Rcc box culvert methodology and designs including computer method

Paper No. 555

RCC BOX CULVERT - METHODOLOGY AND
DESIGNS INCLUDING COMPUTER METHOD†
B.N. Sinha* & R.P. Sharma**

ABSTRACT
Culverts are required to be provided under earth embankment for crossing of water course like streams, Nallas
across the embankment as road embankment can not be allowed to obstruct the natural water way. The culverts
are also required to balance the flood water on both sides of earth embankment to reduce flood level on one side
of road thereby decreasing the water head consequently reducing the flood menace. Culverts can be of different
shapes such as arch, slab and box. These can be constructed with different material such as masonry (brick, stone
etc) or reinforced cement concrete.
Since culvert pass through the earthen embankment, these are subjected to same traffic loads as the road carries
and therefore, required to be designed for such loads. This Paper deals with box culverts made of RCC, with and
without cushion. The size, invert level, layout etc. are decided by hydraulic considerations and site conditions.
The cushion depends on road profile at the culvert location. The scope of this Paper has been further restricted
to the structural design of box. The structural design involves consideration of load cases (box empty, full, sur-
charge loads etc.) and factors like live load, effective width, braking force, dispersal of load through fill, impact
factor, co-efficient of earth pressure etc. Relevant IRC Codes are required to be referred. The structural elements
are required to be designed to withstand maximum bending moment and shear force. The Paper provides full
discussions on the provisions in the Codes, considerations and justification of all the above aspects on design.
Proper design covering these aspects has also been given in the Annexure. To our knowledge, these matters have
neither been covered in any text book nor in any special publication at one place.

1 INTRODUCTION there is no cushion. A box can also be placed within
the embankment where top slab is few meters below the
It is well known that roads are generally constructed
road surface and such boxes are termed with cushion.
in embankment which come in the way of natural flow
The size of box and the invert level depend on the
of storm water (from existing drainage channels). As,
hydraulic requirements governed by hydraulic designs.
such flow cannot be obstructed and some kind of cross The height of cushion is governed by the road profile
drainage works are required to be provided to allow at the location of the culvert. This Paper is devoted to
water to pass across the embankment. The structures to box culverts constructed in reinforced concrete having
accomplish such flow across the road are called culverts, one, two or three cells and varying cushion including no
small and major bridges depending on their span which cushion. The main emphasis is on the methodology of
in turn depends on the discharge. The culvert cover upto design which naturally covers the type of loading as per
waterways of 6 m (IRC:5-19981) and can mainly be of relevant IRC Codes and their combination to produce
two types, namely, box or slab. The box is one which the worst effect for a safe structure. The IS:1893-1984²
has its top and bottom slabs monolithically connected (Clause 6.1.3) provide that box culverts need not be
to the vertical walls. In case of a slab culvert the top designed for earthquake forces, hence no earthquake
slab is supported over the vertical walls (abutments/ forces are considered. Although box of maximum three
piers) but has no monolithic connection between them. cells has been discussed but in practice a box culvert can
A box culvert can have more than single cell and can be have more cells depending on the requirements at site.
placed such that the top slab is almost at road level and Culverts are provided to allow water to pass through

* General Manager
** General Manager } ICT Pvt. Ltd., A-9, Green Park, New Delhi – 110 016,
e-mail : rpsharma@ictonline.com
e-mail : bnsinha@ictonline.com

† Written comments on this paper are invited and will be received upto 5 November 2009.

Journal of the Indian Roads Congress, October-December 2009

190 Sinha & Sharma on

the embankment and follow natural course of flow but for more number of lanes, a situation which occurs on
these are also provided to balance the water level on both widening of the road and frequently encountered for
sides of embankment during floods, such culverts are road development, and whether the culvert designed for
termed as balancers (IRC:78-2000³), although there is no no cushion shall be safe for cushion loads which may
difference in the design. Sometimes the road alignment become a necessity at a future date due to change in road
may cross a stream at an angle other than right angle, profile. If so, up to what height of cushion, the box need
in such situation a skew culvert may be provided. For not be reconstructed. These shall be addressed in this
a smaller span there would be no difference in the Paper giving appropriate solutions as required.
design of culvert but it may require an edge beam and Box culvert has many advantages compared to slab
the layout of wing walls will have to be planned as per culvert or arch culvert. The box is structurally strong,
skew angle. stable and safe and easy to construct. The main
For a box culvert, the top slab is required to withstand advantage is, it can be placed at any elevation within the
dead loads, live loads from moving traffic, earth pressure embankment with varying cushion which is not possible
on sidewalls, water pressure from inside, and pressure for other type of culverts. A multi cell box can cater for
on the bottom slab besides self weight of the slab. The large discharge and can be accommodated within smaller
structure is designed like a rigid frame considering one height of embankment. It does not require separate
meter element and adopting moment distribution method elaborate foundation and can be placed on soft soil by
for obtaining final distributed moments on the basis of providing suitable base slab projection to reduce base
the relative stiffness of the slab and vertical walls. The pressure within the safe bearing capacity of foundation
method is well known and does not need any elucidation. soil. Bearings are not needed. It is convenient to extend
The mid span moments are computed with free supported the existing culvert in the event of widening of the
ends and adjusting it for moments at support obtained carriageway at a later date as per future requirement,
after distribution. The moments at center and supports without any problem of design and/or construction.
for slabs and walls are obtained for various combination 2 CO-EFFICIENT OF EARTH PRESSURE
of loads and the member is designed for the maximum
moment it may be subjected to. Also the shear force at The earth can exert pressure, minimum as active and
a distance of effective depth from the face of wall and maximum as passive, or in between called pressure at rest.
shear stresses it produces in the section is considered in It depends on the condition obtained at site (Terzaghi4
the design. A few things like coefficient of earth pressure and Gulati5). For example in case of a retaining wall
where the wall is free to yield and can move away from
for lateral pressure on walls, effective width (run of
the earth fill the pressure exerted by the earth shall tend
culvert) for live loads and applicability of braking force
to reach active state and thus be minimum. As to reach
on box without cushion (or little cushion) for structural
active state only a small movement is required which
deformation are important items where opinion of the
can normally be achieved in case of a retaining wall,
designers vary and need to be dealt in much detail. These
also before failure of the wall by tilting, the back fill is
affect the design significantly and therefore, required to
bound to reach active state. The wall thus can safely be
be assessed correctly for designing a safe structure. It is
designed for active pressure of earth, with co-efficient
customary to consider box a rigid frame and unit length
applicable for active pressure. In case of an anchored
of box is taken for design by considering the effect of
bulk head, the earth pressure on the anchor plate will
all forces acting on this unit length (generally 1.0 m of
tend to achieve passive state because the anchor plate
box). While calculating weight of cushion on top slab, is dragged against earth and large displacement can be
some designer take average height of earth fill coming allowed, one can consider passive co-efficient for the
over full length of box including sloping side fill. This design of anchor, of course, some factor of safety need be
is not correct and full height of cushion should be taken taken as required displacement to achieve passive state
at the worst section of the box (central portion) will before the bulk head gives way may not be practical. In
be subjected to this load and the section needs to be cases where the structure is constructed before back fill
designed accordingly. earth is placed in position and the situation is such that
A question has been raised frequently whether culverts structure is not in a position to yield on either side, the
designed for four lane divided carriageway are safe earth pressure shall reach a state at rest. In such situation


