 9820
2000 0.355 1.96 × 104
3000 0.533 2.95 × 104
4000 0.710 3.93 × 104
5000 0.888 4.91 × 104
6000 1.07 5.89 × 104
7000 1.24 6.87 × 104
8000 1.42 7.85 × 104
9000 1.60 8.84 × 104
1.00 × 104 1.78 9.82 × 104
2.00 × 104 3.55 1.96 × 105
3.00 × 104 5.33 2.95 × 105
3.03 × 104 5.37 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 0.0174 541
40.0 0.0224 698
50.0 0.0281 873
60.0 0.0337 1050
70.0 0.0393 1220
80.0 0.0449 1400
90.0 0.0505 1570
100 0.0561 1750
200 0.112 3490
300 0.168 5240
400 0.224 6980
500 0.281 8730
600 0.337 1.05 × 104
700 0.393 1.22 × 104
800 0.449 1.40 × 104
900 0.505 1.57 × 104
1000 0.561 1.75 × 104
2000 1.12 3.49 × 104
3000 1.68 5.24 × 104
4000 2.24 6.98 × 104
5000 2.81 8.73 × 104
6000 3.37 1.05 × 105
7000 3.93 1.22 × 105
8000 4.49 1.40 × 105
9000 5.05 1.57 × 105
1.00 × 104 5.61 1.75 × 105
1.70 × 104 9.55 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 0.0425 845
40.0 0.0548 1090
50.0 0.0685 1360
60.0 0.0822 1640
70.0 0.0959 1910
80.0 0.110 2180
90.0 0.123 2450
100 0.137 2730
200 0.274 5450
300 0.411 8180
400 0.548 1.09 × 104
500 0.685 1.36 × 104
600 0.822 1.64 × 104
700 0.959 1.91 × 104
800 1.10 2.18 × 104
900 1.23 2.45 × 104
1000 1.37 2.73 × 104
2000 2.74 5.45 × 104
3000 4.11 8.18 × 104
4000 5.48 1.09 × 105
5000 6.85 1.36 × 105
5840 8.00 1.59 × 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 0.0881 1220
40.0 0.114 1570
50.0 0.142 1960
60.0 0.170 2360
70.0 0.199 2750
80.0 0.227 3140
90.0 0.256 3530
100 0.284 3930
200 0.568 7850
300 0.852 1.18 × 104
400 1.14 1.57 × 104
500 1.42 1.96 × 104
600 1.70 2.36 × 104
700 1.99 2.75 × 104
800 2.27 3.14 × 104
900 2.56 3.53 × 104
1000 2.84 3.93 × 104
2000 5.68 7.85 × 104
2820 8.00 1.11 × 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 0.278 2160
40.0 0.359 2790
50.0 0.449 3490
60.0 0.539 4190
70.0 0.628 4890
80.0 0.718 5590
90.0 0.808 6280
100 0.898 6980
200 1.80 1.40 × 104
300 2.69 2.09 × 104
400 3.59 2.79 × 104
500 4.49 3.49 × 104
600 5.39 4.19 × 104
700 6.28 4.89 × 104
800 7.18 5.59 × 104
891 8.00 6.22 × 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 0.680 3380
40.0 0.877 4360
50.0 1.10 5450
60.0 1.32 6550
70.0 1.53 7640
80.0 1.75 8730
90.0 1.97 9820
100 2.19 1.09 × 104
200 4.38 2.18 × 104
300 6.58 3.27 × 104
365 8.00 3.98 × 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 1.41 4870
40.0 1.82 6280
50.0 2.27 7850
60.0 2.73 9430
70.0 3.18 1.10 × 104
80.0 3.64 1.26 × 104
90.0 4.09 1.41 × 104
100 4.55 1.57 × 104
176 8.00 2.76 × 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 2.61 6630
40.0 3.37 8550
50.0 4.21 1.07 × 104
60.0 5.05 1.28 × 104
70.0 5.89 1.50 × 104
80.0 6.74 1.71 × 104
90.0 7.58 1.92 × 104
95.0 8.00 2.03 × 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 4.45 8660
40.0 5.75 1.12 × 104
50.0 7.18 1.40 × 104
55.7 8.00 1.56 × 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 7.13 1.10 × 104
34.8 8.00 1.23 × 104
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