570
Foundation Design
-750 ) -500 N k n-250 i ( e 0 c r o f r 250 a e h S 500
750 0
1000
2000
3000
4000
5000
6000
7000
(c) 0
) m / N 50 k n i ( 100 e r u s s 150 e r p g n 200 i r a e B
2
250 0
1000
2000
3000
Figure 12.C.18
Examp Example le 12.7 12.7
4000 (d)
5000
6000
7000
(Continued )
Raft Raft Founda Foundatio tion n
Desi Design gn a raft raft foun foundat datio ion n for for the the layo layout ut of colu column mnss show shown n in Figur Figuree 12.C 12.C.1 .19( 9(a). a). All All colu column mnss are are 3 of square shape of size 40 40 cm cm.. ADSP ¼ 80 kN/m kN/m . Use M 15 concrete and Fe 415 steel. Assume 10% as the load of raft and soil above. A. Design Design of Raft Raft Slab
Total vertical column load ¼ ð600 þ 1600 þ 2000 þ 600 þ 800 þ 1800 þ 2000
þ 1000 þ 800 þ 1000 þ 1200 þ 600Þ ¼ 14000 Eccentr Eccentrici icity ty along along the x direc directi tion on is obta obtain ined ed by taki taking ng mome moment nt of column column load loadss about about the the grid 1–1
x ¼
½6ð1600 þ 1800 þ 1000Þ þ 12 ð2000 þ 2000 þ 1200Þ þ 18 ð600 þ 1000 þ 600 Þ 14000
1714 m ¼ 9:1714
ex ¼ 9:1714ð6 þ 3 Þ ¼ 0:1714m Eccentricity along the y direction is obtained by taking moment of column loads about the grid C–C
571
Structural Design of Foundations
) m m ( n o i t c e fl e d m u m i x a M
) N k m ( u e m c r i o x f a r M a e h s
g n ) i d m n e N b k ( m t u n e m i m o x a m . M ) 2 . C . 2 1 n o g ) i n t i c m e r / S a e N n b k i ( s m e t u r n m u e i s s m x e a m M r p o c e e s ( y d u t s e v i t a r a p m o C
8 0 . 8 1 ¼
8 2 / 3 2 3 . 4 2 6
5 0 . 2 1 ¼
5 . 1 / 8 0 . 8 1
3 1 . 8 8 6 ¼
0 2 . 2 3 0 1
5 . 1 / 0 2 . 2 3 0 1
2 2 . 8 5 6 ¼
3 2 3 . 7 8 9
5 . 1 / 3 2 3 . 7 8 9
¼
x
t a m m 6 8 . 5
; m m N k m t a m 6 4 0 2 N 8 0 . 7 k 6 4 4 ¼ 8 6 6 x 2 ¼ 5 6 t . 1 x a 3 6
; m m t m a m N k 7 m 7 2 m 0 2 2 N 8 3 9 . k 6 9 ¼ 6 6 9 x 7 ¼ 2 5 t . 0 x a 4 4
t a
2
7 . C . 2 1 e l b a T
m m 0
2
3 2 3 . 4 2 6
m / 5 . 2 2 N m . m 1 / 6 k 0 3 1 0 2 4 5 ¼ 3 0 . . 4 ¼ 5 x 2 0 6 2
d e n r g o i t s c e a d d f a d a o h o h l l t t i i W W l a n o i t n g i n e s e v d n o C
) y l n o d a F l o E B n g g i n s e i s d u h n t i g w i ( s e D
572
Foundation Design
(d/2+900)
Side d 5 . 0
m m 0 0 7
Corner
400
0 0 7
0.5d
800 kN
0.5d 1600 kN
0.5d
) 0 0 9 + 2 / d (
) 0 0 9 + 2 / d (
400 mm
(d+400)
700 mm
(d+400)
(b1)
(b2)
Critical sections in shear 1 700
2 6000 mm
3 6000 mm
4 6000 mm
700
m m m m 0 0 5 0 7 8
19400 mm
4 -20 mm dia bars @ 260 mm c/c per meter length of the slab
4 legged shear stirrups
(c)
Figure 12.C.19 Raft layout and column loads; (b1) critical section in shear; (b2) critical section in shear; and (c) details of reinforcement along the longitudinal section (Example 12.7).
