RCC Box Culvert Methodology and Designs

* General Manager ICT Pvt. Ltd., A-9, Green Park, New Delhi � 110 016, e-mail : [email protected]

** General Manager e-mail : [email protected]

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

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 !ood water on both sides of earth embankment to reduce !ood level on one side

of road thereby decreasing the water head consequently reducing the !ood 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 traf"c 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 pro"le 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 "ll, impact

factor, co-ef"cient 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 justi"cation 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

It is well known that roads are generally constructed

in embankment which come in the way of natural !ow

of storm water (from existing drainage channels). As,

such !ow cannot be obstructed and some kind of cross

drainage works are required to be provided to allow

water to pass across the embankment. The structures to

accomplish such !ow across the road are called culverts,

small and major bridges depending on their span which

in turn depends on the discharge. The culvert cover upto

waterways of 6 m (IRC:5-19981) and can mainly be of

two types, namely, box or slab. The box is one which

has its top and bottom slabs monolithically connected

to the vertical walls. In case of a slab culvert the top

slab is supported over the vertical walls (abutments/

piers) but has no monolithic connection between them.

A box culvert can have more than single cell and can be

placed such that the top slab is almost at road level and

there is no cushion. A box can also be placed within

the embankment where top slab is few meters below the

road surface and such boxes are termed with cushion.

The size of box and the invert level depend on the

hydraulic requirements governed by hydraulic designs.

The height of cushion is governed by the road pro"le

at the location of the culvert. This Paper is devoted to

box culverts constructed in reinforced concrete having

one, two or three cells and varying cushion including no

cushion. The main emphasis is on the methodology of

design which naturally covers the type of loading as per

relevant IRC Codes and their combination to produce

the worst effect for a safe structure. The IS:1893-1984²

(Clause 6.1.3) provide that box culverts need not be

designed for earthquake forces, hence no earthquake

forces are considered. Although box of maximum three

cells has been discussed but in practice a box culvert can

have more cells depending on the requirements at site.

Culverts are provided to allow water to pass through

Journal of the Indian Roads Congress, October-December 2009

}

190 SINHA & SHARMA ON


the embankment and follow natural course of !ow but

these are also provided to balance the water level on both

sides of embankment during !oods, such culverts are

termed as balancers (IRC:78-2000³), although there is no

difference in the design. Sometimes the road alignment

may cross a stream at an angle other than right angle,

in such situation a skew culvert may be provided. For

a smaller span there would be no difference in the

design of culvert but it may require an edge beam and

the layout of wing walls will have to be planned as per

skew angle.

For a box culvert, the top slab is required to withstand

dead loads, live loads from moving traf"c, earth pressure

on sidewalls, water pressure from inside, and pressure

on the bottom slab besides self weight of the slab. The

structure is designed like a rigid frame considering one

meter element and adopting moment distribution method

for obtaining "nal distributed moments on the basis of

the relative stiffness of the slab and vertical walls. The

method is well known and does not need any elucidation.

The mid span moments are computed with free supported

ends and adjusting it for moments at support obtained

after distribution. The moments at center and supports

for slabs and walls are obtained for various combination

of loads and the member is designed for the maximum

moment it may be subjected to. Also the shear force at

a distance of effective depth from the face of wall and

shear stresses it produces in the section is considered in

the design. A few things like coef"cient of earth pressure

for lateral pressure on walls, effective width (run of

culvert) for live loads and applicability of braking force

on box without cushion (or little cushion) for structural

deformation are important items where opinion of the

designers vary and need to be dealt in much detail. These

affect the design signi"cantly and therefore, required to

be assessed correctly for designing a safe structure. It is

customary to consider box a rigid frame and unit length

of box is taken for design by considering the effect of

all forces acting on this unit length (generally 1.0 m of

box). While calculating weight of cushion on top slab,

some designer take average height of earth "ll coming

over full length of box including sloping side "ll. This

is not correct and full height of cushion should be taken

at the worst section of the box (central portion) will

be subjected to this load and the section needs to be

designed accordingly.

A question has been raised frequently whether culverts

designed for four lane divided carriageway are safe

for more number of lanes, a situation which occurs on

widening of the road and frequently encountered for

road development, and whether the culvert designed for

no cushion shall be safe for cushion loads which may

become a necessity at a future date due to change in road

pro"le. If so, up to what height of cushion, the box need

not be reconstructed. These shall be addressed in this

Paper giving appropriate solutions as required.

Box culvert has many advantages compared to slab

culvert or arch culvert. The box is structurally strong,

stable and safe and easy to construct. The main

advantage is, it can be placed at any elevation within the

embankment with varying cushion which is not possible

for other type of culverts. A multi cell box can cater for

large discharge and can be accommodated within smaller

height of embankment. It does not require separate

elaborate foundation and can be placed on soft soil by

providing suitable base slab projection to reduce base

pressure within the safe bearing capacity of foundation

soil. Bearings are not needed. It is convenient to extend

the existing culvert in the event of widening of the

carriageway at a later date as per future requirement,

without any problem of design and/or construction.

2 CO-EFFICIENT OF EARTH PRESSURE

The earth can exert pressure, minimum as active and

maximum as passive, or in between called pressure at rest.

It depends on the condition obtained at site (Terzaghi4

and Gulati5). For example in case of a retaining wall

where the wall is free to yield and can move away from

the earth "ll the pressure exerted by the earth shall tend

to reach active state and thus be minimum. As to reach

active state only a small movement is required which

can normally be achieved in case of a retaining wall,

also before failure of the wall by tilting, the back "ll is

bound to reach active state. The wall thus can safely be

designed for active pressure of earth, with co-ef"cient

applicable for active pressure. In case of an anchored

bulk head, the earth pressure on the anchor plate will

tend to achieve passive state because the anchor plate

is dragged against earth and large displacement can be

allowed, one can consider passive co-ef"cient for the

design of anchor, of course, some factor of safety need be

taken as required displacement to achieve passive state

before the bulk head gives way may not be practical. In

cases where the structure is constructed before back "ll

earth is placed in position and the situation is such that

structure is not in a position to yield on either side, the

earth pressure shall reach a state at rest. In such situation

191RCC BOX CULVERT- METHODOLOGY AND DESIGNS INCLUDING COMPUTER METHOD


the co-ef"cient of earth pressure shall be more than

the active condition. In case of box since it is con"ned

with earth from both sides the state of earth shall be at

rest and a co-ef"cient more than the active pressure is

normally adopted in the design. The earth is "lled after

construction of the box further the box is not in a position

to move/yield therefore the pressure shall be at rest. The

value is designer�s choice.

The co-ef"cient of earth pressure in case of box is

taken to be 0.333 for a soil having # = 30º equivalent

to active condition by many authors in their books of

design. Some authors take this value = 0.5 for normal

soil having # = 30º. A typical box has been designed

keeping all factors to be same for the two values of earth

pressure co-ef"cient. It is seen that these co-ef"cient

even when taken differently have little effect on the

over all design of the section. To bring out difference

in more appreciable form the two designs are compared

in Table 1. (refer Annex A and Annex B). It is observed

that difference in design of culvert without cushion

is marginal. However, box with cushion shows more

difference.

Considering the situation typical to the box, it is close

to at rest condition and a co-ef"cient higher than active

pressure should be taken. For practical considerations

a value of 0.5 can be taken for earth pressure. Whereas,

there is no point of difference in taking this value for

culverts with cushion, some reservations are shown

where braking force is taken to act on culverts without

cushion, where the box is assumed to deform pressing

against the "ll earth on one side and the pressure can be

different on two sides, at least it may tend to be active

on the side the box is tilting away from the "ll. In design

this difference of earth pressure on two sides of box is

not taken, as the pressure on the passive side, which

depends on amount of deformation of culvert, can not

be evaluated within reasonable limits. However, the

earth pressure on both sides of box before and after

Table 1 Comparison of Moment in kN.m for different Earth Pressure Co-ef!cient 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

deformation can be assumed to be at rest/active pressure

as the earth pressure co-ef"cient has little over all effect

on the structural sizes of box members as already shown

in Table 1 and explained under sub para 2 above. For

A,B,C & D refer Annex A.

3 EFFECTIVE WIDTH

Effective width in the run of culvert (length across span)

is expected to be affected by a moving live load. This

width plays a signi"cant role as far as consideration of

live load in the design of culvert. Where however, there

is large cushion the live load gets dispersed on a very

large area through the "ll and the load per unit area

becomes less and does not remain signi"cant for the

design of box, particularly in comparison to the dead

load due to such large cushion. In case of dead load or

uniform surcharge load the effective width has no role

to play and such loads are to be taken over the entire

area for the design.

Effective width plays an important role for box without

cushion as the live load becomes the main load on the

top slab and to evaluate its effects per unit run for design

as a rigid frame, this load is required to be divided by

the effective width. As such evaluating effective width

correctly is of importance. The relevant IRC Codes,

other Codes, books, theory/concepts are at variance

as far as effective width is concerned and requires

discussions at some length.

It is required to understand the concept behind effective

width. Basically, it is the width of slab perpendicular to

the span which is affected by the load placed on the top

of slab. It shall be related to the area of slab expected

to deform under load. It can be well imagined that this

area of slab which may get affected will depend on how

the slab is supported whether in one direction or both

directions and secondly on the condition of support that

is whether free or continuous or partially or fully "xed.

