A cantilever beam AB of length L = 6.5 ft supports a trapezoidal distributed load of peak intensity q, and minimum intensityq/2, that includes the weight of the beam (see figure). The beam is a steel W 12 x 14 wideflange shape (see Table F-1(a),Appendix F).Calculate the maximum permissible load q based upon (a) an allowable bending stress o,= 18 ksi, (Note: Obtainallowthe moment of inertia and section modulus of the beam from Table F-1(a).) Table F-1(a)Properties of Wide-Flange Sections (W Shapes) - USCS Units (Abridged List)WeightFlangeAxis 1-1Axis 2-2WebDesignationperfootDepth thickness Width ThicknessAreaIbininin.inw 30 x 211 211W 30 x 132 13262.2309077515.11.3210.30066512.97571003.4938.930306151051.0057038012.21963122.25W 24 x 162 16247.72502430.70505151309071.220.875517041410.49.87443W 24 x 946842403.051.9894.027.7700222109W 18 x 119 119W 18 x 7135.120.81901850.6550.4957.90 2537.5011.31.060.810219011702311274491582.691.7071.076460.3W 16 x 100 100W 16 x 77W 16 x 57W 16 x 3129.51700.58510.40.98514901757.101863572.510.455043002750.7600.7150.4407.006.726.41111026924777.057.031.022616.89.131651037.1255313413816.415975837592247243.112.41214.491.601.17W 14 x 120 120W 14 x 82W 14 x 53W 14 x 2635.31451436.24 4950.59014.710.10.94013801901236753.742.481.921.0882.024.015.6051003/00.8550.6608816.05148293B0650353.0139139185.8957.714335554126.07.6902550.42024535.35.658.91W 12 x 87W 12 x 50W 12 x 35W 12 x 145.38 24156324.52.3687.025.6125051512.10.8107401183973.0750.035014.014.610.34.1612212511903700.30002008086563970.6400.5200.2251397471.191.961.540.75339128588.66424561495.185.254.62W 10 x 60w 10 x 45W 10 x 30W 10 x 12176042003500.3000.19060.045.010210.18020.6800.6200.5103414.39 1162302.5713.310.124849.14.3253.41332.0130.08.841055811703244.3816.75.751.3112.03.549873960.21053.81093.902.181.100.785WB x 35WB x 28WB x 21WB x 1535.028.010.38.248.1203100.2858026540.4950.46512798.03122433.513.4542.621.71066632.031.626.164.448.068288110.4000.3159.73.415273.493.291.260.87621.00250024575.348.01821183711.7015.0401Noter Aas 1-1 and2-2 are principal centroidel aesBW 12 × 14-L = 6.5 ft

Answered: Image /qna-images/answer/fc407e9f-dbad-4883-9258-221e4b9ee585.jpg

A cantilever beam AB of length L = 6.5 ft supports a trapezoidal distributed load of peak intensity q, and minimum intensity q/2, that includes the weight of the beam (see figure). The beam is a steel W 12 x 14 wideflange shape (see Table F-1(a), Appendix F). Calculate the maximum permissible load q based upon (a) an allowable bending stress olow = 18 ksi, (Note: Obtain the moment of inertia and section modulus of the beam from Table F-1(a).)

A cantilever beam AB of length L = 6.5 ft supports a trapezoidal distributed load of peak intensity q, and minimum intensity q/2, that includes the weight of the beam (see figure). The beam is a steel W 12 x 14 wideflange shape (see Table F-1(a), Appendix F). Calculate the maximum permissible load q based upon (a) an allowable bending stress olow = 18 ksi, (Note: Obtain the moment of inertia and section modulus of the beam from Table F-1(a).)

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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Question

A cantilever beam AB of length L = 6.5 ft supports a trapezoidal distributed load of peak intensity q, and minimum intensity
q/2, that includes the weight of the beam (see figure). The beam is a steel W 12 x 14 wideflange shape (see Table F-1(a),
Appendix F).
Calculate the maximum permissible load q based upon (a) an allowable bending stress o,
= 18 ksi, (Note: Obtain
allow
the moment of inertia and section modulus of the beam from Table F-1(a).)

Table F-1(a)
Properties of Wide-Flange Sections (W Shapes) - USCS Units (Abridged List)
Weight
Flange
Axis 1-1
Axis 2-2
Web
Designation
per
foot
Depth thickness Width Thickness
Area
Ib
in
in
in.
in
w 30 x 211 211
W 30 x 132 132
62.2
309
0775
15.1
1.32
10.300
665
12.9
757
100
3.49
38.9
303
0615
105
1.00
570
380
12.2
196
312
2.25
W 24 x 162 162
47.7
250
243
0.705
0515
130
907
1.22
0.875
5170
414
10.4
9.87
443
W 24 x 94
684
240
3.05
1.98
94.0
27.7
700
222
109
W 18 x 119 119
W 18 x 71
35.1
20.8
190
185
0.655
0.495
7.90 253
7.50
11.3
1.06
0.810
2190
1170
231
127
449
158
2.69
1.70
71.0
764
60.3
W 16 x 100 100
W 16 x 77
W 16 x 57
W 16 x 31
29.5
170
0.585
10.4
0.985
1490
175
7.10
186
357
2.51
0.455
0430
0275
0.760
0.715
0.440
7.00
6.72
6.41
1110
269
247
77.0
57.0
31.0
226
16.8
9.13
165
103
7.12
553
134
138
16.4
159
758
375
922
472
43.1
12.4
121
4.49
1.60
1.17
W 14 x 120 120
W 14 x 82
W 14 x 53
W 14 x 26
35.3
145
143
6.24 495
0.590
14.7
10.1
0.940
1380
190
123
675
3.74
2.48
1.92
1.08
82.0
24.0
15.6
0510
03/0
0.855
0.660
881
6.05
148
293
B06
503
53.0
139
139
18
5.89
57.7
143
355
541
26.0
7.69
0255
0.420
245
35.3
5.65
8.91
W 12 x 87
W 12 x 50
W 12 x 35
W 12 x 14
5.38 241
563
24.5
2.36
87.0
25.6
125
0515
12.1
0.810
740
118
397
3.07
50.0
350
14.0
14.6
10.3
4.16
122
125
119
0370
0.300
0200
808
656
397
0.640
0.520
0.225
139
747
1.19
1.96
1.54
0.753
391
285
88.6
642
456
149
5.18
5.25
4.62
W 10 x 60
w 10 x 45
W 10 x 30
W 10 x 12
176
0420
0350
0.300
0.190
60.0
45.0
102
10.1
802
0.680
0.620
0.510
341
4.39 116
230
2.57
13.3
10.1
248
49.1
4.32
53.4
133
2.01
30.0
8.84
105
581
170
324
4.38
16.7
5.75
1.31
12.0
3.54
987
396
0.210
53.8
109
3.90
2.18
1.10
0.785
WB x 35
WB x 28
WB x 21
WB x 15
35.0
28.0
10.3
8.24
8.12
0310
0.285
802
654
0.495
0.465
127
98.0
312
243
3.51
3.45
42.6
21.7
106
663
2.03
1.62
6.16
4.44
8.06
828
811
0.400
0.315
9.7
3.41
527
3.49
3.29
1.26
0.876
21.0
0250
0245
75.3
48.0
182
118
371
1.70
15.0
401
Noter Aas 1-1 and2-2 are principal centroidel aes
B
W 12 × 14
-L = 6.5 ft

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