Structural Design of Foundations
y ¼
573
½5ð800 þ 1800 þ 2000 þ 1000Þ þ 10ð600 þ 1600 þ 2000 þ 600Þ 14000
¼ 5:4285 m
e y ¼ 5:42855 ¼ 0:4285m
19:4 11:43 I x ¼ ¼ 2395:16 m4 12 I y ¼
11:4 19:43 12
¼ 6936:31 m4
A ¼ 19:4 11:4 ¼ 221:16 m2 M x ¼ pe y ¼ 14000 0:4285 ¼ 6000 kNm
ð12:C:65Þ
M y ¼ pex ¼ 14000 0:1714 ¼ 2400 kNm
ð12:C:66Þ
P A
¼
14000 ¼ 63:302kN=m2 221:16
Soil pressure at different points is as follows s
s
¼ 63:302
¼
P A
M y I y
x
M x y I x
ð12:C:67Þ
2400 6000 x y ¼ 63:158 1:5269x 0:4745 y 6936:31 2395:16
At corner A–4 s A4
¼ 63:158 þ 0:346 9:7 þ 2:505 5:7 ¼ 80:93 ffi BC of soil ð80kN=m2 Þ
At corner C –4 sC 4
¼ 63:158 þ 0:346 9:72:505 5:7 ¼ 74:225 kN=m2
At corner A–1 s A1
¼ 63:1580:346 9:7 þ 2:505 5:7 ¼ 52:38kN=m2
At corner C –1 sC 1
At corner B–4
¼ 63:1580:346 9:72:505 5:7 ¼ 45:67kN=m2
Foundation Design
574
s B
4 ¼ 63:158 þ 0:346 9:7 ¼ 66:658 kN=m2
At corner B–1
1 ¼ 63:1580:346 9:7 ¼ 59:943kN=m2
s B
In the x direction, the raft is divided in three strips, that is three equivalent beams: 1. Beam A–A with 3.2 m width and soil pressure of 80 kN=m2
ð80 þ 66 :65Þ ¼ 73:32 kN=m2 2 ð66:65 þ 52 :38Þ ¼ 59:52 kN=m2 . Beam C–C with 5.0 m width and soil pressure of
2. Beam B–B with 5.0 m width and soil pressure of 3.
2
The bending moment is obtained by using a coefficient 1/10 and L as the center to center of column distance wL 2 12:C:68 M M 10
þ ¼ ¼
ð
Þ
For strip A–A 2
6 ¼ 288 kNm=m Maximum moment ¼ 10 80
For strip B–B Maximum moment
¼
73:32 62 10
¼ 263:95 kNm=m
For strip C–C
¼ For any strip in the y direction, take M ¼ Maximum moment
For strip 4–4
59:52 62 10
¼ 214:272 kNm=m
wL 2 8
since there is only a two-span equivalent beam. 2
5 ¼ 250 kNm=m Maximum moment ¼ 8 80
The depth of the raft is governed by two-way shear at one of the exterior columns. If the location of critical shear is not obvious, it may be necessary to ffiffiffiffiffi check all possible locations. ffiffiffiffiffi Shear strength of concrete, tc 0:25 f ck 0:25 15 0:97N=mm2 For a corner column d (say C– 1) Perimeter b o 2 2 900 d 1800 mm (Figure 12.C.19(b))
¼
þ
tv
¼ p ¼ p ¼ ¼ þ 1000 ¼ 0:97 ¼ bV d ¼ 1:5ðd þ800 1800Þd u
o
¼ ð d 1200000 þ 1800Þd ¼ 0:97 2
) d þ 1800d 1237113:40 ¼ 0
Structural Design of Foundations
d ¼
1800
575
q ffiffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ð18002 þ 4 1 1237113:40Þ 21
¼ 530:773 mm
For a corner column (say A– 2)
Perimeter bo ¼ 2
tv ¼
d
V u bo d 2
d
) d ¼
1100
2
þ 900
¼
þ ðd þ 400Þ ¼ 2d þ 2200 mm
1:5 1600 1000
ð2d þ 2200Þd
¼ 0:97
þ 1100d 1237113:40 ¼ 0
ð12:C:69Þ
q ffiffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ð11002 þ 4 1 1237113:40Þ 21
¼ 690:811 mm
However, adopt an effective depth of 750 mm and overall depth of 800 mm Reinforcement in the longitudinal direction is given by (considering a 1 m wide strip)
2 s ffiffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi3 4 5
15 1 At ¼ 0:5 415
1
4:6 288 106
2
15 1000 750
1000 750 ¼ 1109:51 mm2
Use 20 mm bars, Af ¼ 314:151 mm2
Number of bars ¼
1109:51
Spacing of long bars ¼
p 202 4
¼ 3:531 ffi 4 bars
1000 p4 202 1109:51
¼ 283:152 mm
Provide 4–20 mm F bars for reinforcement @ 260 mm c/c at top and bottom in both directions. Minimum reinforcement in the slabs ¼ 0:12% 0:12
¼
100
800 1000
¼ 960 mm2 =m < 1109:51 mm2 =m Minimum steel governs in the remaining raft. Critical sections in shear.
