engineering fundamentals
Wide Flange Steel I Beam: W4 × 13
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Glossary » Beams » Simply Supported » Uniformly Distributed Load » Two Equal Spans » Wide Flange Steel I Beam » W4 × 13
Wide Flange Steel I Beam | Single Span | Two Equal Spans | Three Equal Spans | Four Equal Spans

For a simply supported beam in two equal spans, we compute the displacement at the middle of each span w_mid and the maximum normal stress stress_max occuring at the center support of the beam.
The tabulated data listed in this page are calculated based on the area moment of inertia (Ixx = 11.3 in4) for the W4 × 13 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
   
Steel I Beam: W4 × 13 (Wide Flange 4 inch tall × 13 lbf/ft)
L = 3.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
13.0 2.75 × 10-5 32.3
20.0 4.24 × 10-5 49.7
30.0 6.35 × 10-5 74.5
40.0 8.47 × 10-5 99.4
50.0 1.06 × 10-4 124
60.0 1.27 × 10-4 149
70.0 1.48 × 10-4 174
80.0 1.69 × 10-4 199
90.0 1.91 × 10-4 224
100 2.12 × 10-4 248
200 4.24 × 10-4 497
300 6.35 × 10-4 745
400 8.47 × 10-4 994
500 0.00106 1240
600 0.00127 1490
700 0.00148 1740
800 0.00169 1990
900 0.00191 2240
1000 0.00212 2480
2000 0.00424 4970
3000 0.00635 7450
4000 0.00847 9940
5000 0.0106 1.24 × 104
6000 0.0127 1.49 × 104
7000 0.0148 1.74 × 104
8000 0.0169 1.99 × 104
9000 0.0191 2.24 × 104
1.00 × 104 0.0212 2.48 × 104
2.00 × 104 0.0424 4.97 × 104
3.00 × 104 0.0635 7.45 × 104
4.00 × 104 0.0847 9.94 × 104
5.00 × 104 0.106 1.24 × 105
6.00 × 104 0.127 1.49 × 105
7.00 × 104 0.148 1.74 × 105
8.00 × 104 0.169 1.99 × 105
9.00 × 104 0.191 2.24 × 105
1.00 × 105 0.212 2.48 × 105
1.20 × 105 0.253 2.97 × 105
Steel I Beam: W4 × 13 (Wide Flange 4 inch tall × 13 lbf/ft)
L = 5.00 ft
P (lbf/ft) w_max (in) stress_max (psi)
13.0 2.12 × 10-4 89.7
20.0 3.27 × 10-4 138
30.0 4.90 × 10-4 207
40.0 6.54 × 10-4 276
50.0 8.17 × 10-4 345
60.0 9.81 × 10-4 414
70.0 0.00114 483
80.0 0.00131 552
90.0 0.00147 621
100 0.00163 690
200 0.00327 1380
300 0.00490 2070
400 0.00654 2760
500 0.00817 3450
600 0.00981 4140
700 0.0114 4830
800 0.0131 5520
900 0.0147 6210
1000 0.0163 6900
2000 0.0327 1.38 × 104
3000 0.0490 2.07 × 104
4000 0.0654 2.76 × 104
5000 0.0817 3.45 × 104
6000 0.0981 4.14 × 104
7000 0.114 4.83 × 104
8000 0.131 5.52 × 104
9000 0.147 6.21 × 104
1.00 × 104 0.163 6.90 × 104
2.00 × 104 0.327 1.38 × 105
3.00 × 104 0.490 2.07 × 105
4.00 × 104 0.654 2.76 × 105
4.30 × 104 0.703 2.97 × 105
Steel I Beam: W4 × 13 (Wide Flange 4 inch tall × 13 lbf/ft)
L = 10.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
13.0 0.00340 359
20.0 0.00523 552
30.0 0.00784 828
40.0 0.0105 1100
50.0 0.0131 1380
60.0 0.0157 1660
