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DESIGN OF BOX TYPE CULVERT
1 In side diamentions 3.50 m x 3.50 m
2 Super imposed load 12000
3 Live load 45000
4 Wieght of soil 180005 Angle of repose 30 Degree
6 ominal !over top " #ottom 50 mm ominal !over side 50 mm
6 $o!rete %& 20 't( of !on!rete 25000
7 m 13
) Steel 415 150 190
* +hi!,ess of side 'all 330 mm thi!,ness of side 'all is -.
+hi!,ness of top sla# 320 mm -(.(
+hi!,ness of #ottom sla# 350 mm
/ Reinforcement
+op sla# %ain 20 130 mm !"!
Distri#ution 8 130 mm !"!
At supports 8 200 mm !"!
0ottom sla# %ain 20 120 mm !"!
Distri#ution 8 120 mm !"!
At supports 8 300 mm !"! +hrough out sla# at #ottom
Side verti!al 'all erti!al 20 300 mm !"! 0oth side -(.(
Distri#ution 8 130 mm !"!
2 26 mm !"!
* 2 mm $"$
* 13 mm $"!
32
) 2
2 13 mm $"$
3 mm $"$
3(5
*
13 mm $"$
2
12 mm !"!
35
2 * *
24 mm !"! 2 mm $"$ 13 mm $"!
"m3
"m2
"m2
,g"m3
σ!#! "m
2
ater side σst "m2 σ
st "m2
mm Φ
mm Φ
mm Φ
mm Φ
mm Φ
mm Φ
mm Φ
mm Φ
mm Φ
mm Φ
mm Φ
mm Φ
mm Φ
mm Φ
mm Φ
mm Φ mm Φ mm Φ
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p,nand'anaahoo(!o(in
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DSI7 -8 0-9 +:; $ along 'ith the externalloads> Due to smmetr> half offrame ?i(e( AEFD@ of #ox !ulvert is!onsidered for moment distri#ution(Sin!e all the mem#ers have uniformthi!,ness> and uniform diamentions>
the relative stiffness . for AD 'ill#e eFual to 1 'hile the relativestiffness for AE and DF 'ill #e 1"2(
"m2
"m2
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1C 2"3
1"2C 1"3
11"2 11"2
8ix end moments 'ill #e as under G CEEE x 3(*2
&)/346 & m12 12
CEEE x 3.82
/*)51(/ & m12 12
WL Where W is the total tringular earth pressure(12 15
1/ x 3(*2 EEE x 3(*2
x3.82
C 34254 &m12 2 15
& &WL
12 15
&1/ x 3(*2 EEE x 3(*2
x3.82
C &2315 &16)23 C &3/12 2 10
The !"e#$ %&'$(&)*$&!# &' +,((&e% !*$ ,' &--*'$(,$e $,)-e
Fixed End Moments
%em#er D$ DA AD A0 55)5 6525
/*)51(/1 &3/*2* 34254 &)/346 46*52
Hoint D A 12462)(5 1246
%em#er D$ DA AD A0 46*5255)5
Distri#ution fa!tore (33 (6) (6) (33 1/
8ix end moment /*)51(/1 &3/*2* 34254 &)/346 A A
0alan!e &1/641 &3/2*3 361 1531 55)5 1(/1
$arr over 1531 &1/641)1/)
#alan!e &51 &12 13/4 654) 3(*2 m
$arr over 654) &51
#alan!e &21*2 &4365 334 16) )123 1(/1
$arr over 16) &21*2 22/2 D D
#alan!e &55) &1113 1455 )2) 41/2 6/*1)123
$arr over )2) &55)
#alan!e &242 &4*5 3)1 1*6 155514 155
$arr over 1*6 &242 6/*1
#alan!e &62 &124 162 *1
$arr over *1 &62 *12*
#alan!e &2) &54 41 21 8ig 2
$arr over 21 &2)
#alan!e &) &14 1* /
8inal moment 71023 71023 55075 55075
8or horiBontal sla# A0> !arring
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en!e > hd C? 1/ EEE @x 3(*3 & EEE C /9810
2
8ree 0(%( at mid point C6525 x 3(*3
119/44 &m*
et 0(%( at C 11/644 & 55)5 C /45/9 &m
Similarl> free 0(%( at 8 C*12*(2245 x 3(*3
14*/4 &m*
et 0(%( at 8 C 14*/4(416 & )123 C 77881 &m8or verti!al mem#er AD > Simpl supported 0(%( At mid span