It can also be imagined that the width shall be larger if



slab is allowed to slide over support under the load as

in case of freely supported, and the same will reduce if

the slab is restrained from sliding and more the restraint

the less shall be the width. In this view the effective

width shall be least for fully "xed and gradually increase

for partially "xed, increase further for continuous slab

and shall reach maximum for slabs freely supported at

ends. Where support on one side is different than on

the other side the effective width should be obtained

taking this fact in consideration. The distance of the load

from the near support affects effective width, more the

distance larger will be the effective width and will reach

highest when the load is at center. The ratio of breadth

(unsupported edges) and the span also affects effective

width. All factors mentioned above need to be taken

into account while obtaining the effective width.

The IRC:21-20006 Clause 305.16 gives an equation

for obtaining effective width for simply supported and

continuous slab for different ratio of over all width verses

span for these two kinds of supports. The Code does not

provide if one of the support is continuous while other is

simply supported. The Code is silent for other types of

supports such as "xed or partially "xed. Some designers

use this formula and factors for continuous slab is taken

valid for partially restrained support in a situation like

box culvert. This does not appear to be in order. The

reasons for this can be better realized by the explanations

given in sub para 3 above. Nevertheless, effective width

need to be obtained in box type structure also to evaluate

affected area by moving load for considering these in

the design. The design of a typical box of designation

[1/3x3/0] has been done by obtaining effective width

considering varying value of $ such as 2.6, 2.0, 1.0, 0.9,

0.8 & 0 (Table 2). The moment and consequently the

main reinforcement varies signi"cantly with value of $,

the amount of reinforcement increases with $ decreasing.

This is because smaller $ gives smaller effective

width and, therefore, more moment and shear per unit

length (run) of box, as all other dimensions are same

reinforcement increases with decrease in value of $. It

is further observed that MORT&H7 provision in their

standard drawings for a similar culvert and situation falls

between $ value 0 to 1.0. This also indicates that taking

value of $ equivalent to that for continuous slab given

in IRC:21-20006 shall not be correct for box structure. It

may be seen that considering any value for $ shall affect

mainly the top slab. Bottom slab due to dispersal through

walls and box with cushion due to dispersal through "ll

to even the top slab, are not affected much.

The live load moment and shear for the top slab can be

obtained per unit run of box considering effective width

for an assessed value of $. For the bottom slab the live

load shall disperse through the walls and such dispersed

area could over lap for different wheels, therefore,

a uniform distributed load per unit run of box could

be obtained on this basis and used in the analysis. In

other words the effect of live load on bottom slab shall

be as in case of large cushion for top slab explained

under sub para 1. As far as walls are concerned the

loads are uniform and pressure etc all are same per unit

run of culvert and effective width has no role to play.

The braking force acts on the box structure and taking

effective width for top slab different than bottom slab

shall make the analysis cumbersome and may not be

practical. The AASHTO also advocates dispersal for

bottom slab. Jaikrishna and O.P. Jain8 in his book has

considered dispersal of live load through walls for

bottom slab at 45°. However, the MORT&H7 Standard

design do not tally with this provision.

The AASHTO9 for Standard Speci"cations for Highway

Bridges 17th Edition 2002, provides at para 16.6.4.3

under RCC Box that �The width of top slab strip used

for distribution of concentrated wheel loads may be

increased by twice the box height and used for the

distribution of loads to the bottom slab�. This con"rms

what is mentioned in sub para 5 and is alright. However,

any such dispersal for bottom slab different than top

slab shall not be practical when braking force effect is

to be taken, which shall have to be for the same run of

the box structure as a whole (refer para 4).

4 BRAKING FORCE

This is another area where opinion of the designers vary

in two ways "rstly, whether braking force caused by

moving loads shall deform the box structure and should

therefore be considered in the design of box. Secondly,

if it is to be considered what effective width should be

taken to obtain force and moment per unit run of box. Of

course the braking force will affect the global stability

and change the base pressure to some extent. The IRC

Code is silent as far as box is concerned. It will be in

order to neglect effect of braking force on box having

large cushion. In such situation the braking effect will

be absorbed by the cushion itself and no force will be

transmitted to the box beneath. Question will, however,

arise up to what cushion height no braking force need

be taken. This height generally is taken to be 3 m. Thus

no braking force for cushion height of 3 m and more

and full braking force for no cushion, for intermediate



heights of cushion the braking force can be interpolated.

There is no literature on this aspect and the Code is also

not speci"c for box, however, IRC:6-200010 Clause

211.7 mentions that no effect be taken at 3 m below

bed block in case of bridge pear/abutment. Our further

discussions shall be on box without cushion as far as

braking force is concerned.

Braking force by the moving loads on top slab of box

having no cushion shall act on the box structure and

shall deform the box. The question is what length of box

can be considered to share this braking force. In another

words what effective width of box shall be taken to obtain

braking force per unit run of box. One way is to take the

effective width of box same as considered for vertical

effect of moving loads, discussed under para 3 above.

The arguments in favor of this is the same which holds

for effective width for vertical deformation of top slab

under moving loads. Vertical effect as well as braking

effect both are product of the same loads and can affect

the same run of box. In absence of speci"c provision

in Codes in this regard the same effective width can be

taken for both effects for the design of box.

The box is considered a rigid frame for analysis and

design. The braking force can be taken to act on the top

junction of the box causing moment at "xed ends of both

walls and the top and bottom slabs having zero "xed end

moments (IRC:6-200010 Clause 214.7). The moment

distribution is carried out and distributed moments are

obtained at supports. This moment shall be added to the

maximum moment under different conditions for other

loads to get "nal design moments at supports. It may

be mentioned here that the mid span moments are not

affected by braking force moments as the same being

zero at mid span even after distribution. Also braking

force can act in either direction hence the moment

at junctions can reverse in sign and thus needs to be

arithmetically added to moments due to vertical effect

of loads for the design.

It is seen that box without cushion if designed ignoring

braking force effect gives smaller thickness and very

less reinforcement compared to the MORT&H7 standard

designs for similar culvert. In case of 2 m x 2 m box the

distributed moment at junctions works out to about 60%

if braking force is not considered, consequently gives

Table 2 Shows Moment and Reinforcement for Different Values of $ 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

Design " values

Moment in kN.m. Area of reinforcement in mm²

MAB

(Support)

MDC

(Support)

MAB

(Mid-

span)

MDC

(Mid-

span)

Support

A & B

Support

D & C

MAB

(Mid-

span)

MDC

(Mid-

span)

As per

design

carried out

0 119.8 83.6 87.0 47.7 1834.8 1375.3 1331.4 1422.8

0.8 86.4 72.3 61.3 54 1322.6 1189.1 938.1 887.6

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

design of

MORTHS

Standard

design

compares

with values

between

$ = 0 to 1

Standard

design

provide only

reinforce-

ment as

shown

_ _ _ 1398 1398 1005.3 1570.8



lesser thickness and reinforcements. In case of box of

size 6 m x 6 m the braking force effect if not taken gives

lesser moment say around 30% less (Table 3). That is for

larger size of box the effect of braking force becomes

lesser. It, therefore, suggests that for smaller size box

braking force effect has to be taken in design. When,

however, the size is big the braking force will affect the

design marginally. In all cases for box without cushion

braking force need to be considered in the design.

5 IMPACT OF LIVE LOAD

Moving loads create impact when these move over the

deck slab (top slab). The impact depends on the class

and type of load. The IRC:6-2000 Code gives formula to

obtain impact factor for different kind of loads by which

the live load is to be increased to account for impact.

The box without cushion where the top slab will be

subjected to impact is required to be designed for live

loads including such impact loads. Any such impact is

not supposed to act on box with cushion. Hence no such

impact factor shall be considered for box with cushion.

The impact by its very nature is not supposed to act at

lower depth and no impact is considered for the bottom

slab of the box. It does not affect the vertical walls of

the box and not considered in the design.

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

Culvert

Designation[1/6 x 6/ 0] [1/2 x 2/ 0]

LocationSupport

A

Support

DMid AB Mid CD

Support

A

Support

DMid AB Mid CD

M o m e n t w i t h

braking force, in

kN.m.

390 286 244.5 165.2 44 27 42.8 19

Moment without

braking force, in

kN.m.

301 184 244.5 165.2 27.5 8 42.8 19

Reinforcement

with braking force

in mm²

3378 2187 2118 1263 835 504 813 355

Reinforcement

without braking

force in mm²

2607 1407 2118 1263 522 149 813 355

Standard Design

Reinforcement in

mm²

2576 3142 3020 2576 1118 1118 804 804

The IRC:6-200010, Code Clause 211.7 speci"es that

for calculating pressure on the bearings and on the

top surface of the bed blocks, full value of appropriate

impact percentage be allowed. But for design of pier,

abutment below the level of bed block, the appropriate

impact percentage shall be multiplied by the factor given

therein. Accordingly, the impact is to be reduced to 50%

below bed block and zero at 3 m below, proportionately

reducing between this height. Although these provisions

are for bridges but can be applied in case of box structure

in absence of any speci"c provision in the Code for box

in this regard.

The AASHTO9 at para 3.8.1.2 speci"es that impact

shall not be included for culverts having 1m or more

cover. This, however, will be on lower side compared

to considering zero impact for a cover (cushion) of 3 m.

