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Wide Flange Steel I Beam: W12 × 87
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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Three Equal Spans » Wide Flange Steel I Beam » W12 × 87
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 = 740 in4) for the W12 × 87 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: W12 × 87 (Wide Flange 12 inch tall × 87 lbf/ft)
L = 3.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
87.0 3.67 × 10-6 7.95
90.0 3.80 × 10-6 8.23
100 4.22 × 10-6 9.14
200 8.45 × 10-6 18.3
300 1.27 × 10-5 27.4
400 1.69 × 10-5 36.6
500 2.11 × 10-5 45.7
600 2.53 × 10-5 54.9
700 2.96 × 10-5 64.0
800 3.38 × 10-5 73.1
900 3.80 × 10-5 82.3
1000 4.22 × 10-5 91.4
2000 8.45 × 10-5 183
3000 1.27 × 10-4 274
4000 1.69 × 10-4 366
5000 2.11 × 10-4 457
6000 2.53 × 10-4 549
7000 2.96 × 10-4 640
8000 3.38 × 10-4 731
9000 3.80 × 10-4 823
1.00 × 104 4.22 × 10-4 914
2.00 × 104 8.45 × 10-4 1830
3.00 × 104 0.00127 2740
4.00 × 104 0.00169 3660
5.00 × 104 0.00211 4570
6.00 × 104 0.00253 5490
7.00 × 104 0.00296 6400
8.00 × 104 0.00338 7310
9.00 × 104 0.00380 8230
1.00 × 105 0.00422 9140
2.00 × 105 0.00845 1.83 × 104
3.00 × 105 0.0127 2.74 × 104
4.00 × 105 0.0169 3.66 × 104
5.00 × 105 0.0211 4.57 × 104
6.00 × 105 0.0253 5.49 × 104
7.00 × 105 0.0296 6.40 × 104
8.00 × 105 0.0338 7.31 × 104
9.00 × 105 0.0380 8.23 × 104
1.00 × 106 0.0422 9.14 × 104
2.00 × 106 0.0845 1.83 × 105
3.00 × 106 0.127 2.74 × 105
3.25 × 106 0.137 2.97 × 105
Steel I Beam: W12 × 87 (Wide Flange 12 inch tall × 87 lbf/ft)
L = 5.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
87.0 2.83 × 10-5 22.1
90.0 2.93 × 10-5 22.9
100 3.26 × 10-5 25.4
200 6.52 × 10-5 50.8
300 9.78 × 10-5 76.2
400 1.30 × 10-4 102
500 1.63 × 10-4 127
600 1.96 × 10-4 152
700 2.28 × 10-4 178
800 2.61 × 10-4 203
900 2.93 × 10-4 229
1000 3.26 × 10-4 254
2000 6.52 × 10-4 508
3000 9.78 × 10-4 762
4000 0.00130 1020
5000 0.00163 1270
6000 0.00196 1520
7000 0.00228 1780
8000 0.00261 2030
9000 0.00293 2290
1.00 × 104 0.00326 2540
2.00 × 104 0.00652 5080
3.00 × 104 0.00978 7620
4.00 × 104 0.0130 1.02 × 104
5.00 × 104 0.0163 1.27 × 104
6.00 × 104 0.0196 1.52 × 104
7.00 × 104 0.0228 1.78 × 104
8.00 × 104 0.0261 2.03 × 104
9.00 × 104 0.0293 2.29 × 104
1.00 × 105 0.0326 2.54 × 104
2.00 × 105 0.0652 5.08 × 104
3.00 × 105 0.0978 7.62 × 104
4.00 × 105 0.130 1.02 × 105
5.00 × 105 0.163 1.27 × 105
6.00 × 105 0.196 1.52 × 105
7.00 × 105 0.228 1.78 × 105
8.00 × 105 0.261 2.03 × 105
9.00 × 105 0.293 2.29 × 105
1.00 × 106 0.326 2.54 × 105
1.17 × 106 0.381 2.97 × 105
Steel I Beam: W12 × 87 (Wide Flange 12 inch tall × 87 lbf/ft)
L = 10.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
87.0 4.54 × 10-4 88.4
90.0 4.69 × 10-4 91.4
100 5.21 × 10-4 102
200 0.00104 203
300 0.00156 305
400 0.00209 406
500 0.00261 508
600 0.00313 610
700 0.00365 711
