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A Gantry crane is a crane that lifts objects by a hoist, which is fitted in a hoist trolley than can move horizontally on a beam. In the example shown below, the capacity of the hoist is 100 kip and the beam is simply supported with a span of 50 ft. (a) The shear force and bending moment distributions vary with the position a of the hoist trolley. Using shear force and bending moment diagrams, determine expressions for the maximum shear force Vmax and bending moment Mmax as functions of a for 0 < a < 25 ft. (b) Determine the values of a that maximize Vmax and Mmax, and determine these maximum values. (c) Select the lightest permissible wide-flange beam to support the hoist, if the al- lowable flexural stress is 24 ksi and the allowable shearing stress is 14.5 ksi. -50 ft 100 kip

A Gantry crane is a crane that lifts objects by a hoist, which is fitted in a hoist trolley than can move horizontally on a beam. In the example shown below, the capacity of the hoist is 100 kip and the beam is simply supported with a span of 50 ft. (a) The shear force and bending moment distributions vary with the position a of the hoist trolley. Using shear force and bending moment diagrams, determine expressions for the maximum shear force Vmax and bending moment Mmax as functions of a for 0 < a < 25 ft. (b) Determine the values of a that maximize Vmax and Mmax, and determine these maximum values. (c) Select the lightest permissible wide-flange beam to support the hoist, if the al- lowable flexural stress is 24 ksi and the allowable shearing stress is 14.5 ksi. -50 ft 100 kip

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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. A Gantry crane is a crane that lifts objects by a hoist, which is fitted in a hoist trolley than can move horizontally on a beam. In the example shown below, the capacity of the hoist is 100 kip and the beam is simply supported with a span of 50 ft. (a) The shear force and bending moment distributions vary with the position a of the hoist trolley. Using shear force and bending moment diagrams, determine expressions for the maximum shear force Vmax and bending moment Mmax as functions of a for 0 < a < 25 ft. (b) Determine the values of a that maximize Vmax and Mmax, and determine these maximum values. (c) Select the lightest permissible wide-flange beam to support the hoist, if the al- lowable flexural stress is 24 ksi and the allowable shearing stress is 14.5 ksi. 50 ft a 100 kip
Transcribed Image Text:. A Gantry crane is a crane that lifts objects by a hoist, which is fitted in a hoist trolley than can move horizontally on a beam. In the example shown below, the capacity of the hoist is 100 kip and the beam is simply supported with a span of 50 ft. (a) The shear force and bending moment distributions vary with the position a of the hoist trolley. Using shear force and bending moment diagrams, determine expressions for the maximum shear force Vmax and bending moment Mmax as functions of a for 0 < a < 25 ft. (b) Determine the values of a that maximize Vmax and Mmax, and determine these maximum values. (c) Select the lightest permissible wide-flange beam to support the hoist, if the al- lowable flexural stress is 24 ksi and the allowable shearing stress is 14.5 ksi. 50 ft a 100 kip
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
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