70.0 0.0183 1930
80.0 0.0209 2210
90.0 0.0235 2480
100 0.0261 2760
200 0.0523 5520
300 0.0784 8280
400 0.105 1.10 × 104
500 0.131 1.38 × 104
600 0.157 1.66 × 104
700 0.183 1.93 × 104
800 0.209 2.21 × 104
900 0.235 2.48 × 104
1000 0.261 2.76 × 104
2000 0.523 5.52 × 104
3000 0.784 8.28 × 104
4000 1.05 1.10 × 105
5000 1.31 1.38 × 105
6000 1.57 1.66 × 105
7000 1.83 1.93 × 105
8000 2.09 2.21 × 105
9000 2.35 2.48 × 105
1.00 × 104 2.61 2.76 × 105
1.08 × 104 2.81 2.97 × 105
Steel I Beam: W4 × 13 (Wide Flange 4 inch tall × 13 lbf/ft)
L = 15.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
13.0 0.0172 808
20.0 0.0265 1240
30.0 0.0397 1860
40.0 0.0530 2480
50.0 0.0662 3110
60.0 0.0794 3730
70.0 0.0927 4350
80.0 0.106 4970
90.0 0.119 5590
100 0.132 6210
200 0.265 1.24 × 104
300 0.397 1.86 × 104
400 0.530 2.48 × 104
500 0.662 3.11 × 104
600 0.794 3.73 × 104
700 0.927 4.35 × 104
800 1.06 4.97 × 104
900 1.19 5.59 × 104
1000 1.32 6.21 × 104
2000 2.65 1.24 × 105
3000 3.97 1.86 × 105
3140 4.16 1.95 × 105
Steel I Beam: W4 × 13 (Wide Flange 4 inch tall × 13 lbf/ft)
L = 20.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
13.0 0.0544 1440
20.0 0.0837 2210
30.0 0.126 3310
40.0 0.167 4420
50.0 0.209 5520
60.0 0.251 6630
70.0 0.293 7730
80.0 0.335 8840
90.0 0.377 9940
100 0.418 1.10 × 104
200 0.837 2.21 × 104
300 1.26 3.31 × 104
400 1.67 4.42 × 104
500 2.09 5.52 × 104
600 2.51 6.63 × 104
700 2.93 7.73 × 104
800 3.35 8.84 × 104
900 3.77 9.94 × 104
994 4.16 1.10 × 105
Steel I Beam: W4 × 13 (Wide Flange 4 inch tall × 13 lbf/ft)
L = 25.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
13.0 0.133 2240
20.0 0.204 3450
30.0 0.306 5180
40.0 0.409 6900
50.0 0.511 8630
60.0 0.613 1.04 × 104
70.0 0.715 1.21 × 104
80.0 0.817 1.38 × 104
90.0 0.919 1.55 × 104
100 1.02 1.73 × 104
200 2.04 3.45 × 104
300 3.06 5.18 × 104
400 4.09 6.90 × 104
407 4.16 7.03 × 104
Steel I Beam: W4 × 13 (Wide Flange 4 inch tall × 13 lbf/ft)
L = 30.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
13.0 0.275 3230
20.0 0.424 4970
30.0 0.635 7450
40.0 0.847 9940
50.0 1.06 1.24 × 104
60.0 1.27 1.49 × 104
70.0 1.48 1.74 × 104
80.0 1.69 1.99 × 104
90.0 1.91 2.24 × 104
100 2.12 2.48 × 104
196 4.16 4.88 × 104
Steel I Beam: W4 × 13 (Wide Flange 4 inch tall × 13 lbf/ft)
L = 40.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
13.0 0.870 5740
20.0 1.34 8840
30.0 2.01 1.33 × 104
40.0 2.68 1.77 × 104
50.0 3.35 2.21 × 104
60.0 4.02 2.65 × 104
62.1 4.16 2.75 × 104
Steel I Beam: W4 × 13 (Wide Flange 4 inch tall × 13 lbf/ft)
L = 50.0 ft
P (lbf/ft) w_max (in) stress_max (psi)
13.0 2.12 8970
20.0 3.27 1.38 × 104
25.5 4.16 1.76 × 104
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