It is, therefore, suggested that considering full impact

on top slab without cushion and zero impact for 3m

cushion and interpolating impact load for intermediate

height of cushion is on conservative side and can be

safely adopted.

6 SHEAR STRESS

The box is designed for maximum moment for its

concrete section and reinforcements. It is checked for



shear at the critical section and if it exceeds permissible

shear stress for the size of section; mix of concrete and

percentage of reinforcements, the section has to be

increased to bring shear stress within the permissible

limit. Alternatively, the reinforcement can be increased

to increase allowable shear strength. The third option is

to provide stirrups to counter excess shear stress. This

may have to be adopted in situation where thickness

of slab cannot be increased due to certain restrictions.

The top and bottom slabs are needed to be checked

for shear. The vertical walls carry much less loads and

shall be normally safe in shear, therefore, there is no

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

adopted.

It is important to note that IRC:21-20006 under Clause

304.7.1 has given table 12B. Permissible shear stress in

Concrete for checking section for shear stress. The values

given here have been drastically reduced compared to

similar provision in previous Codes and practices. It is

observed that the shear may govern the design of the

section, in particular, box with large cushion.

Critical section for shear is the section at effective depth

from the face of support (face of wall). The effective

depth is the distance of center of tension reinforcement

from the extreme compression face. Where, however,

haunch is provided, an extra depth due to haunch within

a slope of 1V:3H can be considered to increase the

effective depth (IRC:21-20006 Clause 305.5.3). This

should be taken into account while deciding the critical

section. However, for shear stress at the critical section,

the effective depth only without effect of haunch be

taken.

In situation when the section is required to be provided

with shear reinforcement which otherwise is not safe

in shear and only this option is to be adopted, the shear

capacity of the section based on permissible shear stress,

which is based on percentage of tension reinforcement

and concrete mix, is obtained. Shear capacity of

section is deducted from the shear force obtained at

critical section and shear reinforcement is calculated

for the balance shear force and accordingly provided

in addition to other steel. It is obvious that such shear

reinforcement shall be required for the whole length of

box but the distance along the span from the face of wall

up to which these shear reinforcement is to be provided

shall have to be calculated. As the shear is reducing

away from the face of wall, the distance where the

shear force becomes equal to shear capacity of section

(without shear reinforcement) is obtained. The shear

reinforcement shall be provided up to this distance on

both sides of box from near wall. The design at annexure

will further elucidate this.

The box is to be safe in bending as well as in shear. The

box can be designed for maximum shear and checked for

bending, particularly where shear is expected to govern

the design as for box having large cushion. However, the

tension reinforcement has to be provided for the bending

moment in any case.

7 DISTRIBUTION REINFORCEMENTS

The Code IRC:21-20006, in Clause 305.18 provides

for distribution reinforcements. The distribution

reinforcement shall be such as to produce a resisting

moment in direction perpendicular to the span equal

to 0.3 times the moment due to concentrated live loads

plus 0.2 times the moment due to other loads such as

dead load, shrinkage, temperature etc.

In box, moment due to live loads and dead loads

are obtained considering both the loads together. It,

therefore, becomes cumbersome to separate these

two moments to apply above provision of the Code

to calculate distribution reinforcements. To make it

convenient and easy a combined factor for both the

loads, based on weighted average in proportion of their

magnitude, can be worked out to apply for the design.

This has been adopted in the typical design provided

in Annexure.

8 LOAD CASES FOR DESIGN

Mainly three load cases govern the design. These are

given below (Ramamurtham11)

a) Box empty, live load surcharge on top slab of box

and superimposed surcharge load on earth "ll.

b) Box inside full with water, live load surcharge on

top slab and superimposed surcharge load on earth

"ll.

c) Box inside full with water, live load surcharge on

top slab and no superimposed surcharge on earth

"ll.

The above mentioned load cases are to be examined for

box with cushion and without cushion. In case of box



without cushion live load surcharge shall straightway be

considered to act on the top slab, of course with dispersal

through wearing coat and slab thickness as applicable.

In case of box with cushion the live load surcharge

is supposed to disperse through such cushion in both

direction thereby reducing intensity of load on top slab.

This shall be obtained for heaviest live load wheel,

generally 70R(T) vehicle, with due restrictions due to

several wheels placed simultaneously. One question

arises that with increase in cushion height, live load

intensity decreases and eventually falls below the value

equivalent to load of 1.2 m height of earth "ll, in this case

which of the two that is the actual dispersed live load

or superimposed load equivalent to 1.2 m height of "ll

which is more, shall be taken. The answer is dispersed

live load even if it is lower, should be taken. This is

because the highest value of live load has been taken to

obtain this load and no live load can be expected higher

than this. This also explains the fact that with increase

in cushion the live load intensity will decrease which

is natural compared to taking superimposed surcharge

load equivalent to 1.2 m of "ll at a constant rate for all

cushion heights. Further the superimposed live load

equivalent to 1.2 m of "ll is a very general provision

and shall be adopted where it is not practical to obtain

actual live load more accurately as in case of earth

retaining structures.

AASHTO9 provides varying superimposed surcharge

load on earth embankment to consider Equivalent Height

of Soil for Vehicular Loading. Table 3.11.6.4-1 and Table

3.11.6.4-2 give height of earth "ll for Equivalent Height

of Soil for Vehicular Loading. This is in conformity

with varying live load surcharge explained in sub para

2 above.

9 DESIGN OF TYPICAL BOX

Based on the above discussions and clarifications

design of a typical box covering all above mentioned

points are presented as Annexure. The box of 3 m x 3 m

without cushion and with 5 m cushion have been given.

Various load cases have been given for the maximum

design moments. The box has also been checked in

shear and shear reinforcement provided as required.

The relevant parameters are mentioned in the design.

Detailed design of single cell box culvert with and

without cushion have been given. Basically, there is

no difference in design of multi cell box having two,

three or more cells. The bending moment is obtained by

moment distribution considering all the cells together

for different combination of loading and design of

section accomplished for "nal bending moments for that

member. Shear force and resulting shear stress have to

be checked for members independently as done in case

of single cell. A drawing furnishing details of the box

based on detailed design and general arrangement for

site of work as usually required for construction has also

been given as Annex D.

Table 4 Moment and Shear values by Manual Calculation and STAAD. Pro.

Item Location MembersBy Manual

Calculation

Computer

Output by

STAAD.Pro

Remarks

Bending

Moment

(kNm)

Support

MAB

,MBA

,

MAD

, MBC

82.50 83.05

MDC

,MCD

,

MDA

, MCB

95.52 94.66

Mid span

MAB

, MBA

MDC

, MCD

,

MAD

, MBC

69.32

79.34

15.06

69.99

81.70

15.22

Shear

Force

(kN)

At deff

from support for slabsA & B

D & C

112.93

133.06

113.88

102.46

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

5 m cushion have also been done by using STAAD. Pro

computer software and moment and shear as obtained

are compared with that calculated by manual method

of design. These are given in Table 4. It is seen that

they compare well. The design of box can, therefore,

be carried out by STAAD. Pro as well. Input data sheet,

bending moment diagram and shear force diagram as

obtained by STAAD. Pro are given in the Paper at

Annex C. The analysis part to get these design moment

and shear values for relevant members which runs in

number of pages, is not given in the Paper as it will add to

the length without serving much purpose. The STAAD.

Pro is well known computer software commonly used.

Box without cushion : Annex A

Box with cushion : Annex B

Design of box with

cushion by STAAD.Pro. : Annex C

Drawing of the box culverts

for construction purposes : Annex D

10 CONCLUSIONS

i) Box for cross drainage works across high

embankments has many advantages compared to

a slab culvert.

ii) It is easy to add length in the event of widening of

the road.

iii) Box is structurally very strong, rigid and safe.

iv) Box does not need any elaborate foundation and can

easily be placed over soft foundation by increasing

base slab projection to retain base pressure within

safe bearing capacity of ground soil.

v) Box of required size can be placed within the

embankment at any elevation by varying cushion.

This is not possible in case of slab culvert.

vi) Right box can be used for !ow of water in skew

direction by increasing length or providing edge

beam around the box and it is not necessary to

design skew box.

vii) Easy to construct, practically no maintenance, can

have multi-cell to match discharge within smaller

height of embankment.

viii) Small variation in co-ef"cient of earth pressure has

little in!uence on the design of box particularly

without cushion.

ix) For culverts without cushion (or little cushion)

taking effective width as per provision in

IRC:21-2000 corresponding to $ for continuous

slab shall not be correct. It is likely to provide

design moments and shear on lower side hence

not safe.

x) For box without cushion braking force is required

to be considered particularly for smaller span

culverts. Further for distribution of braking force

effects the same effective width as applicable for

vertical application of live load shall be considered.

If braking force is not considered or distributed

over the whole length of box (not restricted within

the effective width) the design shall be unsafe.

xi) It may be seen that $ affects effective width,

mainly applicable for the top slab (particularly

for box without cushion) and braking force. As

regards bottom slab and top and bottom slabs of

box with cushion due to dispersal of loads either

through walls or through "lls effective width loses

its applicability.

xii) The design of box is covered by three load cases

dealt in this paper. The forth situation when whole

box is submerged under water, provide design

moments etc less than given by the three load cases

hence need not be considered.

xiii) The design of box with cushion done by STAAD.

Pro computer software compares very close to

manual design.

