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Wide Flange Steel I Beam: W16 × 31
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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Four Equal Spans » Wide Flange Steel I Beam » W16 × 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 = 375 in4) for the W16 × 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
L = 100 ft
L = 125 ft
L = 150 ft
  
Steel I Beam: W16 × 31 (Wide Flange 16 inch tall × 31 lbf/ft)
L = 3.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 2.39 × 10-6 7.59
40.0 3.09 × 10-6 9.80
50.0 3.86 × 10-6 12.2
60.0 4.63 × 10-6 14.7
70.0 5.40 × 10-6 17.1
80.0 6.18 × 10-6 19.6
90.0 6.95 × 10-6 22.0
100 7.72 × 10-6 24.5
200 1.54 × 10-5 49.0
300 2.32 × 10-5 73.5
400 3.09 × 10-5 98.0
500 3.86 × 10-5 122
600 4.63 × 10-5 147
700 5.40 × 10-5 171
800 6.18 × 10-5 196
900 6.95 × 10-5 220
1000 7.72 × 10-5 245
2000 1.54 × 10-4 490
3000 2.32 × 10-4 735
4000 3.09 × 10-4 980
5000 3.86 × 10-4 1220
6000 4.63 × 10-4 1470
7000 5.40 × 10-4 1710
8000 6.18 × 10-4 1960
9000 6.95 × 10-4 2200
1.00 × 104 7.72 × 10-4 2450
2.00 × 104 0.00154 4900
3.00 × 104 0.00232 7350
4.00 × 104 0.00309 9800
5.00 × 104 0.00386 1.22 × 104
6.00 × 104 0.00463 1.47 × 104
7.00 × 104 0.00540 1.71 × 104
8.00 × 104 0.00618 1.96 × 104
9.00 × 104 0.00695 2.20 × 104
1.00 × 105 0.00772 2.45 × 104
2.00 × 105 0.0154 4.90 × 104
3.00 × 105 0.0232 7.35 × 104
4.00 × 105 0.0309 9.80 × 104
5.00 × 105 0.0386 1.22 × 105
6.00 × 105 0.0463 1.47 × 105
7.00 × 105 0.0540 1.71 × 105
8.00 × 105 0.0618 1.96 × 105
9.00 × 105 0.0695 2.20 × 105
1.00 × 106 0.0772 2.45 × 105
1.21 × 106 0.0936 2.97 × 105
Steel I Beam: W16 × 31 (Wide Flange 16 inch tall × 31 lbf/ft)
L = 5.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 1.85 × 10-5 21.1
40.0 2.38 × 10-5 27.2
50.0 2.98 × 10-5 34.0
60.0 3.57 × 10-5 40.8
70.0 4.17 × 10-5 47.6
80.0 4.77 × 10-5 54.4
90.0 5.36 × 10-5 61.2
100 5.96 × 10-5 68.0
200 1.19 × 10-4 136
300 1.79 × 10-4 204
400 2.38 × 10-4 272
500 2.98 × 10-4 340
600 3.57 × 10-4 408
700 4.17 × 10-4 476
800 4.77 × 10-4 544
900 5.36 × 10-4 612
1000 5.96 × 10-4 680
2000 0.00119 1360
3000 0.00179 2040
4000 0.00238 2720
5000 0.00298 3400
6000 0.00357 4080
7000 0.00417 4760
8000 0.00477 5440
9000 0.00536 6120
1.00 × 104 0.00596 6800
2.00 × 104 0.0119 1.36 × 104
3.00 × 104 0.0179 2.04 × 104
4.00 × 104 0.0238 2.72 × 104
5.00 × 104 0.0298 3.40 × 104
6.00 × 104 0.0357 4.08 × 104
7.00 × 104 0.0417 4.76 × 104
8.00 × 104 0.0477 5.44 × 104
9.00 × 104 0.0536 6.12 × 104
1.00 × 105 0.0596 6.80 × 104
2.00 × 105 0.119 1.36 × 105
3.00 × 105 0.179 2.04 × 105
4.00 × 105 0.238 2.72 × 105
4.37 × 105 0.260 2.97 × 105
Steel I Beam: W16 × 31 (Wide Flange 16 inch tall × 31 lbf/ft)
L = 10.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 2.95 × 10-4 84.4
40.0 3.81 × 10-4 109
50.0 4.77 × 10-4 136
60.0 5.72 × 10-4 163
70.0 6.67 × 10-4 190
80.0 7.63 × 10-4 218
90.0 8.58 × 10-4 245
100 9.53 × 10-4 272
200 0.00191 544
300 0.00286 816
400 0.00381 1090
500 0.00477 1360
600 0.00572 1630
700 0.00667 1900
800 0.00763 2180
900 0.00858 2450
1000 0.00953 2720
2000 0.0191 5440
3000 0.0286 8160
4000 0.0381 1.09 × 104
