The beam shown will be constructed from a standard steel W-shape using an allowable bending stress of 23.1 ksi. Assume P= 32 kips, L4= 4.5 ft, and L2 = 13.5 ft. (a) Determine the minimum section modulus required for this beam. (b) From the table below, select the lightest W shape that can be used for this beam. (c) What is the total weight of the steel beam itself (i.e., not including the loads that are carried by the beam)? P B L1 L2 L1 х—— х d Wide-Flange Sections or W Shapes–U.S. Customary Units

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The beam shown will be constructed from a standard steel W-shape using an allowable bending stress of 23.1 ksi. Assume P = 32 kips,
L1 = 4.5 ft, and L2 = 13.5 ft.
(a) Determine the minimum section modulus required for this beam.
(b) From the table below, select the lightest W shape that can be used for this beam.
(c) What is the total weight of the steel beam itself (i.e., not including the loads that are carried by the beam)?
P
P
B
D
L1
L2
L1
X
Wide-Flange Sections or W Shapes-U.S. Customary Units
Transcribed Image Text:The beam shown will be constructed from a standard steel W-shape using an allowable bending stress of 23.1 ksi. Assume P = 32 kips, L1 = 4.5 ft, and L2 = 13.5 ft. (a) Determine the minimum section modulus required for this beam. (b) From the table below, select the lightest W shape that can be used for this beam. (c) What is the total weight of the steel beam itself (i.e., not including the loads that are carried by the beam)? P P B D L1 L2 L1 X Wide-Flange Sections or W Shapes-U.S. Customary Units
Wide-Flange Sections or W Shapes-U.S. Customary Units
Web
Flange
Flange
Area Depth thickness
by
width
thickness
Designation
S,
A
d
I,
ry
in.?
in.
in.
in.
in.
in.+
in.3
in.
in.+
in.
in.
W24 x 94
27.7
24.3
0.515
9.07
0.875
2700
222
9.87
109
24.0
1.98
24 x 76
22.4
23.9
0.440
8.99
0.680
2100
176
9.69
82.5
18.4
1.92
24 x 68
20.1
23.7
0.415
8.97
0.585
1830
154
9.55
70.4
15.7
1.87
24 x 55
16.2
23.6
0.395
7.01
0.505
1350
114
9.11
29.1
8.30
1.34
W21 x 68
20.0
21.1
0.430
8.27
0.685
1480
140
8.60
64.7
15.7
1.80
21 x 62
18.3
21.0
0.400
8.24
0.615
1330
127
8.54
57.5
14.0
1.77
21 x 50
14.7
20.8
0.380
6.53
0.535
984
94.5
8.18
24.9
7.64
1.30
21 x 44
13.0
20.7
0.350
6.50
0.450
843
81.6
8.06
20.7
6.37
1.26
W18 x 55
16.2
18.1
0.390
7.53
0.630
890
98.3
7.41
44.9
11.9
1.67
18 x 50
14.7
18.0
0.355
7.50
0.570
800
88.9
7.38
40.1
10.7
1.65
18 x 40
11.8
17.9
0.315
6.02
0.525
612
68.4
7.21
19.1
6.35
1.27
18 x 35
10.3
17.7
0.300
6.00
0.425
510
57.6
7.04
15.3
5.12
1.22
W16 x 57
16.8
16.4
0.430
7.12
0.715
758
92.2
6.72
43.1
12.1
1.60
16 x 50
14.7
16.3
0.380
7.07
0.630
659
81.0
6.68
37.2
10.5
1.59
16 x 40
11.8
16.0
0.305
7.00
0.505
518
64.7
6.63
28.9
8.25
1.57
16 x 31
9.13
15.9
0.275
5.53
0.440
375
47.2
6.41
12.4
4.49
1.17
W14 x 68
20.0
14.0
0.415
10.0
0.720
722
103
6.01
121
24.2
2.46
14 x 53
15.6
13.9
0.370
8.06
0.660
541
77.8
5.89
57.7
14.3
1.92
14 x 48
14.1
13.8
0.340
8.03
0.595
484
70.2
5.85
51.4
12.8
1.91
14 x 34
10.0
14.0
0.285
6.75
0.455
340
48.6
5.83
23.3
6.91
1.53
14 x 30
8.85
13.8
0.270
6.73
0.385
291
42.0
5.73
19.6
5.82
1.49
14 x 26
7.69
13.9
0.255
5.03
0.420
245
35.3
5.65
8.91
3.55
1.08
14 x 22
6.49
13.7
0.230
5.00
0.335
199
29.0
5.54
7.00
2.80
1.04
by
Transcribed Image Text:Wide-Flange Sections or W Shapes-U.S. Customary Units Web Flange Flange Area Depth thickness by width thickness Designation S, A d I, ry in.? in. in. in. in. in.+ in.3 in. in.+ in. in. W24 x 94 27.7 24.3 0.515 9.07 0.875 2700 222 9.87 109 24.0 1.98 24 x 76 22.4 23.9 0.440 8.99 0.680 2100 176 9.69 82.5 18.4 1.92 24 x 68 20.1 23.7 0.415 8.97 0.585 1830 154 9.55 70.4 15.7 1.87 24 x 55 16.2 23.6 0.395 7.01 0.505 1350 114 9.11 29.1 8.30 1.34 W21 x 68 20.0 21.1 0.430 8.27 0.685 1480 140 8.60 64.7 15.7 1.80 21 x 62 18.3 21.0 0.400 8.24 0.615 1330 127 8.54 57.5 14.0 1.77 21 x 50 14.7 20.8 0.380 6.53 0.535 984 94.5 8.18 24.9 7.64 1.30 21 x 44 13.0 20.7 0.350 6.50 0.450 843 81.6 8.06 20.7 6.37 1.26 W18 x 55 16.2 18.1 0.390 7.53 0.630 890 98.3 7.41 44.9 11.9 1.67 18 x 50 14.7 18.0 0.355 7.50 0.570 800 88.9 7.38 40.1 10.7 1.65 18 x 40 11.8 17.9 0.315 6.02 0.525 612 68.4 7.21 19.1 6.35 1.27 18 x 35 10.3 17.7 0.300 6.00 0.425 510 57.6 7.04 15.3 5.12 1.22 W16 x 57 16.8 16.4 0.430 7.12 0.715 758 92.2 6.72 43.1 12.1 1.60 16 x 50 14.7 16.3 0.380 7.07 0.630 659 81.0 6.68 37.2 10.5 1.59 16 x 40 11.8 16.0 0.305 7.00 0.505 518 64.7 6.63 28.9 8.25 1.57 16 x 31 9.13 15.9 0.275 5.53 0.440 375 47.2 6.41 12.4 4.49 1.17 W14 x 68 20.0 14.0 0.415 10.0 0.720 722 103 6.01 121 24.2 2.46 14 x 53 15.6 13.9 0.370 8.06 0.660 541 77.8 5.89 57.7 14.3 1.92 14 x 48 14.1 13.8 0.340 8.03 0.595 484 70.2 5.85 51.4 12.8 1.91 14 x 34 10.0 14.0 0.285 6.75 0.455 340 48.6 5.83 23.3 6.91 1.53 14 x 30 8.85 13.8 0.270 6.73 0.385 291 42.0 5.73 19.6 5.82 1.49 14 x 26 7.69 13.9 0.255 5.03 0.420 245 35.3 5.65 8.91 3.55 1.08 14 x 22 6.49 13.7 0.230 5.00 0.335 199 29.0 5.54 7.00 2.80 1.04 by
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