11 ACKNOWLEDGEMENTS

We are thankful to ICT Pvt. Ltd. A-8, Green Park,

New Delhi-110 016 for using its appliances to bring

this paper to the present shape. They are grateful to

Shri A.D. Narain, Executive Director, ICT for his help

in going through the Paper and giving suggestions for

improvements. They are also thankful to S/Shri Jetendra

Kumar Arya and Harjot Singh, Deputy Managers

(Highways) for preparing AUTOCAD drawings and

Mrs. Sonia Kumar, Deputy Manager(IT) for formatting

and typing.



REFERENCES

1. IRC:5-1998, �Standard Speci"cations and Code of

Practice for Road Bridges�, Section I.

2. IS:1893-1984, �Criteria for Earthquake Resistant Design

of Structures�, Fourth Revision.


Practice for Road Bridges�, Section VII, Foundation

and Substructure.

4. Terzaghi and Karl, �Theoretical Soil Mechanics�, John

Wiley and Sons, ING. Tenth Printing, 1962.

5. Gulhati, Shashi K. and Datta, Manoj, �Geotechnical

Engineering�, Tata McGraw-Hill Publishing Company

Limited, 2005.


Practice for Road Bridges�, Section III.

7. MORT&H (Ministry of Road Transport and Highways),

�Standard Drawings for Box Cell Culverts�, New Delhi,

2000.

8. Krishna, Jai and Jain, O.P., �Plain and Reinforced

Concrete�, Volume II, Nem Chand & Bros., Roorkee

(U.P.), 1966.

9. AASHTO (American Association of State Highways

and Transportation Of"cials), �Standard Speci"cations

for Highway Bridges�, 17th Edition, 2002.


Practice for Road Bridges�, Section II.

11. Ramamurtham, S., �Design of Reinforced Concrete

Structures�, Dhanpat Rai Publishing Company, Tenth

Edition, 1985.



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 %Sc (Concrete) 8.33 Mpa

Bottom slab thickness 0.42 m %St (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-ef"cient 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.

ANNEX A

(Para 2)

RCC BOX CULVERT, DESIGNATION: [1/3 x 3/0]

Fig.1 Cross Section of Box (All dimensions are in m)

Fig. 2 Dispersal under Class 70R (T) One Track

(All dimensions are in m)

2 LOAD CALCULATION

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

Speci"cation

(b) Self weight of top slab

= 0.42 x 24 = 10.08 kN/m²

(c) Total = 12.08 kN/m²

2.1.2 Live Load

Consider moving load of 70R(T). The dispersal

and position of load shall be as under:

A B

D C

Dispersal perpendicular to span

= 0.84 + 2 x 0.065 = 0.97 m

Dispersal in span direction

= 4.57 + 2t +2d = 4.57 + 0.13 = 4.70 m



Note :

1) Since the length of wheel is more than total width

of box at top that is 3.84 m further dispersal by

�2d� shall not be possible, hence not taken. In case

where the length of load is less than the width of

box but works out more when �2d� is added, the

dispersed length shall be restricted to top width of

box.

2) As the load of wheel after dispersal does not over

lap, both wheels need to be taken separately.

3) For dispersal refer IRC:21-2000 Clause

305.16.3.

4) Impact as per IRC:6-2000 Clause 211 shall be

taken.

5) This shall be the load when $ 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

2.1.3 Total Load (D.L.+L.L.)

= 12.08 + 95.96 = 108.04 kN/m²

2.2 Bottom Slab

2.2.1 Dead Load

Load from top slab = 12.08 kN/m²

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. 3 Dispersal of wheel loads on bottom slab

(All dimensions are in m)

Fig. 4 Force Diagram for Wall (All dimensions are in m)

Taking reduction for simultaneous additional lane

loadings at 20% (refer IRC:6-2000, Clause 208), the

load on unit area of bottom slab for two track loading

works out to 20.51 kN/m², if one track without reduction

is considered restricting area of dispersal the load per

unit area works out 19.8 kN/m². The dispersed live load

on bottom slab can be taken to be 21 kN/m².

2.2.3 Total Load (DL +LL) = 27.83 + 21 = 48.83 kN/

m² Adopt 50 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 "lls.

Fig. 5 Force Diagram for Wall (All dimensions are in m)

Earth Pressure at base due to live load surcharge

= 1.2 x 18 x 0.5 = 10.8 kN/m²

Earth Pressure at base due to earth "ll

= 18 x 3.42 x 0.5 = 30.78 kN/m²

2.3.2 Case 2 : Box full, Live load surcharge on side

"ll.

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

2.3.3 Case 3 : Box full, no live load surcharge on side

"ll.



Fig. 6 Force Diagram for wall (All dimensions are in m)

Earth Pressure at base due to submerged earth

= 8 x 3.42 x 0.5 = 13.68 kN/m²

Earth Pressure due to live load = 0

2.4 Base Pressure

2.4.1 Dead load

Load from top slab and walls including wearing

course = 27.83 kN/m²

Self weight of bottom slab

= 0.42 x 24 = 10.08 kN/m²


2.4.2 Live Load

There is no live load except coming from top slab

without impact = 21 kN/m²

2.4.3 Base pressure = 58.91 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

= 12.08 x 3.42 x 3.42/12 = 11.77

Fixed end moment due to live load

= 95.96 x 3.42 x 3.42/12 = 93.55

Total "xed end moment = 105.30 kN.m

Mid span moment due to dead load

= 12.08 x 3.42 x 3.42/8 = 17.66

Mid span moment due to live load

= 95.96 x 3.42 x 3.42/8 = 140.30

Total Mid Span Moment = 157.96 kN.m

3.2 Bottom Slab

Fixed end moment due to dead load = 27.13

Fixed end moment due to live load = 20.5


Mid span moment due to dead load = 40.69

Mid span moment due to live load = 30.75


3.3 Side Wall

3.3.1 Case 1 : Box empty, surcharge load on side "ll.

F.E.M at top due to dead load

=

= 12

F.E.M at top due to live load

= 10.8 x 3.42 x 3.42/12 = 10.53

Total F.E.M at top = 22.53 kN.m

F.E.M at base due to dead load

=

= 18 kN.m

F.E.M at base due to live load = 10.53

Total F.E.M at base = 28.53 kN.m


=

= 22.5


= 10.8 x 3.42 x 3.42/8 = 15.79


3.3.2 Case 2 : Box full, live load surcharge on side

"ll.


= 13.68 x 3.42 x 3.42/30 = 5.33

F.E.M at top due to live load = 10.53

Total F.E.M at top slab = 15.86 kN.m


=13.68 x 3.42 x 3.42/20 = 8


Total F.E.M at bottom = 18.53 kN.m


= 13.86 x 3.42 x 3.42/16 = 10





3.3.3 Case 3 : Box full, no live load surcharge

F.E.M at top due to dead load = 5.33

F.E.M due to live load = 0


F.E.M at base due to dead load = 8

F.E.M at base due to live load = 0

Total F.E.M at base = 8 kN.m

Mid span moment due to dead load = 10

Mid span moment due to live load = 0

Total Mid Span Moment = 10 kN.m

4 DISTRIBUTION FACTORS

Junction Members 4EI/L =

K d³/L

SUM

4EI/L

Distri-

bution

factors

A & B AB/AD,

BA/BC

K 0.423

/3.42

2K0.423

/3.42

0.5

0.5

C & D DA/DC,

CD/CB

K 0.423

/3.42

2K 0.423

/3.42

0.5

0.5

5 MOMENT DISTRIBUTION

5.1 F.E.M Due to Dead Load

MAB = MBA = 11.77 kN.m

MDC = MCD = 27.13 kN.m

MAD = MBC = 12 kN.m (case 1), 5.33 kN.m (case 2),

5.33 kN.m (case 3)

MDA = MCB = 18 kN.m (case 1), 8 kN.m (case 2),

8 kN.m (case 3)

5.2 F.E.M Due to Live Load



MAD= MBC =10.53 kN.m (case 1),

10.53 kN.m (case 2), 0 (case 3)

MDA = MCB = 10.53 kN.m (case 1),

10.53 kN.m (case 2), 0 (case 3)

5.3 F.E.M Due to Total Load

MAB = MBA = 105.32 kN.m


MAD= MBC = 22.53 kN.m (case 1),

15.86 kN.m (case 2), 5.33 kN.m (case 3)

MDA = Mcb

= 28.53 kN.m (case 1),

18.53 kN.m (case 2), 8 kN.m (case 3)

5.4 A typical distribution is shown in Table 1. Results

based on similar distribution for other combination

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

Load

Distributed Moments at Supports

RemarksCase

MAB MDC MAD MDA

(MDA) (MCD) (MBC) (MCB)

Dead Load

(1) (-) 10.72 23.74 10.72 (-) 23.74Load on top

slab and

bottom slab

remains

same in all

cases, only

load on side

wall varies.

