# Annular Raft

## Full text

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p = P/A p = P/A p' = M/Z p' = M/Z 2. Size of Raft : 2. Size of Raft : C

Ceennttrraal l DDiiaammeetteer r oof f RRaafft t ((22CC)) == 4.804.80mm D

Deepptth h oof f oo!!nnddaattiioon n aa""oo##e e rraafftt == 2.002.00mm D

DeepptthhooffRRaafftt == 0.\$00.\$0mm %

%nniitt&&eeii''hht t oof f CoConnccrreettee == 2525 S

Saaffe e ""eeaarriinn' ' cacappaacciitt** == 200200

%

%nniitt&&eeii''hhttooffSSooiill == 1818 +ei'ht

+ei'ht of of tan tan == 32003200 +

+iinnddmmoommeenntt == 148148,m,m S

Shheeaar r aat t --aae e D!D!e e tto o +iin+ndd == 1./1./ + +iiddtthhooffRRaafftt == 1.81.8mm + +iiddtthhooffccooll!!mmnn == 0.500.50mm D Deepptthhooffccooll!!mmnn == 0.500.50mm o.

o. of of col!mn col!mn == 44nono 

tteerrnnaal l DDiiaammeetteer r oof f RRaafft t ((22aa)) == \$\$..\$\$0000 mm nntteerrnnaal l DDiia a mmeetteer r oof f RRaafft t ((22"")) == 33..000000 mm

3. Calculation

3. Calculation of of Section PSection Properties :roperties : 

rreeaaooffRRaafftt(()) == 22..1144 S

Seeccttiioon n 66oodd!!ll!!  oof f RRaafft t ((77)) == 22..0022

4. Calcula

4. Calculation of Loads tion of Loads (Self wei(Self weigt !Soil" gt !Soil" :: 

aaccttoorreed d SSeellf f &&eeii''hht t oof f rraafftt == \$\$1100..\$\$55  

aaccttoorreed d oof f &&eeii''hht t oof f ooiil l aa""oo##e e rraafftt == //8888..00//2 2   

otal otal actored 9actored 9ertical :oad on Rertical :oad on Raft aft (;)(;) == 4798.744798.74   

otal otal actored 6oment at Rafactored 6oment at Raft (6)t (6) == 151.23151.23 ,m,m

#. Calculation

#. Calculation of of Stresses on Stresses on Soil :Soil : 6

6aa. . SSttrree == ; ; < < 66 

 77

=

= 182.411182.411   = = 1.5 1.5 > > S-C S-C == 3.3.

6

6iinn. . SSttrree == ; ; , , 66   77 = = 171.217171.217 ? 0.0? 0.0 = = !"#\$" O%  !"#\$" O%  @mm @mm22 m m22 m m33 @m @m22 @m@m22 @m @m22

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\$. Calculation %ending Mo&ents and Sears : \$. Calculation %ending Mo&ents and Sears :

a. 'ue to ertical Load: a. 'ue to ertical Load:

p = P/A

p = P/A == 17&.81417&.814 For , For , r < r < cc \$4 \$4 \$4 \$4 p > a p > a 2 2 where where (1 (1 + + μ)μ)  (1 + μ)  (1 + μ)  (  (1 1 - - μμ)) (1 , A)(1 , A) B

B!!tteer r rraaddii!!  oof f rraafft t ((aa)) == 33..33 mm nnnneer r rraaddii!!  oof f rraafft t (("")) == 11..55 mm C

Ceennttrre e lliinne e rraaddii!!  of of rraafft t ((cc)) == 22..44 mm Radi!