impl supporetd at mid sapn1/ x 3(*3
1"16 x EEE x 3(*3 55*52*
et 0(%( C)123 55)5
C 634/ & EEE C 7197 &m2
3 Case 2 : Dead load and live load from out side and water pressure from inside.
In this !ase > 'ater pressure having an intensit of Bero at A and 9800 x 3(*2 C 3)436
' C 6525
1/ 1/ 1/
Itensit C 1/ A 0 14516
And C 41/2 & 3)436
C 44*4 3(*3
3(*2
D 8 $
41/2 41/2 44*4
' C *12*
8ig 3
8ix end moments 'ill #e as under GC EEE x 3(*3
797/2 & m12 12
CEEE x 3.83
992/9./ & m12 12
WL Where W is the total tringular earth pressure(
12 1
44*4 x 3(*3 EEE x 3(*3
x3.83
C 1/128 &m12 2 10
& &WL
12 15
&44*4 x 3(*3 EEE x 3(*3
x3.83
C 12579 &m12 2 15
The "!"e#$ %&'$(&)*$&!# &' +,((&(e% !*$ ,' &--*'$(e% $,)-e.
Fixed End Moments
%em#er D$ DA AD A0 456/ 6525
//26/(61 &125)/ 1612* &)/)62 23451
Hoint D A 12462)(5 1246
%em#er D$ DA AD A0456/
Distri#ution fa!tore (33 (6) (6) (33 1/ 234518ix end moment //26/(61 &125)/ 1612* &)/)62 A A
0alan!e 2**/) 5))/4 42423 21211 456/ 1 /1
p,nand'anaahoo(!o(in
2C
2C
22C
"m2
At D> is a!ting> in addition to the pressure!onsidered in !ase 1( +he various pressuresare mar,ed in fig 3 (+he verti!al 'alls 'ill thus#e su#e!ted to a net latral pressure of
"m2
"m2 At the +op
"m2 at the #ottom
"m2
%8A0
C'L2 2C
%fd!
C'L2 2C
%8AD
CpL2
%8AD
C2
%8DA
CpL2
%8DA
C2&
+he moment distri#ution !arried out as per ta#le 1 for +,'e 1
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#alan!e &)) &14141 1/265 /632 3(*2
$arr over /632 &))
#alan!e &3211 &6422 4)14 235) 5**13 1(/1
$arr over 235) &3211 44*4 D D
#alan!e &)*6 &15)1 2141 1) 21445**13
$arr over 1) &)*6
#alan!e &35) &)14 524 262 1551* 155
$arr over 262 &35) 2144
#alan!e &*) &1)5 23* 11/
$arr over 11/ &*) *12*
#alan!e &4 &)/ 5* 2/ 8ig 4
$arr over 2/ &4
#alan!e &1 &1/ 26 13
8inal moment 5**13 &5**13 456/ &456/
8or horiBontal sla# A0> !arring
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arth pressure intensit at top C 4 3)436 'C *12* 3)436
8ig 5
arth pressure intensit at 0ottomC 4 6 x 3(*2 C 26/2
In addition to these> the verti!al 'all lsla# su#e!tednto 'ater pressure of intensit K=- at top and 3)4
"m2 at 0ottom> a!ting from inside ( +he lateral pressure on verti!al 'alls Is sho'n in fig 5 and 6
8ix end moments 'ill #e as under G CEEE x 3(*3
797/2 & m12 12
CEEE x 3.83
992/9./ & m12 12
&WL Where W is the total tringular earth pressure(
12 15
4 x 3(*3 EEE x 3(*3
x3.83
C 2209 &m12 2 15
& WL 4*/ & )/*
12 1
&4 x 3(*3 EEE x 3(*3
x3.83
C 5757 &m12 2 10
The "!"e#$ %&'$(&)*$&!# &' +,((&(e% !*$ ,' &--*'$(e% $,)-e.
