r.c.c. box culvert design

7/23/2019 R.C.C. Box Culvert Design

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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 !"!


At supports 8 300 mm !"! +hrough out sla# at #ottom

Side verti!al 'all erti!al 20 300 mm !"! 0oth side -(.(


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

"m3

"m2

"m2

,g"m3

σ!#! "m2

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



p,nand'anaahoo(!o(in

mailto:[email protected]




DSI7 -8 0-9 +:; $<L=+

1 In side diamentions 3(5 x 3(5 m

2 Super imposed load 12

3 Live load 45

4 Wieght of soil 1* 't( of 'ater /*

5 Angle of repose 3 Degree

6 ominal !over top"#ottom 5 mm ominal !over Side 5 mm

6 $o!rete % & 2 't( of !on!rete 25) m 13

) Steel 8 415 1/

15

1 Solution 7enral

8or the purpose of design > one metre length of the #ox is !onsidered(

+he analsis is done for the follo'ing !ases(

?I@ Live load> dead load and earth prssure a!ting > 'ith no 'ater pressure from inside(

?II@ Live and dead load on top and earth pressure a!ting from out side> and 'ater pressure a!ting from ins

'ith no live load on sides

?III@ Dead load and earth pressure a!ting from out side and 'ater pressure from in side(

Let the thi!ness of oriBontal sla# 33 mm C (33 m

erti!al 'all thi!ness 32 mm C (32 m

ffe!tive sla# span 3(5 (33 C 3(*3 m

ffe!tive eight of 'all 3(5 (32 C 3(*2 m

2 Case 1 : Dead and live load from out side of while no water pressure from inside.

Self 'eight og top sla# C (33 x 1 x 1 x EEE C *25

Live load and dead load C 45 EEE C 5)

+otal load on top C 6525

Weight of side 'all C 3(*2 x (32 x EEE C 356 "m

6525 x 3(*3 @? 2 x EEE @C*12*(2

3(*3

.a C1 & sin 3

C1 & (5

C0.5

C1

C (331 sin 3 1 (5 1.5 3

p C EEE x (333 C 1/

Latral pressure due to soil .a x ' x h C (333 x EEE h C 6000 h

en!e total pressure C EEE 6 h

Latral presure inten!it at top C 1/

Latral pressure inten!it at #ottom C EEE 6 x 3.82 C 41/2

' C 6525

1/ 1/

A 0

h 3(*3

1/ 3(*2

6 h

D 8 $

41/2 1/ 22/2

' C *12*

8ig 1

"m3

"m2

"m2 "m3

"m3

σ!#! "m2

-ut side σst "m2

'ater side side σst "m2

"m2

"m2

"m2

∴ <p'ard soil rea!tion at #ase C ?"m2

∴ Latral pressure due to dead load and live load C ;v x .a

"m2

"m2

"m2

8ig 1 sho' the #ox !ulvertframe ABC D> 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



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 <DL /5250

erti!al rea!tionat a and 0 C (5 x 6525 x 3(*2 C 124/28 "m2

Similarl> for the 0ottom sla# D$ !arring <(D(L(loads EEE

erti!al rea!tion at D and $ C (5 x *12*(22 x 3(*3 C 155514

+he #od diagram for various mem#ers> in!luding loading> 0(%( And rea!tions are sho'n in fig(2

8or the verti!al mem#er AD> the horiBontal rea!tion at A is found # ta,ing moments at D(+hus

? &ha x 3(*3 @ 55)5 & EEE EEE x 3.83 x 3(*3 x 1"2

1"2 x 22/2 x 3.83 x 3(*3 x 1"3

&ha x 3(*3 &15/4* 13/355 5635(2

8rom 'hi!h> ha C 4/852


Distri#ution fa!tore for AD and DA= Distri#ution fa!tore for AB and DC=

%8A0

C'L2 2C

%fd!

C'L2 2C

%8AD

C pL2

%8AD

C2

%8DA

CpL2

%8DA

C2&&

+he moment distri#ution !arried out as per ta#le 1 for +,'e 1

"m2(

"m2





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/ 23451

8ix end moment //26/(61 &125)/ 1612* &)/)62 A A

0alan!e &2**/) &5))/4 42423 21211 456/ 1(/1

$arr over 21211 &2**/)