Radi! of of re!ired re!ired moment moment from from centre(r) centre(r) == 1.51.5mm

= = 00..445555 = = 00..22 = = 00..445555 = = ,,11..\$\$00 = = ,,//..//44 = = 3300..0088\$\$ \$4 \$4 = = 22..22 = = ,,11..4422 = = 55..445555 = = ,,44..5555 = = ,,3333..//11 = = 841.217841.217 ,m,m = = 3300..0088\$\$ \$4 \$4 = = 11..5500 = = 33..114400 = =  ,m,m = = 159.133159.133 

).'ue to %ending Mo&ent : ).'ue to %ending Mo&ent :

@m @m22 6 6r1r1 = = p > ap > a22  4 > (3< 4 > (3<μ) * ρμ) * ρ22 , , 1\$ 1\$ >>αα22 (1< (1<μ) * μ) * log log ρρ ,  , 8 >8 >αα22 (3< (3<μ)μ)  < 2 >(1<μ) * K  < 2 >(1<μ) * K 11 , , (1,(1,μ) * K μ) * K 22 * ρ * ρ -2 -2 6 611 = = p > ap > a22  4 > (1<3μ) * ρ 4 > (1<3μ) * ρ22 , , 1\$ 1\$ >>αα22 (1< (1<μ) * μ) * log log ρρ ,  , 8 >8 >αα22 > (1<3 > (1<3μ)μ)  < 2 >(1<μ) * K  < 2 >(1<μ) * K 11 < < (1,(1,μ) * K μ) * K 22* ρ* ρ -2 -2 E Er1r1 = = ρρ, (, (αα22 * ρ * ρ-1-1 ) )

F 11 = = 2> ( 1 <2> ( 1 <αα22)* )* (3+μ)(3+μ) , , 8 8 >>αα44* log α* log α , , 4 4 >>ββ22* (1 - μ)* (1 - μ) , , 8 8 > > (1 (1 < lo'< lo'β)β)

(1<

(1<μμ) ) 1 1 ,, αα22

F 11 = = 4 >4 >αα22* * (3 (3 + + μ)μ) , , 1\$ 1\$ >>αα44* log α* log α , , 1\$ 1\$ >>αα22* * (1+ (1+ μ) μ) * (1 * (1 + log + log β)β)  , 8 > , 8 >αα22 > >ββ22

(1 (1 ,,μμ)) 11,, αα22 α α = " @ a = " @ a β β= c @ a= c @ a ρ ρ= r @ a= r @ a F  F 11 F  F 22 i.Caculation of *M i.Caculation of *M** p > a p > a22  4 > (3<  4 > (3<μ) * ρμ) * ρ22 1\$ > 1\$ >αα22 > (1< > (1<μ) * μ) * log ρlog ρ 8 > 8 >αα22 > (3< > (3<μ)μ)  2 >(1<  2 >(1<μ) * K μ) * K 11  (1,  (1,μ) * K μ) * K 22 * ρ * ρ-2-2 M M(( ii.Caculation of *M ii.Caculation of *M** p > a p > a22  4 > (1<3  4 > (1<3μ) * ρμ) * ρ22 8 > 8 >αα22 > (1<3 > (1<3μ)μ) M M)) iii.Caculation of *+ iii.Caculation of *+** * *((

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p > a p > a 1/2 1/2 * (2 + μ) * (2 + μ) (3 (3 + + μ)μ) = = ,,00..443388 = = ,,22..000044 = = 00..551122 = = 00..3311 1/2 1/2 = = 11..////11 = = ,,11..331133 = = ,,22//..88\$\$// = = 00..88// = = +9.1&+9.1& ,m,m = = 00..//33// = = ,,00..55\$\$ = = 9.7919.791 ,m,m = = 2.8952.895 ,m,m ,otal: ,otal: == = = 832832.2.211 ,N+,N+- -= =  ,N,N+- +-S

Shheeaar r ((EE) ) = = a a < < "" == 1&21&2.2.288 ,N,N

-. Cec for /0ectie 'ept : -. Cec for /0ectie 'ept :

R

Ree!!iirreed d eeeeccttii##e e ddeepptth h ((dd)) == 66

=

= 33\$\$\$\$..003 m3 mmm

;

;rroo##iiddeed d eeeeccttii##e e ddeepptth h ((dd)) == \$\$0000 , , 5500..0000 , , 1100..0000 =

= 54.54. mmmm !"#\$" O%

!"#\$" O%

.