WINBEF Solution:
WINBEF Input
Young’s modulus of soil, E s ¼ 105 kN=m2 , unit weight of soil, gsoil ¼ 20 kN=m3 .
576
Foundation Design
Poisson’s ratio of soil, ns 0:3. Young’s modulus of concrete
¼
p ¼ 5000p ¼ 5000 15 ¼ 19364:92 N=mm ¼ 1:9364 10 kN=m B ¼ breadth of foundation ¼ 1.0 m (considering a 1 m wide strip for design). Moment of inertia of the concrete beam I ¼ ¼ : : ¼ 0:04267 m . Modulus of subgrade reaction, k ¼ ð Þ 0:65 . E f
ffiffi ffi
ffiffi ffi ffi
sck
2
f
k s
¼
1 0 0 83 12 4 E s B E s E f I f 1 n2s
1 B mm
105
12
1:9364
12
1:04
7
10
2
4
h q ffiffi ffi ffi i s ffiffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi s
0:65 105 1000 1 0:32
Bd 3 12
7
59902 ¼ 0:04267 1000 ¼ 59:902 kN=m =mm: 2
Loading Data for WINBEF and Results
The loading data is shown in Figure 12.C.20. Note: In the loading diagram, the load coming on to the beam is taken as maximum of A, B and C strip loads as explained below (see Figure 12.C.19(a)).
Figure 12.C.20
Loading data for WINBEF solution (Example 12.7).
The maximum load on strip 1–1: maximum of A1 (600 kN), B1 (800 kN) and C1 (800 kN), which is 800 kN. The maximum load on strip 2–2: maximum of A2 (1600 kN), B2 (1800 kN) and C2 (1000 kN), which is 1800 kN. The maximum load on strip 3–3: maximum of A3 (2000 kN), B3 (2000 kN) and C3 (1200 kN), which is 2000 kN. The maximum load on strip 4–4: maximum of A4 (600 kN), B4 (1000 kN) and C4 (1000 kN), which is 1000 kN. The details of deflection, bending moment, shear force and bearing pressure are shown in Figure 12.C.21. Please see also comments given in Section 12.C.2.
577
Structural Design of Foundations
3.0 3.5 ) m4.0 m4.5 n i ( 5.0 n 5.5 o i t c 6.0 e l f 6.5 e D7.0 7.5 8.0 0
2000 4000 6000 8000 10000 12000 14000 16000 18000 Length of the beam (in mm) (a)
) m -600 N -400 k n -200 i ( 0 t n e 200 m o 400 m g 600 n i d 800 n e 1000 B
0
2000 4000 6000 8000 10000 12000 14000 16000 18000 Length of the beam (in mm) (b)
-1000 -800 ) -600 N k -400 n i ( -200 e 0 c r 200 o f r 400 a e h 600 S 800 1000 0
2000 4000 6000 8000 10000 12000 14000 16000 18000 Length of the beam (in mm) (c)
Figure 12.C.21 (a) BEF deflection diagram; (b) BEF bending moment diagram; (c) BEF shear force diagram; and (d) BEF bearing pressure diagram (Example 12.7).
Example 12.8
Annular Raft Foundation
Design an annular (circular) raft for a circular tank whose outer diameter is 12 m and is supported by a ring beam of 9 m diameter. The inner diameter of the annulus is 8 m. The factored soil pressure under the raft is 80 kN/m2 and a linearly varying soil pressure due to