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&






#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/


erti!al rea!tionat a and 0 C (5 x 6525 x 3(*2 C 124/28 "m2


erti!al rea!tion at D and $ C (5 x *12* x 3(*2 C 155108



? &ha x 3(*2 @ 456/ & EEE 44*4 x 3.82 x 3(*2 x 1"2

1"2 x 14516 x 3.82 x 3(*2 x 2"3

&ha x 3(*2 &13)44 32)16(16 )6)(*

8rom 'hi!h> ha C 23451

en!e > hd C? 44*4 EEE @x 3(*2 & EEE C 21404

2


119020 &m*

et 0(%( at C 11/2 & 456/ C 73951 &m

Similarl> free 0(%( at 8 C*12* x 3(*2

14*12* &m*

et 0(%( at 8 C 14*12)(*62 & 5**13 C 89315 &m

8or verti!al mem#er AD > Simpl supported 0(%( At mid span

impl supporetd at mid sapn44*4 x 3(*2

1"16 x EEE x 3(*2 2141**

et 0(%( C

5**13 456/

C 51/41 & EEE C 30523 &m2

4 Case 3 : Dead load and live load on top water pressure from inside no live load on side.

in this !ase> it is assume that there is no latral oressure due to live load ( As #efore (

+he top sla# is su#e!ted to a load of JC 6525

and the #ottom sla# is su#e!ted to a load ' C 6525

Itensit C *12* 4 4

Lateral pressure due to dead load C A 0 4

1"3 x 12 C 4

Lateral pressure due to soil C 3(*3

1"3 x 1* C 6 3(*2

en!e earth pressure at depth h is C

4 6 h D 8 $

26/2 26/2 145

"m2(

"m2

2C

2C

22C

"m2

"m2

"m2

"m2

"m2



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


erti!al rea!tionat a and 0 C (5 x 6525 x 3(*2 C 124/28


erti!al rea!tion at D and $ C (5 x *12* x 3(*2 C 155108



? ha x 3(*2 @ 35/2 & EEE 4 x 3.82 x 3(*2 x 1"2

"m2 "

"m2


%8A0

C'L2 2C

%fd!

C'L2 2C

%8AD

CpL2

%8AD

C2&

%8DA

CpL2

%8DA

C2&


"m2(

"m2





& 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


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

Spa!ing of 0ars C Ax1"Ast C 5 x 1 " 3* C 132 sa C 130 mm

e#+e P(!&%e% 8 130 "" ++ !# e,+h ,+e

2C

2C

22C

σst C "mm2 "m3

σ!#! C "mm2 "mm2

Cm!σst

<C1&,"3

RC1"2x! x x ,

%r C = ( 0 (D2 2C

0%x1"σ

stxxDC

mm2

mm Φ #ars3(14xdia2

mm Φ 0ars

mm2

Ast mm2 area on ea!h fa!eC

mm Φ #ars3(14xdia2

mm Φ 0ars



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

, C (323* H C (*/2 = C 1(11

)123

σst "mm2

∴ Ast mm2


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

<C1&,"3

RC1"2x! x x ,

%

0%x1"σstxxDCmm2

3(14xdia2

mm Φ 0ars

mm2

Ast mm2 area on ea!h fa!eC

3(14xdia2

mm Φ 0ars

σst "mm2

2





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

14 n2 & 16) n3 &1256 n & &62*

mm2

mm2

3(14xdia2

mm Φ 0ars

mm Φ #ars

mm2

# n D & dt & ?m & 1@As! 1 ?n & d!@?D & dt& d!@

n2



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


∴ !J "mm2





ide>



2*

55)5

2)(5

6456/

))**1

14



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



*/315

*

e t l a t r a l p r e s s u r e d i a g r a m

16



36

5/2

2)(5

3)42

/25*

1*



or!e

)*

)4

55

mm2

mm2

mm2



-.

'n

&1

& n

mm2



#le



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



7rade of !o %&1 %&15 %&2 %&25 %&3 %&35 %&4

1(2 2( 2(* 3(2 3(6 4( 4(4

?"mm2@ ?"mm2@ ?"mm2@

% 1 3( 3 2(5 25 && &&

% 15 5( 5 4( 4 (6 6

% 2 )( ) 5( 5 (* *

% 25 *(5 *5 6( 6 (/ /

% 3 1( 1 *( * 1( 1% 35 11(5 115 /( / 1(1 11

% 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

7rade of !o %&1 %&15 %&2 %&25 %&3 %&35 %&4

%odular ra

7rade of !on!rete %&15 %&2 %&25 %&3 %&35 %&4

%odular =atio 1*(6) 13(33 1(/* /(33 *(11 )(1* 7rad

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/

(*/ (*/ (*/ (*/ (*/ (*/

()32 1(25 1(244 1(464 1(6*4 1(/3

(433 (66 ()36 (*66 (//) 1(12)

(2*/ (2*/ (2*/ (2*/ (2*/ (2*/

(/4 (/4 (/4 (/4 (/4 (/4

(653 (/14 1(11 1(36 1(52 1(6/*

(314 (44 (534 (62* ()22 (*16

+a#le 1(15( PERISSIBLE DIRECT TENSILE STRESS

+ensilestress"mm2

+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

31?31(11@

1/?1*(6)@

13?13(33@

11?1(/*@

/?/(33@

*?*(11@

)?)(1*@

+a#le 2(1. V:LUES OF DESIGN CONST:NTS

σ!#!

