Data i)Inside dimensions of culvert
=
ii)Grade of concrete
=
iii)Grade of steel
=
iv)External load
=
v)Force on side walls Assumptions
=
i)ermissible stress in concrete * cbc
=
ii)ermissible stress in steel (on faces of members in contact with water or with in a distance of ' mm) * st
iii)ermissible stress in steel (on faces of members on other faces awa+ from water) * st
iv),lear cover
=
=
:
=
a)For forces of members in contact with water
=
b)For forces of members in contact with soil
=
v)Thickness of slab as well as wall Design Constants Modular ratio (m)
=
a)Design constants for faces of maembers in contact with water
K
=
n
= m*cbc
d
=
!
$
=
%&'-σcbc k
K
=
n
"
= = b)Design constants for faces of maembers away from water
=
%&' !&#
= m*cbc
d
k #
!
"
k #
$
=
%&'-*cbc k
Case I)When there is no water in the box culvert : ,onsider ! m len/th of the culvert Top slab : 9oads on to2 slab i)0elf wei/ht of slab ii)1ei/ht of finishin/ iii)External load Total load Effective s2an Fixed end moment at 3 4 5 is
MAB
=
MBA
Maximum 2ositive 5&M at mid s2an
= =
%&' !&.
= = = = = =
.&' %&' ''
=
1l2 !
=
1l2
63
#
6 ottom slab :
7et u2ward 2ressure on bottom slab
=
Fixed end moment at 8 4 , is
=
MDC
=
MCD
Maximum 2ositive 5&M at mid s2an
''
=
1l2 !
=
1l2 6
!ide walls: 9oadin/ on side walls 38 or 5, is identical Fixed end moment at 3 4 5 is
MAB
=
MBC
Fixed end moment at 8 4 , is MDA
=
To calculate maximum 2ositive 5&M $A =
=
1l2 #%
= MCB
=
1l2 %
$B
=
%&'
=
6&#
$
=
%&'-*cbc k
Case I)When there is no water in the box culvert : ,onsider ! m len/th of the culvert Top slab : 9oads on to2 slab i)0elf wei/ht of slab ii)1ei/ht of finishin/ iii)External load Total load Effective s2an Fixed end moment at 3 4 5 is
MAB
=
MBA
Maximum 2ositive 5&M at mid s2an
= =
%&' !&.
= = = = = =
.&' %&' ''
=
1l2 !
=
1l2
63
#
6 ottom slab :
7et u2ward 2ressure on bottom slab
=
Fixed end moment at 8 4 , is
=
MDC
=
MCD
Maximum 2ositive 5&M at mid s2an
''
=
1l2 !
=
1l2 6
!ide walls: 9oadin/ on side walls 38 or 5, is identical Fixed end moment at 3 4 5 is
MAB
=
MBC
Fixed end moment at 8 4 , is MDA
=
To calculate maximum 2ositive 5&M $A =
=
1l2 #%
= MCB
=
1l2 %
$B
=
%&'
=
6&#
9et the 2oint of :ero shear force occurs at a distance 3t the 2oint of :ero shear shear force %&'
x
x 2
=
6&# %&'
x
=
!&;!
=
6&#
=
!%&<
The maximum 2ositive 5&M
"oment Analysis : A
8istribution Factors
%&'%
%&'%
F.E.M
'&'% '&6'
%&%
"'.&% '&6' "!&;# <&< "#&# !&< "%&6! %&%
3'.(3
)3'.(3
5alancin/ ,arr+ over 5alancin/ ,arr+ over 5alancin/ ,arr+ over 5alancin/
<&< !&<
F!"# M$%&!ts
Case II)When culvert is full full of water : Top slab : 9oads on to2 slab i)0elf wei/ht of slab ii)1ei/ht of finishin/ iii)External load
Total load Effective s2an Fixed end moment at 3 4 5 is MAB
=
MBA
Maximum 2ositive 5&M at mid s2an
= = = = = =
.&' %&' ''
=
1l2 !
=
1l2
63
#
6 ottom slab : 7et u2ward 2ressure on bottom slab Fixed end moment at 8 4 , is
MDC
=
MCD
Maximum 2ositive 5&M at mid s2an
= =
''
=
1l2 !