5000 0.0477 1.36 × 104
6000 0.0572 1.63 × 104
7000 0.0667 1.90 × 104
8000 0.0763 2.18 × 104
9000 0.0858 2.45 × 104
1.00 × 104 0.0953 2.72 × 104
2.00 × 104 0.191 5.44 × 104
3.00 × 104 0.286 8.16 × 104
4.00 × 104 0.381 1.09 × 105
5.00 × 104 0.477 1.36 × 105
6.00 × 104 0.572 1.63 × 105
7.00 × 104 0.667 1.90 × 105
8.00 × 104 0.763 2.18 × 105
9.00 × 104 0.858 2.45 × 105
1.00 × 105 0.953 2.72 × 105
1.09 × 105 1.04 2.97 × 105
Steel I Beam: W16 × 31 (Wide Flange 16 inch tall × 31 lbf/ft)
L = 15.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 0.00150 190
40.0 0.00193 245
50.0 0.00241 306
60.0 0.00290 367
70.0 0.00338 429
80.0 0.00386 490
90.0 0.00434 551
100 0.00483 612
200 0.00965 1220
300 0.0145 1840
400 0.0193 2450
500 0.0241 3060
600 0.0290 3670
700 0.0338 4290
800 0.0386 4900
900 0.0434 5510
1000 0.0483 6120
2000 0.0965 1.22 × 104
3000 0.145 1.84 × 104
4000 0.193 2.45 × 104
5000 0.241 3.06 × 104
6000 0.290 3.67 × 104
7000 0.338 4.29 × 104
8000 0.386 4.90 × 104
9000 0.434 5.51 × 104
1.00 × 104 0.483 6.12 × 104
2.00 × 104 0.965 1.22 × 105
3.00 × 104 1.45 1.84 × 105
4.00 × 104 1.93 2.45 × 105
4.85 × 104 2.34 2.97 × 105
Steel I Beam: W16 × 31 (Wide Flange 16 inch tall × 31 lbf/ft)
L = 20.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 0.00473 337
40.0 0.00610 435
50.0 0.00763 544
60.0 0.00915 653
70.0 0.0107 762
80.0 0.0122 871
90.0 0.0137 980
100 0.0153 1090
200 0.0305 2180
300 0.0458 3270
400 0.0610 4350
500 0.0763 5440
600 0.0915 6530
700 0.107 7620
800 0.122 8710
900 0.137 9800
1000 0.153 1.09 × 104
2000 0.305 2.18 × 104
3000 0.458 3.27 × 104
4000 0.610 4.35 × 104
5000 0.763 5.44 × 104
6000 0.915 6.53 × 104
7000 1.07 7.62 × 104
8000 1.22 8.71 × 104
9000 1.37 9.80 × 104
1.00 × 104 1.53 1.09 × 105
2.00 × 104 3.05 2.18 × 105
2.73 × 104 4.16 2.97 × 105
Steel I Beam: W16 × 31 (Wide Flange 16 inch tall × 31 lbf/ft)
L = 25.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 0.0115 527
40.0 0.0149 680
50.0 0.0186 850
60.0 0.0223 1020
70.0 0.0261 1190
80.0 0.0298 1360
90.0 0.0335 1530
100 0.0372 1700
200 0.0745 3400
300 0.112 5100
400 0.149 6800
500 0.186 8500
600 0.223 1.02 × 104
700 0.261 1.19 × 104
800 0.298 1.36 × 104
900 0.335 1.53 × 104
1000 0.372 1.70 × 104
2000 0.745 3.40 × 104
3000 1.12 5.10 × 104
4000 1.49 6.80 × 104
5000 1.86 8.50 × 104
6000 2.23 1.02 × 105
7000 2.61 1.19 × 105
8000 2.98 1.36 × 105
9000 3.35 1.53 × 105
1.00 × 104 3.72 1.70 × 105
1.75 × 104 6.50 2.97 × 105
Steel I Beam: W16 × 31 (Wide Flange 16 inch tall × 31 lbf/ft)
L = 30.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 0.0239 759
40.0 0.0309 980
50.0 0.0386 1220
60.0 0.0463 1470
70.0 0.0540 1710
80.0 0.0618 1960
90.0 0.0695 2200
100 0.0772 2450
200 0.154 4900
300 0.232 7350
400 0.309 9800
500 0.386 1.22 × 104
600 0.463 1.47 × 104
700 0.540 1.71 × 104
800 0.618 1.96 × 104
900 0.695 2.20 × 104
1000 0.772 2.45 × 104
2000 1.54 4.90 × 104
3000 2.32 7.35 × 104
4000 3.09 9.80 × 104
5000 3.86 1.22 × 105
6000 4.63 1.47 × 105
7000 5.40 1.71 × 105
8000 6.18 1.96 × 105
9000 6.95 2.20 × 105
1.00 × 104 7.72 2.45 × 105
1.21 × 104 9.36 2.97 × 105
Steel I Beam: W16 × 31 (Wide Flange 16 inch tall × 31 lbf/ft)