"mm2 τ

m σ!#!

?a@ σst C

14"mm2?8e 25@

,!

!

=!

;!

?M@

?#@ σst C

1/"mm2

,!

!

=!

;!?M@

?! @ σst C

23"mm2?8e 415@

,!

!

=!

;!?M@



=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(

(34 (24 (3) (** 5 ()) (64 1(1/

(35 (25 (3* (/4 55 (*2 (5) 1(43

(36 (25 (3/ 1( 6 (*) (5 1()3(3) (25 (4 1(* 65 (/1 (42 2(14

(3* (26 (41 1(16

(3/ (26 (42 1(25

(4 (26 (43 1(33

(41 (2) (44 1(41

(42 (2) (45 1(5

(43 (2) (46 1(63

(44 (2* (46 1(64

(45 (2* (4) 1()5

(46 (2* (4* 1(**

(4) (2/ (4/ 2(

(4* (2/ (5 2(13

(4/ (2/ (51 2(25

(5 (3

(51 (3

(52 (3

(53 (3

(54 (3

(55 (31

(56 (31

(5) (31

(5* (31

(5/ (31(6 (32

Shear stress t!

100:'

100:'



(61 (32

(62 (32

(63 (32

(64 (32

(65 (33

(66 (33

(6) (33

(6* (33

(6/ (33

() (34

()1 (34

()2 (34

()3 (34

()4 (34

()5 (35

()6 (35

()) (35

()* (35()/ (35

(* (35

(*1 (35

(*2 (36

(*3 (36

(*4 (36

(*5 (36

(*6 (36

(*) (36

(** (3)

(*/ (3)

(/ (3)(/1 (3)

(/2 (3)

(/3 (3)

(/4 (3*

(/5 (3*

(/6 (3*

(/) (3*

(/* (3*

(// (3*

1( (3/

1(1 (3/

1(2 (3/

1(3 (3/

1(4 (3/

1(5 (3/

1(6 (3/

1() (3/

1(* (4

1(/ (4

1(1 (4

1(11 (4

1(12 (4

1(13 (41(14 (4



1(15 (4

1(16 (41

1(1) (41

1(1* (41

1(1/ (41

1(2 (41

1(21 (41

1(22 (41

1(23 (41

1(24 (41

1(25 (42

1(26 (42

1(2) (42

1(2* (42

1(2/ (42

1(3 (42

1(31 (42

1(32 (421(33 (43

1(34 (43

1(35 (43

1(36 (43

1(3) (43

1(3* (43

1(3/ (43

1(4 (43

1(41 (44

1(42 (44

1(43 (44

1(44 (441(45 (44

1(46 (44

1(4) (44

1(4* (44

1(4/ (44

1(5 (45

1(51 (45

1(52 (45

1(53 (45

1(54 (45

1(55 (45

1(56 (45

1(5) (45

1(5* (45

1(5/ (45

1(6 (45

1(61 (45

1(62 (45

1(63 (46

1(64 (46

1(65 (46

1(66 (46

1(6) (461(6* (46



1(6/ (46

1() (46

1()1 (46

1()2 (46

1()3 (46

1()4 (46

1()5 (4)

1()6 (4)

1()) (4)

1()* (4)

1()/ (4)

1(* (4)

1(*1 (4)

1(*2 (4)

1(*3 (4)

1(*4 (4)

1(*5 (4)

1(*6 (4)1(*) (4)