Rcc Box Culvert- Methodology and Designs Including Computer Method 191

the co-efficient of earth pressure shall be more than deformation can be assumed to be at rest/active pressure
the active condition. In case of box since it is confined as the earth pressure co-efficient has little over all effect
with earth from both sides the state of earth shall be at on the structural sizes of box members as already shown
rest and a co-efficient more than the active pressure is in Table 1 and explained under sub para 2 above. For
normally adopted in the design. The earth is filled after A,B,C & D refer Annex A.
construction of the box further the box is not in a position
to move/yield therefore the pressure shall be at rest. The 3 EFFECTIVE WIDTH
value is designer’s choice.
Effective width in the run of culvert (length across span)
The co-efficient of earth pressure in case of box is is expected to be affected by a moving live load. This
taken to be 0.333 for a soil having ф = 30º equivalent width plays a significant role as far as consideration of
to active condition by many authors in their books of live load in the design of culvert. Where however, there
design. Some authors take this value = 0.5 for normal is large cushion the live load gets dispersed on a very
soil having ф = 30º. A typical box has been designed large area through the fill and the load per unit area
keeping all factors to be same for the two values of earth becomes less and does not remain significant for the
pressure co-efficient. It is seen that these co-efficient design of box, particularly in comparison to the dead
even when taken differently have little effect on the load due to such large cushion. In case of dead load or
over all design of the section. To bring out difference uniform surcharge load the effective width has no role
in more appreciable form the two designs are compared to play and such loads are to be taken over the entire
in Table 1. (refer Annex A and Annex B). It is observed area for the design.
that difference in design of culvert without cushion Effective width plays an important role for box without
is marginal. However, box with cushion shows more cushion as the live load becomes the main load on the
difference. top slab and to evaluate its effects per unit run for design
Considering the situation typical to the box, it is close as a rigid frame, this load is required to be divided by
to at rest condition and a co-efficient higher than active the effective width. As such evaluating effective width
pressure should be taken. For practical considerations correctly is of importance. The relevant IRC Codes,
a value of 0.5 can be taken for earth pressure. Whereas, other Codes, books, theory/concepts are at variance
there is no point of difference in taking this value for as far as effective width is concerned and requires
culverts with cushion, some reservations are shown discussions at some length.
where braking force is taken to act on culverts without It is required to understand the concept behind effective
cushion, where the box is assumed to deform pressing width. Basically, it is the width of slab perpendicular to
against the fill earth on one side and the pressure can be the span which is affected by the load placed on the top
different on two sides, at least it may tend to be active of slab. It shall be related to the area of slab expected
on the side the box is tilting away from the fill. In design to deform under load. It can be well imagined that this
this difference of earth pressure on two sides of box is area of slab which may get affected will depend on how
not taken, as the pressure on the passive side, which the slab is supported whether in one direction or both
depends on amount of deformation of culvert, can not directions and secondly on the condition of support that
be evaluated within reasonable limits. However, the is whether free or continuous or partially or fully fixed.
earth pressure on both sides of box before and after It can also be imagined that the width shall be larger if

Table 1 Comparison of Moment in kN.m for different Earth Pressure Co-efficient keeping all other
parameters same

Box Designation [1/3 x 3/ 5] [1/3 x 3/ 0]
Member Ka = 0.333 Ka = 0.5 Ka = 0.333 Ka = 0.5
Support A&B 71.3 82.5 115.8 119.9
Support C&D 83.8 95.5 79.1 83.6
Mid-span AB 80.5 69.3 90.9 86.9
Mid-span DC 85.5 79.3 52.2 47.7


slab is allowed to slide over support under the load as The live load moment and shear for the top slab can be
in case of freely supported, and the same will reduce if obtained per unit run of box considering effective width
the slab is restrained from sliding and more the restraint for an assessed value of α. For the bottom slab the live
the less shall be the width. In this view the effective load shall disperse through the walls and such dispersed
width shall be least for fully fixed and gradually increase area could over lap for different wheels, therefore,
for partially fixed, increase further for continuous slab a uniform distributed load per unit run of box could
and shall reach maximum for slabs freely supported at be obtained on this basis and used in the analysis. In
ends. Where support on one side is different than on other words the effect of live load on bottom slab shall
the other side the effective width should be obtained be as in case of large cushion for top slab explained
taking this fact in consideration. The distance of the load under sub para 1. As far as walls are concerned the
from the near support affects effective width, more the loads are uniform and pressure etc all are same per unit
distance larger will be the effective width and will reach run of culvert and effective width has no role to play.
highest when the load is at center. The ratio of breadth The braking force acts on the box structure and taking
(unsupported edges) and the span also affects effective effective width for top slab different than bottom slab
shall make the analysis cumbersome and may not be
width. All factors mentioned above need to be taken
practical. The AASHTO also advocates dispersal for
into account while obtaining the effective width.
bottom slab. Jaikrishna and O.P. Jain8 in his book has
The IRC:21-20006 Clause 305.16 gives an equation considered dispersal of live load through walls for
for obtaining effective width for simply supported and bottom slab at 45°. However, the MORT&H7 Standard
continuous slab for different ratio of over all width verses design do not tally with this provision.
span for these two kinds of supports. The Code does not The AASHTO9 for Standard Specifications for Highway
provide if one of the support is continuous while other is Bridges 17th Edition 2002, provides at para 16.6.4.3
simply supported. The Code is silent for other types of under RCC Box that “The width of top slab strip used
supports such as fixed or partially fixed. Some designers for distribution of concentrated wheel loads may be
use this formula and factors for continuous slab is taken increased by twice the box height and used for the
valid for partially restrained support in a situation like distribution of loads to the bottom slab”. This confirms
box culvert. This does not appear to be in order. The what is mentioned in sub para 5 and is alright. However,
reasons for this can be better realized by the explanations any such dispersal for bottom slab different than top
given in sub para 3 above. Nevertheless, effective width slab shall not be practical when braking force effect is
need to be obtained in box type structure also to evaluate to be taken, which shall have to be for the same run of
affected area by moving load for considering these in the box structure as a whole (refer para 4).
the design. The design of a typical box of designation
[1/3x3/0] has been done by obtaining effective width 4 BRAKING FORCE
considering varying value of α such as 2.6, 2.0, 1.0, 0.9,
This is another area where opinion of the designers vary
0.8 & 0 (Table 2). The moment and consequently the
in two ways firstly, whether braking force caused by
main reinforcement varies significantly with value of α,
moving loads shall deform the box structure and should
the amount of reinforcement increases with α decreasing.
therefore be considered in the design of box. Secondly,
This is because smaller α gives smaller effective if it is to be considered what effective width should be
width and, therefore, more moment and shear per unit taken to obtain force and moment per unit run of box. Of
length (run) of box, as all other dimensions are same course the braking force will affect the global stability
reinforcement increases with decrease in value of α. It and change the base pressure to some extent. The IRC
is further observed that MORT&H7 provision in their Code is silent as far as box is concerned. It will be in
standard drawings for a similar culvert and situation falls order to neglect effect of braking force on box having
between α value 0 to 1.0. This also indicates that taking large cushion. In such situation the braking effect will
value of α equivalent to that for continuous slab given be absorbed by the cushion itself and no force will be
in IRC:21-20006 shall not be correct for box structure. It transmitted to the box beneath. Question will, however,
may be seen that considering any value for α shall affect arise up to what cushion height no braking force need
mainly the top slab. Bottom slab due to dispersal through be taken. This height generally is taken to be 3 m. Thus
walls and box with cushion due to dispersal through fill no braking force for cushion height of 3 m and more
to even the top slab, are not affected much. and full braking force for no cushion, for intermediate


Table 2 Shows Moment and Reinforcement for Different Values of α Keeping other Parameters Constant as
given here: Box [1/3x3/ 0], Ka = 0.5, steel = Fe 415, concrete = M25, thickness of slabs and walls = 420 mm,
Concrete Unit Weight=24 kN/m3, Soil Unit Weight=18 kN/m3 , Wearing Course Weight = 2 kN/m²

Moment in kN.m. Area of reinforcement in mm²

Mab Mdc Mab Mdc
Design α values Mab Mdc Support Support
(Mid- (Mid- (Mid- (Mid-
(Support) (Support) A&B D&C
span) span) span) span)

