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The strength of a W14x38 rolled-steel beam is increased by attaching a 9x3/4 in plate to its upper flange as shown. Determine the moment of inertia of the composite section with respect to an axis which is parallel to the plate and passes through the centroid C of the composite section. Please refer to the table below for Wide-flange properties.

The strength of a W14x38 rolled-steel beam is increased by attaching a 9x3/4 in plate to its upper flange as shown. Determine the moment of inertia of the composite section with respect to an axis which is parallel to the plate and passes through the centroid C of the composite section. Please refer to the table below for Wide-flange properties.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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The strength of a W14x38 rolled-steel beam is increased by attaching a 9x3/4 in plate to its upper flange as shown.
Determine the moment of inertia of the composite section with respect to an axis which is parallel to the plate and
passes through the centroid C of the composite section.

Please refer to the table below for Wide-flange properties.

APPENDIX B Properties of Rolled-Steel Shapes (U.S. Customary Units) W Shapes (Wide-Flange Shapes) Designation W36 X 302 135 W33 X 201 118 W30 x 173 99 9782885958928892288 W27 X 146 84 W24 X 104 68 W21 x 101 62 44 WI8 X 106 76 W16 X 77 31 26 W14 X 370 145 68 53 43 38 30 26 Area A, in² 88.8 37.3 39.7 35.6 51.0 29.1 59.2 33.7 34.7 43.1 24.8 30.6 20.1 31.1 22.3 14.7 10.3 22.6 16.8 11.8. Depth d, in. 9.13 7.68 109 29.8 21.4 18.3 21.0 13.0 20.7 42.7 24.0 20.0 15.6 12.6 11.2 15.7 32.9 11.5 30.4 29.7 27.4 26.70 24.1 23.7 18.7 18.2 18.0 17.7 16.5 16.4 16.0 15.9 15.7 17.9 14.8 14.3 14.0 Width b, in.. 16.7 12.0 15.0 10,50 14.0 10.0 12.8 8.97 12.3 8.24 6.50 11.2 11.0 Flange 7.50 6.00 10.3 7.12 7.00 5.53 5.50 16.5 15.5 10.1 10.0 8.06 8.00 Thick- ness tin. 1.68 0.790 1.15 0.740 1.07 0.670 0.975 0.640 0.800 0.615 0.450 Web Thick- ness in 0.945 21100 0.600 7800 0.76 0.715 0.505 0.440 0.345 0.715 0.550 0.655 0.520 0.750 0.500 0.585 0.415 0.605 0.460 0.500 0.400 0.350 0.940 0.590 0.680 0.425 0.570 0.355 0.425 0.300 0.455 0.430 0.305 0.275 0.250 2.66 1.66 1.09 0.680 0.855 0.510 0.720 0.415 0.660 0.370 0.530 0.305 11600 686 5900 359 8230 3990 3660 2850 Axis X-X S, in³ rin. 1130 15.4 439 14.0 1910 1330 800 510 3100 258 1830 1110 758 518 375 301 541 12.7 269 11.7 2420 227 1330 127 843 414 11.3 213 10.7 245 199 10.1 154 9.55 81.6 204 146 14.0 13.0 5440 607 1710 232 881 722 541 428 385 291 7.84 7.73 88.9 7.38 57.6 7.04 134 7.00 92.2 6.72 64.7 6.63 47.2 6.41 38.4 6.26 123 103 77.8 62.6 54.6 42.0 9.02 8.54 8.06 F 6.05 6.01 5.89 5.82 in 1300 225 749 187 598 128 443 106 259 70.4 248 57,5 20.7 220 152 40.1 15.3 138 13.9 13.7 14.1 6.77 0.515 0.310 5.87 8.85 13.8 6.73 0.385 0.270 5.73 7.69 13.9 5.03 0.420 0.255 35.3 5.65 6.49 13.7 5.00 0.335 0.230 29.0 5.54 A wide-flange shape is designated