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Wide Flange Steel I Beam: W16 × 31
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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Three 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 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 = 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
   
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 2.58 × 10-6 7.09
40.0 3.33 × 10-6 9.15
50.0 4.17 × 10-6 11.4
60.0 5.00 × 10-6 13.7
70.0 5.83 × 10-6 16.0
80.0 6.67 × 10-6 18.3
90.0 7.50 × 10-6 20.6
100 8.33 × 10-6 22.9
200 1.67 × 10-5 45.7
300 2.50 × 10-5 68.6
400 3.33 × 10-5 91.5
500 4.17 × 10-5 114
600 5.00 × 10-5 137
700 5.83 × 10-5 160
800 6.67 × 10-5 183
900 7.50 × 10-5 206
1000 8.33 × 10-5 229
2000 1.67 × 10-4 457
3000 2.50 × 10-4 686
4000 3.33 × 10-4 915
5000 4.17 × 10-4 1140
6000 5.00 × 10-4 1370
7000 5.83 × 10-4 1600
8000 6.67 × 10-4 1830
9000 7.50 × 10-4 2060
1.00 × 104 8.33 × 10-4 2290
2.00 × 104 0.00167 4570
3.00 × 104 0.00250 6860
4.00 × 104 0.00333 9150
5.00 × 104 0.00417 1.14 × 104
6.00 × 104 0.00500 1.37 × 104
7.00 × 104 0.00583 1.60 × 104
8.00 × 104 0.00667 1.83 × 104
9.00 × 104 0.00750 2.06 × 104
1.00 × 105 0.00833 2.29 × 104
2.00 × 105 0.0167 4.57 × 104
3.00 × 105 0.0250 6.86 × 104
4.00 × 105 0.0333 9.15 × 104
5.00 × 105 0.0417 1.14 × 105
6.00 × 105 0.0500 1.37 × 105
7.00 × 105 0.0583 1.60 × 105
8.00 × 105 0.0667 1.83 × 105
9.00 × 105 0.0750 2.06 × 105
1.00 × 106 0.0833 2.29 × 105
1.30 × 106 0.108 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 1.99 × 10-5 19.7
40.0 2.57 × 10-5 25.4
50.0 3.21 × 10-5 31.8
60.0 3.86 × 10-5 38.1
70.0 4.50 × 10-5 44.5
80.0 5.14 × 10-5 50.8
90.0 5.79 × 10-5 57.2
100 6.43 × 10-5 63.5
200 1.29 × 10-4 127
300 1.93 × 10-4 191
400 2.57 × 10-4 254
500 3.21 × 10-4 318
600 3.86 × 10-4 381
700 4.50 × 10-4 445
800 5.14 × 10-4 508
900 5.79 × 10-4 572
1000 6.43 × 10-4 635
2000 0.00129 1270
3000 0.00193 1910
4000 0.00257 2540
5000 0.00321 3180
6000 0.00386 3810
7000 0.00450 4450
8000 0.00514 5080
9000 0.00579 5720
1.00 × 104 0.00643 6350
2.00 × 104 0.0129 1.27 × 104
3.00 × 104 0.0193 1.91 × 104
4.00 × 104 0.0257 2.54 × 104
5.00 × 104 0.0321 3.18 × 104
6.00 × 104 0.0386 3.81 × 104
7.00 × 104 0.0450 4.45 × 104
8.00 × 104 0.0514 5.08 × 104
9.00 × 104 0.0579 5.72 × 104
1.00 × 105 0.0643 6.35 × 104
2.00 × 105 0.129 1.27 × 105
3.00 × 105 0.193 1.91 × 105
4.00 × 105 0.257 2.54 × 105
4.68 × 105 0.301 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 3.19 × 10-4 78.8
40.0 4.12 × 10-4 102
50.0 5.14 × 10-4 127
60.0 6.17 × 10-4 152
70.0 7.20 × 10-4 178
80.0 8.23 × 10-4 203
90.0 9.26 × 10-4 229
100 0.00103 254
200 0.00206 508
300 0.00309 762