As per 0 119.8 83.6 87.0 47.7 1834.8 1375.3 1331.4 1422.8
design 0.8 86.4 72.3 61.3 54 1322.6 1189.1 938.1 887.6
carried out 0.9 83.1 70.9 58.9 43.6 1272.0 1166.4 901.8 717.8
1.0 80.4 67.0 56.8 46.4 1231.3 1102.1 870.7 726.4
2.0 65.0 64.5 45.2 41.69 995.2 1051.4 692.8 685.8
2.6 59.8 62.8 41.2 41.1 916.0 1033.6 630.4 676.2
As per Standard Standard _ _ _ 1398 1398 1005.3 1570.8
Standard design design
design of compares provide only
MORTHS with values reinforce-
between ment as
α = 0 to 1 shown
heights of cushion the braking force can be interpolated. The box is considered a rigid frame for analysis and
There is no literature on this aspect and the Code is also design. The braking force can be taken to act on the top
not specific for box, however, IRC:6-200010 Clause junction of the box causing moment at fixed ends of both
211.7 mentions that no effect be taken at 3 m below walls and the top and bottom slabs having zero fixed end
bed block in case of bridge pear/abutment. Our further moments (IRC:6-200010 Clause 214.7). The moment
discussions shall be on box without cushion as far as distribution is carried out and distributed moments are
braking force is concerned. obtained at supports. This moment shall be added to the
maximum moment under different conditions for other
Braking force by the moving loads on top slab of box
loads to get final design moments at supports. It may
having no cushion shall act on the box structure and
be mentioned here that the mid span moments are not
shall deform the box. The question is what length of box
affected by braking force moments as the same being
can be considered to share this braking force. In another
zero at mid span even after distribution. Also braking
words what effective width of box shall be taken to obtain
force can act in either direction hence the moment
braking force per unit run of box. One way is to take the
at junctions can reverse in sign and thus needs to be
effective width of box same as considered for vertical
arithmetically added to moments due to vertical effect
effect of moving loads, discussed under para 3 above.
of loads for the design.
The arguments in favor of this is the same which holds
for effective width for vertical deformation of top slab It is seen that box without cushion if designed ignoring
under moving loads. Vertical effect as well as braking braking force effect gives smaller thickness and very
effect both are product of the same loads and can affect less reinforcement compared to the MORT&H7 standard
the same run of box. In absence of specific provision designs for similar culvert. In case of 2 m x 2 m box the
in Codes in this regard the same effective width can be distributed moment at junctions works out to about 60%
taken for both effects for the design of box. if braking force is not considered, consequently gives



lesser thickness and reinforcements. In case of box of The IRC:6-200010, Code Clause 211.7 specifies that
size 6 m x 6 m the braking force effect if not taken gives for calculating pressure on the bearings and on the
lesser moment say around 30% less (Table 3). That is for top surface of the bed blocks, full value of appropriate
larger size of box the effect of braking force becomes impact percentage be allowed. But for design of pier,
lesser. It, therefore, suggests that for smaller size box abutment below the level of bed block, the appropriate
braking force effect has to be taken in design. When, impact percentage shall be multiplied by the factor given
however, the size is big the braking force will affect the therein. Accordingly, the impact is to be reduced to 50%
design marginally. In all cases for box without cushion below bed block and zero at 3 m below, proportionately
braking force need to be considered in the design. reducing between this height. Although these provisions
are for bridges but can be applied in case of box structure
5 IMPACT OF LIVE LOAD in absence of any specific provision in the Code for box
in this regard.
Moving loads create impact when these move over the
deck slab (top slab). The impact depends on the class The AASHTO9 at para 3.8.1.2 specifies that impact
and type of load. The IRC:6-2000 Code gives formula to shall not be included for culverts having 1m or more
obtain impact factor for different kind of loads by which cover. This, however, will be on lower side compared
the live load is to be increased to account for impact. to considering zero impact for a cover (cushion) of 3 m.
The box without cushion where the top slab will be It is, therefore, suggested that considering full impact
subjected to impact is required to be designed for live on top slab without cushion and zero impact for 3m
loads including such impact loads. Any such impact is cushion and interpolating impact load for intermediate
not supposed to act on box with cushion. Hence no such height of cushion is on conservative side and can be
impact factor shall be considered for box with cushion. safely adopted.
The impact by its very nature is not supposed to act at
lower depth and no impact is considered for the bottom 6 SHEAR STRESS
slab of the box. It does not affect the vertical walls of The box is designed for maximum moment for its
the box and not considered in the design. concrete section and reinforcements. It is checked for

Table 3 Comparison of Designs without Braking Force with the Design when Braking Force is Considered

Culvert
[1/6 x 6/ 0] [1/2 x 2/ 0]
Designation
Support Support Support Support
Location Mid AB Mid CD Mid AB Mid CD
A D A D
Moment with
braking force, in 390 286 244.5 165.2 44 27 42.8 19
kN.m.
Moment without
braking force, in 301 184 244.5 165.2 27.5 8 42.8 19
kN.m.
Reinforcement
with braking force 3378 2187 2118 1263 835 504 813 355
in mm²
Reinforcement
without braking 2607 1407 2118 1263 522 149 813 355
force in mm²
Standard Design
Reinforcement in 2576 3142 3020 2576 1118 1118 804 804
mm²


shear at the critical section and if it exceeds permissible away from the face of wall, the distance where the
shear stress for the size of section; mix of concrete and shear force becomes equal to shear capacity of section
percentage of reinforcements, the section has to be (without shear reinforcement) is obtained. The shear
increased to bring shear stress within the permissible reinforcement shall be provided up to this distance on
limit. Alternatively, the reinforcement can be increased both sides of box from near wall. The design at annexure
to increase allowable shear strength. The third option is will further elucidate this.
to provide stirrups to counter excess shear stress. This
The box is to be safe in bending as well as in shear. The
may have to be adopted in situation where thickness
box can be designed for maximum shear and checked for
of slab cannot be increased due to certain restrictions.
bending, particularly where shear is expected to govern
The top and bottom slabs are needed to be checked
the design as for box having large cushion. However, the
for shear. The vertical walls carry much less loads and
tension reinforcement has to be provided for the bending
shall be normally safe in shear, therefore, there is no
moment in any case.
need to check in shear. To make safe in shear one or
any combination of increasing size, increasing tension
reinforcement and/or providing shear stirrups can be 7 DISTRIBUTION REINFORCEMENTS
adopted. The Code IRC:21-20006, in Clause 305.18 provides
It is important to note that IRC:21-20006 under Clause for distribution reinforcements. The distribution
304.7.1 has given table 12B. Permissible shear stress in reinforcement shall be such as to produce a resisting
Concrete for checking section for shear stress. The values moment in direction perpendicular to the span equal
given here have been drastically reduced compared to to 0.3 times the moment due to concentrated live loads
similar provision in previous Codes and practices. It is plus 0.2 times the moment due to other loads such as
observed that the shear may govern the design of the dead load, shrinkage, temperature etc.
section, in particular, box with large cushion. In box, moment due to live loads and dead loads
Critical section for shear is the section at effective depth are obtained considering both the loads together. It,
from the face of support (face of wall). The effective therefore, becomes cumbersome to separate these
depth is the distance of center of tension reinforcement two moments to apply above provision of the Code
from the extreme compression face. Where, however, to calculate distribution reinforcements. To make it
haunch is provided, an extra depth due to haunch within convenient and easy a combined factor for both the
a slope of 1V:3H can be considered to increase the loads, based on weighted average in proportion of their
effective depth (IRC:21-20006 Clause 305.5.3). This magnitude, can be worked out to apply for the design.
should be taken into account while deciding the critical This has been adopted in the typical design provided
section. However, for shear stress at the critical section, in Annexure.
the effective depth only without effect of haunch be
taken. 8 LOAD CASES FOR DESIGN

