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Min. longitudinal spacing 4d40. 52. 0 in.
Min. transverse spacing 4d40. 52. 0 in.
9.5-3
(a) Total load to be supported by the composite section (omit beam weight; check it
later):
Slab: 5
12. 5 85. 36 lb/ft.
For an 18-in. deep beam,
13. 5 79. 04 lb/ft.
Try a W18 86.
0. 85fc´ab AsFy
0. 854a841265, Solution is: a4. 429 in.
yd
2t−a
218. 4
25−4. 429
211. 99 in.
bMnbTy 0. 90126511. 99/12 1138 ft-kips 1067 ft-kips (OK)
Check beam weight:
80. 852230295. 9 ft-kips
bMnbMp698 ft-kips 95.9 ft-kips (OK) UseaW1886
(b) Total load to be supported by the composite section (omit beam weight; check it
later):
Slab: 5
13. 5 70. 45 ft-kips
Try a W18 76.
0. 854a841115, Solution is: a3. 904 in.
yd
2t−a
25
25−3. 904
25. 548 in.
Mn
1
Ty 1
0. 85fc´ab AsFy
0. 854a841265, Solution is: a4. 429in.
yd
2t−a
218. 4
25−4. 492
211. 95 in.
Mn
b
1
b
Ty 1
1. 67 126511. 95
Asa 5/82
40. 306 8 in.2,Ecwc
1.5 fc´1451.5 43492 ksi
′Ec≤RgRpAsaFu
Qn
14. 96 84. 56, round up to 85. total number 285170
Min. longitudinal spacing 4d45/82. 5 in.
Min. transverse spacing 4d45/82. 5 in.
Asa 3/42
40. 441 8 in.2,Ecwc
1.5 fc´1451.5 43492 ksi
′Ec≤RgRpAsaFu
Qn
21. 54 58. 73, round up to 59. total number 259118
For one stud at each section, the required spacing will be
9.6-1
(a) Before concrete cures:
Slab: 4
12 1507. 5375. 0 lb/ft
0. 85fc
′b
0. 854901. 06 in.
Area of transformed concrete C
Fy
324. 5
50 6. 49 in.2
[9-25]
© 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.
Y2t−a
9.6-2
From Problem 9.2-2,
Beams are W18 97
t5in.
b84
384EIs
3842900017500. 214 4 in.
Δconst 5wconstL4
384EIs
50. 160/1230 124
3842900017505. 746 10−2in.
ΔΔ
DΔ
const 0. 2144 0. 05746 0. 271 9 in. Δ2. 63 in.
0. 85fc
′b
0. 854904. 657 in.
Y2t−a
25−4. 657
22. 672 in., dY218. 6 2. 672 21. 27 in.
Taking moments about the bottom of the steel, we get
9.6-3
(a) From Problem 9.3-1, a W12 16 is used, with t4 in., s7ft,L25 ft,
qconst 20 psf, qpart 15 psf, qL125 psf, A992 steel and 4 ksi concrete.
Before concrete cures:
Slab: 4
∑A
9. 420 10. 76 in., ILB 316. 4 in.4
Δpart 5wpartL4
50. 105/1225 124
9.6-4
(a) From Problem 9.4-1, a W21 57 is used, with t6 in., s9ft,L40 ft,
qconst 20 psf, qL250 psf, A992 steel and 4 ksi concrete.
Before concrete cures:
Slab: 6
0. 85fc
′b
0. 8541082. 274 in.
Y2t−a
26−2. 274
24. 863 in.
Taking moments about the bottom of the steel, we get
[9-29]
© 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.
0. 85fc´ab AsFy
0. 854a108810, Solution is: a2. 206in.
yd
2t−a
223. 6
26−2. 206
216. 70 in.
bMnbTy 0. 9081016. 701. 217 104in.-kips 1014 ft-kips
Loads:
[9-30]
© 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.
wu1. 2wD1. 6wL1. 20. 7301. 60. 1801. 164 k/ft
Mu1
81. 164402233 ft-kips
bMnbMp503 ft-kips 233 ft-kips (OK)
After concrete has cured:
wL25092250 lb/ft
Lower-bound moment of inertia:
Effective flange width (40 12/4 120 in. or 912108 in.
