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Chapter 4
4.1 a. Eq. (4.8):
BNNqNcq qcu 2
1
4.2 Eq. (4.17); c = 0:
)4.0(
FS
1
FS
all
BNNq
q
qq
u
all
Q
3
2B
B
26
26
4.3 a. Eq. (4.26):
idsqiqdqsqcicdcscu FFFBNFFFNqFFFNcq
2
1
1
d
F
Chapter 4
27
© 2016 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
kN/m 373.7
)1)(03.48)(5.1)(8.17(
2
1
)2.1)(3.33)(8.172.1(
4
1
all
q
c.
sdqsqdqu FFBNFFNqq
2
1
= 30. From Table 4.2: Nq = 18.4; N = 22.4.
Table 4.3: Fs = 0.6; Fd = 1; Fqs = 1 + tan = 1.577
193.1
3
2
289.01)sin1(tan21 2
B
D
Ff
qd
2
kN/m 368.8
)1)(6.0)(4.22)(3)(5.16(
2
1
)577.1)(193.1)(4.18)(5.16)(2(
4
1
all
q
4.4
20cos
1
2
11 2
all idsqiqdqsqcicdcscFFFBNFFFNqFFFNcB
FS
Q
1
)25)(tan72.20(
tan
d
c
qdcd
F
N
Chapter 4
28
28
605.0
90
20
1
2
qici
FF
4.5 From Eqs. (4.22) and (4.26):
qFFBNFFNqFFNcq dsqdqsqcdcsc2
1
FS
1
all
Chapter 4
29
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
q = (1 17) + (9.69)(0.5) = 21.85 kN/m2
kN 5760
85.21)1)(73.0)(88.10)(2)(69.9)(5.0(
)233.1)(31.1)(66.10)(85.21()257.1)(343.1)(72.20)(70(
3
)3)(2(
all(net)
Q
4.6 c = 0. Eq. (4.26):
dsqdqsqu FFBNFFNqq
2
1
2
2
31
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
4.8 B = B – 2e = 1.5 – (2)(0.15) = 1.2 m; L = 1.5 m
Eq. (4.51):
dsqdqsqu FFBNFFNqq
2
1
1
d
F
Chapter 4
32
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
32
2
kN/m 1571.9
)1)(68.0)(31.56)(2.1)(17(
2
1
)165.1)(58.1)(75.37)(171(
u
q
kN 707.3
4
)5.1)(2.1)(9.1571(
FS
all LBq
Qu
4.9 Eq. (4.55):
)()()()(
ult
all 2
1
44 eseeqseq FNBFNq
BL
Q
Q
2
4
all
4.10 c = 0; = 35
dsqdqsqu FFBNFFNqq
2
1
8.1
qd
Chapter 4
33
© 2016 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
kN/m 12326.6914.540
)1)(1)(03.48)(8.1)(16(
2
1
)127.1)(1)(3.33)(9.0)(16(
u
q
Eq. (4.59):
u
eu
Kq
q
R)(
1
Eq. (4.60):
k
KB
e
aR
. For
5.0
8.1
9.0
B
Df
, a = 1.754; k = 0.8
1232
11)12.0(754.1 )()(
8.0 eu
u
eu q
q
q
. qu(eccentric) = 835.8 kN/m2
Qu = Bqu(e) = (1.8)(835.8) = 1504.4 kN/m
4.11
dsqdqsqu FFBNFFNqq
2
1
q = (2)(105) + (2)(118 – 62.4) = 321.1 lb/ft2
Chapter 4
34
34
4.12
0 ;m 156.0
450
70
ce
Eq. (4.55):
)()()()(
2
ult 2
1eseeqseq FBNFNqBQ
35
© 2016 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
4.13
.0.5)( 16.0
25.2
36.0
;
6
1
and zero between 08.0
5.1
12.0
L
e
B
eLB
So, Case II; Figure 4.26 applies.
From Figure 4.26,
33.0;92.0 21 L
L
L
L
07.2
L
36
36
8.0
4.14 a. From Eq. (4.84):
B
D
ueiu
f
B
e
BqQ
2
)( 121
1
kN/m 1130.9
38
4.1