=
1l2 6
!ide walls: The water 2ressure actin/ in direction o22osite to the external 2ressure will var+ from #&# x = ##%% 7>m = ## K7>m = ?ence net 2ressure for the desi/n of side walls will be 3t to2 i&e&@ at 3 or 5 % =
3t bottom i&e&@ at 8 or ,
=
##
"
MAD
=
MBC
=
1l2 #%
MDA
=
MCB
=
1l2 %
$B
=
%&'
=
;&;
To calculate maximum 2ositive 5&M $A =
"oment Analysis : A
8istribution Factors
%&'%
%&'%
F.E.M
"<&<% #!&;%
"'.&% #!&;% "!'&;' .&;6 "#&;; !&;; "%&;;.
5alancin/ ,arr+ over 5alancin/ ,arr+ over 5alancin/ ,arr+ over
.&;6 !&;;
5alancin/
%&;6
%&'%
F!"# M$%&!ts
3*.++
)3*.++
9et the 2oint of :ero shear force occurs at a distance 3t the 2oint of :ero shear force %&'
x
x 2
=
;&; %&'
x
=
!&;%'
=
;&;
=
!&<
The maximum 2ositive 5&M
The maximum 5&M to which the various sections are subected to in the two cases re The thickness of the slab for culvert will be /overned b+ the thickness obtained from
The to2 and bottom slabs are subected to maximum 2ositive 5&M of '%&## K7m and Design Constants :
*st $
= = =
d
=
!!' %&6'# !&# M%", $&b <<6%%%%
= = Averall de2th assumin/ = =
!&#
!%%%
! mm % mm dia of main bars and clear c ! B '.
3do2t overall thickness of the floor as well as wall slab of the culvert = 3vailable effective de2th(d) = =
mm
.' %
Calculation for area of reinforcement : #) $or top slab : 3st1 for 2ositive 5&M at mid s2an(tension near water face)
3st1
=
M &d&σst
= =
02acin/ usin/ 3Ø
%
02acin/
mm diameter of bars
=
#&!!
= =
#!' #!'
= !; rovide % mm diameter bars C !'% mm c>c
x
%
x !< mm ,>,
!%%%
mm
3st for ne/ative 5&M at su22ort(tension on faces awa+ from water) 8esi/n constants for member havin/ tension on faces awa+ from water *st = !' d
3st2
02acin/ usin/ 3Ø
%&6<% .'
=
'
mm
%&6<%
x
"
=
%
02acin/
= =
= !<6 mm diameter of bars
=
#&!!
= =
#!' #!'
= !; rovide % mm diameter bars C !;% mm c>c
mm2
x
%
x !<6 mm ,>,
!%%%
mm
%) $or bottom slab : 3st1 for 2ositive 5&M at mid s2an(tension near water face)
3st1
=
M &d&σst
= =
02acin/ usin/
%
mm diameter of bars
3Ø
=
#&!!
02acin/
= =
#!' #!'
= !!< rovide % mm diameter bars C !!' mm c>c
x
%
x .. mm ,>,
!%%%
mm
3st for ne/ative 5&M at su22ort(tension on faces awa+ from water) 8esi/n constants for member havin/ tension on faces awa+ from water *st = !' d
3st2
02acin/ usin/ 3Ø
%&6'# .'
=
'
mm
%&6'#
x
"
=
%
02acin/
= =
= ;. mm diameter of bars
=
#&!!
= =
#!' #!'
= #% rovide % mm diameter bars C #%mm c>c
mm2
x
%
x ;. mm ,>,
!%%%
mm
&) $or vertical walls : 3st for mid s2an moment(tension on face awa+ from water)
3st
= %&6<% =
x
!'!&6;6%! mm2
&)Distribution 'einforcement:
3s 2er code for water tanks@ for sections thicker than !%% mm and less than '% mm of thickness eual to or /reater than 'mm two la+ers of reinforcin/ bars shall be 2l In this case thickness of section ercenta/e of distribution reinforcement
=
'%
mm
=
%&#
"
3rea of steel
3rea of steel on each face 02acin/ usin/ 3Ø
02acin/
= =
%&'. %&'. !%%
D
=
<#
=
<#
=
=
#&!!
x
=
.; .;
x mm2
!% mm diameter bars
=
= rovide !% mm diameter of bars C % mm c>c
<
mm2 x # mm
The to2 and bottom slabs are also subected to direct tension due to thrust of water@ t
1.0 DESIGN OF BOX CULVERT
#
x
%
7>mm2
'%
7>mm2
''
K7>m2
!'
K7>m2
.
7>mm2
!!'
7>mm2
!'
7>mm2
# ''
#m
!'