by the letter W followed by the nominal depth in inches and the weight in pounds per foot. 7.07 1990 6.33 677 148 121 9.59 57.7 45.2 X 26.7 19.6 Axis Y-Y S. in³ 156 8.91 7.00 37.7 95.2 32.6 79.8 24.5 40.7 15.7 40.3 14.0 6.37 63.5 3.20 21.2 2.07 5.12 26.9 2.47 43.1 12.1 1.60 28.9 8.25 1.57 12.4 4.49 1.17 3.49 1.12 ·X 241 Tye in. 3.82 2.38 87.3 29.3 24.2 3.56 2.32 14.3 11.3 3.42 2.10 39.4 2.66 27.6 2.61 10.7 1.65 1.22 2.91 1.87 2.89 1.77 1.26 4.27 3.98 2.48 2.46 1.92 1.89 7.88 1.55 5.82 1.49 3.55 2.80 1.08 1.04
Transcribed Image Text:APPENDIX B Properties of Rolled-Steel Shapes (U.S. Customary Units) W Shapes (Wide-Flange Shapes) Designation W36 X 302 135 W33 X 201 118 W30 x 173 99 9782885958928892288 W27 X 146 84 W24 X 104 68 W21 x 101 62 44 WI8 X 106 76 W16 X 77 31 26 W14 X 370 145 68 53 43 38 30 26 Area A, in² 88.8 37.3 39.7 35.6 51.0 29.1 59.2 33.7 34.7 43.1 24.8 30.6 20.1 31.1 22.3 14.7 10.3 22.6 16.8 11.8. Depth d, in. 9.13 7.68 109 29.8 21.4 18.3 21.0 13.0 20.7 42.7 24.0 20.0 15.6 12.6 11.2 15.7 32.9 11.5 30.4 29.7 27.4 26.70 24.1 23.7 18.7 18.2 18.0 17.7 16.5 16.4 16.0 15.9 15.7 17.9 14.8 14.3 14.0 Width b, in.. 16.7 12.0 15.0 10,50 14.0 10.0 12.8 8.97 12.3 8.24 6.50 11.2 11.0 Flange 7.50 6.00 10.3 7.12 7.00 5.53 5.50 16.5 15.5 10.1 10.0 8.06 8.00 Thick- ness tin. 1.68 0.790 1.15 0.740 1.07 0.670 0.975 0.640 0.800 0.615 0.450 Web Thick- ness in 0.945 21100 0.600 7800 0.76 0.715 0.505 0.440 0.345 0.715 0.550 0.655 0.520 0.750 0.500 0.585 0.415 0.605 0.460 0.500 0.400 0.350 0.940 0.590 0.680 0.425 0.570 0.355 0.425 0.300 0.455 0.430 0.305 0.275 0.250 2.66 1.66 1.09 0.680 0.855 0.510 0.720 0.415 0.660 0.370 0.530 0.305 11600 686 5900 359 8230 3990 3660 2850 Axis X-X S, in³ rin. 1130 15.4 439 14.0 1910 1330 800 510 3100 258 1830 1110 758 518 375 301 541 12.7 269 11.7 2420 227 1330 127 843 414 11.3 213 10.7 245 199 10.1 154 9.55 81.6 204 146 14.0 13.0 5440 607 1710 232 881 722 541 428 385 291 7.84 7.73 88.9 7.38 57.6 7.04 134 7.00 92.2 6.72 64.7 6.63 47.2 6.41 38.4 6.26 123 103 77.8 62.6 54.6 42.0 9.02 8.54 8.06 F 6.05 6.01 5.89 5.82 in 1300 225 749 187 598 128 443 106 259 70.4 248 57,5 20.7 220 152 40.1 15.3 138 13.9 13.7 14.1 6.77 0.515 0.310 5.87 8.85 13.8 6.73 0.385 0.270 5.73 7.69 13.9 5.03 0.420 0.255 35.3 5.65 6.49 13.7 5.00 0.335 0.230 29.0 5.54 A wide-flange shape is designated by the letter W followed by the nominal depth in inches and the weight in pounds per foot. 7.07 1990 6.33 677 148 121 9.59 57.7 45.2 X 26.7 19.6 Axis Y-Y S. in³ 156 8.91 7.00 37.7 95.2 32.6 79.8 24.5 40.7 15.7 40.3 14.0 6.37 63.5 3.20 21.2 2.07 5.12 26.9 2.47 43.1 12.1 1.60 28.9 8.25 1.57 12.4 4.49 1.17 3.49 1.12 ·X 241 Tye in. 3.82 2.38 87.3 29.3 24.2 3.56 2.32 14.3 11.3 3.42 2.10 39.4 2.66 27.6 2.61 10.7 1.65 1.22 2.91 1.87 2.89 1.77 1.26 4.27 3.98 2.48 2.46 1.92 1.89 7.88 1.55 5.82 1.49 3.55 2.80 1.08 1.04
–9 in.- C 6.77 in. 3/in. 14.1 in.
Transcribed Image Text:–9 in.- C 6.77 in. 3/in. 14.1 in.
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