. Calculation of Calculation of Reinforce&ent Reinforce&ent :: i. Circumferential Reinforcement: i. Circumferential Reinforcement: = = 883322..220011 HHHHHH 1800. 1800.0000   540.0 I2540.0 I2 = = 1.58&1.58& E Err = = 22>>ρρ 2 2 + 8 + 8 > F  > F  3 3 , 2 , 2* K * K 55 * ρ * ρ -1 -1 F  F 33 = = 3 3 , , 3 3 >>ββ22  (1-μ)  (1-μ)   ,   , 8 8 > 1 <> 1 < αα44 β β22 (3 <(3 <μμ 1 <1 < αα F  F 44 = = 3 >3 >ββ22 *α *α44 , 3 > , 3 >αα44* * (3+μ)(3+μ) , , 8 8 >> αα44 > > (2 (2 < < A)A) β β22 ( ( 1 1 << αα22 (1 - μ)(1 - μ) F  F 55 = = 12 12 >> αα44 F  F 33 F  F 44 F  F 55 i.Caculation of *M i.Caculation of *M** p > a p > a22  4 > (5<  4 > (5<μ) * ρμ) * ρ33  2 > (3<  2 > (3<μ) * K μ) * K 33* ρ* ρ  2 > (1,  2 > (1,μ) * K μ) * K 44* ρ* ρ-3-3  (1<  (1<μ) * K μ) * K 55 * ρ * ρ-1-1 M M(( ii.Caculation of *M ii.Caculation of *M**  4 > (1<5  4 > (1<5μ) * ρμ) * ρ33  2 >(1<3  2 >(1<3μ) * K μ) * K 33 * ρ * ρ M M)) iii.Caculation of *+ iii.Caculation of *+** * *((  6oment (6  6oment (6rr) = a < ") = a < "  6oment (6  6oment (6tt) = a < ") = a < " 0.138 > f  0.138 > f cc > " > " 6 6!!@"d@"d 2 2

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D

Deeii''nneed d rreea a oof f tteeeell == 4529.3784529.378 ;

;rroo##iiddeed d DDiiaammeetteer r oof f ""aarr == 2020mmmm 

rreea a oof f ""aarr == 331144..1155//

S Sppaacciinn' ' == 331144..1155// HHHHHH 452/.38 452/.38 = = \$\$//..33\$\$00 mmmm or a* or a* 1.1.mmmm ;

;rroo##iiddeed d rreea a oof f tteeeell == 3141.5933141.593

= = 111144..445500 HHHHHH 1800 1800.000.000   540.540.0 0 I2I2 = = 2.18&2.18&  R

Ree!!iirreed d rreea a oof f tteeeell == 3355//88..115533

6

6iinn. . rreea a oof f SStteeeell == 0.10.1 HHHHHH  54 540.00.000 100 100 = = //22..000000 P(0" D"0# R"0#(\$"-"#). P(0" D"0# R"0#(\$"-"#). D

Deeii''nneed d rreea a oof f tteeeell == 3598.1533598.153 ;

;rroo##iiddeed d DDiiaammeetteer r oof f ""aarr == 2020mmmm 

rreea a oof f ""aarr == 331144..1155//

S Sppaacciinn' ' == 331144..1155// HHHHHH 35/8.153 35/8.153 = = 88..331111 mmmm or a* or a* 1.1.mmmm ;

;rroo##iiddeed d rreea a oof f tteeeell == 3141.5933141.593

. Cec for Sear : . Cec for Sear :

D

Deeii''n n SShheeaar r ((EE)) == 11\$\$22..002288 

= = 11\$\$22..002288 HHHHHH 180 1800.00.00000  540 540.00.00 = = 00..11\$\$ = = 11000 0 > > tt " " > d> d = = 110000..000000 HHHHHH 180 1800.00.00000  5 540.40.0000 = = 00..332233 JJ Table-19 of IS:4!-"###: Table-19 of IS:4!-"###: pt pt 0 0..2255 00..2233 0 0..55 00..3311 = = .253.253 !"#\$" O%  !"#\$" O%  mm mm22 mm mm22 mm mm22 6 6!!@"d@"d22 mm mm22 mm mm22 mm mm22 mm mm22 mm mm22

ominal Shear tre ( ominal Shear tre (ττ##))