In situation when the section is required to be provided Mainly three load cases govern the design. These are
with shear reinforcement which otherwise is not safe given below (Ramamurtham11)
in shear and only this option is to be adopted, the shear a) Box empty, live load surcharge on top slab of box
capacity of the section based on permissible shear stress, and superimposed surcharge load on earth fill.
which is based on percentage of tension reinforcement
and concrete mix, is obtained. Shear capacity of b) Box inside full with water, live load surcharge on
section is deducted from the shear force obtained at top slab and superimposed surcharge load on earth
critical section and shear reinforcement is calculated fill.
for the balance shear force and accordingly provided c) Box inside full with water, live load surcharge on
in addition to other steel. It is obvious that such shear top slab and no superimposed surcharge on earth
reinforcement shall be required for the whole length of fill.
box but the distance along the span from the face of wall
up to which these shear reinforcement is to be provided The above mentioned load cases are to be examined for
shall have to be calculated. As the shear is reducing box with cushion and without cushion. In case of box


without cushion live load surcharge shall straightway be of Soil for Vehicular Loading. Table 3.11.6.4-1 and Table
considered to act on the top slab, of course with dispersal 3.11.6.4-2 give height of earth fill for Equivalent Height
through wearing coat and slab thickness as applicable. of Soil for Vehicular Loading. This is in conformity
In case of box with cushion the live load surcharge with varying live load surcharge explained in sub para
is supposed to disperse through such cushion in both 2 above.
direction thereby reducing intensity of load on top slab.
This shall be obtained for heaviest live load wheel, 9 DESIGN OF TYPICAL BOX
generally 70R(T) vehicle, with due restrictions due to Based on the above discussions and clarifications
several wheels placed simultaneously. One question design of a typical box covering all above mentioned
arises that with increase in cushion height, live load
points are presented as Annexure. The box of 3 m x 3 m
intensity decreases and eventually falls below the value
without cushion and with 5 m cushion have been given.
equivalent to load of 1.2 m height of earth fill, in this case
Various load cases have been given for the maximum
which of the two that is the actual dispersed live load
or superimposed load equivalent to 1.2 m height of fill design moments. The box has also been checked in
which is more, shall be taken. The answer is dispersed shear and shear reinforcement provided as required.
live load even if it is lower, should be taken. This is The relevant parameters are mentioned in the design.
because the highest value of live load has been taken to Detailed design of single cell box culvert with and
obtain this load and no live load can be expected higher without cushion have been given. Basically, there is
than this. This also explains the fact that with increase no difference in design of multi cell box having two,
in cushion the live load intensity will decrease which three or more cells. The bending moment is obtained by
is natural compared to taking superimposed surcharge moment distribution considering all the cells together
load equivalent to 1.2 m of fill at a constant rate for all for different combination of loading and design of
cushion heights. Further the superimposed live load section accomplished for final bending moments for that
equivalent to 1.2 m of fill is a very general provision member. Shear force and resulting shear stress have to
and shall be adopted where it is not practical to obtain be checked for members independently as done in case
actual live load more accurately as in case of earth of single cell. A drawing furnishing details of the box
retaining structures. based on detailed design and general arrangement for
AASHTO9 provides varying superimposed surcharge site of work as usually required for construction has also
load on earth embankment to consider Equivalent Height been given as Annex D.

Table 4 Moment and Shear values by Manual Calculation and STAAD. Pro.
Computer
By Manual
Item Location Members Output by Remarks
Calculation
STAAD.Pro
MAB,MBA,
82.50 83.05
MAD, MBC
Support
Bending MDC,MCD,
95.52 94.66
Moment MDA, MCB
(kNm) 69.32 69.99
MAB, MBA
Mid span MDC, MCD, 79.34 81.70
MAD, MBC 15.06 15.22
Shear A&B 112.93 113.88
Force At deff from support for slabs
D&C 133.06 102.46
(kN) At deff from top slab for wall A&B 76.51 75.95
At deff from bottom slab for wall D&C 78.40 78.96



The design of the single cell box of size 3 m x 3 m with little influence on the design of box particularly
5 m cushion have also been done by using STAAD. Pro without cushion.
computer software and moment and shear as obtained
are compared with that calculated by manual method ix) For culverts without cushion (or little cushion)
of design. These are given in Table 4. It is seen that taking effective width as per provision in
they compare well. The design of box can, therefore, IRC:21-2000 corresponding to α for continuous
be carried out by STAAD. Pro as well. Input data sheet, slab shall not be correct. It is likely to provide
bending moment diagram and shear force diagram as design moments and shear on lower side hence
obtained by STAAD. Pro are given in the Paper at not safe.
Annex C. The analysis part to get these design moment
x) For box without cushion braking force is required
and shear values for relevant members which runs in
number of pages, is not given in the Paper as it will add to to be considered particularly for smaller span
the length without serving much purpose. The STAAD. culverts. Further for distribution of braking force
Pro is well known computer software commonly used. effects the same effective width as applicable for
vertical application of live load shall be considered.
Box without cushion : Annex A
If braking force is not considered or distributed
Box with cushion : Annex B over the whole length of box (not restricted within
the effective width) the design shall be unsafe.
Design of box with
cushion by STAAD.Pro. : Annex C xi) It may be seen that α affects effective width,
Drawing of the box culverts mainly applicable for the top slab (particularly
for construction purposes : Annex D for box without cushion) and braking force. As
regards bottom slab and top and bottom slabs of
10 CONCLUSIONS box with cushion due to dispersal of loads either
through walls or through fills effective width loses
i) Box for cross drainage works across high
its applicability.
embankments has many advantages compared to
a slab culvert. xii) The design of box is covered by three load cases
ii) It is easy to add length in the event of widening of dealt in this paper. The forth situation when whole
the road. box is submerged under water, provide design
moments etc less than given by the three load cases
iii) Box is structurally very strong, rigid and safe.
hence need not be considered.
iv) Box does not need any elaborate foundation and can
xiii) The design of box with cushion done by STAAD.
easily be placed over soft foundation by increasing
Pro computer software compares very close to
base slab projection to retain base pressure within
safe bearing capacity of ground soil. manual design.

v) Box of required size can be placed within the 11 ACKNOWLEDGEMENTS
embankment at any elevation by varying cushion.
This is not possible in case of slab culvert. We are thankful to ICT Pvt. Ltd. A-8, Green Park,
New Delhi-110 016 for using its appliances to bring
vi) Right box can be used for flow of water in skew
this paper to the present shape. They are grateful to
direction by increasing length or providing edge
Shri A.D. Narain, Executive Director, ICT for his help
beam around the box and it is not necessary to
in going through the Paper and giving suggestions for
design skew box.
improvements. They are also thankful to S/Shri Jetendra
vii) Easy to construct, practically no maintenance, can Kumar Arya and Harjot Singh, Deputy Managers
have multi-cell to match discharge within smaller (Highways) for preparing AUTOCAD drawings and
height of embankment. Mrs. Sonia Kumar, Deputy Manager(IT) for formatting
viii) Small variation in co-efficient of earth pressure has and typing.


REFERENCES 7. MORT&H (Ministry of Road Transport and Highways),
1. IRC:5-1998, “Standard Specifications and Code of “Standard Drawings for Box Cell Culverts”, New Delhi,
Practice for Road Bridges”, Section I. 2000.

2. IS:1893-1984, “Criteria for Earthquake Resistant Design 8. Krishna, Jai and Jain, O.P., “Plain and Reinforced
of Structures”, Fourth Revision. Concrete”, Volume II, Nem Chand & Bros., Roorkee
3. IRC:78-2000, “Standard Specifications and Code of (U.P.), 1966.
Practice for Road Bridges”, Section VII, Foundation 9. AASHTO (American Association of State Highways
and Substructure.
and Transportation Officials), “Standard Specifications
4. Terzaghi and Karl, “Theoretical Soil Mechanics”, John for Highway Bridges”, 17th Edition, 2002.
Wiley and Sons, ING. Tenth Printing, 1962.
10. IRC:6-2000, “Standard Specifications and Code of
5. Gulhati, Shashi K. and Datta, Manoj, “Geotechnical
Practice for Road Bridges”, Section II.
Engineering”, Tata McGraw-Hill Publishing Company
Limited, 2005. 11. Ramamurtham, S., “Design of Reinforced Concrete
6. IRC:21-2000, “Standard Specifications and Code of Structures”, Dhanpat Rai Publishing Company, Tenth
Practice for Road Bridges”, Section III. Edition, 1985.