800 0.00417 813
900 0.00469 914
1000 0.00521 1020
2000 0.0104 2030
3000 0.0156 3050
4000 0.0209 4060
5000 0.0261 5080
6000 0.0313 6100
7000 0.0365 7110
8000 0.0417 8130
9000 0.0469 9140
1.00 × 104 0.0521 1.02 × 104
2.00 × 104 0.104 2.03 × 104
3.00 × 104 0.156 3.05 × 104
4.00 × 104 0.209 4.06 × 104
5.00 × 104 0.261 5.08 × 104
6.00 × 104 0.313 6.10 × 104
7.00 × 104 0.365 7.11 × 104
8.00 × 104 0.417 8.13 × 104
9.00 × 104 0.469 9.14 × 104
1.00 × 105 0.521 1.02 × 105
2.00 × 105 1.04 2.03 × 105
2.92 × 105 1.52 2.97 × 105
Steel I Beam: W12 × 87 (Wide Flange 12 inch tall × 87 lbf/ft)
L = 15.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
87.0 0.00230 199
90.0 0.00238 206
100 0.00264 229
200 0.00528 457
300 0.00792 686
400 0.0106 914
500 0.0132 1140
600 0.0158 1370
700 0.0185 1600
800 0.0211 1830
900 0.0238 2060
1000 0.0264 2290
2000 0.0528 4570
3000 0.0792 6860
4000 0.106 9140
5000 0.132 1.14 × 104
6000 0.158 1.37 × 104
7000 0.185 1.60 × 104
8000 0.211 1.83 × 104
9000 0.238 2.06 × 104
1.00 × 104 0.264 2.29 × 104
2.00 × 104 0.528 4.57 × 104
3.00 × 104 0.792 6.86 × 104
4.00 × 104 1.06 9.14 × 104
5.00 × 104 1.32 1.14 × 105
6.00 × 104 1.58 1.37 × 105
7.00 × 104 1.85 1.60 × 105
8.00 × 104 2.11 1.83 × 105
9.00 × 104 2.38 2.06 × 105
1.00 × 105 2.64 2.29 × 105
1.30 × 105 3.43 2.97 × 105
Steel I Beam: W12 × 87 (Wide Flange 12 inch tall × 87 lbf/ft)
L = 20.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
87.0 0.00726 354
90.0 0.00751 366
100 0.00834 406
200 0.0167 813
300 0.0250 1220
400 0.0334 1630
500 0.0417 2030
600 0.0500 2440
700 0.0584 2840
800 0.0667 3250
900 0.0751 3660
1000 0.0834 4060
2000 0.167 8130
3000 0.250 1.22 × 104
4000 0.334 1.63 × 104
5000 0.417 2.03 × 104
6000 0.500 2.44 × 104
7000 0.584 2.84 × 104
8000 0.667 3.25 × 104
9000 0.751 3.66 × 104
1.00 × 104 0.834 4.06 × 104
2.00 × 104 1.67 8.13 × 104
3.00 × 104 2.50 1.22 × 105
4.00 × 104 3.34 1.63 × 105
5.00 × 104 4.17 2.03 × 105
6.00 × 104 5.00 2.44 × 105
7.00 × 104 5.84 2.84 × 105
7.31 × 104 6.10 2.97 × 105
Steel I Beam: W12 × 87 (Wide Flange 12 inch tall × 87 lbf/ft)
L = 25.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
87.0 0.0177 552
90.0 0.0183 571
100 0.0204 635
200 0.0407 1270
300 0.0611 1900
400 0.0815 2540
500 0.102 3170
600 0.122 3810
700 0.143 4440
800 0.163 5080
900 0.183 5710
1000 0.204 6350
2000 0.407 1.27 × 104
3000 0.611 1.90 × 104
4000 0.815 2.54 × 104
5000 1.02 3.17 × 104
6000 1.22 3.81 × 104
7000 1.43 4.44 × 104
8000 1.63 5.08 × 104
9000 1.83 5.71 × 104
1.00 × 104 2.04 6.35 × 104
2.00 × 104 4.07 1.27 × 105
3.00 × 104 6.11 1.90 × 105
4.00 × 104 8.15 2.54 × 105
4.68 × 104 9.53 2.97 × 105
Steel I Beam: W12 × 87 (Wide Flange 12 inch tall × 87 lbf/ft)
L = 30.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
87.0 0.0367 795
90.0 0.0380 823
100 0.0422 914
200 0.0845 1830
300 0.127 2740
400 0.169 3660
500 0.211 4570
600 0.253 5490
700 0.296 6400
