rafter foundation calculations

8/21/2019 Rafter Foundation Calculations

1/8

7 0 0 m m

0.5d

( d / 2 + 9 0 0 ) 0

. 5 d

1600 kN

700 mmCorner

(d/2+900)

7 0 0

(d+400)

0.5d

( d / 2 + 9 0 0 )

0.5d400

800 kNSide

Critical sections in shear

(b1) (b2)

(c)

6000 mm 6000 mm 6000 mm700 700

4321

19400 mm

7 5 0 m m

8 0 0 m m

4 -20 mm dia bars @ 260 mm c/c

per meter length of the slab4 legged shear stirrups

(d+400)

400 mm

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).

572 Foundation Design


2/8

Example 12.7 Raft Foundation

Design a raft foundation for the layout of columns shown in Figure 12.C.19(a). All columns are

of square shape of size 40 40 cm. ADSP ¼ 80 kN/m3. Use M 15 concrete and Fe 415 steel.Assume 10% as the load of raft and soil above.

A. Design of Raft Slab

Total vertical column load ¼ ð600 þ 1600 þ 2000 þ 600 þ 800 þ 1800 þ 2000þ 1000 þ 800 þ 1000 þ 1200 þ 600Þ ¼ 14000

Eccentricity along thex direction is obtained by taking moment of column loads about the

grid 1–1

x ¼ 6ð1600 þ 1800 þ 1000Þ þ 12ð2000 þ 2000 þ 1200Þ þ 18ð600 þ 1000 þ 600Þ½

14000

¼ 9:1714 m

ex ¼ 9:1714ð6 þ 3Þ ¼ 0:1714m

Eccentricity along the y direction is obtained by taking moment of column loads about thegrid C–C

700060005000

(c)

(d)

40003000200010000

750

500

2500

-250

-500

-750

S h e a r f o r c e ( i n k N )

70006000500040003000200010000

250

200

150

100

50

0

B e a r i n g p r e s s u r e ( i n k N / m 2 )

Figure 12.C.18 (Continued )



3/8

T a b l e 1 2 . C . 7

C o m p a r a t i v e s t u d y ( s e

e c o m m e n t s i n S e c t i o n 1 2 . C . 2

) .

M a x i m u m b e a r i n g

p r e s s u r e ( k N / m 2 )

M a x i m u m b e n d i n g

m

o m e n t ( k N m )

M a x i m u m

s h e a r

f o r c e ( k N )

M a x i m u m d

e fl e c t i o n ( m m )

C o n v e n t i o n a l

d e

s i g n

W i t h f a c t o r e d

l o a d

6 2 4 . 3

2 3

9 8 7

. 3 2 3

1 0 3 2 . 2 0

6 2 4 . 3

2 3 / 2 8 ¼

1 8 . 0

8

W i t h d e s i g n

l o a d

6 2 4 . 3

2 3 / 1 . 5

¼

4 1 6 . 2

2

9 8 7

. 3 2 3 / 1 . 5 ¼

6 5 8 . 2

2

1 0 3 2 . 2 0

/ 1 . 5 ¼

6 8 8 . 1

3

1 8 . 0

8 / 1 . 5 ¼

1 2 . 0

5

D e s i g

n u s i n g B E F

( w

i t h d e s i g n l o a d o n l y )

2 0 5 . 0

5 0 k N / m 2

a t

x

¼

0 m m

4 4 0

. 5 7 6 k N m a t

x

¼

6 6 8 0 m m ;

2 9 9 . 9

3 7 k N m

a t x

¼

2 2 2 7 m m

6 3 1 . 6 2 8

k N a t

x

¼

6 6 8 0 m m ;

5 6 4 . 4

0 6 k N

a t x

¼

7 2 4 m m

5 . 8

6 m m a t x

¼

0 m m

Structural Design of Foundations 571


4/8

y ¼ 5ð800 þ 1800 þ 2000 þ 1000Þ þ 10ð600 þ 1600 þ 2000 þ 600Þ½

14000 ¼ 5:4285 m

e y ¼ 5:42855 ¼ 0:4285m

I x ¼19:4 11:43

12 ¼ 2395:16 m4

I y ¼11:4 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

A¼

14000

221:16¼ 63:302kN=m2

Soil pressure at different points is as follows

s ¼P

A

M y

I y

x M x

I x

y ð12:C:67Þ

s ¼ 63:302 2400

6936:31x

6000

2395:16 y ¼ 63:158 1:5269x 0:4745 y

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=m2Þ

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 ¼ 63:1580:346 9:72:505 5:7 ¼ 45:67kN=m2

At corner B–4



5/8

s B4 ¼ 63:158 þ 0:346 9:7 ¼ 66:658 kN=m2

At corner B–1

s B

1

¼63:158

0:346

9:7

¼59:943kN=m2

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

2. Beam B–B with 5.0 m width and soil pressure of ð80 þ 66:65Þ

2 ¼ 73:32 kN=m2

3. Beam C–C with 5.0 m width and soil pressure of ð66:65 þ 52:38Þ

2 ¼ 59:52 kN=m2.

