Box Culvert Design Calculation

Reference

Calculation

Output

 Ac

 Area of concrete concrete

 Acc

 Area of concrete concrete in compression

 As

 Area of tension reinforcement reinforcement Minimum area of tension reinforcement

s min

av

Length of that part of member traversed by shear failure plane

b

With (breath) or effective width of section

c

Cover to outer diameter  

d 7c

ffective depth of section !asic force used in defining compressive forces

7t

!asic force used in defining tie forces

f cu

Characteristic Characteristic strength of concrete

f s

stimated design service stress in the tension reinforcement reinforcement

f y

Characteristic Characteristic strength of reinforcement

"

#hear modulus

$

%$Ma%imum hori&ontal force $ori&ontal force in % direction

$y

$ori&ontal force in y direction

h

Overall depth

'L

'nife edge load

L l%

Critical perimeter   imension of element on % direction

ly

imension of element on y direction

l&

imension of element on & direction

M M%

esign ultimate resistance moment Moment on % a%is

My

Moment on y a%is

M&

Moment on & a%is



#urcharge load

r

*nternal radius of bend

#L#

#erviceability lilimit st state

+

+raction force

t

+hic,ness of the element

-L#

-ltimate lilimit st state

.

#hea #hearr for force ce due due to to des desig ign n ult ultim imat ate e loa loads ds or desi design gn ulti ultima mate te valu value e of of a concentrated load

v

esign shear stress

vc

esign shear stress in concrete

%

/eutral a%is depth

%0

istance fr from 1 a%is to to th the ce centroid of of an an el element

y' 

istance from 2 a%is to the centroid of an element

&

Lever arm

&0

ist istan ance ce from from 2 3 1 plan plane e to to poi point nt wher where e the the cons consid ider ered ed resu result ltan antt force acting

 β

¿s

Coefficient4 Coefficient4 variously defined4 as appropriate #train in tension reinforcement reinforcement

δ 

/ominal range of movement

φ

#oil friction angle4 or diameter 

σ a γ 

γ fL γ f  3 3

 Active earth pressure pressure -nit weight of soil 5artial load factor  5artial load factor 

oc6 /o6 DESIGN UNIT

esigned

ate

E C

EPC DIVISION

Chec,ed

ate

CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB)

8ob Code

5age

Reference

Calculation

Output

oc6 /o6 D E C

DESIGN UNIT

esigned

ate

EPC DIVISION

Chec,ed

ate

CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB)

8ob Code

5age

Reference

Calculation

Output

oc6 /o6 D E C

EPC DIVISION

esigned Chec,ed

ate ate

CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB)

8ob Code

5age

DESIGN UNIT

Reference

Calculation

Output

oc6 /o6 D E C

DESIGN UNIT

esigned

ate

EPC DIVISION

Chec,ed

ate

CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB)

8ob Code

5age

Reference

Calculation

Output

oc6 /o6 D E C

DESIGN UNIT

esigned

ate

EPC DIVISION

Chec,ed

ate

CENTRAL ENGINEERING CONSULTANCY BUREAU (CECB)

8ob Code

5age

Reference

Calculation

Output

Design of Box Culve! Ground Level

X hs

A

B H

hw

Y

hw

h l

D

C

hs

7igure 9: imentional 5roperties h

;

:6<

m

l

;

:6=

m

$

;

>6<

m

#afe !earing 5ressure

;

:=9 ,/?m<

#ection +hic,ness Main R?7

;

96<

m

;

:<

mm

Cover to R?7

;

=

mm

"rade of Concrete

;

<=

/?mm<

Bc

;

<

,/?m

Bs

;

<9

,/?m

Bw

;

F0

;

#oil Cover 4

( hw 4 h

;

span?(:9 @:=))

5roperties of #oil

D6E: ,/?m <=

o

" # Pe$%nen! Lo%&s

:6:

ead Loads +he nominal dead doad consist of the weight of the materials and the part of the structure

