A simple beam AB is loaded as shown in the figure.

(a) Calculate the required section modulus S if sallow 518,000 psi, L = 32 ft, P = 2900 lb, and q = 450 lb/ft. Then select a suitable I-beam (S shape) from Table F-2(a), Appendix F, and recalculate S taking into account the weight of the beam. Select a new beam size if necessary.

(b) What is the maximum load P that can be applied to your final beam selection in part (a)?

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Table F-2(a) Properties of I-Beam Sections (S Shapes) USCS Units (Abridged List) Flange Designation $ 24 X 100 $24 x 80 $20 × 96 $20 X 75 $18 X 70 $ 18 X 54.7 $15 x 50 $15 X 42.9 $12 X 50 $ 12 x 35 $10 x 35 $ 10 X 25.4 $8 X 23 $8 X 18.4 S6 x 17.2 $6 x 12.5 $4X9.5 $4 x 7.7 Weight per Web Average Foot Area Depth Thickness Width Thickness 1 lb in² in. in. in. in. 100 80.0 96.0 28.2 20.3 75.0 22.0 20.0 70.0 54.7 50.0 42.9 50.0 35.0 35.0 25.4 23.0 18.4 17.3 12.5 29.3 24.0 23.5 24.0 9.50 7.70 20.5 18.0 16.0 18.0 14.7 15.0 12.6 15.0 14.6 12.0 10.2 12.0 10.3 10.0 7.45 10.0 6.76 5.40 8.00 5.06 6.00 3.66 6.00 0.745 0.500 2.79 4.00 2.26 4.00 0.800 0.635 0.711 0.461 0.550 0.411 8.00 0.441 0.594 0.311 7.25 7.00 0.687 5.48 0.428 5.08 0.465 0.232 7.20 6.39 0.326 0.193 6.25 6.00 5.64 5.50 4.17 0.271 4.00 4.94 4.66 3.57 3.33 2.80 2.66 0.870 0.870 0.622 0.622 0.920 0.795 1280 0.691 923 0.691 801 0.491 0.491 0.425 0.425 S in* in³ 0.359 0.359 2380 199 2100 175 0.659 303 0.544 228 0.293 0.293 1670 165 128 485 446 Axis 1-1 147 123 26.2 22.0 103 89.0 50.6 38.1 64.7 16.2 57.5 14.4 7.71 49.9 7.62 29.5 64.7 5.75 15.6 59.4 5.95 14.3 r T in. in¹ 9.01 47.4 13.1 9.47 42.0 12.0 6.70 24.0 7.07 20.7 3.09 3.26 8.74 2.28 7.34 2.45 6.76 3.38 1.56 6.05 3.03 Axis 2-2 4.27 3.69 S in³ 2.29 1.80 0.887 1.64 0.748 4.55 15.6 5.69 1.03 4.72 9.84 3.88 0.980 29.4 3.78 8.30 3.36 0.899 24.6 4.07 6.73 2.89 0.950 r in. 13.9 1.33 9.25 1.16 5.53 5.19 1.27 1.34 7.69 1.08 6.91 1.14 1.03 1.06 1.28 1.08 2.05 0.795 1.84 0.827 0.673 0.702 0.635 0.564 0.562 0.576