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The simply supported beam shown below is made of air-dried Douglas fir with an allowable flexural stress of 2000 psi and an allowable shearing stress of 85 psi. Select the lightest standard structural timber that can be used to support the load shown in the figure. 4.5 ft 8000 lb 4.5 ft

The simply supported beam shown below is made of air-dried Douglas fir with an allowable flexural stress of 2000 psi and an allowable shearing stress of 85 psi. Select the lightest standard structural timber that can be used to support the load shown in the figure. 4.5 ft 8000 lb 4.5 ft

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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TABLE A-1 Wide-Flange Beams (U.S. Customary Units) FLANGE Desig nation W36 X 230 X 160 W33 X 201 x 152 X 130 W30 X 132 X 108 W27 X 146 X 94 W24 X 104 X 84 X 62 W21 x 101 X 83 X 62 W18 X 97 X 76 X 60 W16 X 100 X 67 X 40 x 26 W14 X 120 X 82 X 43 X 30 W12 X 96 X 65 x 50 X 30 W10 X 60 X 45 X 30 X 22 W8 X 40 X 31 X 24 X 15 W6 X 25 X 16 W5 X 16 W4 X 13 Area (10²) 67.6 47.0 59.1 44.7 38.3 38.9 31.7 42.9 27.7 30.6 24.7 18.2 29.8 24.3 18.3 28.5 22.3 17.6 29.4 19.7 11.8 7.68 35.3 24.1 12.6 8.85 28.2 19.1 14.7 8.79 17.6 13.3 8.84 6.49 11,7 9.13 7.08 4.44 7.34 4.74 4.68 3.83 Depth (in.) 35.90 36.01 H 33.68 33.49 33.09 30.31 29.83 27.38 26.92 24.06 24.10 23.74 21.36 21.43 20.99 18.59 1821 18.24 16,97 16.33 16.01 15.69 14.48 14.31 13.66 13.84 12.71 12.12 12.19 12.34 10.22 10.10 10.47 10.17 8.25 8.00 7.93 8.11 6.38 6.28 5.01 4.16 for Width (in.) 16.470 12.000 15.745 11.565 11.510 10.545 10.475 13.965 9.990 12.750 9.020 7,040 12.290 8.355 8.240 11.145 11.035 7.555 10.425 10.235 6.995 5.500 14.670 10.130 7.995 6.730 12.160 12.000 8.080 6.520 10.080 8.020 5.810 5.750 8.070 7.995 6.495 4.015 6.080 4.030 5.000 4.060 Thick- ness (in.) 1.260 1.020 1.150 1.055 0.855 1.000 0.760 0.975 0.745 0.750 0.770 0.590 0.800 0.835 0.615 0.870 0.680 0.695 0.985 0.665 0.505 0.345 0.940 0.855 0.530 0.385 0.900 0.605 0.640 0.440 0.680 0.620 0.510 0.360 0.560 0.435 0.400 0.315 0.455 0.405 0.360 0.345 Web Thick- ness (in.) 0.760 0.650 0.715 0.635 0.580 0.615 0.545 0.605 0.490 0.500 0.470 0.430 0.500 0.515 0.400 0.535 0.425 0.415 0.585 0.395 0.305 0.250 0.590 0.510 0.305 0.270 0.550 0.390 0.370 0.260 0.420 0.350 0.300 0.240 0.360 0.285 0.245 0.245 0.320 0.260 0.240 0.280 I (in*) 15000 9750 11500 8160 6710 5770 4470 5630 3270 3100 2370 1550 2420 1830 1330 1750 1330 984 1490 954 518 301 1380 882 428 291 833 $33 394 238 341 248 170 118 146 110 82.8 48.0 53.4 32.1 21.3 11.3 AXTS X-X S (in³) 837 542 684 487 406 380 299 411 243 258 196 131 227 171 127 188 146 108 175 117 64.7 38.4 190 123 62.7 42.0 131 87.9 64.7 38.6 66.7 49.1 32.4 23.2 35.5 27.5 20.9 11.8 16.7 10.2 8.51 5.46 H X-X' (in) 14.9 14.4. 