@mm @mm22

J of Steel (p J of Steel (ptt))

ττcc

;ermii"le Shear tre (

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### DESIGN OF ANNULAR RAFT :

1. Materials :

1. Materials :

G

Grraadde e oof f CCoonnccrreettee == 2525

G

= = 0.30.3 p = P/A p = P/A p' = M/Z p' = M/Z 2. Size of Raft : 2. Size of Raft : C

Ceennttrraal l DDiiaammeetteer r oof f RRaafft t ((22CC)) == 4.804.80mm D

Deepptth h oof f oo!!nnddaattiioon n aa""oo##e e rraafftt == 2.002.00mm D

DeepptthhooffRRaafftt == 0.\$00.\$0mm %

%nniitt&&eeii''hht t oof f CoConnccrreettee == 2525 S

Saaffe e ""eeaarriinn' ' cacappaacciitt** == 200200

%

%nniitt&&eeii''hhttooffSSooiill == 1818 +

+eeii''hhttooffaann == 32003200 +

+iinnddmmoommeenntt == 148148,m,m S

Shheeaar r aat t --aae e D!D!e e tto o ++iinndd == 1./1./ +

+iiddtthhooffRRaafftt == 1.81.8mm 

tteerrnnaal l DDiiaammeetteer r oof f RRaafft t ((22aa)) == \$\$..\$\$0000 mm nntteerrnnaal l DDiia a mmeetteer r oof f RRaafft t ((22"")) == 33..000000 mm +

+iiddtthhooffccooll!!mmnn == 0.500.50mm D

Deepptthhooffccooll!!mmnn == 0.500.50mm o.

o. of of col!mn col!mn == 44nono

3. Calculati

3. Calculation of on of Section PSection Properties :roperties : 

rreeaaooffRRaafftt(()) == 22..1144 S

Seeccttiioon n 66oodd!!ll!!  oof f RRaafft t ((77)) == 22..0022

4. Calculation o

4. Calculation of Loads (Self weigt !Sof Loads (Self weigt !Soil" :il" : 

aaccttoorreed d SSeellf f &&eeii''hht t oof f rraafftt == \$\$1100..\$\$55  

aaccttoorreed d oof f &&eeii''hht t oof f ooiil l aa""oo##e e rraafftt == //8888..00//2 2   

otal otal actored 9actored 9ertical :oad on Rertical :oad on Raft aft (;)(;) == 4798.744798.74   

otal otal actored actored 6oment d!e to &ind 6oment d!e to &ind at Raft (6)at Raft (6) == 151.23151.23 ,m,m

#. Calculation %ending Mo&ents and Sears : #. Calculation %ending Mo&ents and Sears :

a. 'ue to ertical Load: a. 'ue to ertical Load:

p = P/A

p = P/A == 17&.81417&.814 For , For , r \$ r \$ cc \$4 \$4 \$4 \$4 p > a p > a @mm @mm22 @mm @mm22 ;oion rario ( ;oion rario (μμ)) @mm @mm22 m m22 m m33 @m @m22 6 6r2r2 = = p > ap > a22  4 > (3< 4 > (3<μ) * ρμ) * ρ22 , , 1\$ 1\$ >α22 (1< (1<μ) * μ) * log log ρρ , , 8 8 > > (3<(3<μ)μ)  < 2 >(1< < 2 >(1<μ) * K'μ) * K'11 , , (1,(1,μ) * K'μ) * K'22 * ρ * ρ-2-2 6 622 = = p > ap > a22  4 > (1<3 4 > (1<3μ) * ρμ) * ρ22 , , 1\$ 1\$ >α22 (1< (1<μ) * μ) * log log ρρ , , 8 8 >(1<3>(1<3μ)μ)  < 2 >(1< < 2 >(1<μ) * K'μ) * K'11 , , (1,(1,μ) * K'μ) * K'22* ρ* ρ-2-2 E Er2r2 = =  ( (ρρ,, ρρ-1-1)) c c " " a a

