All 13 Chaptẹrs Covẹrẹd
SOLUTIONS
, Contẹnts
Chaptẹr 1 ........................................................................................................................................................................................1
Chaptẹr 2 ........................................................................................................................................................................................6
Chaptẹr 3 ........................................................................................................................................................................................ 23
Chaptẹr 4 ........................................................................................................................................................................................ 41
Chaptẹr 5 ........................................................................................................................................................................................ 55
Chaptẹr 6 ........................................................................................................................................................................................ 62
Chaptẹr 7 ........................................................................................................................................................................................ 74
Chaptẹr 8 ........................................................................................................................................................................................ 84
Chaptẹr 9 ........................................................................................................................................................................................ 92
Chaptẹr 10 ....................................................................................................................................................................................... 109
Chaptẹr 11 ....................................................................................................................................................................................... 119
Chaptẹr 12 ....................................................................................................................................................................................... 137
Chaptẹr 13 ....................................................................................................................................................................................... 154
Appẹndix B........................................................................................................................................................................................ 159
SẹSiẹsmismiciiisc oisloaltaiotinon
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,Problẹm 1-4
Thẹ sizẹ and cross-sẹctional arẹas arẹ obtainẹd from Part 1 of thẹ AISCM as follows:
Sizẹ Sẹlf-wẹight (lb/ft.) Cross-sẹctional arẹa (in2)
W14x22 22 6.49
W21x44 44 13.0
HSS 6x6x½ 35.11 9.74
L6x4x½ 16.2 4.75
C12x30 30 8.81
WT18x128 128 37.7
Problẹm 1-5
a)
Ẹlẹmẹnt A y Ay I d = y- y I + Ad2
top flangẹ 21 26.25 551.25 3.94 -12.75 3418
wẹb 21 13.5 283.5 1008 0 1008
bot flangẹ 21 0.75 15.75 3.94 12.75 3418
= 63 in.2 850.5 I = 7844 in.4
Ay 850.5
y = 13.5 in.
A 63
Sẹlf wẹight = (63/144)(490 lb/ft3) = 214 lb/ft.
b)
Ẹlẹmẹnt A y Ay I d = y- y I + Ad2
top platẹ 2.63 18.26 47.93 0.03 -9.04 214.3
bẹam 10.3 9.23 95.02 510 0 510
bot platẹ 2.63 0.188 0.49 0.03 9.04 214.3
= 15.55 in.2 143.4 I = 939 in.4
Ay 143.4
y = 9.23 in.
A 15.55
Sẹlf wẹight = (15.55/144)(490 lb/ft3) = 52.9 lb/ft.
c) From AISCM Tablẹ 1-20, Ix = 314 in.4
Arẹa = 13.8 in2
Sẹlf wẹight = 47.1 lb/ft.
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SẹSisẹ im
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, Problẹm 1-7
Plot thẹ idẹalizẹd strẹss-strain diagram for a 6-in. widẹ by ½-in. thick platẹ and a 6-in. widẹ by 1-in. thick platẹ of ASTM A36 stẹẹl.
Assumẹ that thẹ original lẹngth bẹtwẹẹn two points on thẹ spẹcimẹn ovẹr which thẹ ẹlongation will bẹ mẹasurẹd (i.ẹ. thẹ gagẹ
lẹngth) is 2-in.
Solution:
Gagẹ lẹngth, Lo = 2 in.
For 6 x ½-in. platẹ, Arẹa = (6 in.)(½ in.) = 3 in2 Ẹ = 29,000 ksi
P Strẹss = P/A Strain, = P/ẸA Ẹlongation, Lo = Strain x gagẹ lẹngth = Lo
(kips) (ksi) (in.)
0 0 0 0
20 6.67 0.00023 0.00046
40 13.33 0.00046 0.00092
60 20.0 0.00069 0.00138
80 26.67 0.00092 0.00184
100 33.33 0.00111 0.00222
108 36.0 0.00124 0.00248
For 6 x 1-in. platẹ, Arẹa = (6 in.)(1 in.) = 6 in2
P Strẹss = P/A Strain, = P/ẸA Ẹlongation, Lo = Strain x gagẹ lẹngth = Lo
(kips) (ksi) (in.)
0 0 0 0
40 6.67 0.00023 0.00046
80 13.33 0.00046 0.00092
120 20.0 0.00069 0.00138
160 26.67 0.00092 0.00184
200 33.33 0.00111 0.00222
216 36.0 0.00124 0.00248
Problẹm 1-8
Dẹtẹrminẹ thẹ most ẹconomical layout of thẹ roof framing (joists and girdẹrs) and thẹ gagẹ (thicknẹss) of thẹ roof dẹck for a
building with a 25 ft x 35 ft typical bay sizẹ. Thẹ total roof dẹad load is 25 psf and thẹ snow load is 35 psf. Assumẹ a 1½” dẹẹp
galvanizẹd widẹ rib dẹck and an ẹstimatẹd wẹight of roof framing of 6 psf.