Fixed End Moments
%em#er D$ DA AD A0 35/2 6525 3
//26/(61 5)5) &22/ &)/)62 C
Hoint D A 12462)(5 1246
%em#er D$ DA AD A035/2
Distri#ution fa!tore (33 (6) (6) (33 4 *
8ix end moment //26/(61 5)5) &22/ &)/)62 A A
0alan!e &35/ &)1* 5464) 2)324 35/2 1(/1
$arr over 2)324 &35/4*)4*
#alan!e &/1* &1*216 2333/ 116) 3(*2
$arr over 116) &/1*
#alan!e &3*/ &))* 6)2 336 4/646 1(/1
$arr over 336 &3*/ D D
#alan!e &112 &224 25/3 12/) 145164/646
/
$arr over 12/) &112
#alan!e &432 &*64 6)5 33) 1551* 155
$arr over 33) &432 52
#alan!e &112 &225 2** 144
$arr over 144 &112 *12*
#alan!e &4* &/6 )5 3) 8ig 4
$arr over 3) &4*
#alan!e &12 &25 32 16
8inal moment 4/646 &4/646 35/2 &35/2
8or horiBontal sla# A0> !arring for the 0ottom sla# D$ !arring in!luding loading> 0(%( And rea!tions are sho'n in fig(6
"m2 "
"m2
p,nand'anaahoo(!o(in
%8A0
C'L2 2C
%fd!
C'L2 2C
%8AD
CpL2
%8AD
C2&
%8DA
CpL2
%8DA
C2&
+he moment distri#ution !arried out as per ta#le 1 for +,'e 1
"m2(
"m2
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& 1"2 x 14516 x 3.82 x 3(*2 x 1"3
&ha x 3(*2 &13)44 2/1*4(* & 3534
8rom 'hi!h> ha C 5200
en!e > hd C? 14516 x 3(*2 @& 4 x 3(*2 & 52 7245./
2
8ree 0(%( at mid point C6525 x 3(*3
119/44 &m*
et 0(%( at C 11/644 & 35/2 C 83742 &m
Similarl> free 0(%( at 8 C*12* x 3(*3
14*/4 &m*
et 0(%( at 8 C 14*/4(416 & 4/646 C 99258 &m
8or verti!al mem#er AD > Simpl supported 0(%( At mid span
Simpl supporetd at mid sapn C4 x 3(*3
1"16 x EEE x 3(*3 5/)3(/*
et 0(%( C4/646 35/2
C 42))4 5/)4 C 48748 &m2
5 Design of top slab :
Mid section
+he top sla# is su#e!ted to follo'ing values of 0(%( and dire!t for!e
$ase 0(%( at $enter ?@ 0(%( at ends ?A@ Dire!t for!e ?ha@
?i@ 6456/ 55)5 46*52
?II@ )3/51 456/ 23451
?II@ *3)42 35/2 52
+he se!tion 'ill #e design for maximum 0(%( C 83742 N "
!( ,$e( '&%e !(+e
= 15 't( of !on!rete C EEE
= ) 't of 'ater C /*
m = 13 for 'ater side f
m!C
13 x )C 0.378 . C (3
13 x ) 15
= 1 & (3)* " 3 C 0.874 H C (*
= (5 x ) x (*) x (3)* C 1.155 = C 1(1
P(!&%e !e( ,-- $h&+#e'' C 320 mm so effe!tive thi!,nesss C 270 mm
= 1(155 x 1 x 2) 8421/794 83742000 O.6.
