The beam shown will be constructed from a standard steel W-shape using an allowable bending stress of 83.4 ksi. Assume P = 49 kips, L₁ = 7.8 ft, and L2 = 23.4 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)? L₁ B L2 Wide-Flange Sections or W Shapes-U.S. Customary Units L₁ Y bf D he X

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 beam shown will be constructed from a
standard steel W-shape using an allowable
bending stress of 83.4 ksi. Assume P = 49 kips,
L₁ = 7.8 ft, and L₂ = 23.4 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)?
L₁
B
L2
Wide-Flange Sections or W Shapes-U.S. Customary Units
L₁
Y
bf
D
X
Transcribed Image Text:The beam shown will be constructed from a standard steel W-shape using an allowable bending stress of 83.4 ksi. Assume P = 49 kips, L₁ = 7.8 ft, and L₂ = 23.4 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)? L₁ B L2 Wide-Flange Sections or W Shapes-U.S. Customary Units L₁ Y bf D X
Wide-Flange Sections or W Shapes-U.S. Customary Units
Flange
thickness
4
Designation
X
W24 x 94
24 x 76
24 x 68
24 x 55
W21 x 68
21 x 62
21 x 50
21 x 44
lb
W18 x 55
18 x 50
18 x 40
18 x 35
W16 x 57
16 x 50
10 AJ
16 x 40
16 x 31
W14 x 68
14 x 53
14 x 48
14 x 34
14 x 30
14 x 26
14 x 22
(a) Smin
in.3
(b) W
i
i
(c) W=
i
Web
Area Depth thickness
A
d
"
in.²
27.7
22.4
20.1
16.2
20.0
18.3
Un
14.7
Answer:
120
13.0
16.2
14.7
11.8
10.3
16.8
14.7
11.8
9.13
in.
24.3
23.9
23.7
23.6
21.1
21.0
30.0
20.8
20.7
=
18.1
18.0
17.9
17.7
20.0
14.0
15.6 13.9
14.1
13.8
10.0
14.0
14.0
8.85 13.8
7.69 13.9
6.49
13.7
16.4
16.3
16.0
15.9
in.
0.515
0.440
0.415
0.395
0.430
0.400
0.380
0.350
1
0.390
9:30
0.355
www
0.315
0.300
-
0.430
0.380
wwwww
0.305
0.275
0.415
0.370
0.340
0.285
0.270
0.255
0.230
Flange
width
by
in.
9.07
8.99
8.97
7.01
8.27
8.24
co
6.53
6.50
7.53
7.50
6.02
6.00
7.12
7.07
7.00
5.53
10.0
8.06
8.03
6.75
6.73
5.03
5.00
in.
0.875
0.680
0.585
0.505
0.685
0.615
0.535
0450
0.450
B
0.630
0.050
0.570
www
0.525
0128
0.425
0.715
0.630
0.505
0.440
0.720
0.660
0.595
0.455
0.385
0.420
0.335
Ix
in.4
2700
2100
1830
1350
1480
1330
984
843
890
800
612
510
758
659
518
375
722
541
484
340
291
245
199
Sg
in.³
222
176
154
114
140
127
94.5
81.6
92.2
81.0
64.7
47.2
98.3 7.41
88.9
7.38
68.4
7.21
57.6 7.04
103
r₂ 1,
in.
in.¹
9.87 109
9.69
9.55
9.11
77.8
70.2
48.6
42.0
35.3
29.0
8.18
2.00
8.06
8.60 64.7 15.7
8.54 57.5
14.0
340
24.9
20.7
6.72
6.68
82.5
70.4
29.1
43.1
37.2
6.63 28.9
6.41
12.4
44.9
40.1
19.1
15.3
5.65
5.54
6.01 121
5.89
5.85
5.83
5.73
Sy
in.3³
24.0
18.4
15.7
8.30
7.64
(27
6.37
12.1
10.5
8.25
4.49
11.9
10.7
6.35 1.27
5.12
1.22
24.2
14.3
57.7
51.4
23.3
6.91
19.6
5.82
8.91 3.55
7.00 2.80
r₂
in.
1.98
1.92
12.8
1.87
1.34
1.80
1.77
1.30
1.26
1.67
1.0/
1.65
1.60
1.59
1.57
1.17
2.46
1.92
1.91
1.53
1.49
1.08
1.04
Transcribed Image Text:Wide-Flange Sections or W Shapes-U.S. Customary Units Flange thickness 4 Designation X W24 x 94 24 x 76 24 x 68 24 x 55 W21 x 68 21 x 62 21 x 50 21 x 44 lb W18 x 55 18 x 50 18 x 40 18 x 35 W16 x 57 16 x 50 10 AJ 16 x 40 16 x 31 W14 x 68 14 x 53 14 x 48 14 x 34 14 x 30 14 x 26 14 x 22 (a) Smin in.3 (b) W i i (c) W= i Web Area Depth thickness A d " in.² 27.7 22.4 20.1 16.2 20.0 18.3 Un 14.7 Answer: 120 13.0 16.2 14.7 11.8 10.3 16.8 14.7 11.8 9.13 in. 24.3 23.9 23.7 23.6 21.1 21.0 30.0 20.8 20.7 = 18.1 18.0 17.9 17.7 20.0 14.0 15.6 13.9 14.1 13.8 10.0 14.0 14.0 8.85 13.8 7.69 13.9 6.49 13.7 16.4 16.3 16.0 15.9 in. 0.515 0.440 0.415 0.395 0.430 0.400 0.380 0.350 1 0.390 9:30 0.355 www 0.315 0.300 - 0.430 0.380 wwwww 0.305 0.275 0.415 0.370 0.340 0.285 0.270 0.255 0.230 Flange width by in. 9.07 8.99 8.97 7.01 8.27 8.24 co 6.53 6.50 7.53 7.50 6.02 6.00 7.12 7.07 7.00 5.53 10.0 8.06 8.03 6.75 6.73 5.03 5.00 in. 0.875 0.680 0.585 0.505 0.685 0.615 0.535 0450 0.450 B 0.630 0.050 0.570 www 0.525 0128 0.425 0.715 0.630 0.505 0.440 0.720 0.660 0.595 0.455 0.385 0.420 0.335 Ix in.4 2700 2100 1830 1350 1480 1330 984 843 890 800 612 510 758 659 518 375 722 541 484 340 291 245 199 Sg in.³ 222 176 154 114 140 127 94.5 81.6 92.2 81.0 64.7 47.2 98.3 7.41 88.9 7.38 68.4 7.21 57.6 7.04 103 r₂ 1, in. in.¹ 9.87 109 9.69 9.55 9.11 77.8 70.2 48.6 42.0 35.3 29.0 8.18 2.00 8.06 8.60 64.7 15.7 8.54 57.5 14.0 340 24.9 20.7 6.72 6.68 82.5 70.4 29.1 43.1 37.2 6.63 28.9 6.41 12.4 44.9 40.1 19.1 15.3 5.65 5.54 6.01 121 5.89 5.85 5.83 5.73 Sy in.3³ 24.0 18.4 15.7 8.30 7.64 (27 6.37 12.1 10.5 8.25 4.49 11.9 10.7 6.35 1.27 5.12 1.22 24.2 14.3 57.7 51.4 23.3 6.91 19.6 5.82 8.91 3.55 7.00 2.80 r₂ in. 1.98 1.92 12.8 1.87 1.34 1.80 1.77 1.30 1.26 1.67 1.0/ 1.65 1.60 1.59 1.57 1.17 2.46 1.92 1.91 1.53 1.49 1.08 1.04
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