#tructural

-nit Weight of Concrete shall be ta,en as < ,/?m

ngineering

!ecouse of the arching of soil4 chec, whether the depth above culvert is

esign in

G  % width of culvert ( in which case limit depth to  % width )

preactice (Roger 3

;

epth of cover ($)

westbroo,)

 % width

(page3D)

;

>6< 

m :6H

%

;

6E

m

 % width I ;

>6<

m

epth limited to

;

6E m

;

6E

#o

#urcharge on Roof  #urcharge 5resure (r) r

#oil ngineering (#pangler J $andy)

;

DH

%

<9 ,/?m<

C%sses of 'on&ui! ins!%ll%!ion 'onsi&e %s Di!' Con&ui! Di!' Con&ui!

A ditch conduit is defined as one which is instaled in a relatively narrow ditch dug in passive or undisturbed soil and wich is then covered with earth bac,fill6

Celon Ele'!i'i! Bo%&

C E

oc6 /o6

D%$ S%fe!

esigned

Envion$en!%l *

Chec,ed

S.M.P

ate ate

:69=6<9:9

B

8ob Code

Civil S!u'!ue +%in!%n%n'e

Reference

5age

Calculation

: Output

+%xi$u$ lo%& on &i!' 'on&i!ion

epth of cover

;

>6<

m

Su'%ge on Roof  #urcharge 5resure (r) < (r) ; Cd6B6!d Cd

;

µ0

;

;

'

4

:3e-2Kµ0($?!d) <6'6µ0 tan φ0

:3sin φ :sin φ

µ0

3

coedicient of friction between fill material and side of ditch

' !d

3  Active Lateral earth pressure coeficient 3 $ori&ontal width of ditch at top of conduit

B

3

-nit weight (wet density) of filling material

$

3

$eight of fill above top of conduite

Cd

3

Load coeficient for ditch condition

#o4 '

;

:3sin φ

!d ;

6H9 m4 Consider :m length of Roof slab

:sin φ ; µ0

tan φ0

;

96HH

<6'6K06($?!d) ;

96>H

Cd

#tructural

;

969H

:6<

;

:69

(r)

;

Cd6B6!d<

(r)

;

:9:69

,/?m<

$ori&ontal arth 5ressure

ngineering

esign in

*f the bac,fill properties are ,nown4

preactice

*f wall friction is to be ignored

(δ = 0 )

(Roger 3 westbroo,)

'9

;

:3sin F0

;

96=>>

(page3D)

'a

;

( :3sin F0 ) ? ( :sin F0 )

;

969H

 ma%

;

B6'a6h

;

<9

%

96: %

D6:

; >6D ,/?m< ep

;

<9

%

; :=6<

Celon Ele'!i'i! Bo%&

C

D%$ S%fe!

96: % ,/?m<



; ma% 3 ep



;

=E6

:6D

,/?m<

oc6 /o6 esigned

S.M.P

ate

:69=6<9:9

E B

Envion$en!%l *

Chec,ed

ate

Civil S!u'!ue +%in!%n%n'e

8ob Code

5age

Reference  AA#$+O

Calculation

Output

, # Ve!i'%l Live Lo%&s

6>6:  7or 7ill epths $  E feet (<99 mm) and Culvert Clear #pan Length4 +he effect of live load is neglected in design when the depth of fill is more than

E feet - # .&os!%!i' Pessue (In!en%l)

 ip

; C6h ;

D6E: %

; :H6HE

:6> ,/?m<

/ # An%lsis

Reinforced Concrete

Constant '

;

h



;

:6<:

Manual

,:

;

':

;

<6<:

(ref3=6:)

,

;

'

;

6<:

,=

;

<'

;

=6

,>

;

<'>

;

D6

,E

;

'E

;

::6H

esigners

l

6:

N

hs hw



Load Case 39: +esting Condition

6:6: $ydrostatic 5ressure3(*nternal) Reinforced

A

M A ;

B

Concrete esigners

M! ; ip6h<6'6,> H96,:6, ;

qip

96DD ,/6m?m

Manual (ref3=6:)