Ast C
*3)42 C 23/5
15 x (*)4 x 2)
using A C C3(14 x 2 x 2
C 3144 x1 4
Spa!ing of 0ars C x1"Ast 314 x 1 " 2365 C 133 sa C 130 mm
e#+e P(!&%e% 20 130 "" ++
:+*,- :'$ ;(!&%e% 1 x 314 " 13 C 2415
0end half #ars up near support at distan!e of L"5 C 3(*3 " 5 C (* m
Area of distri#utionn steel C (3 &(1 x? 32 & 1
C (24M
45 & 1
C (24 x 32 x 1 C )5/ E
using 8 A C C3(14 x * x *
C 54 x1 4
2C
2C
22C
σst C "mm2 "m3
σ!#! C "mm2 "mm2
Cm!σst
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Section at supports :-
%aximum 0(%(C 55)5 &m( +here is dire!t !ompression of 46*52 also(
0ut it effe!t is not !onsidered #e!ause the sla# is a!tuall reinfor!ed #oth at top and #ottom (
Sin!e steel is at top C 1/ !on!rete % 2
, C (323* H C (*/2 = C 1(11
C55)5
C 1241/ x (*/2 x 2)
Area availa#le from the #ars #entup from the middle se!tion C 2415 " 2 C 12*
124 N 12*
6 Design of bottom slab:
+he #ottom sla# has the follo'ing value of 0(%( and dire!t for!e(
$ase 0(%( at $enter ?8@ 0(%( at ends ?D@ Dire!t for!e ?ha@
?i@ ))**1 )123 6/*1
?II@ */315 5**13 2144
?II@ //25* 4/646 )246
+he se!tion 'ill #e design for maximum 0(%( C 99258 N "
!( ,$e( '&%e !(+e
= 15 't( of !on!rete C EEE
= ) 't of 'ater C /*
m = 13 for 'ater side f
m!C
13 x )C 0.378 . C (3
13 x ) 15
= 1 & (3)* " 3 C 0.874 H C (*
= (5 x ) x (*) x (3)* C 1.155 = C 1(1
C//25*416
C 2/4 mm D 344 mm1 x 1(155
P(!&%e $h&+#e'' ! )!$$!" '-,) D 350 mm so that d C 300 mm
Ast C//25*416 C 2523
15 x (*)4 x 3
using mm #ars A C C3(14 x 2 x 2
C 3144 x1 4
Spa!ing of 0ars C x1"Ast 314 x 1 " 2523 C 124 sa C 120 mm
e#+e P(!&%e% 20 120 "" ++
:+*,- :'$ ;(!&%e% 1 x 314 " 12 C 261)
0end half #ars up near support at distan!e of L"5 C 3(*3 " 5 C (* m
Area of distri#utionn steel C (3 &(1 x? 35 & 1
C (23 M45 & 1
C (23 x 35 x 1 C * 4
using 8 mm #ars A C C3(14 x * x *
C 54 x1 4
Spa!ing of 0ars C Ax1"Ast C 5 x 1 " 4 C 126 sa C 120 mm
e#+e P(!&%e% 8 120 "" ++ !# e,+h ,+e
Section at supports :-
%aximum 0(%(C )123 &m( +here is dire!t !ompression of 6/*1 also(
0ut it effe!t is not !onsidered #e!ause the sla# is a!tuall reinfor!ed #oth at top and #ottom (
Sin!e steel is at top C 1/ !on!rete % 2
σst "mm2
∴ Ast mm2
p,nand'anaahoo(!o(in
mm2
en!e these #ars 'ill serve the purpose( o'ever> provide * mm dia( Additional #ars 2 mm !"!
σst C "mm2 "m3
σ!#! C "mm2 "mm2
Cm!σst
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1/ x (*/2 x 3
Area availa#le from the #ars #entup from the middle se!tion C 261) " 2 C 13*
13/) O 13* 8ail > hen!e additional reinfor!ement 'ill provided(
Additional reinfor!emet reFuired C **(6)
using 8 mm #ars A C C3(14 x * x *
C 54 x1 4
Spa!ing of 0ars C Ax1"Ast C 5 x 1 " */ C 56) sa C 5/0 mme#+e P(!&%e% 8 300 "" ++ $h(!*=h$ !*$ $he '-,)> ,$ &$' )!$$!".
) De'&=# ! '&%e ,--?
