363107901-SOlution-Steel-By-William-T-Segui-001-pdf

CHAPTER 1 - INTRODUCTION
1.5-1
(a)
P  2067  1340 lb
f  P  1340  68. 02 psi
19. 7
A
(b) Since E  f ,
68. 02
 f 
 2. 35  10 −6
E
29, 000, 000
f  68. 0 psi
  2. 35  10 −6
1.5-2
(a)
L  9/ sin 45 °  12. 73 ft
ΔL  L  8. 9  10 −4  12. 73  12  0. 136 in.
(b)
ΔL  0. 136 in.
f  E  8. 9  10 −4  29, 000  25. 81 ksi
P  fA  25. 811. 31  33. 8 kips
P  33. 8 kips
1.5-3
(a)
(b)
2
0. 5 2
A  d 
 0. 196 3 in. 2
4
4
f  P  5000  25, 470 psi
0. 1963
A
−3
  ΔL  6. 792  10  8. 49  10 −4
L
8
25, 470
E  f 
 3. 0  10 7 psi
8. 49  10 −4
F u  P u  14, 700  74, 900 psi
0. 1963
A
E  30, 000 ksi
F u  74. 9 ksi
[1-1]
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1.5-4
Spreadsheet results:
(a) (b)
Load Stress
(lb)
(psi)
microstrain
2,000 10,186
2,500
3,000
3,500
4,000
4,500
5,000
12,732
15,279
17,825
20,372
22,918
25,465
47
220
500
950
1,111
1,200
1,702
30,000
Stress (psi)
25,000
20,000
15,000
10,000
5,000
0
0.000000
0.000500
0.001000
0.001500
0.002000
Strain
(c)
Slope  9,210,000 psi  modulus of elasticity
[1-2]
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1.5-5 (Note: These results are very approximate and depend on how the curves are
drawn.)
(a)
80
Stress (ksi)
70
60
50
40
30
20
10
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.008
0.01
0.012
Strain
60
Stress (ksi)
50
40
30
20
10
0
0
0.002
0.004
0.006
Strain
(b)
F prop ≈ 47 ksi
(c)
E ≈ 40/0. 004  10, 000 ksi
(d)
F y ≈ 52 ksi
(e)
F u ≈ 70 ksi
[1-3]
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(f)
2
0. 5 2
A  d 
 0. 196 3 in. 2
4
4
10
f P 
 50. 94 ksi
0. 1963
A
 r ≈ 0. 0015,
 r   r L  0. 00158  0. 012 in.
 r  0. 012 in.
1.5-6
Spreadsheet results:
(a)
Load
Elongation
Stress
(kips)
(in.)
(ksi)
0
1.0
2.0
2.5
3.5
5.0
6.0
7.0
8.0
9.0
10.0
11.5
12.0
0
0.0010
0.0014
0.0020
0.0024
0.0036
0.0044
0.0050
0.0060
0.0070
0.0080
0.0120
0.0180
0
5.094
10.19
12.74
17.83
25.47
30.57
35.66
40.75
45.85
50.94
58.58
61.13
0.002
0.004
Strain
0
0.0005
0.0007
0.0010
0.0012
0.0018
0.0022
0.0025
0.0030
0.0035
0.0040
0.0060
0.0090
(b)
70
Stress (ksi)
60
50
40
30
20
10
0
0
0.006
0.008
0.01
Strain
[1-4]
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E≈
(c)
38
 13, 600 ksi
0. 0028
E ≈ 13, 600 ksi
(d)
F pl ≈ 38 ksi
(e)
F y ≈ 60 ksi
1.5-7
Spreadsheet results:
(a)
Load Elongation x 103
(kip s)
( in.)
0
0
0.5
0.16
1
0.352
1.5
0.706
2
1.012
2.5
1.434
3
1.712
3.5
1.986
4
2.286
4.5
2.612
5
2.938
5.5
3.274
6
3.632
6.5
3.976
7
4.386
7.5
4.64
8
4.988
8.5
5.432
9
5.862
9.5
6.362
10
7.304
10.5
8.072
11
9.044
11.5
11.31
12
14.12
12.5
20.044
13
29.106
S tress
( ksi)
0
2.5
5
7.5
10
12.5
15
17.5
20
22.5
25
27.5
30
32.5
35
37.5
40
42.5
45
47.5
50
52.5
55
57.5
60
62.5
65
St rain x 10 3
(in./in .)
0
0.080
0.176
0.353
0.506
0.717
0.856
0.993
1.143
1.306
1.469
1.637
1.816
1.988
2.193
2.320
2.494
2.716
2.931
3.181
3.652
4.036
4.522
5.655
7.060
10.02
14.55
[1-5]
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(b)
70
S tress (ksi)
60
50
40
30
20
10
0
0
2
4
6
8
10
12
14
16
M icro stra in
(c)
Using the dashed line, E ≈
56
 15, 600 ksi
5. 6 − 2  10 −3
E ≈ 16, 000 ksi
(d)
F pl ≈ 42 ksi
(e)
F y ≈ 58 ksi
[1-6]
© 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.