D q = qip ressures

C

MC ;

M ; Ma6 'E

B.M.D

,> :6<:> ,/6m?m

;

6:6< 7le%ure due to weight of wall Wall weight ( " )

;

hw6B6h

;

E6<

: ; <6"

;

:96<9 ,/?m<

l6hw

,/?m

Reinforced Concrete

A

M A ;

B

esigners Manual

G

M! ; :6l<6' :<6,:6,

G

;

96<< ,/6m?m

(ref3=6:) D q! ressures

C

MC ;

B.M.D

M ; Ma6 '= ' ;

396D>

,/6m?m

6:6 7le%ure due to weight of Roof  

;

:

hs6Bc

;

6E

oc6 /o6

,/?m<

C E B

D%$ S%fe!

esigned

Envion$en!%l *

Chec,ed

ate

Civil S!u'!ue +%in!%n%n'e

8ob Code

5age

Reference

S.M.P

Calculation A

B

D

M! ;

MC ;

M

; 6l<

C B.M.D

:<6,: ;

396=

,/6m?m

 Addition of moment for Load case 9: 5osition

$ydrost3 atic

Bf

uls3 Mb

Walls

Roof 

Walls  Roof 

Bf 

uls3 Mb

 A and !

96DD

:6

:6E

96<<

396=

396:

:6

396:D

:6:D

C and 

:6<<

:6

:6>9

396D>

396=

3:6<

:6

3:6E=

396:=

Roof mid3 #pan

96DD

:6

:6E

96<<

:69

:6

:6=

<6E

!ase mid3 #pan

:6<<

:6

:6>9

<6=

:6

6
=699

:6

3<6EE

396>

:6

3:69<

36D9

Walls middle

P 3<69H

PP 96E<

PP

PP

:6=

96E<

396E

396=

+able 3 9: 7i%ed end mement of the wall for $ydrostatic load M A

;

W6L

;

MC

W6L

:= ;

:9

:6H9> ,/6m?m

Ma%imum (3ve) moment

;

<6: ,/6m?m

;

W6L

(Where % is 96=L from C)

<6 ;

3:69 ,/6m?m

P Calculation of moment at mid span of walls done by apro%imatly by adding moment transferred to mid span from 7M to the Ma%imum negative meoment occurred at 96=L after moment distribution PP Moment at mid span of the wall is calculated by considering full bending Calculation of midspan moment due to wall load /iutral a%is depth from A 6<

;

96
Load Case 39< Culvert empty and trench filled

Lateral soil pressurees giving rise to fle%ture in the structure QQis the rectanguler pressure and Q epQ is the triangular pressure 6<6: +rianguler 5ressure4 ep Reinforced Concrete

A

B

M A ;

M! ; ep6h<6'6,> H96,:6,

esigners

; 396D: ,/6m?m

Manual (ref3=6:) qep

qep ressures

C

D

:69=6<9:9

< Output

M A ;

q = q! ressures

ate

MC ;

M ; M A6 'E

B.M.D

,> ;

3:6: ,/6m?m

+otal uls

oc6 /o6 C E B

S.M.P

D%$ S%fe!

esigned

Envion$en!%l *

Chec,ed

ate

Civil S!u'!ue +%in!%n%n'e

8ob Code

5age

Reference

Calculation 6<6< #urcharge on walls4

M A ;

M! ;

MC ;

B

M

; 6h 6' :<6,:

Concrete

D

; 3>6>< ,/6m?m

esigners (ref3=6:)

A

<

Reinforced

Manual

ate

6<6 #urcharge on Roof 4r 

M A ;

M! ;

MC ;

C B.M.D

ressures A

B

M

<

; 6l

:<6,: ;

3>6=

D

,/6m?m

C B.M.D

ressures

 Addition of moment for Load Case < +otal (#urvice)

Bf 

3>6=

3:H6<<

:6

3<<6>9

3:6<

3>6=

3:>6H<

:6

3<6HH

3>6><

:69

:>6
D6>9

:6

:6=E

3:6:

3>6><

<6=

:>6
:96E9

:6

:=6:<

P

PP

:6

:6D

396>

3>6=

H6H=

:6

D6:

Walls J #urcharg Roof( LC3:) 3e (Roof)

5osotion

ep



 A and !