+he side 'all has the follo'ing value of 0(%( and dire!t for!e(
$ase 0(%( at $enter ?8@ 0(%( at ends ?D@ Dire!t for!e ?ha@
?i@ )1/) )123 155514
?II@ 3523 5**13 1551*
?II@ 4*)4* 4/646 1551*
+he se!tion 'ill #e design for maximum 0(%( C 71023 N "> ,#% %&(e+$ !(+e C 155514
!!entri!it C)123 x 1
C 45) mm155514
proposed thi!,ness of side 'all JC 33 mm ∴ e " D 45) " 33 C 1(3* N 1(5
thi!,ness of side 'all is -.
Let us reinfor!e the se!tion 'ith 20 300 mm !"! provided on #oth fa!es> as sho
in fig xxx ( With !over of 5 mm and D C 33 mm
As! C Ast C1
x3(14 x 2 x 2
C 14)3 4
+he depth of (A( is !omputed from follo'ing expressionG
n
3 3 nC e
D& dt
# n ?m &1@ As! n & d!& m Ast
D & dt & n 2
n n
or
1 n33 & 5 &
n 12 x
14)x n & 5 x
2 3 n
1 n12 x
14)x n & 5 & 13 x
14)x 33 & 5
2 n n
5 n 2* &n
n & 5 x&16
3 nC 45) 115
5 n1256
x n & 5 &EEE
x 2* & nn n
14 n & 16) &1256 &&62*
nC 5)2
5 n 1256 &62*
&3*/*6)
EEEn n
multipl # n
14 n2 & 16) n3 &1256 n & &62*C 5)2
5 n2 1256 n& 62* & 3*/*6) EEE n
mm2
mm2
3(14xdia2
mm Φ 0ars
mm Φ #ars
mm2
# n D & dt & ?m & 1@As! 1 ?n & d!@?D & dt& d!@
n2
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2*6 n2 14/6)333 n & 253*45/)33
&146 n2 & 13)11333 n & &24)565/)33 C 16)
&*)6 n2 *226* n & 14*53/5* C
S!-= $h&' $(&,- ,#% e((!( e =e$> # C 91.47 mm
? 5 x /1(4) 12 x 14)
? /1(4) & 5 @ &13 x 14)
/1(4) /1(4)x ? 33 & 5 & /1(4) @
or 45)34 13)(3 x 41(4) & 14/ x 1**(53 C 233*3
C155514
C /./5 N 7 Stress is less than permissi233*3
Also stress in steel t Cm !J
?D&d!&n@ C13 x 6(65
x ? 33 & 5 & /1(4) @n /1(4)
C 178.2 "mm2 N 190 "mm2 O.6.
Stress in steel is less than permissia#le en!e se!tion is -(.(
n3
n3
∴ !J
p,nand'anaahoo(!o(in
∴ !J "mm2
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p,nand'anaahoo(!o(in
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ide>
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2*
55)5
2)(5
6456/
))**1
14
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e t l a t r a l p r e s s u r e d i a g r a m
456/
2)(5
)3/51
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*/315
*
t l a t r a l p r e s s u r e d i a g r a m
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36
5/2
2)(5
3)42
/25*
1*
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or!e
)*
)4
55
mm2
mm2
mm2
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or!e
)*
)4
55
mm2
mm2
mm2
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-.
'n
&1
& n
mm2
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#le
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B!@ +*-e($'
2 26 mm !"!
* 2 mm $"$
* 13 mm $"!
32
) 2
2 13 mm $"$
3 mm $"$
3(5
*
13 mm $"$
2
12 mm !"!
35
2 * *
24 mm !"! 2 mm $"$ 13 mm $"!
