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(a) Construct a free body diagram (FBD) of the floor beam, with all necessarv labels. (b) Determine the support reactions at A and D. (c) Construct shear force and bending moment diagrams for the floor beam. (d) Derive equation of beam deflection under the uniformly distributed load, in terms of E, I, and distance x.

(a) Construct a free body diagram (FBD) of the floor beam, with all necessarv labels. (b) Determine the support reactions at A and D. (c) Construct shear force and bending moment diagrams for the floor beam. (d) Derive equation of beam deflection under the uniformly distributed load, in terms of E, I, and distance x.

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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683 APPENDIX B Properties of Rolled-Steel Shapes (SI Units) Continued from page 681 W Shapes (Wide-Flange Shapes) Flange Web Thick- Axis X-X Axis Y-Y Thick- Width br, mm S. 10° mm 10 mm mm Area Depth ness S, ness Ty Designationt A, mm? d, mm 1o° mm 10 mm E mm fw, mm mm W310 x 143 18200 323 310 22.9 14.0 347 2150 138 112 728 78.5 107 13600 312 305 17.0 10.9 248 1600 135 81.2 531 77.2 74 9420 310 205 16.3 9.40 163 1050 132 23.4 228 49.8 60 7550 302 203 13.1 7.49 128 844 130 18.4 180 49.3 52 6650 318 167 13.2 7.62 119 747 133 10.2 122 39.1 102 87.5 37.9 44.5 5670 312 166 11.2 6.60 99.1 633 132 8.45 38.6 38.7 4940 310 165 9.65 5.84 84.9 547 131 7.20 38.4 32.7 4180 312 102 10.8 6.60 64.9 416 125 1.94 21.5 23.8 3040 305 101 6.73 5.59 42.9 280 119 1.17 23.1 19.6 21200 12900 98.2 55.8 742 433 W250 × 167 31.8 19.6 290 264 19.2 298 2060 118 68.1 101 264 257 11.9 164 1240 113 65.8 80 10200 257 254 15.6 9.4 126 983 111 42.9 338 65.0 67 8580 257 204 15.7 8.89 103 805 110 22.2 218 51.1 58 7420 252 203 13.5 8.00 87.0 690 108 18.7 185 50.3 15.2 6.95 49.1 6260 247 202 11.0 7.37 71.2 574 106 151 49.3 44.8 5700 267 148 13.0 7.62 70.8 531 111 94.2 34.8 32.7 4190 259 146 9.14 6.10 49.1 380 108 4.75 65.1 33.8 28.4 3630 259 102 10.0 6.35 40.1 308 105 1.79 35.1 22.2 22.3 2850 254 102 6.86 5.84 28.7 226 100 1.20 23.8 20.6 W200 x 86 11000 222 209 20.6 13.0 94.9 852 92.7 31.3 300 53.3 71 9100 216 206 17.4 10.2 76.6 708 91.7 25.3 246 52.8 7550 210 205 14.2 9.14 7.87 59 60.8 582 89.7 20.4 200 51.8 52 6650 206 204 12.6 52.9 511 89.2 17.7 174 51.6 46.1 5880 203 203 11.0 7.24 45.8 451 88.1 15.4 152 51.3 41.7 5320 4570 205 166 11.8 7.24 40.8 398 87.6 9.03 109 41.1 35.9 165 92.3 10.2 10.2 201 6.22 34.4 342 86.9 7.62 40.9 31.3 3970 210 134 6.35 31.3 298 88.6 4.07 60.8 32.0 26.6 3390 207 133 8.38 5.84 25.8 249 87.1 3.32 49.8 31.2 22.5 2860 206 102 8.00 6.22 20.0 193 83.6 1.42 27.9 22.3 19.3 2480 203 102 6.48 5.84 16.5 162 81.5 1.14 22.5 21.4 W150 x 37.1 4740 162 154 11.6 8.13 22.2 274 68.6 7.12 91.9 38.6 29.8 3790 157 153 9.27 6.60 17.2 220 67.6 5.54 72.3 38.1 24 3060 160 102 10.3 6.60 13.4 167 66.0 1.84 36.1 24.6 18 2290 153 102 7.11 5.84 9.20 120 63.2 1.24 24.6 23.3 13.5 1730 150 100 5.46 4.32 6.83 91.1 62.7 0.916 18.2 23.0 W130 x 28.1 23.8 3590 131 128 10.9 6.86 10.9 167 55.1 3.80 59.5 32.5 3040 127 127 9.14 6.10 8.91 140 54.1 3.13 49.2 32.0 w100 x 19.3 2470 106 103 8.76 7.11 4.70 89.5 43.7 1.61 31.1 25.4 IA wide-flange shape ts destgnated by the letter W folowed by the norntnal depth in mtlltrneters and the mass in kılograms per meter.
