This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
159
Chapter 16
16.1
.28
°
=
′
φ
From Table 16.1, =
c
N31.61;
=
q
N
17.81;
=
γ
N
13.70
2
kN/m 499.4=
++=
++
′
==
2
1
5.3
1
2
1
5.3
1
all γqc
s
u
γBNqNNc
F
q
q
16.2 For square footing, Eq. (16.12) is used.
16.3
.35
°
=
′
φ
From Table 16.1, =
c
N57.75;
=
q
N
41.44;
=
γ
N
45.41
16.4
.0
°
=
′
φ
From Table 16.1, =
c
N5.7;
=
q
N
1;
=
γ
N
0
2
1
1
u
q
160
16.5
.28
°
=
′
φ
From Table 16.2, =
c
N25.80;
=
q
N
14.72;
=
γ
N
16.72
For a continuous foundation with vertical loading, all inclination factors and
shape factors are equal to one. So,
16.6
.28
°
=
′
φ
From Table 16.2, =
c
N25.80;
=
q
N
14.72;
γ
N
= 16.72
s
F
For vertical loading, all inclination factors are equal to one.
γs
161
© 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.
1=
γd
λ
2
kN/m 745.5
=
+
+
=
)1)(6.0)(72.16)(0.2)(19(
2
1
)224.1)(531.1)(72.14)(5.1)(19()3.1)(57.1)(80.25)(31(
5.3
1
all
q
16.7 γ = 115 lb/ft
3
;
1100
=
′
c
lb/ft
2
;
°
=
′
35
φ
; D
f
= 3.5 ft; B = 5 ft; factor of safety = 4
+
)1)(03.48)(0.5)(115(
2
1
4
all
16.8 γ = 16.5 kN/m
3
; 41=
u
c kN/m
3
;
0
=
′
φ
; D
f
= 1.5 m; factor of safety = 5
162
© 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.
3.1
0.2
5.1
4.014.01 =
+=
+= B
D
λ
f
cd
1)sin1(tan21 2=
′
−
′
+=
B
D
λf
qd
φφ
1=
γd
λ
2
kN/m 59.7=
++= )1)(0)(0.2)(5.16(
2
1
)1)(1)(5.1)(5.16()3.1)(14.5)(41(
5
1
all
q
16.9 Eq. (16.12):
γqcu
BNγqNNcq
′
++
′
=4.03.1
16.10 Since the groundwater table is 0.25 m below the footing, it represents Case III in
Figure 16.6.
163
© 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.
4.18=++= )]84.9)(5.1)(66.10)(4.0()21.14)(17()09.27)(32)(3.1[(
771
5.1
2
s
F
16.11
.29
°
=
′
φ
From Table 16.1, =
c
N34.24;
=
q
N
19.98;
=
γ
N
16.18
all
s
F
16.12
°
=
′
27
φ
;
38
=
′
c
kN/m
2
; B = 2.25 m; D
f
= 2 m; α = 12°
Using Eq. (16.31) which provides the vertical component of the inclined loading,
++
′
=
γiγdγsγqiqdqsqcicdcsc
s
λλλγBNλλλqNλλλNc
F
q2
11
all
90
90
qi
°
ci
164
509.127tan1tan1 =+=
′
+=
φ
L
B
λ
qs
27.1
25.2
2
)27sin1(27tan21)sin1(tan21
22
=
−+=
′
−
′
+= B
D
λ
f
qd
φφ
12
cos
all(i)
16.13 γ = 17 kN/m
3
;
48
=
′
c
kN/m
2
;
°
=
′
31
φ
; factor of safety = 4.5
1
165
© 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.