Without

braking Force

(2) (-) 6.96 19.15 6.96 (-) 19.15

(3) (-) 6.96 19.15 6.96 (-) 19.15

Live Load

(1) (-) 61.17 6.38 61.17 (-) 6.38

(2) (-) 61.17 6.38 61.17 (-) 6.38

(3) (-) 55.91 1.12 55.91 (-) 1.12

Total Load

(1) (-) 71.89 30.12 71.89 (-) 30.12

(2) (-) 68.13 25.53 68.13 (-)25.53

(3) (-) 62.87 20.27 62.87 (-) 20.27

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

= 86.07

157.96 - 68.13

= 89.83

157.96 - 62.87

=95.09

The Walls

bends

outwardly in

all three casesMDC 71.45 - 30.12

= 41.33

71.45 - 25.53

= 45.92

71.45 - 20.27

= 51.18

MAD 38.29 - (71.89 + 30.12)/2

= (-)12.72

25.79 - (68.13 + 25.53)/2

= (-) 21.04

10 - (62.87 + 20.27)/2

= (-) 31.57

6 BRAKING FORCE

6.1 LOAD: 70R(T), one wheel load is considered as there is no over lapping.

No impact as per IRC:6-2000 Clause 214.2.

The braking force shall be 20 & for the "rst lane load

The braking force = 350 x 20/100 = 70 kN

Load on top of box which will affect the box = 3.84 x 70/4.7 = 57.19 kN

6.2 Moment Due to Braking Force

MAD

= MDA

= MCB

= MBC

= 57.19 x 3.42/2

= 97.79 kN.m

The moments at top and bottom slab ends shall all

be zero.

After distribution of moments among all the

members a moment of 48.9 kN.m is obtained at

all ends. This moment is added to the maximum

moments obtained for various combination of

loadings at the ends of members to get design

moments. Since braking force can also act from

the reverse direction the moment at junctions are

added irrespective of its sign.

7 DESIGN OF SECTION

7.1 Design Moments

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

Provided 362 mm is safe

Check for Shear

Shear force at deff

from face of wall

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

permissible

Permissible shear stress

Increase tension steel to increase permissible shear

stress.

Required steel

Hence, provide tension steel = 2076 mm² in place

of 1849.6 mm² required for moment only.

7.3 Bottom Slab

B.M. (Max) = 79.02 kN.m

Provided 337 mm is O.K.

Check for Shear

Shear Stress = 0.1613 N/mm² < 0.2715 N/mm²

permissible, hence safe.

7.4 Side Walls

Moment at junction are same as slabs hence same

tensile bars shall continue.

Check for Shear

= 18.460 + 17.545 = 36.01 kN

RD = 18.468 + 35.090 = 53.56 kN

S.F. at deff from

= 53.56 � 11.92 � 4.45 = 37.19 kN

S.F. at deff from

= 30.796 kN

Maximum Shear Stress (near base) = 0.100 N/mm² (safe)



ANNEX B

(Para 2)

RCC BOX CULVERT, DESIGNATION: [1/3 x 3/5]1 SALIENT FEATURES

Same as for box [1/3 x 3/0] given in Annex A,

except the cushion which is 5.0 m total height

above top slab.

Fig. 1 Section of box culvert (All dimensions are in m)

2 LOAD CALCULATION

2.1 Top Slab

2.1.1 Dead Load

a) Cushion = 5 x 18 = 90 kN/m²

b) Self weight of top slab = 0.42 x 24 =10.08 kN/m²

c) Total = 100.08 kN/m²

2.1.2 Live Load

Consider moving load of 70R (T). The dispersal

and position of load shall be as under:

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

The larger of the two that is 4.52 kN/m² is considered.

Note:

1) As the load of wheel after dispersal over lap both

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.

2.1.3 Total load = 104.6 kN/m²

2.2 Bottom Slab

2.2.1 Dead Load

Load from top slab including cushion

=100.08 kN/m²

Load of walls

= 2 x 3 x 0.42 x 24/3.84 = 15.75 kN/m²

Total load = 115.83 kN/m²

Live Load

Load from top slab without impact

= 4.52 kN/m²

Note: Some designers take further dispersal of live

load from top slab. Although further dispersal through

walls can not be denied but will affect only marginally,

therefore, the load on top without impact can be taken

for bottom slab also, which is already without impact

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 "lls.

Fig. 3 : Force diagram for vertical wall (All dimensions are in m)

A

D

B

C



Pressure due to live load surcharge

= 1.2 x 18 x 0.5 = 10.80 kN/m²

Pressure due to earth surcharge

= 5 x 18 x 0.5 = 45 kN/m²

Pressure due to earth "ll

= 0.5 x 18 x 3.42 = 30.78 kN/m²

Case 2 : Box full, Live load surcharge on side "ll.

Fig. 5 Force Diagram for wall

Water pressure inside and outside will balance each

other and hence not taken.

Pressure due to live load surcharge

= 10.8 = 10.8 kN/m²

Pressure due to earth surcharge

= 45 = 45 kN/m²

Pressure due to submerged earth

= 0.5 x (18-10) x 3.42 = 13.68 kN/m²

2.3.2 Case 3 : Box full, no live load surcharge on

side "ll.

2.4 Base Pressure

Dead load

Load from top slab and walls including cushion

= 115.83 kN/m²

Self weight of bottom slab

= 0.42 x 24 =10.08 kN/m²


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


= 100.08 x 3.42 x 3.42 /12 = 97.55

Fixed end moment due to live load

= 4.52 x 3.42 x 3.42/12 = 4.41



=100.08 x 3.42 x 3.42/8 = 146.32


= 4.52 x 3.42 x 3.42/8 = 6.61

Total Mid Span Moment =152.93 kN.m

3.2 Bottom Slab


=115.83 x 3.42 x 3.42/12 = 112.9

Fixed end moment due to live load = 4.41



= 115.83 x 3.42 x 3.42/8 = 169.35



3.3 Side Wall

3.3.1 Case 1 : Box empty, surcharge load on side "ll


= 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



= 43.86+30.78 x 3.42 x 3.42/20 = 61.86 kN.m




= 45 x 3.42 x 3.42/8+30.78 x 3.42 x 3.42/16 = 88.29

Fig. 4 Force Diagram for wall (All dimensions are in m)

Pressure due to submerged earth =13.68 kN/m²

Pressure due to earth surcharge = 45 kN/m²



Mid span moment due to live load = 10.8 x 3.42 x 3.42/8 = 15.79

Total Mid Span Moment =104.08 kN.m

3.3.2 Case 2 : Box full, live load surcharge on side "ll.

F.E.M at top due to dead load = 43.86+13.68 x 3.42 x 3.42/30 = 49.19

F.E.M at top due to live load = 10.53


F.E.M at base due to dead load = 43.86+13.68 x 3.42 x 3.42/20 = 51.86


Total F.E.M at bottom = 62.39 kN.m

Mid span moment due to dead load = 65.79+13.68 x 3.42 x 3.42/16 = 75.79



3.3.3 Case 3 : Box full, no live load surcharge

F.E.M at top due to dead load = 43.86 + 5.33 = 49.19 kN.m

F.E.M due to live load = 0

Total F.E.M at top = 49.19

F.E.M at base due to dead load = 43.86 + 8 = 51.86

F.E.M at base due to live load = 0


Mid span moment due to dead load = 65.79 + 13.68 x 3.42 x 3.42/16 = 75.79

Mid span moment due to live load = 0


4 DISTRIBUTION FACTORS ARE SAME

AS OBTAINED FOR BOX WITHOUT

CUSHION

5 MOMENT DISTRIBUTION

5.1 F.E.M Due to Dead Load


MDC = MCD = 112.90 kN.m

MAD = MBC = 55.86 kN.m (case 1),

49.19 kN.m (case 2), 49.19 kN.m (case 3)


51.86 kN.m (case 2), 51.86 kN.m (case 3)

5.2 F.E.M Due to Live Load




10.53 kN.m(case 2), 0 (case 3)


0.53 kN.m (case 2), 0 (case 3)

5.3 F.E.M Due to Total Load

MAB = MBA = 101.95 kN.m

MDC = MCD = 117.31 kN.m


59.72 kN.m(case 2), 49.19 kN.m (case 3)


62.39 kN.m (case 2), 51.86 kN.m (case 3)

A typical distribution is shown in Table 1. Results based

on similar distribution for other combination of loads

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

Load

Distributed Moments at Supports

RemarksCase

MAB MDC MAD MDA

(MBA) (MCD) (MBC) (MCB)

Dead Load

(1) (-) 75.54 88.55 75.54 (-) 88.55

Load on top slab and bottom

slab remains same in all

cases, only load on side wall

varies.

No braking force need be

considered due to cushion.

(2) (-) 71.79 83.97 71.79 (-) 83.97

(3) (-) 71.79 83.97 71.79 (-) 83.97

Live Load

(1) (-) 7.47 7.47 7.47 (-) 7.47

(2) (-) 7.47 7.47 7.47 (-) 7.47

(3) (-) 2.20 2.20 2.20 (-) 2.20

Total Load

(1) (-) 83.00 96.02 83.00 (-) 96.02

(2) (-) 79.25 91.43 79.25 (-)91.43

(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 = 78.94When surcharge is not

taken the Wall bends

outwardly.

MDC

175.96 - 96.02 = 79.94 175.96 - 91.43 = 84.53 175.96 - 86.17 = 89.79

MAD

104.08 - (83+96.02)/2

= 14.57

91.58 - (79.25+91.43)/2

= 6.24

75.79 - (73.99+86.17)/2

= (-) 4.29

6 DESIGN OF SECTION

Table 4 Moment and Reinforcement at Salient Section

Member MAB MDCMid span

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

Maximum moment support/mid span = 83.0 kN.m

Depth required =

Check for Shear



Provide shear reinforcement

Shear capacity

= 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

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.

Then,

and x = 0.543 m, say 600 mm

Provide shear reinforcement upto 600 mm from

face of near wall on both sides.