Transcribed Image Text:683 APPENDIX B Properties of Rolled-Steel Shapes (SI Units) Continued from page 681 W Shapes (Wide-Flange Shapes) Flange Web Thick- Axis X-X Axis Y-Y Thick- Width br, mm S. 10° mm 10 mm mm Area Depth ness S, ness Ty Designationt A, mm? d, mm 1o° mm 10 mm E mm fw, mm mm W310 x 143 18200 323 310 22.9 14.0 347 2150 138 112 728 78.5 107 13600 312 305 17.0 10.9 248 1600 135 81.2 531 77.2 74 9420 310 205 16.3 9.40 163 1050 132 23.4 228 49.8 60 7550 302 203 13.1 7.49 128 844 130 18.4 180 49.3 52 6650 318 167 13.2 7.62 119 747 133 10.2 122 39.1 102 87.5 37.9 44.5 5670 312 166 11.2 6.60 99.1 633 132 8.45 38.6 38.7 4940 310 165 9.65 5.84 84.9 547 131 7.20 38.4 32.7 4180 312 102 10.8 6.60 64.9 416 125 1.94 21.5 23.8 3040 305 101 6.73 5.59 42.9 280 119 1.17 23.1 19.6 21200 12900 98.2 55.8 742 433 W250 × 167 31.8 19.6 290 264 19.2 298 2060 118 68.1 101 264 257 11.9 164 1240 113 65.8 80 10200 257 254 15.6 9.4 126 983 111 42.9 338 65.0 67 8580 257 204 15.7 8.89 103 805 110 22.2 218 51.1 58 7420 252 203 13.5 8.00 87.0 690 108 18.7 185 50.3 15.2 6.95 49.1 6260 247 202 11.0 7.37 71.2 574 106 151 49.3 44.8 5700 267 148 13.0 7.62 70.8 531 111 94.2 34.8 32.7 4190 259 146 9.14 6.10 49.1 380 108 4.75 65.1 33.8 28.4 3630 259 102 10.0 6.35 40.1 308 105 1.79 35.1 22.2 22.3 2850 254 102 6.86 5.84 28.7 226 100 1.20 23.8 20.6 W200 x 86 11000 222 209 20.6 13.0 94.9 852 92.7 31.3 300 53.3 71 9100 216 206 17.4 10.2 76.6 708 91.7 25.3 246 52.8 7550 210 205 14.2 9.14 7.87 59 60.8 582 89.7 20.4 200 51.8 52 6650 206 204 12.6 52.9 511 89.2 17.7 174 51.6 46.1 5880 203 203 11.0 7.24 45.8 451 88.1 15.4 152 51.3 41.7 5320 4570 205 166 11.8 7.24 40.8 398 87.6 9.03 109 41.1 35.9 165 92.3 10.2 10.2 201 6.22 34.4 342 86.9 7.62 40.9 31.3 3970 210 134 6.35 31.3 298 88.6 4.07 60.8 32.0 26.6 3390 207 133 8.38 5.84 25.8 249 87.1 3.32 49.8 31.2 22.5 2860 206 102 8.00 6.22 20.0 193 83.6 1.42 27.9 22.3 19.3 2480 203 102 6.48 5.84 16.5 162 81.5 1.14 22.5 21.4 W150 x 37.1 4740 162 154 11.6 8.13 22.2 274 68.6 7.12 91.9 38.6 29.8 3790 157 153 9.27 6.60 17.2 220 67.6 5.54 72.3 38.1 24 3060 160 102 10.3 6.60 13.4 167 66.0 1.84 36.1 24.6 18 2290 153 102 7.11 5.84 9.20 120 63.2 1.24 24.6 23.3 13.5 1730 150 100 5.46 4.32 6.83 91.1 62.7 0.916 18.2 23.0 W130 x 28.1 23.8 3590 131 128 10.9 6.86 10.9 167 55.1 3.80 59.5 32.5 3040 127 127 9.14 6.10 8.91 140 54.1 3.13 49.2 32.0 w100 x 19.3 2470 106 103 8.76 7.11 4.70 89.5 43.7 1.61 31.1 25.4 IA wide-flange shape ts destgnated by the letter W folowed by the norntnal depth in mtlltrneters and the mass in kılograms per meter.
Figure 1 illustrates a cross-section of an aircraft fuselage. The floor beam of the aircraft is supported by the fuselage at its both ends. The floor beam has an I-shaped cross-section and is subjected to 1.2 kN/m uniformly distributed load at its center. It is assumed that the fuselage only exerts vertical reactions on the ends of the beam and El is constant. 1.2 kN/m D -2.4 m- 0.6 m 0.C Figure 1: Cross-section of an aircraft fuselage. (a) Construct a free body diagram (FBD) of the floor beam, with all necessarv labels. (b) Determine the support reactions at A and D. (c) Construct shear force and bending moment diagrams for the floor beam. (d) Derive equation of beam deflection under the uniformly distributed load, in terms of E, I, and distance x. (e) Determine the maximum deflection of the floor beam in terms of E and I. (f) If the floor beam is made of rolled-steel W250x58 with Young's modulus of 200 GPa, calculate the maximum deflection of the floor beam to the nearest mm.
Transcribed Image Text:Figure 1 illustrates a cross-section of an aircraft fuselage. The floor beam of the aircraft is supported by the fuselage at its both ends. The floor beam has an I-shaped cross-section and is subjected to 1.2 kN/m uniformly distributed load at its center. It is assumed that the fuselage only exerts vertical reactions on the ends of the beam and El is constant. 1.2 kN/m D -2.4 m- 0.6 m 0.C Figure 1: Cross-section of an aircraft fuselage. (a) Construct a free body diagram (FBD) of the floor beam, with all necessarv labels. (b) Determine the support reactions at A and D. (c) Construct shear force and bending moment diagrams for the floor beam. (d) Derive equation of beam deflection under the uniformly distributed load, in terms of E, I, and distance x. (e) Determine the maximum deflection of the floor beam in terms of E and I. (f) If the floor beam is made of rolled-steel W250x58 with Young's modulus of 200 GPa, calculate the maximum deflection of the floor beam to the nearest mm.
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