400 0.00412 1020
500 0.00514 1270
600 0.00617 1520
700 0.00720 1780
800 0.00823 2030
900 0.00926 2290
1000 0.0103 2540
2000 0.0206 5080
3000 0.0309 7620
4000 0.0412 1.02 × 104
5000 0.0514 1.27 × 104
6000 0.0617 1.52 × 104
7000 0.0720 1.78 × 104
8000 0.0823 2.03 × 104
9000 0.0926 2.29 × 104
1.00 × 104 0.103 2.54 × 104
2.00 × 104 0.206 5.08 × 104
3.00 × 104 0.309 7.62 × 104
4.00 × 104 0.412 1.02 × 105
5.00 × 104 0.514 1.27 × 105
6.00 × 104 0.617 1.52 × 105
7.00 × 104 0.720 1.78 × 105
8.00 × 104 0.823 2.03 × 105
9.00 × 104 0.926 2.29 × 105
1.00 × 105 1.03 2.54 × 105
1.17 × 105 1.20 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 0.00161 177
40.0 0.00208 229
50.0 0.00260 286
60.0 0.00312 343
70.0 0.00365 400
80.0 0.00417 457
90.0 0.00469 515
100 0.00521 572
200 0.0104 1140
300 0.0156 1720
400 0.0208 2290
500 0.0260 2860
600 0.0312 3430
700 0.0365 4000
800 0.0417 4570
900 0.0469 5150
1000 0.0521 5720
2000 0.104 1.14 × 104
3000 0.156 1.72 × 104
4000 0.208 2.29 × 104
5000 0.260 2.86 × 104
6000 0.312 3.43 × 104
7000 0.365 4.00 × 104
8000 0.417 4.57 × 104
9000 0.469 5.15 × 104
1.00 × 104 0.521 5.72 × 104
2.00 × 104 1.04 1.14 × 105
3.00 × 104 1.56 1.72 × 105
4.00 × 104 2.08 2.29 × 105
5.00 × 104 2.60 2.86 × 105
5.20 × 104 2.71 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 0.00510 315
40.0 0.00658 407
50.0 0.00823 508
60.0 0.00988 610
70.0 0.0115 711
80.0 0.0132 813
90.0 0.0148 915
100 0.0165 1020
200 0.0329 2030
300 0.0494 3050
400 0.0658 4070
500 0.0823 5080
600 0.0988 6100
700 0.115 7110
800 0.132 8130
900 0.148 9150
1000 0.165 1.02 × 104
2000 0.329 2.03 × 104
3000 0.494 3.05 × 104
4000 0.658 4.07 × 104
5000 0.823 5.08 × 104
6000 0.988 6.10 × 104
7000 1.15 7.11 × 104
8000 1.32 8.13 × 104
9000 1.48 9.15 × 104
1.00 × 104 1.65 1.02 × 105
2.00 × 104 3.29 2.03 × 105
2.92 × 104 4.81 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 0.0125 492
40.0 0.0161 635
50.0 0.0201 794
60.0 0.0241 953
70.0 0.0281 1110
80.0 0.0321 1270
90.0 0.0362 1430
100 0.0402 1590
200 0.0804 3180
300 0.121 4760
400 0.161 6350
500 0.201 7940
600 0.241 9530
700 0.281 1.11 × 104
800 0.321 1.27 × 104
900 0.362 1.43 × 104
1000 0.402 1.59 × 104
2000 0.804 3.18 × 104
3000 1.21 4.76 × 104
4000 1.61 6.35 × 104
5000 2.01 7.94 × 104
6000 2.41 9.53 × 104
7000 2.81 1.11 × 105
8000 3.21 1.27 × 105
9000 3.62 1.43 × 105
1.00 × 104 4.02 1.59 × 105
1.87 × 104 7.52 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 0.0258 709
40.0 0.0333 915
50.0 0.0417 1140
60.0 0.0500 1370
70.0 0.0583 1600
80.0 0.0667 1830
90.0 0.0750 2060
100 0.0833 2290
200 0.167 4570
300 0.250 6860
400 0.333 9150
500 0.417 1.14 × 104
600 0.500 1.37 × 104
700 0.583 1.60 × 104
800 0.667 1.83 × 104
900 0.750 2.06 × 104