1(** (4*

1(*/ (4*

1(/ (4*

1(/1 (4*

1(/2 (4*

1(/3 (4*

1(/4 (4*

1(/5 (4*

1(/6 (4*

1(/) (4*

1(/* (4*1(// (4*

2( (4/

2(1 (4/

2(2 (4/

2(3 (4/

2(4 (4/

2(5 (4/

2(6 (4/

2() (4/

2(* (4/

2(/ (4/

2(1 (4/

2(11 (4/

2(12 (4/

2(13 (5

2(14 (5

2(15 (5

2(16 (5

2(1) (5

2(1* (5

2(1/ (5

2(2 (5

2(21 (52(22 (5



2(23 (5

2(24 (5

2(25 (51

2(26 (51

2(2) (51

2(2* (51

2(2/ (51

2(3 (51

2(31 (51

2(32 (51

2(33 (51

2(34 (51

2(35 (51

2(36 (51

2(3) (51

2(3* (51

2(3/ (51

2(4 (512(41 (51

2(42 (51

2(43 (51

2(44 (51

2(45 (51

2(46 (51

2(4) (51

2(4* (51

2(4/ (51

2(5 (51

2(51 (51

2(52 (512(53 (51

2(54 (51

2(55 (51

2(56 (51

2(5) (51

2(5* (51

2(5/ (51

2(6 (51

2(61 (51

2(62 (51

2(63 (51

2(64 (51

2(65 (51

2(66 (51

2(6) (51

2(6* (51

2(6/ (51

2() (51

2()1 (51

2()2 (51

2()3 (51

2()4 (51

2()5 (512()6 (51



2()) (51

2()* (51

2()/ (51

2(* (51

2(*1 (51

2(*2 (51

2(*3 (51

2(*4 (51

2(*5 (51

2(*6 (51

2(*) (51

2(** (51

2(*/ (51

2(/ (51

2(/1 (51

2(/2 (51

2(/3 (51

2(/4 (512(/5 (51

2(/6 (51

2(/) (51

2(/* (51

2(// (51

3( (51

3(1 (51

3(2 (51

3(3 (51

3(4 (51

3(5 (51

3(6 (513() (51

3(* (51

3(/ (51

3(1 (51

3(11 (51

3(12 (51

3(13 (51

3(14 (51

3(15 (51



#d %&15 %&2 %&25 %&3 %&35 %&4

(1* (1* (1/ (2 (2 (2(25 (22 (22 (23 (23 (23 (23

(5 (2/ (3 (31 (31 (31 (32

()5 (34 (35 (36 (3) (3) (3*

1( (3) (3/ (4 (41 (42 (42

1(25 (4 (42 (44 (45 (45 (46

1(5 (42 (45 (46 (4* (4/ (4/

1()5 (44 (4) (4/ (5 (52 (52

2( (44 (4/ (51 (53 (54 (55

2(25 (44 (51 (53 (55 (56 (5)

2(5 (44 (51 (55 (5) (5* (6

2()5 (44 (51 (56 (5* (6 (623( and a#ove (44 (51 (5) (6 (62 (63

-ver all depth of sla# 3 or more 2)5 25 225 2 1)5 15 or less

κ 1( 1(5 1(1 1(15 1(2 1(25 1(3

7rade of !on!rete %&15 %&2 %&25 %&3 %&35 %&4

1(6 1(* 1(/ 2(2 2(3 2(5

e of !on!re 1 15 2 25 3 35 4 45

&& (6 (* (/ 1 1(1 1(2 1(3

;lain %(S( 0ars (:(S(D( 0ars

% 15 (6 5* (/6 6

% 2 (* 44 1(2* 45

% 25 (/ 3/ 1(44 4

% 3 1 35 1(6 36

% 35 1(1 32 1()6 33

% 4 1(2 2/ 1(/2 3

% 45 1(3 2) 2(* 2*

% 5 1(4 25 2(24 26

+a#le 3(1( Pe("&''&)-e 'he,( '$(e'' T,)-e τ+ &# +!#+(e$e AIS ? 45/2000

1As

;ermissi#le shear stress in !on!rete t! "mm2

N (15

+a#le 3(2( F,+!( !

+a#le 3(3( ,@&"*" 'he,( '$(e'' τ!(m,@

&# +!#+(e$e AIS ? 45/2000

τ!(max

+a#le 3(4. Pe("&''&)-e B!#% '$(e'' T,)-e τ)%

&# +!#+(e$e AIS ? 45/2000

#d? " mm2

+a#le 3(5. Dee-!;"e#$ Le#=$h &# $e#'&!#

7rade of!on!rete τ

#d

? " mm2@ ,d

C Ld

Φ τ#d

? " mm2@ ,d

C Ld

Φ



alue of angle

tan Degree sin !os

(1* 1 (1) (/*

(1/ 11 (1/ (/*

(21 12 (21 (/*

(23 13 (23 (/)

(25 14 (24 (/)

(2) 15 (26 (/)

(2/ 16 (2* (/6

(31 1) (2/ (/6

(32 1* (31 (/5

(34 1/ (33 (/5

(36 2 (34 (/4(3* 21 (36 (/3

(4 22 (3) (/3

(42 23 (3/ (/2

(45 24 (41 (/2

(4) 25 (42 (/1

(5* 3 (5 (*)

() 35 (5) (*2

(*4 4 (64 ())

1( 45 ()1 ()1

1(1/ 5 ()) (64

1(43 55 (*2 (5)

1()3 6 (*) (52(14 65 (/1 (42



5

1(4

r.c.c. box culvert design

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