6.2 Bottom Slab

Maximum Moment support/mid span = 96.02 kN.m

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

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

Balance shear force

= 133.95 � 100.760 =33.19 kN

x is the distance from face of wall where shear

force equals shear capacity of the section

Then,

and x = 0.613 m say 650 mm

Provide shear reinforcement upto 650 mm from

face of near wall on both sides.

6.3 Side Walls

Maximum moments at junctions of slabs and

walls are same as slabs. Hence provide same

reinforcements as slabs at junctions/supports.

Check for Shear

Maximum shear near top at deff

from top slab is

obtained as under :

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



ANNEX C

(Para 9)

RCC BOX CULVERT, DESIGNATION: [1/3 x 3/5]

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;



105 0.57 3.42 0; 106 0.57 3.42 1.6416; 107 0.57 3.42 3.284;

108 0.57 3.42 4.926; 109 0.57 3.42 6.568; 110 0.57 3.42 8.21;

111 0.57 3.42 9.852; 112 0.57 3.42 11.494; 113 0.57 3.42 13.136;

114 0.57 3.42 14.778; 115 0.57 3.42 16.42; 116 0.57 3.42 18.062;

117 0.57 3.42 19.704; 118 1.14 3.42 0; 119 1.14 3.42 1.6416;

120 1.14 3.42 3.284; 121 1.14 3.42 4.926; 122 1.14 3.42 6.568;

123 1.14 3.42 8.21; 124 1.14 3.42 9.852; 125 1.14 3.42 11.494;

126 1.14 3.42 13.136; 127 1.14 3.42 14.778; 128 1.14 3.42 16.42;

129 1.14 3.42 18.062; 130 1.14 3.42 19.704; 131 1.71 3.42 0;

132 1.71 3.42 1.6416; 133 1.71 3.42 3.284; 134 1.71 3.42 4.926;

135 1.71 3.42 6.568; 136 1.71 3.42 8.21; 137 1.71 3.42 9.852;

138 1.71 3.42 11.494; 139 1.71 3.42 13.136; 140 1.71 3.42 14.778;

141 1.71 3.42 16.42; 142 1.71 3.42 18.062; 143 1.71 3.42 19.704;

144 2.28 3.42 0; 145 2.28 3.42 1.6416; 146 2.28 3.42 3.284;

147 2.28 3.42 4.926; 148 2.28 3.42 6.568; 149 2.28 3.42 8.21;

150 2.28 3.42 9.852; 151 2.28 3.42 11.494; 152 2.28 3.42 13.136;

153 2.28 3.42 14.778; 154 2.28 3.42 16.42; 155 2.28 3.42 18.062;

156 2.28 3.42 19.704; 157 2.85 3.42 0; 158 2.85 3.42 1.6416;

159 2.85 3.42 3.284; 160 2.85 3.42 4.926; 161 2.85 3.42 6.568;

162 2.85 3.42 8.21; 163 2.85 3.42 9.852; 164 2.85 3.42 11.494;

165 2.85 3.42 13.136; 166 2.85 3.42 14.778; 167 2.85 3.42 16.42;

168 2.85 3.42 18.062; 169 2.85 3.42 19.704; 170 3.42 3.42 0;

171 3.42 3.42 1.6416; 172 3.42 3.42 3.284; 173 3.42 3.42 4.926;

174 3.42 3.42 6.568; 175 3.42 3.42 8.21; 176 3.42 3.42 9.852;

177 3.42 3.42 11.494; 178 3.42 3.42 13.136; 179 3.42 3.42 14.778;

180 3.42 3.42 16.42; 181 3.42 3.42 18.062; 182 3.42 3.42 19.704; 183 0 0.855 0;

184 0 0.855 1.6416; 185 0 0.855 3.284; 186 0 0.855 4.926; 187 0 0.855 6.568;

188 0 0.855 8.21; 189 0 0.855 9.852; 190 0 0.855 11.494; 191 0 0.855 13.136;

192 0 0.855 14.778; 193 0 0.855 16.42; 194 0 0.855 18.062; 195 0 0.855 19.704;

196 3.42 0.855 0; 197 3.42 0.855 1.6416; 198 3.42 0.855 3.284;

199 3.42 0.855 4.926; 200 3.42 0.855 6.568; 201 3.42 0.855 8.21;

202 3.42 0.855 9.852; 203 3.42 0.855 11.494; 204 3.42 0.855 13.136;

205 3.42 0.855 14.778; 206 3.42 0.855 16.42; 207 3.42 0.855 18.062;

208 3.42 0.855 19.704; 209 0 1.71 0; 210 0 1.71 1.6416; 211 0 1.71 3.284;

212 0 1.71 4.926; 213 0 1.71 6.568; 214 0 1.71 8.21; 215 0 1.71 9.852;

216 0 1.71 11.494; 217 0 1.71 13.136; 218 0 1.71 14.778; 219 0 1.71 16.42;

220 0 1.71 18.062; 221 0 1.71 19.704; 222 3.42 1.71 0; 223 3.42 1.71 1.6416;

224 3.42 1.71 3.284; 225 3.42 1.71 4.926; 226 3.42 1.71 6.568;

227 3.42 1.71 8.21; 228 3.42 1.71 9.852; 229 3.42 1.71 11.494;

230 3.42 1.71 13.136; 231 3.42 1.71 14.778; 232 3.42 1.71 16.42;

233 3.42 1.71 18.062; 234 3.42 1.71 19.704; 235 0 2.565 0; 236 0 2.565 1.6416;

237 0 2.565 3.284; 238 0 2.565 4.926; 239 0 2.565 6.568; 240 0 2.565 8.21;

241 0 2.565 9.852; 242 0 2.565 11.494; 243 0 2.565 13.136; 244 0 2.565 14.778;

245 0 2.565 16.42; 246 0 2.565 18.062; 247 0 2.565 19.704; 248 3.42 2.565 0;

249 3.42 2.565 1.6416; 250 3.42 2.565 3.284; 251 3.42 2.565 4.926;

252 3.42 2.565 6.568; 253 3.42 2.565 8.21; 254 3.42 2.565 9.852;

255 3.42 2.565 11.494; 256 3.42 2.565 13.136; 257 3.42 2.565 14.778;

258 3.42 2.565 16.42; 259 3.42 2.565 18.062; 260 3.42 2.565 19.704;



MEMBER INCIDENCES

1 1 2; 2 2 3; 3 3 4; 4 4 5; 5 5 6; 6 6 7; 7 7 8; 8 8 9; 9 9 10; 10 10 11;

11 11 12; 12 12 13; 13 14 15; 14 15 16; 15 16 17; 16 17 18; 17 18 19; 18 19 20;

19 20 21; 20 21 22; 21 22 23; 22 23 24; 23 24 25; 24 25 26; 25 27 28; 26 28 29;

27 29 30; 28 30 31; 29 31 32; 30 32 33; 31 33 34; 32 34 35; 33 35 36; 34 36 37;

35 37 38; 36 38 39; 37 40 41; 38 41 42; 39 42 43; 40 43 44; 41 44 45; 42 45 46;

43 46 47; 44 47 48; 45 48 49; 46 49 50; 47 50 51; 48 51 52; 49 53 54; 50 54 55;

51 55 56; 52 56 57; 53 57 58; 54 58 59; 55 59 60; 56 60 61; 57 61 62; 58 62 63;

59 63 64; 60 64 65; 61 66 67; 62 67 68; 63 68 69; 64 69 70; 65 70 71; 66 71 72;

67 72 73; 68 73 74; 69 74 75; 70 75 76; 71 76 77; 72 77 78; 73 79 80; 74 80 81;

75 81 82; 76 82 83; 77 83 84; 78 84 85; 79 85 86; 80 86 87; 81 87 88; 82 88 89;

83 89 90; 84 90 91; 85 1 14; 86 14 27; 87 27 40; 88 40 53; 89 53 66; 90 66 79;

91 2 15; 92 15 28; 93 28 41; 94 41 54; 95 54 67; 96 67 80; 97 3 16; 98 16 29;

99 29 42; 100 42 55; 101 55 68; 102 68 81; 103 4 17; 104 17 30; 105 30 43;

106 43 56; 107 56 69; 108 69 82; 109 5 18; 110 18 31; 111 31 44; 112 44 57;

113 57 70; 114 70 83; 115 6 19; 116 19 32; 117 32 45; 118 45 58; 119 58 71;

120 71 84; 121 7 20; 122 20 33; 123 33 46; 124 46 59; 125 59 72; 126 72 85;

127 8 21; 128 21 34; 129 34 47; 130 47 60; 131 60 73; 132 73 86; 133 9 22;

134 22 35; 135 35 48; 136 48 61; 137 61 74; 138 74 87; 139 10 23; 140 23 36;

141 36 49; 142 49 62; 143 62 75; 144 75 88; 145 11 24; 146 24 37; 147 37 50;

148 50 63; 149 63 76; 150 76 89; 151 12 25; 152 25 38; 153 38 51; 154 51 64;

155 64 77; 156 77 90; 157 13 26; 158 26 39; 159 39 52; 160 52 65; 161 65 78;

162 78 91; 163 92 93; 164 93 94; 165 94 95; 166 95 96; 167 96 97; 168 97 98;

169 98 99; 170 99 100; 171 100 101; 172 101 102; 173 102 103; 174 103 104;