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where where

B

B!!tteer r rraaddii!!  oof f rraafft t ((aa)) == 33..33 mm nnnneer r rraaddii!!  oof f rraafft t (("")) == 11..55 mm C

Ceennttrre e lliinne e rraaddii!!  of of rraafft t ((cc)) == 22..44 mm Radi!

Radi! of of re!ired re!ired moment moment from from centre(r) centre(r) == 3.33.3mm

= = 00..445555 = = 00..22 = = 11..000000 = = 33..1100 = = ,,1133..333311 = = 3300..0088\$\$ \$4 \$4 = = 1133..220000 = = 00..000000 = = 22\$\$..440000 = = //..\$\$4455 = = ,,//..333322 = = 173.85 ,m173.85,m = = 3300..0088\$\$ \$4 \$4 = = ..\$\$0000 = = 1155..220000 = = +219.214+219.214 ,m,m = = .. 

).'ue to %ending Mo&ent : ).'ue to %ending Mo&ent : p' = M/Z p' = M/Z == 5.5975.597 For , For , r \$ r \$ cc 1/2 1/2 1/2 1/2 p > a p > a 1/2 1/2 F F11 = = F F 11< 8 < 8 >( >( 1 1 << log β ) * log β ) * ( 1 - α( 1 - α22)) F F22== F F 22 , , ( ( 8 8 >> β β22 ) * ( 1 - α ) * ( 1 - α22)) α α = " @ a = " @ a β β= c @ a= c @ a ρ ρ= r @ a= r @ a F F11 F F22 i.Caculation of *M i.Caculation of *M** p > a p > a22  4 > (3<  4 > (3<μ) * ρμ) * ρ22 1\$ > (1< 1\$ > (1<μ) μ) * * log ρlog ρ 8 > (3< 8 > (3<μ)μ)  2 >(1<  2 >(1<μ) * K'μ) * K'11  (1,  (1,μ) * K'μ) * K'22 * ρ * ρ-2-2 M M(( ii.Caculation of *M ii.Caculation of *M** p > a p > a22  4 > (1<3  4 > (1<3μ) * ρμ) * ρ22 8 > (1<3 8 > (1<3μ)μ) M M)) iii.Caculation of *+ iii.Caculation of *+** * *(( @m @m22 6 6rr = = p p > > aa22  4 > (5< 4 > (5<μ) * ρμ) * ρ33 < < 2 2 >(3<>(3<μ) * K'μ) * K' 3 3 * ρ * ρ  < 2 > (1, < 2 > (1,μ) * K'μ) * K'44 * ρ * ρ -- < (1< < (1<μ) * K'μ) * K' 5 5 * ρ * ρ -1 -1 6 6rr = = p p > > aa22  4 > (1<5 4 > (1<5μ) * ρμ) * ρ33 < < 2 2 >(1<3>(1<3μ) * K'μ) * K' 3 3 * ρ * ρ  , 2 > (1, , 2 > (1,μ) * K'μ) * K'44 * ρ * ρ -3 -3  < (1< < (1<μ) * K'μ) * K' 5 5 * ρ * ρ -1 -1 E Err = = 22>>ρρ22 + 8 + 8 > F > F 3 3 , , 22* K'* K'55 * ρ * ρ -1 -1 F F33 =  = F F 33 , , 33 * * ( ( 1 1 - - αα44)) β β22 F F44 = = F F 44  <   < 3 3 >>ββ22 (1 - α (1 - α44 ) )

