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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Four 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 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 = 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 3.40 × 10-6 8.52
90.0 3.52 × 10-6 8.81
100 3.91 × 10-6 9.79
200 7.82 × 10-6 19.6
300 1.17 × 10-5 29.4
400 1.56 × 10-5 39.2
500 1.96 × 10-5 49.0
600 2.35 × 10-5 58.8
700 2.74 × 10-5 68.5
800 3.13 × 10-5 78.3
900 3.52 × 10-5 88.1
1000 3.91 × 10-5 97.9
2000 7.82 × 10-5 196
3000 1.17 × 10-4 294
4000 1.56 × 10-4 392
5000 1.96 × 10-4 490
6000 2.35 × 10-4 588
7000 2.74 × 10-4 685
8000 3.13 × 10-4 783
9000 3.52 × 10-4 881
1.00 × 104 3.91 × 10-4 979
2.00 × 104 7.82 × 10-4 1960
3.00 × 104 0.00117 2940
4.00 × 104 0.00156 3920
5.00 × 104 0.00196 4900
6.00 × 104 0.00235 5880
7.00 × 104 0.00274 6850
8.00 × 104 0.00313 7830
9.00 × 104 0.00352 8810
1.00 × 105 0.00391 9790
2.00 × 105 0.00782 1.96 × 104
3.00 × 105 0.0117 2.94 × 104
4.00 × 105 0.0156 3.92 × 104
5.00 × 105 0.0196 4.90 × 104
6.00 × 105 0.0235 5.88 × 104
7.00 × 105 0.0274 6.85 × 104
8.00 × 105 0.0313 7.83 × 104
9.00 × 105 0.0352 8.81 × 104
1.00 × 106 0.0391 9.79 × 104
2.00 × 106 0.0782 1.96 × 105
3.00 × 106 0.117 2.94 × 105
3.03 × 106 0.119 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 2.63 × 10-5 23.7
90.0 2.72 × 10-5 24.5
100 3.02 × 10-5 27.2
200 6.04 × 10-5 54.4
300 9.06 × 10-5 81.6
400 1.21 × 10-4 109
500 1.51 × 10-4 136
600 1.81 × 10-4 163
700 2.11 × 10-4 190
800 2.42 × 10-4 218
900 2.72 × 10-4 245
1000 3.02 × 10-4 272
2000 6.04 × 10-4 544
3000 9.06 × 10-4 816
4000 0.00121 1090
5000 0.00151 1360
6000 0.00181 1630
7000 0.00211 1900
8000 0.00242 2180
9000 0.00272 2450
1.00 × 104 0.00302 2720
2.00 × 104 0.00604 5440
3.00 × 104 0.00906 8160
4.00 × 104 0.0121 1.09 × 104
5.00 × 104 0.0151 1.36 × 104
6.00 × 104 0.0181 1.63 × 104
7.00 × 104 0.0211 1.90 × 104
8.00 × 104 0.0242 2.18 × 104
9.00 × 104 0.0272 2.45 × 104
1.00 × 105 0.0302 2.72 × 104
2.00 × 105 0.0604 5.44 × 104
3.00 × 105 0.0906 8.16 × 104
4.00 × 105 0.121 1.09 × 105
5.00 × 105 0.151 1.36 × 105
6.00 × 105 0.181 1.63 × 105
7.00 × 105 0.211 1.90 × 105
8.00 × 105 0.242 2.18 × 105
9.00 × 105 0.272 2.45 × 105
1.00 × 106 0.302 2.72 × 105
1.09 × 106 0.330 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 4.20 × 10-4 94.7
90.0 4.35 × 10-4 97.9
100 4.83 × 10-4 109
200 9.66 × 10-4 218
300 0.00145 326
400 0.00193 435
500 0.00242 544
600 0.00290 653
700 0.00338 762
800 0.00386 870
900 0.00435 979
1000 0.00483 1090
2000 0.00966 2180
3000 0.0145 3260
4000 0.0193 4350
5000 0.0242 5440
6000 0.0290 6530
7000 0.0338 7620
8000 0.0386 8700
9000 0.0435 9790
1.00 × 104 0.0483 1.09 × 104
2.00 × 104 0.0966 2.18 × 104
3.00 × 104 0.145 3.26 × 104
4.00 × 104 0.193 4.35 × 104
5.00 × 104 0.242 5.44 × 104
6.00 × 104 0.290 6.53 × 104
7.00 × 104 0.338 7.62 × 104
8.00 × 104 0.386 8.70 × 104
9.00 × 104 0.435 9.79 × 104
1.00 × 105 0.483 1.09 × 105
2.00 × 105 0.966 2.18 × 105
2.73 × 105 1.32 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 0.00213 213
90.0 0.00220 220
100 0.00245 245
200 0.00489 490
300 0.00734 734
400 0.00978 979
500 0.0122 1220
600 0.0147 1470
700 0.0171 1710
800 0.0196 1960
900 0.0220 2200
1000 0.0245 2450
2000 0.0489 4900
3000 0.0734 7340
4000 0.0978 9790
5000 0.122 1.22 × 104
6000 0.147 1.47 × 104
7000 0.171 1.71 × 104
8000 0.196 1.96 × 104
9000 0.220 2.20 × 104
1.00 × 104 0.245 2.45 × 104
2.00 × 104 0.489 4.90 × 104
3.00 × 104 0.734 7.34 × 104
4.00 × 104 0.978 9.79 × 104
5.00 × 104 1.22 1.22 × 105
6.00 × 104 1.47 1.47 × 105
7.00 × 104 1.71 1.71 × 105
8.00 × 104 1.96 1.96 × 105
9.00 × 104 2.20 2.20 × 105
1.00 × 105 2.45 2.45 × 105
