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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 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 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.

 Steel I Beam: W12 × 87 (Wide Flange 12 inch tall × 87 lbf/ft) L = 3.00 ft (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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