B
Bq
22.3435.751
)]65.22)()(17)(4.0()28.25)(17)(2()41.40)(48)(3.1[(
5.4
1
all
+=
++=
(a)
2
all
1160
B
q=
(b)
From Eqs. (a) and (b),
B
B
22.3435.751
1160
2
+=
By trial and error, B ≈
1.21 m
16.14 γ = 121 lb/ft
3
;
0
=
′
c
;
°
=
′
26
φ
; factor of safety = 2.5
1
16.15 γ = 17 kN/m
3
;
48
=
′
c
kN/m
2
;
°
=
′
31
φ
; factor of safety = 4.5
++
11
Trial 1: Assume B = 1.25 m
631.1
67.32
63.20
11 =
+=
+=
c
q
cs
N
N
L
B
λ
404.1
25.1
2
tan)4.0(1tan)4.0(1
11
=
+=
+=
−−
B
D
λ
f
cd
6.131tan1tan1 =+=
′
+=
φ
L
B
λ
qs
286
.
1
25.1
2
tan)31sin1(31tan21tan)sin1(tan21
1212
=
−+=
′
−
′
+=
−−
B
D
λ
f
qd
φφ
6.04.01 =
−= L
B
λ
γs
γd
167
© 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.
1176)1)(5.1176())((
22
allall
≈== BqQ
kN, which is slightly higher than 1160 kN,
and therefore acceptable for design.
Design B
= 1 m
16.16 γ = 16 kN/m
3
;
0
=
′
c
;
°
=
′
29
φ
, D
f
= 1.3 m; B = 1.75 m; and x = 0.25 m
From Table 16.2:
=
q
N
16.44;
=
γ
N
19.34
1
all
s
F
16.17 γ = 118 lb/ft
3
,
700
=
′
c
lb/ft
2
,
°
=
′
33
φ
, D
f
= 4.5 ft, B = 6.25 ft, and x = 0.75 ft
168
For vertical load [Eq. (16.44)]:
1
4
all
16.18 γ = 16 kN/m
3
;
0
=
′
c
;
°
=
′
29
φ
, D
f
= 1.3 m; B = 1.75 m; and x = 0.25 m
From Table 16.2:
=
q
N
16.44;
=
γ
N
19.34
1
Eq. (16.48):
( )
(eccentric) (centric) (centric)
1 1
k
u u u k
e
Q Q a Q R
B
= − = −
(eccentric) (centric)
u u k
16.19 γ = 17 kN/m
3
;
0
=
′
c
;
°
=
′
34
φ
, D
f
= 1.2 m; B = 1.8 m; e = 0.3 m; and α = 10°
170
B′ = 1.8 – (2)(0.3) = 1.2 m
Since it is a continuous foundation, all shape factors are equal to one.
1
)(
ueiu
B
′
φ
171
u
q
is the ultimate bearing capacity with vertical centric load. Since it is a
continuous foundation, all shape factors are equal to one.
1
CRITICAL THINKING PROBLEM
C.16.1 The footing is placed at a depth of 1.5 m.
a.
B = 1 m
Eq. (16.49):
=25
)mm(
05.0
60
net
e
d
S
F
N
q
net
25
05.0
172
kN 71
3
)1)(8.212(
3
))((
2
net
net-all
≈== Aq
Q
B = 1.5 m
+
)mm(3.0
2
60
e
S
BN
3
3
net-all
B = 2 m
+
)mm(3.0
2
60
e
S
BN
net
25
2
08.0
173
© 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.
kN 229
3
)2)(7.114(
3
))((
2
net
net-all
≈== Aq
Q
B = 3 m
Eq. (16.50):
+
=25
)mm(3.0
08.0
2
60
net
e
d
S
F
B
BN
q
3
3
net-all
The design chart is shown.
174
b. For any design footing size B,
appliednetall
QQ ≥
−
(1)
c.
φ
′ = 33º; cʹ = 0;
=
q
N
32.33;
=
γ
N
31.94 (Table 16.1); B = 2.25 m
−
netallnet-all
d. The net allowable column load calculated by Terzaghi’s bearing capacity
equation (Part c) is significantly higher than that calculated by the method
Trusted by Thousands of
Students
Here are what students say about us.
Resources
Company
Copyright ©2022 All rights reserved. | CoursePaper is not sponsored or endorsed by any college or university.