All 13 Chapters Covered
SOLUTIONS
, Contents
Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Chapter 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Chapter 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .159
@Seismicisolation
@Seismicisolation
,Problem 1-4
The size and cross-sectional areas are obtained from Part 1 of the AISCM as follows:
Size Self-weight (lb/ft.) Cross-sectional area (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
Problem 1-5
a)
Element A y Ay I d = y- y I + Ad2
top flange 21 26.25 551.25 3.94 -12.75 3418
web 21 13.5 283.5 1008 0 1008
bot flange 21 0.75 15.75 3.94 12.75 3418
Σ= 63 in.2 850.5 I = 7844 in.4
ΣAy 850.5
y= = = 13.5 in.
ΣA 63
Self weight = (63/144)(490 lb/ft3) = 214 lb/ft.
b)
Element A y Ay I d = y- y I + Ad2
top plate 2.63 18.26 47.93 0.03 -9.04 214.3
beam 10.3 9.23 95.02 510 0 510
bot plate 2.63 0.188 0.49 0.03 9.04 214.3
Σ= 15.55 in.2 143.4 I = 939 in.4
ΣAy 143.4
y= = = 9.23 in.
ΣA 15.55
Self weight = (15.55/144)(490 lb/ft3) = 52.9 lb/ft.
c) From AISCM Table 1-20, Ix = 314 in.4
Area = 13.8 in2
Self weight = 47.1 lb/ft.
1
@Seismicisolation
@Seismicisolation
, Problem 1-7
Plot the idealized stress-strain diagram for a 6-in. wide by ½-in. thick plate and a 6-in. wide by 1-in.
thick plate of ASTM A36 steel. Assume that the original length between two points on the specimen
over which the elongation will be measured (i.e. the gage length) is 2-in.
Solution:
Gage length, Lo = 2 in.
For 6 x ½-in. plate, Area = (6 in.)(½ in.) = 3 in2
E = 29,000 ksi
P Stress = P/A Strain, ε = P/EA Elongation, ΔLo = Strain x gage length = εLo
(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. plate, Area = (6 in.)(1 in.) = 6 in2
P Stress = P/A Strain, ε = P/EA Elongation, ΔLo = Strain x gage length = εLo
(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
Problem 1-8
Determine the most economical layout of the roof framing (joists and girders) and the gage
(thickness) of the roof deck for a building with a 25 ft x 35 ft typical bay size. The total roof dead
load is 25 psf and the snow load is 35 psf. Assume a 1½” deep galvanized wide rib deck and an
estimated weight of roof framing of 6 psf.
*Assume beams (or joists) span the 35’ direction
* Assume 3-span condition
*Total roof load = (25psf + 35psf) – 6psf = 54psf
2
@Seismicisolation
@Seismicisolation
SOLUTIONS
, Contents
Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Chapter 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Chapter 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Chapter 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Chapter 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Chapter 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Chapter 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Chapter 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Chapter 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Chapter 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
Appendix B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .159
@Seismicisolation
@Seismicisolation
,Problem 1-4
The size and cross-sectional areas are obtained from Part 1 of the AISCM as follows:
Size Self-weight (lb/ft.) Cross-sectional area (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
Problem 1-5
a)
Element A y Ay I d = y- y I + Ad2
top flange 21 26.25 551.25 3.94 -12.75 3418
web 21 13.5 283.5 1008 0 1008
bot flange 21 0.75 15.75 3.94 12.75 3418
Σ= 63 in.2 850.5 I = 7844 in.4
ΣAy 850.5
y= = = 13.5 in.
ΣA 63
Self weight = (63/144)(490 lb/ft3) = 214 lb/ft.
b)
Element A y Ay I d = y- y I + Ad2
top plate 2.63 18.26 47.93 0.03 -9.04 214.3
beam 10.3 9.23 95.02 510 0 510
bot plate 2.63 0.188 0.49 0.03 9.04 214.3
Σ= 15.55 in.2 143.4 I = 939 in.4
ΣAy 143.4
y= = = 9.23 in.
ΣA 15.55
Self weight = (15.55/144)(490 lb/ft3) = 52.9 lb/ft.
c) From AISCM Table 1-20, Ix = 314 in.4
Area = 13.8 in2
Self weight = 47.1 lb/ft.
1
@Seismicisolation
@Seismicisolation
, Problem 1-7
Plot the idealized stress-strain diagram for a 6-in. wide by ½-in. thick plate and a 6-in. wide by 1-in.
thick plate of ASTM A36 steel. Assume that the original length between two points on the specimen
over which the elongation will be measured (i.e. the gage length) is 2-in.
Solution:
Gage length, Lo = 2 in.
For 6 x ½-in. plate, Area = (6 in.)(½ in.) = 3 in2
E = 29,000 ksi
P Stress = P/A Strain, ε = P/EA Elongation, ΔLo = Strain x gage length = εLo
(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. plate, Area = (6 in.)(1 in.) = 6 in2
P Stress = P/A Strain, ε = P/EA Elongation, ΔLo = Strain x gage length = εLo
(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
Problem 1-8
Determine the most economical layout of the roof framing (joists and girders) and the gage
(thickness) of the roof deck for a building with a 25 ft x 35 ft typical bay size. The total roof dead
load is 25 psf and the snow load is 35 psf. Assume a 1½” deep galvanized wide rib deck and an
estimated weight of roof framing of 6 psf.
*Assume beams (or joists) span the 35’ direction
* Assume 3-span condition
*Total roof load = (25psf + 35psf) – 6psf = 54psf
2
@Seismicisolation
@Seismicisolation