ANNEX A
(Para 2)
RCC BOX CULVERT, DESIGNATION: [1/3 x 3/0]

1 SALIENT FEATURES
Clear span 3 m Concrete grade M25 = 25 Mpa
Clear height 3 m Steel grade Fe 415 = 415 Mpa
Top slab thickness 0.42 m БSc (Concrete) 8.33 Mpa
Bottom slab thickness 0.42 m БSt (Steel) 200 Mpa
Side wall thickness 0.42 m Modular ratio 10
Unit weight of concrete 24 kN/m3 n (for depth of neutral axis) 0.294
Unit weight of earth 18 kN/m3 j (for effective depth) 0.902
Unit weight of water 10 kN/m3 k (for moment of resistance) 1.105 Mpa
Co-efficient of earth pressure at rest 0.5 All dimensions are in meter unless
Total cushion on top 0.0 m mentioned otherwise.
Thickness of wearing coat 0.065 m All moments are in kN. m and shear force
Carriageway 8 lane divided in kN unless mentioned otherwise.

A B

D C

Fig.1 Cross Section of Box (All dimensions are in m)
2 LOAD CALCULATION and position of load shall be as under:
2.1 Top Slab
2.1.1 Dead Load
(a) Weight of wearing course
= 0.065 x 22 = 1.43 kN/m²
Adopt minimum of 2 kN/m² as per MOST
Specification
(b) Self weight of top slab Fig. 2 Dispersal under Class 70R (T) One Track
= 0.42 x 24 = 10.08 kN/m² (All dimensions are in m)

(c) Total = 12.08 kN/m² Dispersal perpendicular to span
= 0.84 + 2 x 0.065 = 0.97 m
2.1.2 Live Load
Dispersal in span direction
Consider moving load of 70R(T). The dispersal = 4.57 + 2t +2d = 4.57 + 0.13 = 4.70 m


Note : Taking reduction for simultaneous additional lane
1) Since the length of wheel is more than total width loadings at 20% (refer IRC:6-2000, Clause 208), the
of box at top that is 3.84 m further dispersal by load on unit area of bottom slab for two track loading
“2d” shall not be possible, hence not taken. In case works out to 20.51 kN/m², if one track without reduction
where the length of load is less than the width of is considered restricting area of dispersal the load per
box but works out more when “2d” is added, the unit area works out 19.8 kN/m². The dispersed live load
dispersed length shall be restricted to top width of on bottom slab can be taken to be 21 kN/m².
box.
2.2.3 Total Load (DL +LL) = 27.83 + 21 = 48.83 kN/
2) As the load of wheel after dispersal does not over m² Adopt 50 kN/m²
lap, both wheels need to be taken separately.
2.3 Side Wall
3) For dispersal refer IRC:21-2000 Clause
305.16.3. 2.3.1 Case 1: Box empty, earth pressure with live load
surcharge equivalent to 1.2 m height of earth on
4) Impact as per IRC:6-2000 Clause 211 shall be both sides fills.
taken.
5) This shall be the load when α is zero and live load
is taken to disperse through wearing coat only.
Load per unit area
= 350/4.7 x 0.97 = 76.77 kN/m²
Impact factor for 70R(T) shall be 25 % as per Clause
211.3 (a) (i) of IRC:6-2000
Load including impact = 95.96 kN/m² Fig. 4 Force Diagram for Wall (All dimensions are in m)

2.1.3 Total Load (D.L.+L.L.) Earth Pressure at base due to live load surcharge
= 12.08 + 95.96 = 108.04 kN/m² = 1.2 x 18 x 0.5 = 10.8 kN/m²

2.2 Bottom Slab Earth Pressure at base due to earth fill
= 18 x 3.42 x 0.5 = 30.78 kN/m²
2.2.1 Dead Load
2.3.2 Case 2 : Box full, Live load surcharge on side
Load from top slab = 12.08 kN/m² fill.
Load of walls = 2 x 3 x 0.42 x 24/3.84 = 15.75 kN/m²
Total Load = 27.83 kN/m²
2.2.2 Live Load
The Live Load on top of box will disperse through
walls and when arranged on the carriage way
(lengthwise of the box) the distribution shall be as
under : Fig. 5 Force Diagram for Wall (All dimensions are in m)
Water pressure inside and out side will balance each
other and hence not taken.
Earth Pressure at base due to live load surcharge
= 10.8 kN/m²
Earth Pressure at base due to submerged earth
= (18-10) x 3.42 x 0.5 = 13.68 kN/m²

Fig. 3 Dispersal of wheel loads on bottom slab 2.3.3 Case 3 : Box full, no live load surcharge on side
(All dimensions are in m) fill.


Total fixed end moment = 47.63 kN.m
Mid span moment due to dead load = 40.69
Mid span moment due to live load = 30.75
Total Mid Span Moment = 71.45 kN.m
3.3 Side Wall
Fig. 6 Force Diagram for wall (All dimensions are in m) 3.3.1 Case 1 : Box empty, surcharge load on side fill.
Earth Pressure at base due to submerged earth F.E.M at top due to dead load
= 8 x 3.42 x 0.5 = 13.68 kN/m²
= = 12
Earth Pressure due to live load = 0

2.4 Base Pressure F.E.M at top due to live load
= 10.8 x 3.42 x 3.42/12 = 10.53
2.4.1 Dead load
Total F.E.M at top = 22.53 kN.m
Load from top slab and walls including wearing F.E.M at base due to dead load
course = 27.83 kN/m²
Self weight of bottom slab =
= 18 kN.m
= 0.42 x 24 = 10.08 kN/m²
F.E.M at base due to live load = 10.53
Total F.E.M at base = 28.53 kN.m
2.4.2 Live Load
Mid span moment due to dead load
There is no live load except coming from top slab
without impact = 21 kN/m² = = 22.5
2.4.3 Base pressure = 58.91 kN/m² (Is safe for a S.B.C
of 150 kN/m²) Mid span moment due to live load
= 10.8 x 3.42 x 3.42/8 = 15.79
3 MOMENT CALCULATION Total Mid Span Moment = 38.29 kN.m
3.1 Top Slab 3.3.2 Case 2 : Box full, live load surcharge on side
Fixed end moment due to dead load fill.
= 12.08 x 3.42 x 3.42/12 = 11.77 F.E.M at top due to dead load
Fixed end moment due to live load = 13.68 x 3.42 x 3.42/30 = 5.33
= 95.96 x 3.42 x 3.42/12 = 93.55 F.E.M at top due to live load = 10.53
Total fixed end moment = 105.30 kN.m Total F.E.M at top slab = 15.86 kN.m
Mid span moment due to dead load F.E.M at base due to dead load
= 12.08 x 3.42 x 3.42/8 = 17.66 =13.68 x 3.42 x 3.42/20 =8
Mid span moment due to live load F.E.M at base due to live load = 10.53
= 95.96 x 3.42 x 3.42/8 = 140.30
Total F.E.M at bottom = 18.53 kN.m
3.2 Bottom Slab = 13.86 x 3.42 x 3.42/16 = 10
Fixed end moment due to dead load = 27.13 Mid span moment due to live load = 15.79
Fixed end moment due to live load = 20.5 Total Mid Span Moment = 25.79 kN.m


