The (10+0.5R)-ft-long steel column is an W8 x 40 section that is fixed at both ends. The midpoint of the column is braced by two cables that prevent displacement in the x- direction. Determine the critical value of the axial load P. Use E = 29 x 10° psi for steel. Where R=37 (10+0.5R) ft

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Publisher:Segui, William T.
Chapter10: Plate Girders
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Problem 10.7.9P
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Q. 3 The (10+0.5R)-ft-long steel column is an W8 x 40 section
that is fixed at both ends. The midpoint of the column is
braced by two cables that prevent displacement in the x-
direction. Determine the critical value of the axial load P.
Use E = 29 x 10° psi for steel.
Where R=37
(10+0.5R) ft
Transcribed Image Text:Q. 3 The (10+0.5R)-ft-long steel column is an W8 x 40 section that is fixed at both ends. The midpoint of the column is braced by two cables that prevent displacement in the x- direction. Determine the critical value of the axial load P. Use E = 29 x 10° psi for steel. Where R=37 (10+0.5R) ft
Wide-Flange Sections or W Shapes FPS Units
Flange
Web
X-x axis
y-y axis
Area Depth
thickness
width
thickness
Designation
A
by
in. x Ib/ft
in?
in.
in.
in.
in.
in
in
in.
in
in
in.
740
W12 x 87
W12 x 50
W12 x 45
W12 x 26
W12 x 22
W12 X 16
W12 X 14
W10 X 100
WI0 X 54
25.6
14.7
12.53
12.19
12.06
12.22
12.31
11.99
12.125
8.080
5.38
5.18
241
56.3
50.0
17.3
4.66
2.82
2.36
39.7
13.9
12.4
5.34
2.31
1.41
1.19
3.07
1.96
0.515
0.370
0.335
0.230
0.260
0.220
0.810
0.640
118
64.7
394
8.045
6,490
13.2
7.65
6.48
4.71
4.16
4.030
3.990
3.970
0.575
0.380
0.425
0.265
0.225
350
204
156
103
88.6
58.1
33.4
25.4
17.1
14.9
5.15
5.17
4.91
4.67
1.94
1.51
0.847
0.773
0.753
11.91
0.200
4.62
29.4
15.8
13.3
11.5
8.84
2.65
2.56
2.01
1.98
1.37
0.874
0.810
0.785
11.10
10.09
10.340
10.030
0.680
1.120
0.615
0.620
0.530
623
303
248
209
170
96.3
68.9
53.8
112
4.60
207
103
53.4
45.0
40.0
0.370
0.350
0.315
0.300
4.37
4.32
4.27
4.38
4.14
3.95
3.90
20.6
13.3
11.3
5.75
2.14
1.45
1.10
60.0
10.10
9.92
10.47
8.020
7.985
5.810
W10 x 45
W10 x 39
W10 x 30
W10 X 19
W10 X 15
WI0 X 12
49.1
42.1
32.4
18.8
13.8
10.9
5.62
4.41
3.54
10.24
9.99
9.87
0.250
0.230
0.190
4.020
4.000
3.960
0.510
0.395
0.270
16.7
4.29
2.89
2.18
0.210
272
228
W8 x 67
W8 x 58
W8 x 48
W8 x 40
W8 x 31
W8 x 24
W8 X 15
9.00
8.75
0.570
0.510
8.280
8.220
0.935
0.810
0.685
3.72
3.65
88.6
75.1
60.9
21.4
18.3
2.12
2.10
2.08
2.04
2.02
19.7
60.4
17.1
52.0
14.1
8.50
0.400
8.110
184
43.3
3.61
3.53
15.0
11.7
9.13
7.08
8.25
8.00
7.93
8.11
0.360
0.285
0.245
0.245
8.070
146
35.5
27.5
20.9
11.8