1000 0.833 2.29 × 104
2000 1.67 4.57 × 104
3000 2.50 6.86 × 104
4000 3.33 9.15 × 104
5000 4.17 1.14 × 105
6000 5.00 1.37 × 105
7000 5.83 1.60 × 105
8000 6.67 1.83 × 105
9000 7.50 2.06 × 105
1.00 × 104 8.33 2.29 × 105
1.30 × 104 10.8 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 0.0816 1260
40.0 0.105 1630
50.0 0.132 2030
60.0 0.158 2440
70.0 0.184 2850
80.0 0.211 3250
90.0 0.237 3660
100 0.263 4070
200 0.527 8130
300 0.790 1.22 × 104
400 1.05 1.63 × 104
500 1.32 2.03 × 104
600 1.58 2.44 × 104
700 1.84 2.85 × 104
800 2.11 3.25 × 104
900 2.37 3.66 × 104
1000 2.63 4.07 × 104
2000 5.27 8.13 × 104
3000 7.90 1.22 × 105
4000 10.5 1.63 × 105
5000 13.2 2.03 × 105
6000 15.8 2.44 × 105
6030 15.9 2.45 × 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 0.199 1970
40.0 0.257 2540
50.0 0.321 3180
60.0 0.386 3810
70.0 0.450 4450
80.0 0.514 5080
90.0 0.579 5720
100 0.643 6350
200 1.29 1.27 × 104
300 1.93 1.91 × 104
400 2.57 2.54 × 104
500 3.21 3.18 × 104
600 3.86 3.81 × 104
700 4.50 4.45 × 104
800 5.14 5.08 × 104
900 5.79 5.72 × 104
1000 6.43 6.35 × 104
2000 12.9 1.27 × 105
2470 15.9 1.57 × 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 0.413 2840
40.0 0.533 3660
50.0 0.667 4570
60.0 0.800 5490
70.0 0.933 6400
80.0 1.07 7320
90.0 1.20 8230
100 1.33 9150
200 2.67 1.83 × 104
300 4.00 2.74 × 104
400 5.33 3.66 × 104
500 6.67 4.57 × 104
600 8.00 5.49 × 104
700 9.33 6.40 × 104
800 10.7 7.32 × 104
900 12.0 8.23 × 104
1000 13.3 9.15 × 104
1190 15.9 1.09 × 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 0.766 3860
40.0 0.988 4980
50.0 1.24 6220
60.0 1.48 7470
70.0 1.73 8710
80.0 1.98 9960
90.0 2.22 1.12 × 104
100 2.47 1.24 × 104
200 4.94 2.49 × 104
300 7.41 3.73 × 104
400 9.88 4.98 × 104
500 12.4 6.22 × 104
600 14.8 7.47 × 104
643 15.9 8.00 × 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 1.31 5040
40.0 1.69 6500
50.0 2.11 8130
60.0 2.53 9760
70.0 2.95 1.14 × 104
80.0 3.37 1.30 × 104
90.0 3.79 1.46 × 104
100 4.21 1.63 × 104
200 8.43 3.25 × 104
300 12.6 4.88 × 104
377 15.9 6.13 × 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 2.09 6380
40.0 2.70 8230
50.0 3.37 1.03 × 104
60.0 4.05 1.23 × 104
70.0 4.72 1.44 × 104
80.0 5.40 1.65 × 104
90.0 6.07 1.85 × 104
100 6.75 2.06 × 104
200 13.5 4.12 × 104
235 15.9 4.84 × 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 3.19 7880
40.0 4.12 1.02 × 104
50.0 5.14 1.27 × 104
60.0 6.17 1.52 × 104
70.0 7.20 1.78 × 104
80.0 8.23 2.03 × 104
90.0 9.26 2.29 × 104
100 10.3 2.54 × 104
154 15.9 3.92 × 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 7.79 1.23 × 104
40.0 10.0 1.59 × 104
50.0 12.6 1.99 × 104
60.0 15.1 2.38 × 104
63.2 15.9 2.51 × 104
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