175 105 106; 176 106 107; 177 107 108; 178 108 109; 179 109 110; 180 110 111;

181 111 112; 182 112 113; 183 113 114; 184 114 115; 185 115 116; 186 116 117;

187 118 119; 188 119 120; 189 120 121; 190 121 122; 191 122 123; 192 123 124;

193 124 125; 194 125 126; 195 126 127; 196 127 128; 197 128 129; 198 129 130;

199 131 132; 200 132 133; 201 133 134; 202 134 135; 203 135 136; 204 136 137;

205 137 138; 206 138 139; 207 139 140; 208 140 141; 209 141 142; 210 142 143;

211 144 145; 212 145 146; 213 146 147; 214 147 148; 215 148 149; 216 149 150;

217 150 151; 218 151 152; 219 152 153; 220 153 154; 221 154 155; 222 155 156;

223 157 158; 224 158 159; 225 159 160; 226 160 161; 227 161 162; 228 162 163;

229 163 164; 230 164 165; 231 165 166; 232 166 167; 233 167 168; 234 168 169;

235 170 171; 236 171 172; 237 172 173; 238 173 174; 239 174 175; 240 175 176;

241 176 177; 242 177 178; 243 178 179; 244 179 180; 245 180 181; 246 181 182;

247 92 105; 248 105 118; 249 118 131; 250 131 144; 251 144 157; 252 157 170;

253 93 106; 254 106 119; 255 119 132; 256 132 145; 257 145 158; 258 158 171;

259 94 107; 260 107 120; 261 120 133; 262 133 146; 263 146 159; 264 159 172;

265 95 108; 266 108 121; 267 121 134; 268 134 147; 269 147 160; 270 160 173;

271 96 109; 272 109 122; 273 122 135; 274 135 148; 275 148 161; 276 161 174;

277 97 110; 278 110 123; 279 123 136; 280 136 149; 281 149 162; 282 162 175;

283 98 111; 284 111 124; 285 124 137; 286 137 150; 287 150 163; 288 163 176;

289 99 112; 290 112 125; 291 125 138; 292 138 151; 293 151 164; 294 164 177;

295 100 113; 296 113 126; 297 126 139; 298 139 152; 299 152 165; 300 165 178;

301 101 114; 302 114 127; 303 127 140; 304 140 153; 305 153 166; 306 166 179;

307 102 115; 308 115 128; 309 128 141; 310 141 154; 311 154 167; 312 167 180;

313 103 116; 314 116 129; 315 129 142; 316 142 155; 317 155 168; 318 168 181;

319 104 117; 320 117 130; 321 130 143; 322 143 156; 323 156 169; 324 169 182;

325 183 184; 326 184 185; 327 185 186; 328 186 187; 329 187 188; 330 188 189;



331 189 190; 332 190 191; 333 191 192; 334 192 193; 335 193 194; 336 194 195;

337 196 197; 338 197 198; 339 198 199; 340 199 200; 341 200 201; 342 201 202;

343 202 203; 344 203 204; 345 204 205; 346 205 206; 347 206 207; 348 207 208;

349 209 210; 350 210 211; 351 211 212; 352 212 213; 353 213 214; 354 214 215;

355 215 216; 356 216 217; 357 217 218; 358 218 219; 359 219 220; 360 220 221;

361 222 223; 362 223 224; 363 224 225; 364 225 226; 365 226 227; 366 227 228;

367 228 229; 368 229 230; 369 230 231; 370 231 232; 371 232 233; 372 233 234;

373 235 236; 374 236 237; 375 237 238; 376 238 239; 377 239 240; 378 240 241;

379 241 242; 380 242 243; 381 243 244; 382 244 245; 383 245 246; 384 246 247;

385 248 249; 386 249 250; 387 250 251; 388 251 252; 389 252 253; 390 253 254;

391 254 255; 392 255 256; 393 256 257; 394 257 258; 395 258 259; 396 259 260;

397 1 183; 398 183 209; 399 209 235; 400 235 92; 401 2 184; 402 184 210;

403 210 236; 404 236 93; 405 3 185; 406 185 211; 407 211 237; 408 237 94;

409 4 186; 410 186 212; 411 212 238; 412 238 95; 413 5 187; 414 187 213;

415 213 239; 416 239 96; 417 6 188; 418 188 214; 419 214 240; 420 240 97;

421 7 189; 422 189 215; 423 215 241; 424 241 98; 425 8 190; 426 190 216;

427 216 242; 428 242 99; 429 9 191; 430 191 217; 431 217 243; 432 243 100;

433 10 192; 434 192 218; 435 218 244; 436 244 101; 437 11 193; 438 193 219;

439 219 245; 440 245 102; 441 12 194; 442 194 220; 443 220 246; 444 246 103;

445 13 195; 446 195 221; 447 221 247; 448 247 104; 449 91 208; 450 208 234;

451 234 260; 452 260 182; 453 90 207; 454 207 233; 455 233 259; 456 259 181;

457 89 206; 458 206 232; 459 232 258; 460 258 180; 461 88 205; 462 205 231;

463 231 257; 464 257 179; 465 87 204; 466 204 230; 467 230 256; 468 256 178;

469 86 203; 470 203 229; 471 229 255; 472 255 177; 473 85 202; 474 202 228;

475 228 254; 476 254 176; 477 84 201; 478 201 227; 479 227 253; 480 253 175;

481 83 200; 482 200 226; 483 226 252; 484 252 174; 485 82 199; 486 199 225;

487 225 251; 488 251 173; 489 81 198; 490 198 224; 491 224 250; 492 250 172;

493 80 197; 494 197 223; 495 223 249; 496 249 171; 497 79 196; 498 196 222;

499 222 248; 500 248 170;