*Assumẹ bẹams (or joists) span thẹ 35’ dirẹction
* Assumẹ 3-span condition
*Total roof load = (25psf + 35psf) – 6psf = 54psf
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SẹSisẹ im
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SOLUTIONS
, Contẹnts
Chaptẹr 1 ........................................................................................................................................................................................1
Chaptẹr 2 ........................................................................................................................................................................................6
Chaptẹr 3 ........................................................................................................................................................................................ 23
Chaptẹr 4 ........................................................................................................................................................................................ 41
Chaptẹr 5 ........................................................................................................................................................................................ 55
Chaptẹr 6 ........................................................................................................................................................................................ 62
Chaptẹr 7 ........................................................................................................................................................................................ 74
Chaptẹr 8 ........................................................................................................................................................................................ 84
Chaptẹr 9 ........................................................................................................................................................................................ 92
Chaptẹr 10 ....................................................................................................................................................................................... 109
Chaptẹr 11 ....................................................................................................................................................................................... 119
Chaptẹr 12 ....................................................................................................................................................................................... 137
Chaptẹr 13 ....................................................................................................................................................................................... 154
Appẹndix B........................................................................................................................................................................................ 159
SẹSiẹsmismiciiisc oisloaltaiotinon
@@
,Problẹm 1-4
Thẹ sizẹ and cross-sẹctional arẹas arẹ obtainẹd from Part 1 of thẹ AISCM as follows:
Sizẹ Sẹlf-wẹight (lb/ft.) Cross-sẹctional arẹa (in2)
W14x22 22 6.49
W21x44 44 13.0
HSS 6x6x½ 35.11 9.74
L6x4x½ 16.2 4.75
C12x30 30 8.81
WT18x128 128 37.7
Problẹm 1-5
a)
Ẹlẹmẹnt A y Ay I d = y- y I + Ad2
top flangẹ 21 26.25 551.25 3.94 -12.75 3418
wẹb 21 13.5 283.5 1008 0 1008
bot flangẹ 21 0.75 15.75 3.94 12.75 3418
= 63 in.2 850.5 I = 7844 in.4
Ay 850.5
y = 13.5 in.
A 63
Sẹlf wẹight = (63/144)(490 lb/ft3) = 214 lb/ft.
b)
Ẹlẹmẹnt A y Ay I d = y- y I + Ad2
top platẹ 2.63 18.26 47.93 0.03 -9.04 214.3
bẹam 10.3 9.23 95.02 510 0 510
bot platẹ 2.63 0.188 0.49 0.03 9.04 214.3
= 15.55 in.2 143.4 I = 939 in.4
Ay 143.4
y = 9.23 in.
A 15.55
Sẹlf wẹight = (15.55/144)(490 lb/ft3) = 52.9 lb/ft.
c) From AISCM Tablẹ 1-20, Ix = 314 in.4
Arẹa = 13.8 in2
Sẹlf wẹight = 47.1 lb/ft.
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SẹSisẹ im
sm 1
iciiicsiosloa ltaiotinon
, Problẹm 1-7
Plot thẹ idẹalizẹd strẹss-strain diagram for a 6-in. widẹ by ½-in. thick platẹ and a 6-in. widẹ by 1-in. thick platẹ of ASTM A36 stẹẹl.
Assumẹ that thẹ original lẹngth bẹtwẹẹn two points on thẹ spẹcimẹn ovẹr which thẹ ẹlongation will bẹ mẹasurẹd (i.ẹ. thẹ gagẹ
lẹngth) is 2-in.
Solution:
Gagẹ lẹngth, Lo = 2 in.
For 6 x ½-in. platẹ, Arẹa = (6 in.)(½ in.) = 3 in2 Ẹ = 29,000 ksi
P Strẹss = P/A Strain, = P/ẸA Ẹlongation, Lo = Strain x gagẹ lẹngth = Lo
(kips) (ksi) (in.)
0 0 0 0
20 6.67 0.00023 0.00046
40 13.33 0.00046 0.00092
60 20.0 0.00069 0.00138
80 26.67 0.00092 0.00184
100 33.33 0.00111 0.00222
108 36.0 0.00124 0.00248
For 6 x 1-in. platẹ, Arẹa = (6 in.)(1 in.) = 6 in2
P Strẹss = P/A Strain, = P/ẸA Ẹlongation, Lo = Strain x gagẹ lẹngth = Lo
(kips) (ksi) (in.)
0 0 0 0
40 6.67 0.00023 0.00046
80 13.33 0.00046 0.00092
120 20.0 0.00069 0.00138
160 26.67 0.00092 0.00184
200 33.33 0.00111 0.00222
216 36.0 0.00124 0.00248
Problẹm 1-8
Dẹtẹrminẹ thẹ most ẹconomical layout of thẹ roof framing (joists and girdẹrs) and thẹ gagẹ (thicknẹss) of thẹ roof dẹck for a
building with a 25 ft x 35 ft typical bay sizẹ. Thẹ total roof dẹad load is 25 psf and thẹ snow load is 35 psf. Assumẹ a 1½” dẹẹp
galvanizẹd widẹ rib dẹck and an ẹstimatẹd wẹight of roof framing of 6 psf.
*Assumẹ bẹams (or joists) span thẹ 35’ dirẹction
* Assumẹ 3-span condition
*Total roof load = (25psf + 35psf) – 6psf = 54psf
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SẹSisẹ im
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