(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.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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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.
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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