A simple beam of length L = 5 m carries a uniform load of intensity q = 5.8 kN/m and a concentrated load 22.5 kN (see figure).

(a) Assuming sallow = 110 MPa, calculate the required section modulus S. Then select the most economical wide-flange beam (W shape) from Table F-1(b) in Appendix F, and recalculate S, taking into account the weight of the beam. Select a new beam if necessary.

(b) Repeat part (a), but now assume that the design requires that the W shape must be used in weak axis bending (i.e., it must bend about the 2–2
(or y) axis of the cross-section).

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Table F-1(a) Properties of Wide-Flange Sections (W Shapes) USCS Units (Abridged List) Flange Weight per Designation Foot W 30 x 211 W 30 x 132 W 24 x 162 W 24 X 94 W 18 X 119 W 18 x 71 W 16 x 100 W 16 X 77 W 16 X 57 W 16 X 31 W 14 X 120 W 14 X 82 W 14 X 53 W 14 X 26 W 12 X 87 W 12 X 50 W 12 X 35 W 12 x 14 W 10 X 60 W 10 X 45 W 10 x 30 W 10 x 12 W8 x 35 W 8 x 28 W8 X 21 W8 X 15 lb in² in. 211 132 162 94.0 119 71.0 100 77.0 57.0 31.0 120 82.0 53.0 26.0 87.0 50.0 35.0 14.0 60.0 45.0 30.0 12.0 Web Area Depth Thickness Width Thickness in. 0.775 0.615 35.0 28.0 21.0 15.0 62.2 38.9 47.7 27.7 35.1 19.0 20.8 18.5 35.3 24.0 15.6 30.9 30.3 29.5 17.0 22.6 16.5 16.8 16.4 9.13 15.9 7.69 25.0 24.3 25.6 12.5 14.6 12.2 10.3 12.5 4.16 11.9 6.16 4.44 17.6 10.2 13.3 10.1 8.84 10.5 3.54 9.87 10.3 8.12 8,24 8.06 8.28 8.11 0.705 0.515 14.5 0.590 14.3 0.510 13.9 0.370 13.9 0.255 in. 0.655 11.3 0.495 7.64 15.1 10.5 0.585 10.4 0.455 10.3 0.430 7.12 0.275 5.53 0.420 0.350 0.300 0.190 0.310 0.285 0.250 0.245 13.0 1.22 9.07 0.875 14.7 10.1 8.06 5.03 0.515 12.1 0.370 0.300 0.200 in. 1.32 1.00 10.1 8.02 5.81 3.96 8.02 6.54 5.27 4.01 1.06 0.810 0.810 8.08 0.640 6.56 0.520 3.97 0.225 0.985 0.760 0.715 0.440 0.940 0.855 0.660 0.420 0.680 0.620 0.510 0.210 0.495 0.465 0.400 0.315 Axis 1-1 1 in* 10300 665 12.9 757 5770 380 12.2 196 S r in³ in. 5170 414 10.4 443 2700 222 9.87 109 1 inª 2190 231 7.90 253 1170 127 7.50 60.3 1380 190 881 123 541 245 1490 175 7.10 1110 134 7.00 758 92.2 6.72 375 47.2 6.41 124 88.6 186 138 6.24 495 6.05 148 77.8 5.89 57.7 35.3 5.65 8.91 341 248 170 32.4 4.38 53.8 10.9 3.90 43.1 740 118 5.38 241 391 64.2 5.18 285 45.6 5.25 14.9 4.62 56.3 24.5 2.36 66.7 4.39 116 49.1 4.32 53.4 16.7 2.18 127 3.51 42.6 31.2 98.0 24.3 3.45 21.7 75.3 18.2 3.49 9.77 48.0 11.8 3.29 3.41 Axis 2-2 S in³ 100 37.2 r in. 68.4 3.05 24.0 1.98 3.49 2.25 44.9 2.69 15.8 1.70 35.7 2.51 26.9 2.47 12.1 1.60 4.49 1.17 67.5 29.3 3.74 2.48 14.3 1.92 3.55 1.08 39.7 3.07 13.9 1.96 7.47 1.54 1.19 10.6 0.753 23.0 2.57 13.3 2.01 5.75 1.37 1.10 0.785 2.03 6.63 1.62 3.71 1.26 1.70 0.876