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CHAPTER 4 -COMPRESSION MEMBERS
4.3-1
2. 65 45. 28
4. 71 E
Fy
4. 71 29000
50 113. 4
2. 65 135. 8
4. 71 E
Fy
4. 71 29000
50 113. 4
4.3-2
rKL
r1. 025 12
3. 68 81. 52
4. 71 E
Fy
4. 71 29000
35 135. 6
4.3-3
4.3-4
(a) Lc
rKL
r0. 6515 12
4.3-5
(a) Lc
rKL
r0. 813 12
2. 48 50. 32
Since Lc/r50. 32 113. 4, use AISC Eq. E3-2:
c
1. 67 597. 1 kips Pn
c
(b) From Manual Table 4-14, for Lc/r50. 32 and Fy50 ksi,
c
c
c
4.3-6
Since Lc/r42. 83 113. 4, use AISC Eq. E3-2:
[4-3]
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c
1. 67 919. 2 kips Pn
c
(b) From Manual Table 4-14, for Lc/r42. 83 and Fy50 ksi,
c
c
c
4.3-7
(a) Let PucPn
4.3-8
[4-4]
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or posted to a publicly accessible website, in whole or in part.
4.4-1
Compute the overall, or flexural, buckling strength.
Fy
46 118
Since 87.8 118, use AISC Equation E3-2.
The nominal strength is
Check width-thickness ratios. From the dimensions and properties table in the Manual,
the width-thickness ratio for the larger overall dimension is
The ratio for the smaller dimension is
From AISC Table B4.1, case 12 (and Figure 4.9 in this book), the upper limit for
nonslender elements is
tand b
tare 1.40 E
Fy
strength must be computed. (Although the limiting width-thickness ratio is labeled b/t
in the table, that is a generic notation, and it applies to h/tas well.)
For the larger dimension,
Since 54. 5 45. 55,
Feℓ
From AISC Table E7-1, Case b,
The elastic buckling stress is
Feℓc2r
2
Fy1. 38 35. 15
54. 5
24636. 44 ksi
The unreduced length of the longer side can be taken as
and the effective width is
Feℓ
27. 39
27. 39 8. 41 in.
For the smaller dimension,
Theeffectivecross-sectionalareais
The nominal compressive strength is
4.4-2
Compute the overall, or flexural, buckling strength.
Since 87.20 113.4, use AISC Equation E3-2.
The nominal strength is
Check width-thickness ratios. From the dimensions and properties table in the Manual,
the width-thickness ratio of the web is
tw
From AISC Table B4.1 (and Figure 4.9 in this book), the upper limit for nonslender
Since h
tw
1.49 E
Fy
, the web is slender.
For the flange,
For the web,
[4-7]
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Since 47. 37, beb, andthereisnoreductioninarea. Pn855 kips
4.6-1
From the column load tables for Lc18 ft, a W14 74 has a design strength of 563
kips. UseaW1474
From the column load tables for Lc18 ft, a W14 82 has an allowable strength of
413 kips. UseaW1482
Try W16 77 (a nonslender shape), Ag22. 6 in.2,ry2.47 in.
∴Fcr 0. 658Fy/FeFy0. 65860/37.436030. 67 ksi
Compute the overall, or flexural, buckling strength.
[4-8]
© 2018 Cengage Learning®. All Rights Reserved. May not be scanned, copied or duplicated,
or posted to a publicly accessible website, in whole or in part.
Since 87.8 103.5, use AISC Equation E3-2.
The nominal flexural buckling strength is
Check width-thickness ratios. From the dimensions and properties table in the Manual,
the width-thickness ratio of the web is
tw
From AISC Table B4.1 (and Figure 4.9 in this book), the upper limit for nonslender
elements is
tw
Fy
For the flange,
For the web,
UseaW1667
(b-2) Assume Fcr 25 ksi
[4-9]
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or posted to a publicly accessible website, in whole or in part.