14.0 13.5 13.2 12.2 11.9 Y 11.4 10.9 10.1 9.79 9.23 9.02 8.67 8.54 7.82 7.73 7.47 7.10 6.96 6.63 6.26 6.24 6.05 5.82 5.73 5.44 5.28 5.18 5.21 4.39 4.33 4.38 4.27 3.53 3.47 3.42 3.29 2.70 2.60 2.13 1.72 Courtesy of the American Institute of Steel Construction. *W means wide-flange beam, followed by the nominal dopth in inches, then the weight in pounds per foot of length. I (in¹) 940 295 749 273 218 196 146 443 124 259 94.4 34.5 248 81.4 57.5 201 152 50.1 186 119 28.9 9.59 495 148 45.2 19.6 270 174 56.3 20.3 116 $3.4 16.7 11.4 49.1 37.1 18.3 3.41 17.1 4.43 7.51 3.86 AXIS Y-Y S (in³) 114 49.1 95.2 47.2 37.9 37.2 27.9 63.5 24.8 40.7 20.9 9.80 40.3 19.5 13.9 36.1 27.6 13.3 35.7 23.2 8.25 3.49 67.5 29.3 11.3 5.82 44.4 29.1 13.9 6.24 23.0 13.3 5.75 3.97 12.2 9.27 5.63 1.70 5.61 2.20 3.00 1.90 3.73 2.50 3.56 2.47 2.39 2.25 2.15 3.21 2.12 2.91 1.95 1.38 2.89 1.83 1.77 2.65 2.61 1.69 2.52 2.46 1.57 1.12 3.74 2.48 1.89 1.49 3.09 3.02 1.96 1.52 2.57 2.01 1.37 1.33 2.04 2.02 1.61 0.876 1.52 0.967 1.27 1.00
Transcribed Image Text:TABLE A-1 Wide-Flange Beams (U.S. Customary Units) FLANGE Desig nation W36 X 230 X 160 W33 X 201 x 152 X 130 W30 X 132 X 108 W27 X 146 X 94 W24 X 104 X 84 X 62 W21 x 101 X 83 X 62 W18 X 97 X 76 X 60 W16 X 100 X 67 X 40 x 26 W14 X 120 X 82 X 43 X 30 W12 X 96 X 65 x 50 X 30 W10 X 60 X 45 X 30 X 22 W8 X 40 X 31 X 24 X 15 W6 X 25 X 16 W5 X 16 W4 X 13 Area (10²) 67.6 47.0 59.1 44.7 38.3 38.9 31.7 42.9 27.7 30.6 24.7 18.2 29.8 24.3 18.3 28.5 22.3 17.6 29.4 19.7 11.8 7.68 35.3 24.1 12.6 8.85 28.2 19.1 14.7 8.79 17.6 13.3 8.84 6.49 11,7 9.13 7.08 4.44 7.34 4.74 4.68 3.83 Depth (in.) 35.90 36.01 H 33.68 33.49 33.09 30.31 29.83 27.38 26.92 24.06 24.10 23.74 21.36 21.43 20.99 18.59 1821 18.24 16,97 16.33 16.01 15.69 14.48 14.31 13.66 13.84 12.71 12.12 12.19 12.34 10.22 10.10 10.47 10.17 8.25 8.00 7.93 8.11 6.38 6.28 5.01 4.16 for Width (in.) 16.470 12.000 15.745 11.565 11.510 10.545 10.475 13.965 9.990 12.750 9.020 7,040 12.290 8.355 8.240 11.145 11.035 7.555 10.425 10.235 6.995 5.500 14.670 10.130 7.995 6.730 12.160 12.000 8.080 6.520 10.080 8.020 5.810 5.750 8.070 7.995 6.495 4.015 6.080 4.030 5.000 4.060 Thick- ness (in.) 1.260 1.020 1.150 1.055 0.855 1.000 0.760 0.975 0.745 0.750 0.770 0.590 0.800 0.835 0.615 0.870 0.680 0.695 0.985 0.665 0.505 0.345 0.940 0.855 0.530 0.385 0.900 0.605 0.640 0.440 0.680 0.620 0.510 0.360 0.560 0.435 0.400 