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Cancel Anytime. = = ,,55..88\$\$ = = ,,00..448855 = = 12.00012.000 = = 00..3311 1/2 1/2 = = 2211..220000 = = ,,3388..2255 = = ,,00..\$\$88 = = 88..440000 = = +3.112+3.112 ,m,m = = 1100..000000 = = ,,2222..22//\$\$ = = +1.22+1.22 ,m,m = = .337.337 ,m,m ,otal: ,otal: == = = 1717.&.&9393 ,N+,N+- -= = +22+22.23&.23& ,N+- ,N+-S Shheeaar r ((EE) ) = = a a < < "" == ..333377 ,N,N

\$. Cec for /0ectie 'ept : \$. Cec for /0ectie 'ept :

R

Ree!!iirreed d eeeeccttii##e e ddeepptth h ((dd)) == 66

0.138 > fc > " 0.138 > fc > "

=

= 11\$\$55..//1 m1 mmm

;

;rroo##iiddeed d eeeeccttii##e e ddeepptth h ((dd)) == \$\$0000 , , 5500..0000 , , 1100..0000 =

= 54.54. mmmm !"#\$" O%

!"#\$" O%

-. Calculation of

-. Calculation of ReinReinforce&ent :force&ent : i.

i. CircumferenCircumferential tial ReinforcemeReinforcement:nt:

= = 1100..\$\$//33 HHHHHH 1800 1800.00.00   540.0 I2540.0 I2 = = .325.325 F F33 F F44 F F55 i.Caculation of *M i.Caculation of *M** p > a p > a22  4 > (5<  4 > (5<μ) * ρμ) * ρ33  2 > (3<  2 > (3<μ) * K'μ) * K'33* ρ* ρ  2 > (1,  2 > (1,μ) * K'μ) * K'44* ρ* ρ-3-3  (1<  (1<μ) * K'μ) * K'55 * ρ * ρ-1-1 M M(( ii.Caculation of *M ii.Caculation of *M**  4 > (1<5  4 > (1<5μ) * ρμ) * ρ33  2 >(1<3  2 >(1<3μ) * K'μ) * K'33 * ρ * ρ M M)) iii.Caculation of *+ iii.Caculation of *+** * *((  6oment (6  6oment (6rr) = a < ") = a < "  6oment (6  6oment (6tt) = a < ") = a < " 6 6!!@"d@"d22

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= = 222200..2233\$\$ HHHHHH 1800 1800.000.000   540.540.0 0 I2I2 = = .42.42  R

Ree!!iirreed d rreea a oof f tteeeell == \$\$22\$\$..228800

6

6iinn. . rreea a oof f SStteeeell == 0.10.1 HHHHHH  5 54040.00.00 100 100 = = //22..000000 P(0" M0#0-- R"0#(\$"-"#)6 P(0" M0#0-- R"0#(\$"-"#)6 D

Deeii''nneed d rreea a oof f tteeeell == 972.972. ;

;rroo##iiddeed d DDiiaammeetteer r oof f ""aarr == 2020mmmm 

rreea a oof f ""aarr == 331144..1155//

S Sppaacciinn' ' == 331144..1155// HHHHHH /2.000 /2.000 = = 332233..2200/ m/ mmm or a* or a* 1.1.mmmm ;

;rroo##iiddeed d rreea a oof f tteeeell == 3141.5933141.593

. Cec for Sear : . Cec for Sear :

D

Deeii''n n SShheeaar r ((EE)) == 00..3333 

= = 00..3333 HHHHHH 180 1800.00.00000  540 540.00.00 = = 00..000000 = = 11000 0 > > tt " " > d> d = = 110000..000000 HHHHHH 180 1800.00.00000  5 54040.00.00 = = 00..332233 JJ Table-19 of IS:4!-"###: Table-19 of IS:4!-"###: pt pt 0 0..2255 00..2233 0 0..55 00..3311 = = .253.253 !"#\$" O%  !"#\$" O%  6 6!!@"d@"d22 mm mm22 mm mm22 mm mm22 mm mm22 mm mm22

ominal Shear tre ( ominal Shear tre (ττ##))

@mm @mm22

J of Steel (p J of Steel (ptt))

ττcc

;ermii"le Shear tre (

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