396D:

3>6><

396:

C and 

3:6:

3>6><

Roof mid3 #pan

396D:

!ase mid3 #pan Walls middle

+otal -6L6#6

7i%ed end mement of the wall due to ep M A

;

W6L

MC

;

:= ;

:9

:6EH ,/6m?m

;

Ma%imum (3ve) moment

;

(Where % is 96=L from C)

<6<
; 6<

W6L

3:69 ,/6m?m

Load Case 39

6<6: +his is load case 9<  $ydrostatic load from Load case 9:

5osotion

L6C69< (#ervice)

$ydrost6 (#ervice)

+otal (#ervice)

L6C69< (-6L6#6)

$ydrost6 (-6L6#6)

 A and !

3:H6<<

96DD

3:=6<

3<<6>9

:6E

3<:6<

C and 

3:>6H<

:6<<

3:H69

3<6HH

:6>9

3<<6DH

Roof mid3 #pan

D6>9

96DD

:96HD

:6=E

:6E

:6DH

!ase mid3 #pan

:96E9

:6<<

:<69<

:=6:<

:6>9

:H6E

Walls middle

H6H=

3<69H

6=D

D6:

3<6EE

H6

+otal

(-6L6#6)

:69=6<9:9

 Output

oc6 /o6 C E B

D%$ S%fe!

esigned

Envion$en!%l *

Chec,ed 8ob Code

Civil S!u'!ue +%in!%n%n'e

Reference

S.M.P

Calculation

Load Case 39:

$ydrostatic 5ressure

;

:H6HE

,/?m<

Weight of walls

;

:96<9

,/?m<

Weight of Roof  7loor

;

D6H9

,/?m<

+otal 5ressure

;

H6E

,/?m<

+otal 5ressure =6<

I

:=9 ,/?m<

hence o,

Load Case 39<

Weight of walls

;

:96<9

,/?m<

Weight of Roof  7loor

;

D6H9

,/?m<

#urcharge on Roof

;

DH699

,/?m<

+otal 5ressure

;

::=6E9

,/?m<

+otal 5ressure =6

I

:=9 ,/?m<

hence o,

Load Case 39

Weight of walls

;

:96<9

,/?m<

Weight of Roof  7loor

;

D6H9

,/?m<

#urcharge on Roof

;

DH699

,/?m<

$ydrostatic 5ressure

;

:H6HE

,/?m<

+otal 5ressure

;

:<<6
,/?m<

+otal 5ressure

I

:=9 ,/?m<

hence o,

4 # U5L5S5 of 6lex!ue

Ma%imum Moments ,/6m?m Member

$ogging

#agging

Roof

3<<6>9

(L6C39:)

:6DH

(L6C39)

Walls

3<6HH

(L6C39<)

D6:

(L6C39<)

!ase

3<6HH

(L6C39<)

:H6E

(L6C39)

i 3 #labs Ma%imum Moment

;

:69=6<9:9

ate 5age

 Output

0 # Ce'1 on goun& s%fe 2e%ing 3essue

=6:

ate

<6:=

,/6m?m

oc6 /o6 C E B

Envion$en!%l *

esigned Chec,ed

Civil S!u'!ue +%in!%n%n'e

8ob Code

D%$ S%fe!

Reference

S.M.P

ate ate

:69=6<9:9

5age

=

Calculation

Output

Design C%l'ul%!ion fo Box C ulve!