0. 6Fcr
0. 62526. 3 in.2
ry
2. 49 86. 75 200 (OK)
ry
2. 47 87. 45 200 (OK)
4. 71 E
Fy
4. 71 29000
60 103. 5 87. 45
4.6-2
LcKL 2. 02040 ft
(a-1) Pu1. 2D1. 6L1. 21101. 6110308 kips
From the column load tables for Lc40 ft, a W12 120 has a design strength of 339
ry
ry
1. 69 284. 0 200
ry
ry
2. 63 182. 5 200
4. 71 E
Fy
4. 71 29000
55 108. 2 182. 5
∴Fcr 0. 877Fe0. 8778. 5947. 537 ksi
ry
ry
2. 74 175. 2 200
Fe2E
ry
ry
2. 72 176. 5 200
[4-11]
© 2018 Cengage Learning®. All Rights Reserved. May not be scanned, copied or duplicated,
or posted to a publicly accessible website, in whole or in part.
Fe2E
0. 6Fcr
0. 6845. 8 in.2
ry
ry
2. 74 175. 2 200
4. 71 E
Fy
4. 71 29000
55 108. 2 175. 2
4.6-3
LcKL 2. 11225. 2 ft
(a) Pu1. 2D1. 6L1. 21001. 6300600. 0 kips
HSS 16 12 3
4.6-4
LcKL 0. 81512 ft
4.6-5
LcKL 2. 11225. 2 ft
4.6-6
LcKL 0. 81512 ft
4.6-7
Pu1. 2D1. 6L1. 2901. 6260524 kips
LcKL 0. 6515. 339. 965 say 10 ft
4.6-8
PaDL90 260 350 kips
4.6-9
c
4.7-1
[4-14]
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or posted to a publicly accessible website, in whole or in part.
4.7-2
For an HSS 10 65/16, Ag8. 76 in.2,rx3. 66 in., ry2. 47 in., and there are
no slender elements (see Manual Table 1-12A).
c
1. 67 205. 0 kips Pn
c
4.7-3
[4-15]
© 2018 Cengage Learning®. All Rights Reserved. May not be scanned, copied or duplicated,
or posted to a publicly accessible website, in whole or in part.
Since Lc/r62. 95 103. 5, use AISC Eq. E3-2:
4.7-4
From the column load tables for Lc12 ft, try a W14 74
Lcx
22
4.7-5
From the column load tables for Lc15ft,therearenoW8orW10shapeswith
enough strength. Try a W12 230 :
cPn2450 kips for Lc15 ft
Lcx
rx/ry
35
1. 80 19. 44 ft 15 ft
For Lc19 ft, cPn2150 kips 2280 kips (N.G.)
Try a W14 233:
KxL
rx/ry
35
1. 62 21. 60 ft 15 ft
c
Lcx
rx/ry
35
1. 80 19. 44 ft 15 ft
For Lc19 ft, Pn
c
1430 kips 1520 kips (N.G.)
Try a W12 252:
Lcx
35
c
Try a W14 233:
Lcx
rx/ry
35
1. 62 21. 60 ft 15 ft
For Lc21. 60 ft, Pn
c
1530 kips 1520 kips (OK)
4.7-6
The x-axis strength will control when rx/ryLcx
Lcy
2. 0. This is true for all
rectangular HSS.
4.7-7
Lcx KxL27 ft, Lcy KyL15 ft
rx
rx
3. 85 84. 16 Lcy
ry
ry
3. 25 55. 38
4. 71 E
Fy
4. 71 29000
46 118. 3
Since Lc/r84. 16 118. 3, use AISC Eq. E3-2:
Fcr 0. 658Fy/FeFy0. 65846/40.414628. 57 ksi
Fcr
39. 09 38. 13
Since 54. 5 38. 13,
Feℓ
54. 5
The unreduced length of the longer side can be taken as
Fcr
Fcr
39. 09
39. 09 7. 246 in.
Theeffectivecross-sectionalareais
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