L = 40.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 0.0756 1350
40.0 0.0976 1740
50.0 0.122 2180
60.0 0.146 2610
70.0 0.171 3050
80.0 0.195 3480
90.0 0.220 3920
100 0.244 4350
200 0.488 8710
300 0.732 1.31 × 104
400 0.976 1.74 × 104
500 1.22 2.18 × 104
600 1.46 2.61 × 104
700 1.71 3.05 × 104
800 1.95 3.48 × 104
900 2.20 3.92 × 104
1000 2.44 4.35 × 104
2000 4.88 8.71 × 104
3000 7.32 1.31 × 105
4000 9.76 1.74 × 105
5000 12.2 2.18 × 105
6000 14.6 2.61 × 105
6820 16.6 2.97 × 105
Steel I Beam: W16 × 31 (Wide Flange 16 inch tall × 31 lbf/ft)
L = 50.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 0.185 2110
40.0 0.238 2720
50.0 0.298 3400
60.0 0.357 4080
70.0 0.417 4760
80.0 0.477 5440
90.0 0.536 6120
100 0.596 6800
200 1.19 1.36 × 104
300 1.79 2.04 × 104
400 2.38 2.72 × 104
500 2.98 3.40 × 104
600 3.57 4.08 × 104
700 4.17 4.76 × 104
800 4.77 5.44 × 104
900 5.36 6.12 × 104
1000 5.96 6.80 × 104
2000 11.9 1.36 × 105
2670 15.9 1.81 × 105
Steel I Beam: W16 × 31 (Wide Flange 16 inch tall × 31 lbf/ft)
L = 60.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 0.383 3040
40.0 0.494 3920
50.0 0.618 4900
60.0 0.741 5880
70.0 0.865 6860
80.0 0.988 7840
90.0 1.11 8820
100 1.24 9800
200 2.47 1.96 × 104
300 3.71 2.94 × 104
400 4.94 3.92 × 104
500 6.18 4.90 × 104
600 7.41 5.88 × 104
700 8.65 6.86 × 104
800 9.88 7.84 × 104
900 11.1 8.82 × 104
1000 12.4 9.80 × 104
1290 15.9 1.26 × 105
Steel I Beam: W16 × 31 (Wide Flange 16 inch tall × 31 lbf/ft)
L = 70.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 0.709 4130
40.0 0.915 5330
50.0 1.14 6670
60.0 1.37 8000
70.0 1.60 9330
80.0 1.83 1.07 × 104
90.0 2.06 1.20 × 104
100 2.29 1.33 × 104
200 4.58 2.67 × 104
300 6.87 4.00 × 104
400 9.15 5.33 × 104
500 11.4 6.67 × 104
600 13.7 8.00 × 104
694 15.9 9.25 × 104
Steel I Beam: W16 × 31 (Wide Flange 16 inch tall × 31 lbf/ft)
L = 80.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 1.21 5400
40.0 1.56 6970
50.0 1.95 8710
60.0 2.34 1.04 × 104
70.0 2.73 1.22 × 104
80.0 3.12 1.39 × 104
90.0 3.51 1.57 × 104
100 3.90 1.74 × 104
200 7.81 3.48 × 104
300 11.7 5.22 × 104
400 15.6 6.97 × 104
407 15.9 7.08 × 104
Steel I Beam: W16 × 31 (Wide Flange 16 inch tall × 31 lbf/ft)
L = 90.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 1.94 6830
40.0 2.50 8820
50.0 3.13 1.10 × 104
60.0 3.75 1.32 × 104
70.0 4.38 1.54 × 104
80.0 5.00 1.76 × 104
90.0 5.63 1.98 × 104
100 6.25 2.20 × 104
200 12.5 4.41 × 104
254 15.9 5.60 × 104
Steel I Beam: W16 × 31 (Wide Flange 16 inch tall × 31 lbf/ft)
L = 100 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 2.95 8440
40.0 3.81 1.09 × 104
50.0 4.77 1.36 × 104
60.0 5.72 1.63 × 104
70.0 6.67 1.90 × 104
80.0 7.63 2.18 × 104
90.0 8.58 2.45 × 104
100 9.53 2.72 × 104
167 15.9 4.53 × 104
Steel I Beam: W16 × 31 (Wide Flange 16 inch tall × 31 lbf/ft)
L = 125 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 7.21 1.32 × 104
40.0 9.31 1.70 × 104
50.0 11.6 2.13 × 104
60.0 14.0 2.55 × 104
68.2 15.9 2.90 × 104
Steel I Beam: W16 × 31 (Wide Flange 16 inch tall × 31 lbf/ft)
L = 150 ft
P (lbf/ft) w_max (in) stress_max (psi)
31.0 15.0 1.90 × 104
32.9 15.9 2.02 × 104
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