3.3.3 Case 3 : Box full, no live load surcharge Mad = Mbc = 12 kN.m (case 1), 5.33 kN.m (case 2),
F.E.M at top due to dead load = 5.33 5.33 kN.m (case 3)
F.E.M due to live load = 0 Mda = Mcb = 18 kN.m (case 1), 8 kN.m (case 2),
Total F.E.M at top = .33 kN.m
5 8 kN.m (case 3)
F.E.M at base due to dead load = 8
5.2 F.E.M Due to Live Load
F.E.M at base due to live load = 0
Total F.E.M at base = 8 kN.m Mab = Mba = 93.55 kN.m
Mid span moment due to dead load = 10
Mdc = Mcd = 20.50 kN.m
Mid span moment due to live load = 0
Mad= Mbc =10.53 kN.m (case 1),
Total Mid Span Moment = 10 kN.m
10.53 kN.m (case 2), 0 (case 3)
4 DISTRIBUTION FACTORS Mda = Mcb = 10.53 kN.m (case 1),
10.53 kN.m (case 2), 0 (case 3)
Junction Members 4EI/L = SUM Distri-
K d³/L 4EI/L bution 5.3 F.E.M Due to Total Load
factors
Mab = Mba = 105.32 kN.m
A&B AB/AD, K 0.423 2K0.423 0.5
BA/BC /3.42 /3.42 0.5 Mdc = Mcd = 47.63 kN.m
C&D DA/DC, K 0.423 2K 0.423 0.5 Mad= Mbc = 22.53 kN.m (case 1),
CD/CB /3.42 /3.42 0.5 15.86 kN.m (case 2), 5.33 kN.m (case 3)

5 MOMENT DISTRIBUTION Mda = Mcb = 28.53 kN.m (case 1),
18.53 kN.m (case 2), 8 kN.m (case 3)
5.1 F.E.M Due to Dead Load
5.4 A typical distribution is shown in Table 1. Results
Mab = Mba = 11.77 kN.m based on similar distribution for other combination
Mdc = Mcd = 27.13 kN.m are given in Table 2.

Table 1 Moment Distribution for Total Load for Top & Bottom Slabs and Case 1 Loads for Walls

Joint A B C D
Member AB AD BA BC CB CD DC DA
D.F 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500
F.E.M -105.320 22.530 105.320 -22.530 28.530 -47.63 47.63 -28.530
DIST. 41.39 41.39 -41.39 -41.39 9.55 9.55 -9.55 -9.55
C.O. -20.69 -4.78 20.693 4.776 -20.693 -4.776 4.776 20.693
DIST. 12.73 12.73 -12.73 -12.73 12.73 12.73 -12.73 -12.73
C.O. -6.37 -6.37 6.367 6.367 -6.367 -6.367 6.37 6.367
DIST. 6.37 6.37 -6.37 -6.37 6.37 6.37 -6.37 -6.37
C.O. -3.18 -3.18 3.184 3.184 -3.184 -3.184 3.184 3.184
DIST. 3.18 3.18 -3.18 -3.18 3.18 3.18 -3.18 -3.18
C.O. -1.59 -1.59 1.592 1.592 -1.592 -1.592 1.592 1.592
DIST. 1.59 1.59 -1.59 -1.59 1.59 1.59 -1.59 -1.59
FINAL -71.89 71.89 71.89 -71.89 30.12 -30.12 30.12 -30.12



Table 2 Support Moments

Distributed Moments at Supports
Load Mab Mdc Mad Mda Remarks
Case
(Mda) (Mcd) (Mbc) (Mcb)
(1) (-) 10.72 23.74 10.72 (-) 23.74
Load on top
Dead Load (2) (-) 6.96 19.15 6.96 (-) 19.15
slab and
(3) (-) 6.96 19.15 6.96 (-) 19.15 bottom slab
(1) (-) 61.17 6.38 61.17 (-) 6.38 remains
Live Load (2) (-) 61.17 6.38 61.17 (-) 6.38 same in all
(3) (-) 55.91 1.12 55.91 (-) 1.12 cases, only
(1) (-) 71.89 30.12 71.89 (-) 30.12 load on side
Total Load (2) (-) 68.13 25.53 68.13 (-)25.53 wall varies.
Without
(3) (-) 62.87 20.27 62.87 (-) 20.27
braking Force
Maximum All cases 71.89 30.12 71.89 30.12
Table 3 Mid Span Moments (Total Loads only)
Member Case 1 Case 2 Case 3 Remarks
Mab 157.96 - 71.89 157.96 - 68.13 157.96 - 62.87 The Walls
= 86.07 = 89.83 =95.09 bends
Mdc 71.45 - 30.12 71.45 - 25.53 71.45 - 20.27 outwardly in
= 41.33 = 45.92 = 51.18 all three cases
Mad 38.29 - (71.89 + 30.12)/2 25.79 - (68.13 + 25.53)/2 10 - (62.87 + 20.27)/2
= (-)12.72 = (-) 21.04 = (-) 31.57

6 BRAKING FORCE The moments at top and bottom slab ends shall all
6.1 LOAD: 70R(T), one wheel load is considered as be zero.
there is no over lapping. After distribution of moments among all the
No impact as per IRC:6-2000 Clause 214.2. members a moment of 48.9 kN.m is obtained at
all ends. This moment is added to the maximum
The braking force shall be 20 % for the first lane
load moments obtained for various combination of
loadings at the ends of members to get design
The braking force = 350 x 20/100 = 70 kN
moments. Since braking force can also act from
Load on top of box which will affect the box the reverse direction the moment at junctions are
= 3.84 x 70/4.7 = 57.19 kN added irrespective of its sign.
6.2 Moment Due to Braking Force 7 DESIGN OF SECTION
MAD = MDA = MCB = MBC = 57.19 x 3.42/2 7.1 Design Moments
= 97.79 kN.m
Table 4

Load Case Maximum Distributed Moments at Supports
Mab Mdc Mad Mda
Total Load Maximum of all cases 71.89 30.12 71.89 30.12
Braking Force Distributed Moments at support 48.90 48.90 48.90 48.90
Design Moments Support Moments including braking 120.79 79.02 120.79 79.02


Table 5 Moment and Reinforcement at Salient Section

Member MAB MDC Mid span
AB DC AD
Moment in kN.m 120.79 79.02 95.09 51.18 31.57
Area of steel in mm² 1849.6 1299.8 1456 841.8 483.4

7.2 Top Slab
Maximum moment support/mid span including

breaking = 120.79 kN.m
Check for Shear

Provided 362 mm is safe
Shear Stress = 0.1613 N/mm² < 0.2715 N/mm²
permissible, hence safe.
Check for Shear 7.4 Side Walls
Shear force at deff from face of wall Moment at junction are same as slabs hence same
tensile bars shall continue.

Shear Stress = 0.3247 N/mm² > 0.312 N/mm²
permissible

Permissible shear stress
Check for Shear

Increase tension steel to increase permissible shear
stress.
= 18.460 + 17.545 = 36.01 kN
Required steel
RD = 18.468 + 35.090 = 53.56 kN
S.F. at deff from

= 53.56 – 11.92 – 4.45 = 37.19 kN
Hence, provide tension steel = 2076 mm² in place
of 1849.6 mm² required for moment only. S.F. at deff from
7.3 Bottom Slab
B.M. (Max) = 79.02 kN.m

= 30.796 kN

Provided 337 mm is O.K. Maximum Shear Stress (near base) = 0.100 N/mm² (safe)