33 3(5 33
m Φ
mm Φ
mm Φ
mm Φ
mm Φ
mm Φ
mm Φ
m Φ mm Φ mm Φ
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7rade of !o %&1 %&15 %&2 %&25 %&3 %&35 %&4 #
1(2 2( 2(* 3(2 3(6 4( 4(4(
(
(
1(
1(
?"mm2@ ?"mm2@ ?"mm2@ 1(
% 1 3( 3 2(5 25 && && 1(
% 15 5( 5 4( 4 (6 6 2(
% 2 )( ) 5( 5 (* * 2(
% 25 *(5 *5 6( 6 (/ / 2(
% 3 1( 1 *( * 1( 1 2(
% 35 11(5 115 /( / 1(1 11 3( an
% 4 13( 13 1( 1 1(2 12
% 45 14(5 145 11( 11 1(3 13
% 5 16( 16 12( 12 1(4 14
-ver all de
7rade of !o %&1 %&15 %&2 %&25 %&3 %&35 %&4
%odular ra
7rade of
7rade of !on!rete %&15 %&2 %&25 %&3 %&35 %&4
%odular =atio 1*(6) 13(33 1(/* /(33 *(11 )(1* 7rade of !on!re
5 ) *(5 1 11(5 13
/3(33 /3(33 /3(33 /3(33 /3(33 /3(33
(4 (4 (4 (4 (4 (4
(*6) (*6) (*6) (*6) (*6) (*6)
(*6) 1(214 1(4)4 1()34 1(//4 2(254
()14 1 1(214 1(42/ 1(643 1(*5)
(32/ (32/ (32/ (32/ (32/ (32/ % 15
(*/ (*/ (*/ (*/ (*/ (*/ % 2
()32 1(25 1(244 1(464 1(6*4 1(/3 % 25
(433 (66 ()36 (*66 (//) 1(12) % 3
(2*/ (2*/ (2*/ (2*/ (2*/ (2*/ % 35
(/4 (/4 (/4 (/4 (/4 (/4 % 4
(653 (/14 1(11 1(36 1(52 1(6/* % 45
+a#le 1(15( PERISSIBLE DIRECT TENSILE STRESS+a#le 3(1
1
+ensilestress"mm2
N
+a#le 1(16(( Pe("&''&)-e '$(e'' +!#+(e$e AIS ? 45/2000
7rade of!on!rete
;ermission stress in !ompression ?"mm2@ ;ermissi#le stress in #ond ?Average@ forplain #ars in tention ?"mm2@0ending α
!#! Dire!t ?α!!@
.g"m2 .g"m2 in ,g"m2
+a#le 1(1*( ODUL:R R:TIO
+a#le31?31(11@
1/?1*(6)@
13?13(33@
11?1(/*@
/?/(33@
*?*(11@
)?)(1*@
τ!(
+a#le 2(1. V:LUES OF DESIGN CONST:NTS
σ!#!
"mm2 τ#d ? " mm2
m σ!#!
?a@ σst C
14"mm2?8e 25@
,!
!
=! 7rade of
!on!rete;!?M@
?#@ σst C
1/"mm2
,!
!
=!
;!?M@
?! @ σst C
23"mm2
,!
!
=!
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(314 (44 (534 (62* ()22 (*16 % 5
=eifor!ement M alue of angle
M-2! M-2! Degree sin !os tan
bd bd 1 (1) (/* (1*
(15 (1* (1* (15 11 (1/ (/* (1/
(16 (1* (1/ (1* 12 (21 (/* (21
(1) (1* (2 (21 13 (23 (/) (23
(1* (1/ (21 (24 14 (24 (/) (25
(1/ (1/ (22 (2) 15 (26 (/) (2)
(2 (1/ (23 (3 16 (2* (/6 (2/
(21 (2 (24 (32 1) (2/ (/6 (31
(22 (2 (25 (35 1* (31 (/5 (32
(23 (2 (26 (3* 1/ (33 (/5 (34
(24 (21 (2) (41 2 (34 (/4 (36
(25 (21 (2* (44 21 (36 (/3 (3*
(26 (21 (2/ (4) 22 (3) (/3 (4
(2) (22 (3 (5 23 (3/ (/2 (42
(2* (22 (31 (55 24 (41 (/2 (45
(2/ (22 (32 (6 25 (42 (/1 (4)
(3 (23 (33 (65 3 (5 (*) (5*
(31 (23 (34 () 35 (5) (*2 ()
(32 (24 (35 ()5 4 (64 ()) (*4
(33 (24 (36 (*2 45 ()1 ()1 1(
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d %&15 %&2 %&25 %&3 %&35 %&4
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