The bending moment is obtained by using a coefficient 1/10 and L as the center to center of

column distance

þ M ¼ M ¼ wL 210

ð12:C:68Þ

For strip A–A

Maximum moment ¼ 80 62

10 ¼ 288 kNm=m

For strip B–B

Maximum moment ¼ 73:32 62

10 ¼ 263:95 kNm=m

For strip C–C

Maximum moment ¼ 59:52 62

10 ¼ 214:272 kNm=m

For any strip in the y direction, take M ¼ wL 28

since there is only a two-span equivalent beam.

For strip 4–4

Maximum moment ¼ 80 52

8 ¼ 250 kNm=m

The depth of the raft is governed by two-wayshear at one of the exterior columns. If the location

of critical shear is not obvious, it may be necessary to check all possible locations.

Shear strength of concrete, tc ¼ 0:25 ffiffiffiffiffi f ck p ¼ 0:25 ffiffiffiffiffi 15p ¼ 0:97N=mm2

For a corner column (say C– 1)

Perimeter bo ¼ 2 d 2 þ 900 ¼ d þ 1800 mm (Figure 12.C.19(b))

tv ¼ V ubod

¼ 1:5 800 1000ðd þ 1800Þd ¼ 0:97

¼ 1200000ðd þ 1800Þd ¼ 0:97

) d 2 þ 1800d 1237113:40 ¼ 0



6/8

d ¼1800

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið18002 þ 4 1 1237113:40Þ

q 2 1

¼ 530:773 mm

For a corner column (say A– 2)

Perimeter bo ¼ 2 d

2 þ 900

þ d þ 400ð Þ ¼ 2d þ 2200 mm

tv ¼ V u

bod ¼

1:5 1600 1000

ð2d þ 2200Þd ¼ 0:97

d 2 þ 1100d 1237113:40 ¼ 0 ð12:C:69Þ

) d ¼1100

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið11002 þ 4 1 1237113:40Þ

q 2 1

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)

At ¼ 0:5 15

4151

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

4:6 288 106

15 1000 7502

s 2

4

3

51000 750 ¼ 1109:51 mm2

Use 20 mm bars, Af ¼ 314:151 mm2

Number of bars ¼1109:51

p4

202 ¼ 3:531 ffi 4 bars

Spacing of long bars ¼1000 p

4202

1109:51¼ 283:152 mm

Provide 4–20 mmF bars for reinforcement @ 260 mm c/c at top and bottom in both directions.

Minimum reinforcement in the slabs ¼ 0:12%

¼0:12

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 InputYoung’s modulus of soil, E s ¼ 10

5 kN=m2, unit weight of soil, gsoil ¼ 20 kN=m3.



7/8

Poisson’s ratio of soil, ns ¼ 0:3.Young’s modulus of concrete

E f ¼ 5000 ffiffiffiffiffiffiffisck p ¼ 5000 ffiffiffiffiffi15

p ¼ 19364:92 N=mm2 ¼ 1:9364 107 kN=m2

B¼ breadth of foundation¼ 1.0 m (considering a 1 m wide strip for design).Moment of inertia of the concrete beam I f ¼ Bd 312 ¼ 1:00:8

3

12 ¼ 0:04267 m4.

Modulus of subgrade reaction, k s ¼ 1 BðmmÞ 0:65 ffiffiffiffiffiffiffi

E s B4

E f I f

12

q h i E s1n2s .

k s ¼ 0:651000

105

1 0:32 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

105 1:041:9364 107 0:04267

12

s ¼ 59902

1000 ¼ 59:902 kN=m2=mm:

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)).

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 inFigure 12.C.21. Please see also comments given in Section 12.C.2.

Figure 12.C.20 Loading data for WINBEF solution (Example 12.7).



8/8

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. Thefactored soil pressure under the raft is 80 kN/m2 and a linearly varying soil pressure due to

180001600014000120001000080006000400020000

8.07.57.06.56.05.5

5.04.54.0

3.53.0

D e f l e c t i o

n ( i n m m )

Length of the beam (in mm)

(a)

180001600014000120001000080006000400020000

1000

800

600

400

200

0

-200

-400

-600

B e n d i n g m o m e n t ( i n k N

- m )


(b)

(c)

180001600014000120001000080006000400020000

1000800600400200

0-200-400-600-800

-1000

S h e a r f o r c e ( i n k N )


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).


rafter foundation calculations

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