ANNEX B
(Para 2)
1 SALIENT FEATURES The larger of the two that is 4.52 kN/m² is considered.
Same as for box [1/3 x 3/0] given in Annex A, Note:
except the cushion which is 5.0 m total height
1) As the load of wheel after dispersal over lap both
above top slab.
wheels need to be taken together.
2) For dispersal refer IRC:21-2000 Clause 305.16.4.
3) No impact as per IRC:6-2000 Clause 211.7 (c) due
to cushion more than 3.0 m.
A B
2.1.3 Total load = 104.6 kN/m²
2.2 Bottom Slab
2.2.1 Dead Load
Load from top slab including cushion
D C
=100.08 kN/m²
Fig. 1 Section of box culvert (All dimensions are in m) Load of walls
2 LOAD CALCULATION = 2 x 3 x 0.42 x 24/3.84 = 15.75 kN/m²
2.1 Top Slab Total load = 115.83 kN/m²
2.1.1 Dead Load Live Load
a) Cushion = 5 x 18 = 90 kN/m² Load from top slab without impact
= 4.52 kN/m²
b) Self weight of top slab = 0.42 x 24 =10.08 kN/m²
Note: Some designers take further dispersal of live
c) Total = 100.08 kN/m²
load from top slab. Although further dispersal through
2.1.2 Live Load walls can not be denied but will affect only marginally,
therefore, the load on top without impact can be taken
Consider moving load of 70R (T). The dispersal
for bottom slab also, which is already without impact
and position of load shall be as under:
in this case.
2.2.2 Total load =115.83 + 4.52 = 120.35 kN/m²
2.3 Side Wall
2.3.1 Case 1: Box empty, earth pressure with live load
surcharge equivalent to 1.2 m height of earth on
both sides fills.
Fig. 2 Dispersal of live load (All dimensions are in m)
Dispersed area when 1 track loading is considered
= 12.9 x 14.57 = 187.95 m²
Load per unit area when 1 track load (covering
2-lanes) is considered = 700/187.95 = 3.724 kN/m²
Load per unit area when 2 track load (covering
4-lanes) is considered
= 1400 x 0.8/17 x 14.57 = 4.52 kN/m² Fig. 3 : Force diagram for vertical wall (All dimensions are in m)


Pressure due to live load surcharge 2.4 Base Pressure
= 1.2 x 18 x 0.5 = 10.80 kN/m²
Dead load
Pressure due to earth surcharge Load from top slab and walls including cushion
= 5 x 18 x 0.5 = 45 kN/m² = 115.83 kN/m²
Self weight of bottom slab
Pressure due to earth fill
= 0.42 x 24 =10.08 kN/m²
= 0.5 x 18 x 3.42 = 30.78 kN/m²
Case 2 : Box full, Live load surcharge on side fill. Live Load
There is no live load except coming from top slab
without impact = 4.52 kN/m²
2.4.1 Base pressure = 130.43 kN/m²
(Is safe for a S.B.C of 150 kN/m²)
3 MOMENT CALCULATION
3.1 Top Slab
Fixed end moment due to dead load
Fig. 4 Force Diagram for wall (All dimensions are in m)
= 100.08 x 3.42 x 3.42 /12 = 97.55
Fixed end moment due to live load
Water pressure inside and outside will balance each = 4.52 x 3.42 x 3.42/12 = 4.41
other and hence not taken. Total fixed end moment = 101.96 kN.m
Pressure due to live load surcharge Mid span moment due to dead load
= 10.8 = 10.8 kN/m² =100.08 x 3.42 x 3.42/8 = 146.32
Mid span moment due to live load
Pressure due to earth surcharge = 4.52 x 3.42 x 3.42/8 = 6.61
= 45 = 45 kN/m²
Total Mid Span Moment =152.93 kN.m
Pressure due to submerged earth 3.2 Bottom Slab
= 0.5 x (18-10) x 3.42 = 13.68 kN/m² Fixed end moment due to dead load
2.3.2 Case 3 : Box full, no live load surcharge on =115.83 x 3.42 x 3.42/12 = 112.9
side fill. Fixed end moment due to live load = 4.41
Total fixed end moment = 117.31 kN.m
= 115.83 x 3.42 x 3.42/8 = 169.35
Mid span moment due to live load = 6.61
3.3 Side Wall
3.3.1 Case 1 : Box empty, surcharge load on side fill
F.E.M at top due to dead load
= 45 x 3.42 x 3.42/12 +30.78 x 3.42 x 3.42/30 = 55.86
F.E.M at top due to live load
= 10.8 x 3.42 x 3.42/12 = 10.53
F.E.M at base due to dead load
= 43.86+30.78 x 3.42 x 3.42/20 = 61.86 kN.m
Fig. 5 Force Diagram for wall F.E.M at base due to live load = 10.53
Pressure due to submerged earth =13.68 kN/m² Total F.E.M at base = 72.39 kN.m
Pressure due to earth surcharge = 45 kN/m² = 45 x 3.42 x 3.42/8+30.78 x 3.42 x 3.42/16 = 88.29


Mid span moment due to live load 4 DISTRIBUTION FACTORS ARE SAME
= 10.8 x 3.42 x 3.42/8 = 15.79 AS OBTAINED FOR BOX WITHOUT
Total Mid Span Moment =104.08 kN.m CUSHION
3.3.2 Case 2 : Box full, live load surcharge on side fill. 5 MOMENT DISTRIBUTION
F.E.M at top due to dead load 5.1 F.E.M Due to Dead Load
= 43.86+13.68 x 3.42 x 3.42/30 = 49.19 Mab = Mba = 97.54 kN.m
F.E.M at top due to live load = 10.53 Mdc = Mcd = 112.90 kN.m
Mad = Mbc = 55.86 kN.m (case 1),
F.E.M at base due to dead load 49.19 kN.m (case 2), 49.19 kN.m (case 3)
= 43.86+13.68 x 3.42 x 3.42/20 = 51.86
Mda = Mcb = 61.86 kN.m (case 1),
F.E.M at base due to live load = 10.53
51.86 kN.m (case 2), 51.86 kN.m (case 3)
Total F.E.M at bottom = 62.39 kN.m
5.2 F.E.M Due to Live Load
= 65.79+13.68 x 3.42 x 3.42/16 = 75.79 Mab = Mba = 4.41 kN.m
Mid span moment due to live load = 15.79 Mdc = Mcd = 4.41 kN.m
Total Mid Span Moment = 91.58 kN.m Mad = Mbc = 10.53 kN.m (case 1),
3.3.3 Case 3 : Box full, no live load surcharge 10.53 kN.m(case 2), 0 (case 3)
F.E.M at top due to dead load Mda = Mcb = 10.53 kN.m (case 1),
= 43.86 + 5.33 = 49.19 kN.m 0.53 kN.m (case 2), 0 (case 3)
F.E.M due to live load =0 5.3 F.E.M Due to Total Load
Total F.E.M at top = 49.19 Mab = Mba = 101.95 kN.m
F.E.M at base due to dead load Mdc = Mcd = 117.31 kN.m
= 43.86 + 8 = 51.86 Mad = Mbc = 66.39 kN.m (case 1),
F.E.M at base due to live load = 0 59.72 kN.m(case 2), 49.19 kN.m (case 3)
Total F.E.M at base = 51.86 kN.m Mda = Mcb = 72.39 kN.m (case 1),
Mid span moment due to dead load 62.39 kN.m (case 2), 51.86 kN.m (case 3)
= 65.79 + 13.68 x 3.42 x 3.42/16 = 75.79
A typical distribution is shown in Table 1. Results based
Mid span moment due to live load = 0 on similar distribution for other combination of loads
Total Mid Span Moment = 75.79 kN.m were done and given in Table 2.
Table 1 Moment Distribution for Total Load on Top & Bottom Slab and Case 1 Load on Walls
Joint A B C D
Member AB AD BA BC CB CD DC DA
D.F 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500
F.E.M -101.955 66.39 101.955 -66.389 72.389 -117.307 117.307 -72.389
DIST. 17.78 17.78 -17.78 -17.78 22.46 22.46 -22.46 -22.46
C.O. -8.89 -11.23 8.892 11.229 -8.892 -11.229 11.229 8.892
DIST. 10.06 10.06 -10.06 -10.06 10.06 10.06 -10.06 -10.06
C.O. -5.03 -5.03 5.030 5.030 -5.030 -5.030 5.030 5.030
DIST. 5.03 5.03 -5.03 -5.03 5.03 5.03 -5.03 -5.03
C.O. -2.52 -2.52 2.515 2.515 -2.515 -2.515 2.515 2.515
DIST. 2.52 2.52 -2.52 -2.52 2.52 2.52 -2.52 -2.52
C.O. -1.26 -1.26 1.258 1.258 -1.258 -1.258 1.258 1.258
DIST. 1.26 1.26 -1.26 -1.26 1.26 1.26 -1.26 -1.26
FINAL -83.00 83.00 83.00 -83.00 96.02 -96.02 96.02 -96.02