0.315 0.455 0.405 0.360 0.345 Web Thick- ness (in.) 0.760 0.650 0.715 0.635 0.580 0.615 0.545 0.605 0.490 0.500 0.470 0.430 0.500 0.515 0.400 0.535 0.425 0.415 0.585 0.395 0.305 0.250 0.590 0.510 0.305 0.270 0.550 0.390 0.370 0.260 0.420 0.350 0.300 0.240 0.360 0.285 0.245 0.245 0.320 0.260 0.240 0.280 I (in*) 15000 9750 11500 8160 6710 5770 4470 5630 3270 3100 2370 1550 2420 1830 1330 1750 1330 984 1490 954 518 301 1380 882 428 291 833 $33 394 238 341 248 170 118 146 110 82.8 48.0 53.4 32.1 21.3 11.3 AXTS X-X S (in³) 837 542 684 487 406 380 299 411 243 258 196 131 227 171 127 188 146 108 175 117 64.7 38.4 190 123 62.7 42.0 131 87.9 64.7 38.6 66.7 49.1 32.4 23.2 35.5 27.5 20.9 11.8 16.7 10.2 8.51 5.46 H X-X' (in) 14.9 14.4. 14.0 13.5 13.2 12.2 11.9 Y 11.4 10.9 10.1 9.79 9.23 9.02 8.67 8.54 7.82 7.73 7.47 7.10 6.96 6.63 6.26 6.24 6.05 5.82 5.73 5.44 5.28 5.18 5.21 4.39 4.33 4.38 4.27 3.53 3.47 3.42 3.29 2.70 2.60 2.13 1.72 Courtesy of the American Institute of Steel Construction. *W means wide-flange beam, followed by the nominal dopth in inches, then the weight in pounds per foot of length. I (in¹) 940 295 749 273 218 196 146 443 124 259 94.4 34.5 248 81.4 57.5 201 152 50.1 186 119 28.9 9.59 495 148 45.2 19.6 270 174 56.3 20.3 116 $3.4 16.7 11.4 49.1 37.1 18.3 3.41 17.1 4.43 7.51 3.86 AXIS Y-Y S (in³) 114 49.1 95.2 47.2 37.9 37.2 27.9 63.5 24.8 40.7 20.9 9.80 40.3 19.5 13.9 36.1 27.6 13.3 35.7 23.2 8.25 3.49 67.5 29.3 11.3 5.82 44.4 29.1 13.9 6.24 23.0 13.3 5.75 3.97 12.2 9.27 5.63 1.70 5.61 2.20 3.00 1.90 3.73 2.50 3.56 2.47 2.39 2.25 2.15 3.21 2.12 2.91 1.95 1.38 2.89 1.83 1.77 2.65 2.61 1.69 2.52 2.46 1.57 1.12 3.74 2.48 1.89 1.49 3.09 3.02 1.96 1.52 2.57 2.01 1.37 1.33 2.04 2.02 1.61 0.876 1.52 0.967 1.27 1.00
The simply supported beam shown below is made of air-dried Douglas fir with an allowable flexural stress of 2000 psi and an allowable shearing stress of 85 psi. Select the lightest standard structural timber that can be used to support the load shown in the figure. 4.5 ft 8000 lb 4.5 ft 4
Transcribed Image Text:The simply supported beam shown below is made of air-dried Douglas fir with an allowable flexural stress of 2000 psi and an allowable shearing stress of 85 psi. Select the lightest standard structural timber that can be used to support the load shown in the figure. 4.5 ft 8000 lb 4.5 ft 4
Expert Solution
Step 1

To Find :

The lightest standard timber that can be used for support.

Given :

The allowable flexural stress is σa=2000psi

The allowable shear stress is τa=85psi

Free body diagram :

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