Prob. 4 (30 pts) A simply supported beam with w10:12 steel wide-flange shape is loaded as shown in Figure. The reactions at A and B are also given in Figure. (A) Using Singularity functions, find the moment equation and determine the maximum normal stress at D. (B) Find the deflection at D, (x=7 ft) if E=30x10³ ksi. Wide-Flange Sections or W Shapes FPS Units Designation in. x b/ft W12 x 87 W12 x 50 W12 x 45 W12 x 26 W12 x 22 W12 x 16 W12 x 14 6X OLA W10 x 100 W10 54 15.8 W10 x 45 13.3 10,10 11.5 9.92 10,47 5.62 10.24 4.41 9.99 3.54 9.87 VID x 30 W10 x 19 15 x 12 W x 67 W8 x 58 W X4 W x 40 x 31 5x24 W6 x 25 W6 x 20 W6 x 16 9 Area Depth A d in² 25.6 14.7 13.2 W6 x 9 12.53 12.19 12.06 7.65 12.22 6.48 12.31 4.71 11.99 4.16 11.91 8.84 19.7 17.1 14.1 11.7 9.13 11.10 10.09 7.08 4.44 9.00 8.75 8.50 8.25 8.00 7.93 K11 7.34 6.38 5.87 6.20 4.74 6.28 4.43 5.99 3.55 2.68 5.90 Web thickness L 0.515 0.370 0.315 0.230 0.260 0.220 0.200 0.370 0.350 0.315 0.300 0.250 0.230 0.190 0.570 0.510 0.680 10.340 10.030 0.400 0.360 0.285 0.245 0.245 Flange 0.320 0.260 0.360 0.230 0.230 0.170 width b T inª 12.125 0.810 740 8.080 0.640 8.045 0.575 350 6.490 0,380 204 4.030 0.425 156 3.990 3.970 8.020 7.985 5.810 thickness 4 4.020 4.000 3,960 0.365 0.225 1.130 0.615 0.630 0.530 0.510 0.395 6.270 0.210 0.935 0.810 0.400 0.315 103 88.6 8.280 272 8.220 228 8.110 0.685 184 8.070 0.560 146 7.995 0.435 110 6.495 4.015 6,080 6.000 4.000 0.405 5.990 0.360 4.000 0.280 3940 0.215 0.455 0.365 X-Xaxi S in² 118 3 kips/ft 623 112 303 60.0 248 209 170 13 kip 3 ft 32.4 18.8 68.9 13.8 53.8 10.9 J in I in 4.60 4.37 103 48.0 53.4 16.7 2.70 41.4 13.4 2.66 10.2 2.60 32.1 29.1 22.1 5.38 241 39.7 3.07 64.7 5.18 13.9 1.96 58.1 5.15 50.0 124 194 31.4 5.17 17.3 5.34 25.4 4.91 4.66 2.31 17.1 4.67 2.82 1.41 14.9 4.62 2.36 1.19 8 kips y-y axis S 53.4 F in² in 207 40.0 20.6 2.65 2.56 2.01 4.27 1.98 4.38 1.37 4.14 4.29 2.14 0.874 1.95 2.89 1.45 0.810 3.90 2.18 1.10 0785 88.6 21.4 2.12 52.0 3.65 75.1 18.3 2.10 361 60.9 15.0 2.08 60.4 3.72 43.3 35.5 1.91 49.1 122 2.04 21.5 3.47 37.1 9:27 20.9 3.42 11.8 3.29 D 133 11.3 16.7 5.75 18.3 3.41 1.70 1.51 0.347 9.72 256 7.31 2.49 1.50 16.4 5.56 247 2.19 1.11 0.773 0.753 2.02 1.61 0.876 17.1 5.61 1.52 133 4.41 1.50 4.43 2.20 0.966 1.46 9.32 3.11 0.918 0.905 E 3 kips/ft 13 kip 3 ft

Fig: 1