Table 2 Support Moments
Distributed Moments at Supports
Load Mab Mdc Mad Mda Remarks
Case
(Mba) (Mcd) (Mbc) (Mcb)
(1) (-) 75.54 88.55 75.54 (-) 88.55
Dead Load (2) (-) 71.79 83.97 71.79 (-) 83.97
(3) (-) 71.79 83.97 71.79 (-) 83.97 Load on top slab and bottom
(1) (-) 7.47 7.47 7.47 (-) 7.47 slab remains same in all
Live Load (2) (-) 7.47 7.47 7.47 (-) 7.47 cases, only load on side wall
(3) (-) 2.20 2.20 2.20 (-) 2.20 varies.
(1) (-) 83.00 96.02 83.00 (-) 96.02 No braking force need be
Total Load (2) (-) 79.25 91.43 79.25 (-)91.43 considered due to cushion.
(3) (-) 73.99 86.17 73.99 (-) 86.17
Maximum All cases 83.00 96.02 83.00 96.02
Table 3 Mid Span Moments

Member Case 1 Case 2 Case 3 Remarks
MAB 152.93 - 83.0 = 69.93 152.93 - 79.25 = 73.68 152.93 - 73.99 = 78.94
When surcharge is not
MDC 175.96 - 96.02 = 79.94 175.96 - 91.43 = 84.53 175.96 - 86.17 = 89.79 taken the Wall bends
104.08 - (83+96.02)/2 91.58 - (79.25+91.43)/2 75.79 - (73.99+86.17)/2 outwardly.
MAD
= 14.57 = 6.24 = (-) 4.29

6 DESIGN OF SECTION
Table 4 Moment and Reinforcement at Salient Section

Mid span
Member Mab Mdc
AB DC AD
Moment in kN.m 83.0 96.02 78.94 89.79 14.57
Area of steel in mm² 1271 1579 1209 1477 223

6.1 Top Slab Check for Shear
Maximum moment support/mid span = 83.0 kN.m
Depth required =



Provide shear reinforcement Balance shear force
Shear capacity = 133.95 – 100.760 =33.19 kN
= 0.2623 x 1000 x 362 = 94953N = 94.95 kN
Balance Shear = 113.80 – 94.95 = 18.85 kN
Take spacing 250 c/c of 8 mm

x is the distance from face of wall where shear
force equals shear capacity of the section

Then,
Shear capacity of section
= 0.2623 x 362 = 94.95kN

Say x is the distance from the face of wall where
shear force equals shear capacity of the section. and x = 0.613 m say 650 mm
Then, Provide shear reinforcement upto 650 mm from
face of near wall on both sides.
6.3 Side Walls
and x = 0.543 m, say 600 mm
Maximum moments at junctions of slabs and
Provide shear reinforcement upto 600 mm from walls are same as slabs. Hence provide same
face of near wall on both sides. reinforcements as slabs at junctions/supports.
6.2 Bottom Slab
Check for Shear
Maximum Moment support/mid span = 96.02 kN.m
Maximum shear near top at deff from top slab is
obtained as under :

Provided = 420 – 75 – 8 = 337 mm is o.k.

Fig. 6 Shear force at dig. (All dimensions are in m)
Check for Shear

Shear Stress = 0.3975 N/mm²

Provide shear reinforcements
Shear Capacity
= 0.299 x 337 x 1000 = 100763 N =100.76 kN


ANNEX C
(Para 9)
STAAD. Pro : Structural Analysis and Design Software
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 17-Dec-08
END JOB INFORMATION
INPUT WIDTH 79
* ANALYSIS FOR LIVE LOAD
*

*BOTTOM SLAB
*LONGITUDINAL MEMBER
* TRANSVERSE MEMBER
*TOP SLAB
*LONGITUDINAL MEMBER
* TRANSVERSE MEMBER
* VERTICAL WALL
*
UNIT METER kN
JOINT COORDINATES
1 0 0 0; 2 0 0 1.6416; 3 0 0 3.284; 4 0 0 4.926; 5 0 0 6.568; 6 0 0 8.21;
7 0 0 9.852; 8 0 0 11.494; 9 0 0 13.136; 10 0 0 14.778; 11 0 0 16.42;
12 0 0 18.062; 13 0 0 19.704; 14 0.57 0 0; 15 0.57 0 1.6416; 16 0.57 0 3.284;
17 0.57 0 4.926; 18 0.57 0 6.568; 19 0.57 0 8.21; 20 0.57 0 9.852;
21 0.57 0 11.494; 22 0.57 0 13.136; 23 0.57 0 14.778; 24 0.57 0 16.42;
25 0.57 0 18.062; 26 0.57 0 19.704; 27 1.14 0 0; 28 1.14 0 1.6416;
29 1.14 0 3.284; 30 1.14 0 4.926; 31 1.14 0 6.568; 32 1.14 0 8.21;
33 1.14 0 9.852; 34 1.14 0 11.494; 35 1.14 0 13.136; 36 1.14 0 14.778;
37 1.14 0 16.42; 38 1.14 0 18.062; 39 1.14 0 19.704; 40 1.71 0 0;
41 1.71 0 1.6416; 42 1.71 0 3.284; 43 1.71 0 4.926; 44 1.71 0 6.568;
45 1.71 0 8.21; 46 1.71 0 9.852; 47 1.71 0 11.494; 48 1.71 0 13.136;
49 1.71 0 14.778; 50 1.71 0 16.42; 51 1.71 0 18.062; 52 1.71 0 19.704;
53 2.28 0 0; 54 2.28 0 1.6416; 55 2.28 0 3.284; 56 2.28 0 4.926;
57 2.28 0 6.568; 58 2.28 0 8.21; 59 2.28 0 9.852; 60 2.28 0 11.494;
61 2.28 0 13.136; 62 2.28 0 14.778; 63 2.28 0 16.42; 64 2.28 0 18.062;
65 2.28 0 19.704; 66 2.85 0 0; 67 2.85 0 1.6416; 68 2.85 0 3.284;
69 2.85 0 4.926; 70 2.85 0 6.568; 71 2.85 0 8.21; 72 2.85 0 9.852;
73 2.85 0 11.494; 74 2.85 0 13.136; 75 2.85 0 14.778; 76 2.85 0 16.42;
77 2.85 0 18.062; 78 2.85 0 19.704; 79 3.42 0 0; 80 3.42 0 1.6416;
81 3.42 0 3.284; 82 3.42 0 4.926; 83 3.42 0 6.568; 84 3.42 0 8.21;
85 3.42 0 9.852; 86 3.42 0 11.494; 87 3.42 0 13.136; 88 3.42 0 14.778;
89 3.42 0 16.42; 90 3.42 0 18.062; 91 3.42 0 19.704; 92 0 3.42 0;
93 0 3.42 1.6416; 94 0 3.42 3.284; 95 0 3.42 4.926; 96 0 3.42 6.568;
97 0 3.42 8.21; 98 0 3.42 9.852; 99 0 3.42 11.494; 100 0 3.42 13.136;
101 0 3.42 14.778; 102 0 3.42 16.42; 103 0 3.42 18.062; 104 0 3.42 19.704;

Rcc box culvert methodology and designs including computer method

Rcc box culvert methodology and designs including computer method

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to Rcc box culvert methodology and designs including computer method

Similar to Rcc box culvert methodology and designs including computer method (20)

Recently uploaded

Recently uploaded (20)

Rcc box culvert methodology and designs including computer method