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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 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 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 3.67 × 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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (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 (lbf/ft) (in) (psi) 87.0 11.1 1.38 × 104 90.0 11.5 1.43 × 104 98.4 12.5 1.56 × 104