1.21 × 105 2.97 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 0.00672 379
90.0 0.00696 392
100 0.00773 435
200 0.0155 870
300 0.0232 1310
400 0.0309 1740
500 0.0386 2180
600 0.0464 2610
700 0.0541 3050
800 0.0618 3480
900 0.0696 3920
1000 0.0773 4350
2000 0.155 8700
3000 0.232 1.31 × 104
4000 0.309 1.74 × 104
5000 0.386 2.18 × 104
6000 0.464 2.61 × 104
7000 0.541 3.05 × 104
8000 0.618 3.48 × 104
9000 0.696 3.92 × 104
1.00 × 104 0.773 4.35 × 104
2.00 × 104 1.55 8.70 × 104
3.00 × 104 2.32 1.31 × 105
4.00 × 104 3.09 1.74 × 105
5.00 × 104 3.86 2.18 × 105
6.00 × 104 4.64 2.61 × 105
6.82 × 104 5.27 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 0.0164 592
90.0 0.0170 612
100 0.0189 680
200 0.0377 1360
300 0.0566 2040
400 0.0755 2720
500 0.0943 3400
600 0.113 4080
700 0.132 4760
800 0.151 5440
900 0.170 6120
1000 0.189 6800
2000 0.377 1.36 × 104
3000 0.566 2.04 × 104
4000 0.755 2.72 × 104
5000 0.943 3.40 × 104
6000 1.13 4.08 × 104
7000 1.32 4.76 × 104
8000 1.51 5.44 × 104
9000 1.70 6.12 × 104
1.00 × 104 1.89 6.80 × 104
2.00 × 104 3.77 1.36 × 105
3.00 × 104 5.66 2.04 × 105
4.00 × 104 7.55 2.72 × 105
4.37 × 104 8.24 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 0.0340 852
90.0 0.0352 881
100 0.0391 979
200 0.0782 1960
300 0.117 2940
400 0.156 3920
500 0.196 4900
600 0.235 5880
700 0.274 6850
800 0.313 7830
900 0.352 8810
1000 0.391 9790
2000 0.782 1.96 × 104
3000 1.17 2.94 × 104
4000 1.56 3.92 × 104
5000 1.96 4.90 × 104
6000 2.35 5.88 × 104
7000 2.74 6.85 × 104
8000 3.13 7.83 × 104
9000 3.52 8.81 × 104
1.00 × 104 3.91 9.79 × 104
2.00 × 104 7.82 1.96 × 105
3.00 × 104 11.7 2.94 × 105
3.03 × 104 11.9 2.97 × 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 0.108 1510
90.0 0.111 1570
100 0.124 1740
200 0.247 3480
300 0.371 5220
400 0.495 6960
500 0.618 8700
600 0.742 1.04 × 104
700 0.866 1.22 × 104
800 0.989 1.39 × 104
900 1.11 1.57 × 104
1000 1.24 1.74 × 104
2000 2.47 3.48 × 104
3000 3.71 5.22 × 104
4000 4.95 6.96 × 104
5000 6.18 8.70 × 104
6000 7.42 1.04 × 105
7000 8.66 1.22 × 105
8000 9.89 1.39 × 105
9000 11.1 1.57 × 105
1.00 × 104 12.4 1.74 × 105
1.71 × 104 21.1 2.97 × 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 0.263 2370
90.0 0.272 2450
100 0.302 2720
200 0.604 5440
300 0.906 8160
400 1.21 1.09 × 104
500 1.51 1.36 × 104
600 1.81 1.63 × 104
700 2.11 1.90 × 104
800 2.42 2.18 × 104
900 2.72 2.45 × 104
1000 3.02 2.72 × 104
2000 6.04 5.44 × 104
3000 9.06 8.16 × 104
4000 12.1 1.09 × 105
4150 12.5 1.13 × 105
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 0.545 3410
90.0 0.563 3530
100 0.626 3920
200 1.25 7830
300 1.88 1.18 × 104
400 2.50 1.57 × 104
500 3.13 1.96 × 104
600 3.76 2.35 × 104
700 4.38 2.74 × 104
800 5.01 3.13 × 104
900 5.63 3.53 × 104
1000 6.26 3.92 × 104
2000 12.5 7.83 × 104
2000 12.5 7.84 × 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 1.01 4640
90.0 1.04 4800
100 1.16 5330
200 2.32 1.07 × 104
300 3.48 1.60 × 104
400 4.64 2.13 × 104
500 5.80 2.67 × 104
600 6.96 3.20 × 104
700 8.12 3.73 × 104
800 9.28 4.27 × 104
900 10.4 4.80 × 104
1000 11.6 5.33 × 104
1080 12.5 5.76 × 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 1.72 6060
90.0 1.78 6270
100 1.98 6960
200 3.96 1.39 × 104
300 5.94 2.09 × 104
400 7.91 2.79 × 104
500 9.89 3.48 × 104
600 11.9 4.18 × 104
633 12.5 4.41 × 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 2.76 7670
90.0 2.85 7930
100 3.17 8810
200 6.34 1.76 × 104
300 9.51 2.64 × 104
395 12.5 3.48 × 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 4.20 9470
90.0 4.35 9790
100 4.83 1.09 × 104
200 9.66 2.18 × 104
259 12.5 2.82 × 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 10.3 1.48 × 104
90.0 10.6 1.53 × 104
100 11.8 1.70 × 104
106 12.5 1.81 × 104
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