49.1
12.2
9.27
5.63
1.70
0.560
7.995
0.435
110
3.47
37.1
0.400
0.315
82.8
3.42
3.29
6.495
18.3
1.61
4.44
4.015
48.0
3.41
0.876
W6 x 25
W6 x 20
W6 x 16
W6 X 15
W6 X 12
W6 X 9
7.34
0.455
6.38
6.20
6.28
0.320
53.4
16.7
2.70
2.66
2.60
2.56
2.49
2.47
17.1
13.3
4.43
9.32
2.99
6.080
5.61
1.52
5.87
0.260
6.020
0.365
41.4
13.4
4.41
1.50
4.74
0.260
4.030
5.990
0.405
32.1
10.2
9.72
7.31
5.56
2.20
0.966
4.43
5.99
0.230
0.260
29.1
3.11
1.46
3.55
2.68
0.230
0.170
6.03
0.280
0.215
22.1
1.50
1.11
0.918
0.905
4.000
5.90
3.940
16.4
2.19
Transcribed Image Text:Wide-Flange Sections or W Shapes FPS Units Flange Web X-x axis y-y axis Area Depth thickness width thickness Designation A by in. x Ib/ft in? in. in. in. in. in in in. in in in. 740 W12 x 87 W12 x 50 W12 x 45 W12 x 26 W12 x 22 W12 X 16 W12 X 14 W10 X 100 WI0 X 54 25.6 14.7 12.53 12.19 12.06 12.22 12.31 11.99 12.125 8.080 5.38 5.18 241 56.3 50.0 17.3 4.66 2.82 2.36 39.7 13.9 12.4 5.34 2.31 1.41 1.19 3.07 1.96 0.515 0.370 0.335 0.230 0.260 0.220 0.810 0.640 118 64.7 394 8.045 6,490 13.2 7.65 6.48 4.71 4.16 4.030 3.990 3.970 0.575 0.380 0.425 0.265 0.225 350 204 156 103 88.6 58.1 33.4 25.4 17.1 14.9 5.15 5.17 4.91 4.67 1.94 1.51 0.847 0.773 0.753 11.91 0.200 4.62 29.4 15.8 13.3 11.5 8.84 2.65 2.56 2.01 1.98 1.37 0.874 0.810 0.785 11.10 10.09 10.340 10.030 0.680 1.120 0.615 0.620 0.530 623 303 248 209 170 96.3 68.9 53.8 112 4.60 207 103 53.4 45.0 40.0 0.370 0.350 0.315 0.300 4.37 4.32 4.27 4.38 4.14 3.95 3.90 20.6 13.3 11.3 5.75 2.14 1.45 1.10 60.0 10.10 9.92 10.47 8.020 7.985 5.810 W10 x 45 W10 x 39 W10 x 30 W10 X 19 W10 X 15 WI0 X 12 49.1 42.1 32.4 18.8 13.8 10.9 5.62 4.41 3.54 10.24 9.99 9.87 0.250 0.230 0.190 4.020 4.000 3.960 0.510 0.395 0.270 16.7 4.29 2.89 2.18 0.210 272 228 W8 x 67 W8 x 58 W8 x 48 W8 x 40 W8 x 31 W8 x 24 W8 X 15 9.00 8.75 0.570 0.510 8.280 8.220 0.935 0.810 0.685 3.72 3.65 88.6 75.1 60.9 21.4 18.3 2.12 2.10 2.08 2.04 2.02 19.7 60.4 17.1 52.0 14.1 8.50 0.400 8.110 184 43.3 3.61 3.53 15.0 11.7 9.13 7.08 8.25 8.00 7.93 8.11 0.360 0.285 0.245 0.245 8.070 146 35.5 27.5 20.9 11.8 49.1 12.2 9.27 5.63 1.70 0.560 7.995 0.435 110 3.47 37.1 0.400 0.315 82.8 3.42 3.29 6.495 18.3 1.61 4.44 4.015 48.0 3.41 0.876 W6 x 25 W6 x 20 W6 x 16 W6 X 15 W6 X 12 W6 X 9 7.34 0.455 6.38 6.20 6.28 0.320 53.4 16.7 2.70 2.66 2.60 2.56 2.49 2.47 17.1 13.3 4.43 9.32 2.99 6.080 5.61 1.52 5.87 0.260 6.020 0.365 41.4 13.4 4.41 1.50 4.74 0.260 4.030 5.990 0.405 32.1 10.2 9.72 7.31 5.56 2.20 0.966 4.43 5.99 0.230 0.260 29.1 3.11 1.46 3.55 2.68 0.230 0.170 6.03 0.280 0.215 22.1 1.50 1.11 0.918 0.905 4.000 5.90 3.940 16.4 2.19
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