#m
K7>m2
'' ' mm or diameter of bar which ever is more %
mm
#%%
mm
6% #&*cbc
=
6% #
m*cbc B
= *st
= x
! .
m*cbc B =
x
= "
!# %& %& #
x
%&6'#
= *st !
= "
!# %&! %&! #
=
!#
!#
x
.
x
.
B
=
%&6'#
.
x
%&
!#
x
.
x
.
B
=
%&6<%
x
.
x
%&6<%
x
%&!
K7>m K7>m K7>m K7>m B
%&!'
B
%&!'
=
#&#
=
<#
x
#&# !
x
#&#
=
'.&
x
#&#
x
#&#
=
m
K7m
<#
6 =
6'&6
K7m
K7m
=
''
=
'%&%
=
x
#&# !
x
#&#
x
#&#
x
#&#
x
#&# #%
x
#&#
x
#&# %
x
#&#
x
#&#
x
! #
K7m
''
6 =
.&;
=
!'
=
'&'
=
!'
=
6&
x
!'
K7
K7m
K7m
K7m !'
x
from 3 or 5&
!' #&#
x
x x
#&# !'
x
x
x
=
6&#
"
%&'
x
!'
x #&#
m x
!&;!!
K7m
C
%&'%
%&'%
%&'%
%&'%
%&'%
'.&% "'&6' !&;# "<&< #&# "!&< %&6! "%&%
"'&'% "'&6'
"'%&%% %&;
"<&<
'&#
"!&<
!&#!
"%&%
%&##
6& %&; "!%&< '&# "&
"6& "%&; !%&< "'&# &
3'.(3
)3'.(3
)22.22
22.22
)22.22
K7>m K7>m K7>m K7>m B
%&!'
B
%&!'
=
#&#
=
<#
x
#&# !
x
#&#
=
'.&
x
#&#
x
#&#
=
<#
K7m
6 =
6'&6
K7m
K7m =
''
=
'%&%
=
x
#&# !
x
#&#
x
#&#
x
#&#
K7m
''
6 =
.&;
K7m
:er at to2 to !%%%
!'
=
!6
K7m
=
!6
x
#&# #%
x
#&#
x
#&# %
x
#&#
x
#&#
x
! #
<&< =
!6 ;&;
x
K7m
!6
K7m
K7
C
%&'%
%&'%
%&'%
%&'%
%&'%
'.&% "#!&;% !'&;' ".&;6 #&;; "!&;; %&;;.
<&<% "#!&;%
"'%&%% ;&;'
".&;6
.&;
"!&;;
!&6.
";&; ;&;' "!&;6 .&; "#&. !&6. "%&;
;&; ";&;' !&;6 ".&; #&. "!&6. %&;
"%&;6
"%&;6
%&.
%&.
"%&.
3*.++
)3*.++
)10.22
10.22
)10.22
x
from 3 or 5&
!6 #&#
x
x x
#&# !6
x
x
x
=
"
%&'
x
!6
;&;
m x
!&;%'
x #&#
K7m erred above have been marked as below aximum 5&M an+ where in the box section& 3 <&<6 Knm 2roducin/ tension near the water face&
#;&6#
3*.1
& 8
ver of
' mm '
B
%
.' mm " mm
'
"
%
'%%#%%%% %&6'# !<
x
%
x
!!'
mm2
x
%
%
"
#;6#%%%% '
x
x
%
%
!'
<<6%%%% %&6<% ..
x mm2
%
x
!!'
x
%
%
"
%%%% '
x
x
%
#'!%%%%% '
%
!'
x
!'
the minimum reinforcement in each of the two directions shall be linearl+ reduced from %&# D aced one near each face of the section to meet the reuirements of minimum reinforcement&
%&#
"
%&
'%
"
!%%
x
'%
"
!%%
'%%
#
!%
x
!%%%
x
!%
mm2
!%%%
he ma/nitude of which is ver+ small and hence ne/lected&
K7>m2
!'
K7>m2
!!'
!'
K7>m2
3
8
5
,
!'
K7>m
!&;!!
x
!&;!!
x
D
%&'% '%&%% "%&; "'&#
!&;!
"!&#! "%&## 22.22
!&%;
!&;!! #
D
%&'% '%&%% ";&;' ".&; "!&6.
"%&. 10.22
!&;%'
#;&6#
x
!&;%'
*0.03
x
!&;%' #
#;&6# 5 #;&6#
3*.1
& , &
6-.6(
&
or !%% mm thick sections to %&D for '% mm thick sections &3lso in case of concret
sections