Use b108 in.
0. 85fc
′b
0. 8541082. 206 in.
Y2t−a
26−2. 206
24. 897 in.
Taking moments about the bottom of the steel, we get
[9-31]
© 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.
2. 0 −1. 239 0. 761 in.
Required Is50. 730/1240 124
9.6-5
(a) From Problem 9.4-2, a W14 22 is used, with t4 in., s8ft,L27 ft,
qconst 20 psf, qpart 20 psf, qL120 psf, A992 steel and 4 ksi concrete.
Before concrete cures:
Slab: 4
0. 85fc
′b
0. 854811. 178 in.
Y2t−a
∑A
12. 98 11. 98 in., ILB 540. 7 in.4
Δpart 5wpartL4
50. 160/1227 124
9.7-1
(a) Lower-bound moment of inertia:
0. 85fc
Use CV′515 kips.
From CT,0.85fc
0. 854a72515, Solution is: a2. 104 in.
Y2t−a
24. 5 −2. 104
23. 448 in.
∑A
20. 60 15. 0 in. ILB 1289 in.4
9.7-2
Steel headed stud anchors:
Asa 3/42
40. 441 8 in.2,Ecwc
1.5 fc´1451.5 43492 ksi
′Ec≤RgRpAsaFu
0.85 fc´bt 0. 854904. 5 −2765. 0 kips
Since AsFyis the smallest of the three possibilities, C735 kips, and there is full
0. 85fc
′b
0. 854902. 402 in.
Moment arm for concrete compressive force is
9.7-3
Asa 3/42
40. 441 8 in.2,Ecwc
1.5 fc´1451.5 43492 ksi
[9-35]
© 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.
′Ec≤RgRpAsaFu
0.85 fc´bt 0. 854664. 5 −1. 5673. 2 kips
Since ∑Qnis the smallest of the three possibilities, C173.2 kips, there is partial
173. 2 Fybft′−FyAs−bft′0
173. 2 505. 03t′−507. 69 −5. 03t′0, Solution is: t′0. 420 1
Since tf0. 420 in., the PNA is at the bottom of the flange.
∑A
5. 577 9. 505 in.
0. 85fc
′b
0. 854660. 771 8 in.
Moment arm for concrete compressive force is
y
̄t−a
9.7-4
ThebeamisaW1840.
Asa 3/42
40. 441 8 in.2,Ecwc
1.5 fc´1451.5 43492 ksi
′Ec≤RgRpAsaFu
0.85 fc´bt 0. 8541204. 5 −1. 51224 kips
Since ∑Qnis the smallest of the three possibilities, C292.9 kips, there is partial
[9-37]
© 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.
composite action, and the PNA is in the steel section. Determine whether the PNA is in
∑A
8. 829 11. 88 in.
0. 85fc
′b
0. 8541200. 717 9 in.
Moment arm for concrete compressive force is
y
̄t−a
211. 88 4. 5 −0. 7179
216. 02 in.
Moment arm for compressive force in the steel is
[9-38]
© 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.
Before the concrete cures,
wu1. 20. 47131. 60. 2000. 885 6 kips/ft
Mu1
80. 8856402177 ft-kips
Ma1
80. 6713402134 ft-kips
Mnx
b
Mpx
b
196 ft-kips 134 ft-kips (OK)
After the concrete cures,
9.8-1
From the solution to Problem 9.7-3, for ¾-in. studs and fc´ 4ksi,Qn 17.23 kips
0.85 fc´bt 0. 854664. 5 −1. 5673. 2 kips
0. 85fc´b258. 5
0. 854661. 152 in.
Y2t−a
24. 5 −1. 152
23. 924 in.
9.8-2
0.85 fc´bt 0. 854905−2918. 0 kips
0. 85fc´b378. 4
0. 854901. 237 in.
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