The beam shown will be constructed from a standard steel W-shape using an allowable bending stress of 97.3 ksi. Assume P = 48 kips, L₁ = 7.6 ft, and L₂ = 22.8 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)? A LI P BO L2 P L₁ D X
The beam shown will be constructed from a standard steel W-shape using an allowable bending stress of 97.3 ksi. Assume P = 48 kips, L₁ = 7.6 ft, and L₂ = 22.8 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)? A LI P BO L2 P L₁ D X
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:The beam shown will be constructed from a standard steel W-shape using an allowable bending stress of 97.3 ksi. Assume P = 48 kips,
L₁ = 7.6 ft, and L2 = 22.8 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)?
A
y
L₁
Designation
W24 x 94
24 x 76
24 × 68
24 x 55
W21 x 68
21 x 62
21 x 50
21 x 44
W18 x 55
18 x 50
18 x 40
18 x 35
W16 x 57
16 x 50
16 x 40
16 x 31
W14 × 68
14 x 53
14 x 48
14 x 34
14 x 30
14 x 26
14 x 22
Answer:
Wide-Flange Sections or W Shapes-U.S. Customary Units
(a) Smin = i
(b) Wi
(c) W = i
P
B
Web
Area Depth thickness
A
d
tw
in.²
27.7
22.4
20.1
16.2
20.0
18.3
14.7
13.0
16.2
14.7
11.8
10.3
20.0
15.6
in.
24.3
23.9
23.7
23.6
21.1
21.0
20.8
20.7
14.1
10.0
L2
18.1
18.0
17.9
17.7
8.85
7.69 13.9
6.49
13.7
in.
0.515
0.440
0.415
0.395
16.8
16.4
14.7
16.3
11.8
16.0
9.13 15.9
14.0
13.9
13.8
14.0
0.285
13.8 0.270
0.255
0.230
0.430
0.400
0.380
0.350
lb
0.390
0.355
0.315
0.300
0.430
0.380
0.305
0.275
0.415
0.370
0.340
in.³
X i
с
in.
9.07
8.99
8.97
7.01
8.27
8.24
6.53
6.50
Flange Flange
width
thickness
bf
tf
in.
0.875
0.680
0.585
0.505
7.53
7.50
6.02
6.00
7.12
7.07
7.00
5.53
P
10.0
L₁
8.06
8.03
6.75
6.73
5.03
5.00
0.685
0.615
0.535
0.450
0.630
0.570
0.525
0.425
0.715
0.630
0.505
0.440
0.720
0.660
0.595
0.455
0.385
0.420
0.335
D
X
I₂
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
S₂
in.³
222
176
154
114
140
127
94.5
81.6
98.3
88.9
68.4
57.6
92.2
81.0
64.7
47.2
103
77.8
70.2
48.6
42.0
35.3
29.0
in.
9.87
9.69
9.55
9.11
8.60
8.54
8.18
8.06
7.41
7.38
7.21
7.04
6.72
6.68
6.63
6.41
6.01
5.89
5.85
5.83
5.73
5.65
5.54
Iy
in.4
109
d
82.5
70.4
29.1
64.7
57.5
24.9
20.7
44.9
40.1
19.1
15.3
121
57.7
51.4
23.3
19.6
THE
8.91
7.00
X-=-X
Sy
in.³
24.0
18.4
15.7
8.30
15.7
14.0
7.64
6.37
43.1
12.1
37.2 10.5
28.9
8.25
12.4
4.49
11.9
10.7
6.35
5.12
Y
b₂
Fy
in.
1.98
1.92
1.87
1.34
1.80
1.77
1.30
1.26
1.67
1.65
1.27
1.22
1.60
1.59
1.57
1.17
24.2
2.46
14.3
1.92
12.8
1.91
6.91 1.53
5.82
1.49
3.55
1.08
2.80 1.04
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