800 0.338 7310
900 0.380 8230
1000 0.422 9140
2000 0.845 1.83 × 104
3000 1.27 2.74 × 104
4000 1.69 3.66 × 104
5000 2.11 4.57 × 104
6000 2.53 5.49 × 104
7000 2.96 6.40 × 104
8000 3.38 7.31 × 104
9000 3.80 8.23 × 104
1.00 × 104 4.22 9.14 × 104
2.00 × 104 8.45 1.83 × 105
2.97 × 104 12.5 2.71 × 105
Steel I Beam: W12 × 87 (Wide Flange 12 inch tall × 87 lbf/ft)
L = 40.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
87.0 0.116 1410
90.0 0.120 1460
100 0.133 1630
200 0.267 3250
300 0.400 4880
400 0.534 6500
500 0.667 8130
600 0.801 9750
700 0.934 1.14 × 104
800 1.07 1.30 × 104
900 1.20 1.46 × 104
1000 1.33 1.63 × 104
2000 2.67 3.25 × 104
3000 4.00 4.88 × 104
4000 5.34 6.50 × 104
5000 6.67 8.13 × 104
6000 8.01 9.75 × 104
7000 9.34 1.14 × 105
8000 10.7 1.30 × 105
9000 12.0 1.46 × 105
9390 12.5 1.53 × 105
Steel I Beam: W12 × 87 (Wide Flange 12 inch tall × 87 lbf/ft)
L = 50.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
87.0 0.283 2210
90.0 0.293 2290
100 0.326 2540
200 0.652 5080
300 0.978 7620
400 1.30 1.02 × 104
500 1.63 1.27 × 104
600 1.96 1.52 × 104
700 2.28 1.78 × 104
800 2.61 2.03 × 104
900 2.93 2.29 × 104
1000 3.26 2.54 × 104
2000 6.52 5.08 × 104
3000 9.78 7.62 × 104
3850 12.5 9.77 × 104
Steel I Beam: W12 × 87 (Wide Flange 12 inch tall × 87 lbf/ft)
L = 60.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
87.0 0.588 3180
90.0 0.608 3290
100 0.676 3660
200 1.35 7310
300 2.03 1.10 × 104
400 2.70 1.46 × 104
500 3.38 1.83 × 104
600 4.05 2.19 × 104
700 4.73 2.56 × 104
800 5.41 2.93 × 104
900 6.08 3.29 × 104
1000 6.76 3.66 × 104
1850 12.5 6.78 × 104
Steel I Beam: W12 × 87 (Wide Flange 12 inch tall × 87 lbf/ft)
L = 70.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
87.0 1.09 4330
90.0 1.13 4480
100 1.25 4980
200 2.50 9960
300 3.76 1.49 × 104
400 5.01 1.99 × 104
500 6.26 2.49 × 104
600 7.51 2.99 × 104
700 8.76 3.48 × 104
800 10.0 3.98 × 104
900 11.3 4.48 × 104
1000 12.5 4.98 × 104
1000 12.5 4.98 × 104
Steel I Beam: W12 × 87 (Wide Flange 12 inch tall × 87 lbf/ft)
L = 80.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
87.0 1.86 5660
90.0 1.92 5850
100 2.14 6500
200 4.27 1.30 × 104
300 6.41 1.95 × 104
400 8.54 2.60 × 104
500 10.7 3.25 × 104
587 12.5 3.82 × 104
Steel I Beam: W12 × 87 (Wide Flange 12 inch tall × 87 lbf/ft)
L = 90.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
87.0 2.98 7160
90.0 3.08 7410
100 3.42 8230
200 6.84 1.65 × 104
300 10.3 2.47 × 104
366 12.5 3.01 × 104
Steel I Beam: W12 × 87 (Wide Flange 12 inch tall × 87 lbf/ft)
L = 100 ft
P (lbf/ft) w_max (in) stress_max (psi)
87.0 4.54 8840
90.0 4.69 9140
100 5.21 1.02 × 104
200 10.4 2.03 × 104
240 12.5 2.44 × 104
Steel I Beam: W12 × 87 (Wide Flange 12 inch tall × 87 lbf/ft)
L = 125 ft
P (lbf/ft) w_max (in) stress_max (psi)
87.0 11.1 1.38 × 104
90.0 11.5 1.43 × 104
98.4 12.5 1.56 × 104
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