4#

H6:

U5L5S5 of 6lex!ue

 Analysis was carried out for several load cases of various loading arrangements to find out the ma%imum effect on the !o% culvert iameter of main reinforcement

;

:<

mm

iameter of secondary reinforcement

;

:<

mm

#ection +hic,ness

;

Ma%imum !ending Moment

;

<99 mm <6:=

,/6m?m

 Assume severe environment condition4 for driving rain ;

Cover  ;

ffective depth4 d

<99

3

= 3

=

mm

H

d

; :D

mm

; :D ,

mm < ; M ? (bd f cu)

<

; (<6:=%:9  ?(:999%:D %<=) H

;

969

<

I 96:=H

$ence no compression r?f is reuired M &

; (96E>f )As& ; (: 3 :6:f y As? f cubd) d

euation : euation =

from these two euations

&

; d (96=(96<=3,?96D):?<

&

; d U96=(96<=3969?96D):?< ;

::6:

I 96D=9 d

+a,e  as 96D=d 

; 96D=

d

; 96D=

%

:D

mm

; :<

H6:6: Design of $%in einfo'e$en!  As ; M ? 96E>f y&  As re

; <6:= %:9H ? 96E>%H9%:< ; -se

+

:<

mm

;


=<

mm
 As pro

mm
=<

mm
+ini$u$ %e% of $%in %info'e$en! fo sl%2s

:99As ? bad

; :99%=
; 969

T 96:

Main r?f   T

$ence o6,

H6<

Design fo Se% Reinfo'e$en!

Chec, shear in -6L6#6 on roof and floor slabs +a,e Load case 9< #hear across support

;

( ::=6E9 3

Wt of !ase % Bf )

;

:9D69E ,/?m<

",

7

,08

+herefore shear in the support ; ;

C E B

:9D69E % :6< ?< H=6= ,/?m

D%$ S%fe!

oc6 /o6 esigned

Envion$en!%l *

Chec,ed

ate

Civil S!u'!ue +%in!%n%n'e

8ob Code

5age

Reference

S.M.P

Calculation ;

H=6= ,/?m

ffective depth4 d

;

:D mm

+ension steel across shear plane

; 1:< 3<=9 c?c ;

:99 % =< :999%:D

!# E::9

ffective depth

vc

5art 9:

;

969

;

:D mm

; 96>D%N(:99As?bd):?6(99?d):??:6<= ;

table 6: esign shear stress

v

96=

; .?bd ; (H=6=%:9)?(:999%:D) ;

v

H6 !s E::9

96 /?mm<

I

vc

$ence o6,

Ce'1 in U5L5S5 on !e %2ili! of !e 9%ll !o !%s$i! !e %xi%l lo%&s

+reat as a column with bending at right angle to wall

Chec, h?hw

6D66H6< 666:

; ;

:6> ? E6= I

96< :<

hence column is short !# E::9 indicates that the effect of the a%ial load may be ignored if this force does not e%ceed 96:6f cu6(c6s6a6)

hence

96:6fcu6(C6#6A)

-ltimate Load ?m?Wall

;

96: %

9

;

H99

,/?m

;

:?<( DH69 % 

;

%

<99 :6>

96<

%

:<9 ,/?m I

% :6 :6>

H99

% <%:6 )

,/?m

hence o6,6 +he above calculation assumes that the wall is cosidered as reignfoced and not mass concrete vertical R?7 provided

;

so Area 5ercentage of Concrete area

1

:<

G

<99

:::69

mm<

;

:::69

%

:999 % +his is

S

;

;

:99

:D

96>=D V G

Minimum of 96V

:69=6<9:9

H Output

esign shear force4 . design

:99 As?bd

ate

96 V

hence o6,6

< Layers

oc6 /o6 C E B

D%$ S%fe!

esigned

Envion$en!%l *

Chec,ed

ate

Civil S!u'!ue +%in!%n%n'e

8ob Code

5age

Reference

Calculation

S.M.P

ate

:69=6<9:9

> Output

oc6 /o6 C E B

D%$ S%fe!

esigned

Envion$en!%l *

Chec,ed

ate

Civil S!u'!ue +%in!%n%n'e

8ob Code

5age

S.M.P

ate

:69=6<9:9

E