START GROUP DEFINITION

MEMBER

_TS 253 TO 318

_TS1 247 TO 252 319 TO 324

_BS 91 TO 156

_BS1 85 TO 90 157 TO 162

_DBS 1 TO 84 163 TO 246 325 TO 396

END GROUP DEFINITION

DEFINE MATERIAL START

ISOTROPIC MATERIAL1

E 3.05e+007

POISSON 0.196183

ISOTROPIC MATERIAL2

E 3.05e+007

POISSON 0.196183

DENSITY 24

END DEFINE MATERIAL

MEMBER PROPERTY AMERICAN

85 TO 90 157 TO 162 247 TO 252 319 TO 324 PRIS YD 0.42 ZD 0.821

91 TO 156 253 TO 318 PRIS YD 0.42 ZD 1.642



401 TO 444 453 TO 496 PRIS YD 0.42 ZD 1.642

1 TO 12 73 TO 84 163 TO 174 235 TO 246 PRIS YD 0.42 ZD 0.285

13 TO 72 175 TO 234 PRIS YD 0.42 ZD 0.57

397 TO 400 445 TO 452 497 TO 500 PRIS YD 0.42 ZD 0.821

325 TO 396 PRIS YD 0.42 ZD 0.855

CONSTANTS

MATERIAL MATERIAL1 MEMB 1 TO 84 163 TO 246 325 TO 396

MATERIAL MATERIAL2 MEMB 85 TO 162 247 TO 324 397 TO 500

SUPPORTS

1 TO 91 ELASTIC MAT DIRECT Y SUBGRADE 20400

*DEFINE MOVING LOAD

* IMPACT FACTOR 1

* REDUCTION OF LOAD 20%

*TYPE 1 LOAD 28 28 28 28 28 28 28 28 28 28

*DIST 0.46 0.46 0.46 0.46 0.46 0.46 0.46 0.46 0.46

*TYPE 2 LOAD 28 28 28 28 28 28 28 28 28 28

*DIST 0.46 0.46 0.46 0.46 0.46 0.46 0.46 0.46 0.46

*TYPE 3 LOAD 68 68 68 68 48 48 32

*DIST 1.37 3.05 1.37 2.13 1.52 3.96

*TYPE 4 LOAD 68 68 68 68 48 48 32

*DIST 1.37 3.05 1.37 2.13 1.52 3.96

*TYPE 5 LOAD 27 27 27 27 46 46 11 11

*DIST 3 3 3 4.3 1.2 3.2 1.1

*TYPE 6 LOAD 27 27 27 27 46 46 11 11

*DIST 3 3 3 4.3 1.2 3.2 1.1

LOAD 1

MEMBER LOAD

253 TO 318 UNI GY -16.55

247 TO 252 319 TO 324 UNI GY -8.275

*LOAD 2

MEMBER LOAD

253 TO 318 UNI GY -148

247 TO 252 319 TO 324 UNI GY -74

1 TO 12 73 TO 84 UNI GY -30.24

*ACTIVE EARTH PRESSURE ON BOTH SIDE OF WALL

* COEFFICIENT OF ACTIVE EARTH PRESSURE = KA=0.5

* CALCULATION IS BASED ON 0.50x20xWxH

* LOAD 3

MEMBER LOAD

400 448 TRAP GX 0 6.318

399 447 TRAP GX 6.318 12.64

398 446 TRAP GX 12.64 18.95

397 445 TRAP GX 18.95 25.27

404 408 412 416 420 424 428 432 436 440 444 TRAP GX 0 12.64

403 407 411 415 419 423 427 431 435 439 443 TRAP GX 12.64 25.27

402 406 410 414 418 422 426 430 434 438 442 TRAP GX 25.27 37.91

401 405 409 413 417 421 425 429 433 437 441 TRAP GX 37.91 50.54

452 500 TRAP GX -6.318 0 -6.318



451 499 TRAP GX -12.64 -6.318 -12.64

450 498 TRAP GX -18.95 -12.64 -18.95

449 497 TRAP GX -25.27 -18.95 -25.27

456 460 464 468 472 476 480 484 488 492 496 TRAP GX 0 -12.64

455 459 463 467 471 475 479 483 487 491 495 TRAP GX -12.64 -25.27

454 458 462 466 470 474 478 482 486 490 494 TRAP GX -25.27 -37.91

453 457 461 465 469 473 477 481 485 489 493 TRAP GX -37.91 -50.54

* VALUE USED 0.50 x 18 x 1.20 x W

* SURCHARGE LOAD

MEMBER LOAD

397 TO 400 445 TO 448 UNI GX 45.812

449 TO 452 497 TO 500 UNI GX -45.812

401 TO 444 UNI GX 91.62

453 TO 496 UNI GX -91.62

253 TO 318 UNI GY -7.42

247 TO 252 319 TO 324 UNI GY -3.71

PRINT SUPPORT INFORMATION

*LOAD 4 MOVING LOAD

*LOAD GENERATION 16 ADD LOAD 1

*TYPE 1 0 3.42 12.12 XINC 0.5

*TYPE 2 0 3.42 14.18 XINC 0.5

*TYPE 1 0 3.42 16.22 XINC 0.5

*TYPE 2 0 3.42 18.28 XINC 0.5

*TYPE 5 0 3.42 20.15 XINC 0.5

*TYPE 6 0 3.42 21.95 XINC 0.5


*TYPE 1 0.5 8.42 12.12 XINC 0.5

*TYPE 2 0.5 8.42 14.18 XINC 0.5

*TYPE 1 0.5 8.42 16.22 XINC 0.5

*TYPE 2 0.5 8.42 18.28 XINC 0.5

*TYPE 5 0.5 8.42 20.15 XINC 0.5

*TYPE 6 0.5 8.42 21.95 XINC 0.5


*TYPE 1 1 8.42 12.12 XINC 0.5

*TYPE 2 1 8.42 14.18 XINC 0.5

*TYPE 1 1 8.42 16.22 XINC 0.5

*TYPE 2 1 8.42 18.28 XINC 0.5

*TYPE 5 1 8.42 20.15 XINC 0.5

*TYPE 6 1 8.42 21.95 XINC 0.5


*TYPE 1 1.5 8.42 12.12 XINC 0.5

*TYPE 2 1.5 8.42 14.18 XINC 0.5

*TYPE 1 1.5 8.42 16.22 XINC 0.5

*TYPE 2 1.5 8.42 18.28 XINC 0.5

*TYPE 5 1.5 8.42 20.15 XINC 0.5

*TYPE 6 1.5 8.42 21.95 XINC 0.5


*TYPE 1 2 8.42 12.12 XINC 0.5

*TYPE 2 2 8.42 14.18 XINC 0.5

*TYPE 1 2 8.42 16.22 XINC 0.5

*TYPE 2 2 8.42 18.28 XINC 0.5

*TYPE 5 2 8.42 20.15 XINC 0.5

*TYPE 6 2 8.42 21.95 XINC 0.5


*TYPE 1 2.5 8.42 12.12 XINC 0.5

*TYPE 2 2.5 8.42 14.18 XINC 0.5

*TYPE 1 2.5 8.42 16.22 XINC 0.5

*TYPE 2 2.5 8.42 18.28 XINC 0.5

*TYPE 5 2.5 8.42 20.15 XINC 0.5

*TYPE 6 2.5 8.42 21.95 XINC 0.5


*TYPE 1 3.995 8.42 12.12 XINC 0.5

*TYPE 2 3.995 8.42 14.18 XINC 0.5

*TYPE 1 3.995 8.42 16.22 XINC 0.5

*TYPE 2 3.995 8.42 18.28 XINC 0.5

*TYPE 5 6.01 8.42 20.15 XINC 0.5

*TYPE 6 6.01 8.42 21.95 XINC 0.5

* IMPACT FACTOR 1


*TYPE 1 LOAD 28 28 28 28 28 28 28 28 28 28

*DIST 0.46 0.46 0.46 0.46 0.46 0.46 0.46 0.46 0.46

*TYPE 2 LOAD 28 28 28 28 28 28 28 28 28 28

*DIST 0.46 0.46 0.46 0.46 0.46 0.46 0.46 0.46 0.46

*TYPE 3 LOAD 68 68 68 68 48 48 32

*DIST 1.37 3.05 1.37 2.13 1.52 3.96

*TYPE 4 LOAD 68 68 68 68 48 48 32

*DIST 1.37 3.05 1.37 2.13 1.52 3.96

*TYPE 5 LOAD 27 27 27 27 46 46 11 11

*DIST 3 3 3 4.3 1.2 3.2 1.1

*TYPE 6 LOAD 27 27 27 27 46 46 11 11

*DIST 3 3 3 4.3 1.2 3.2 1.1

*LOAD 5 MOVING LOAD


*TYPE 3 0 8.42 12.13 XINC 0.5

*TYPE 4 0 8.42 14.06 XINC 0.5

*TYPE 3 0 8.42 16.12 XINC 0.5

*TYPE 4 0 8.42 18.08 XINC 0.5

*TYPE 5 0 8.42 19.93 XINC 0.5



*TYPE 6 0 8.42 21.73 XINC 0.5


*TYPE 3 0.5 8.42 12.63 XINC 0.5

*TYPE 4 0.5 8.42 14.56 XINC 0.5

*TYPE 3 0.5 8.42 16.62 XINC 0.5

*TYPE 4 0.5 8.42 18.58 XINC 0.5

*TYPE 5 0.5 8.42 20.43 XINC 0.5

*TYPE 6 0.5 8.42 22.23 XINC 0.5


*TYPE 3 1 8.42 12.63 XINC 0.5

*TYPE 4 1 8.42 14.56 XINC 0.5

*TYPE 3 1 8.42 16.62 XINC 0.5

*TYPE 4 1 8.42 18.58 XINC 0.5

*TYPE 5 1 8.42 20.43 XINC 0.5

*TYPE 6 1 8.42 22.23 XINC 0.5


*TYPE 3 1.5 8.42 12.63 XINC 0.5

*TYPE 4 1.5 8.42 14.56 XINC 0.5

*TYPE 3 1.5 8.42 16.62 XINC 0.5

*TYPE 4 1.5 8.42 18.58 XINC 0.5

*TYPE 5 1.5 8.42 20.43 XINC 0.5

*TYPE 6 1.5 8.42 22.23 XINC 0.5


*TYPE 3 2.395 8.42 12.63 XINC 0.5

*TYPE 4 2.395 8.42 14.56 XINC 0.5

*TYPE 3 2.395 8.42 16.62 XINC 0.5

*TYPE 4 2.395 8.42 18.58 XINC 0.5

*TYPE 5 6.01 8.42 20.43 XINC 0.5

*TYPE 6 6.01 8.42 22.23 XINC 0.5


*TYPE 3 3 8.42 12.63 XINC 0.5

*TYPE 4 3 8.42 14.56 XINC 0.5

*TYPE 3 3 8.42 16.62 XINC 0.5

*TYPE 4 3 8.42 18.58 XINC 0.5

*TYPE 5 3 8.42 20.43 XINC 0.5

*TYPE 6 3 8.42 22.23 XINC 0.5


*TYPE 3 3.5 8.42 12.63 XINC 0.5

*TYPE 4 3.5 8.42 14.56 XINC 0.5

*TYPE 3 3.5 8.42 16.62 XINC 0.5

*TYPE 4 3.5 8.42 18.58 XINC 0.5

*TYPE 5 3.5 8.42 20.43 XINC 0.5

*TYPE 6 3.5 8.42 22.23 XINC 0.5


*TYPE 3 5 8.42 12.63 XINC 0.5

*TYPE 4 5 8.42 14.56 XINC 0.5

*TYPE 3 5 8.42 16.62 XINC 0.5

*TYPE 4 5 8.42 18.58 XINC 0.5

*TYPE 5 5 8.42 20.43 XINC 0.5

*TYPE 6 5 8.42 22.23 XINC 0.5

* IMPACT FACTOR 1


*TYPE 5 LOAD 27 27 27 27 46 46 11 11

*DIST 3 3 3 4.3 1.2 3.2 1.1

*TYPE 6 LOAD 27 27 27 27 46 46 11 11

*DIST 3 3 3 4.3 1.2 3.2 1.1

*LOAD 1 MOVING LOAD


*TYPE 5 0 8.42 20.43 XINC 0.5

*TYPE 6 0 8.42 22.23 XINC 0.5

*TYPE 5 0 8.42 20.23 XINC 0.5

*TYPE 6 0 8.42 22.23 XINC 0.5

*TYPE 5 0 8.42 20.23 XINC 0.5

*TYPE 6 0 8.42 22.23 XINC 0.5

*TYPE 5 0 8.42 20.23 XINC 0.5

*TYPE 6 0 8.42 22.23 XINC 0.5

*TYPE 5 0 8.42 20.23 XINC 0.5

*TYPE 6 0 8.42 22.23 XINC 0.5


*TYPE 5 1.5 8.42 20.43 XINC 0.5

*TYPE 6 1.5 8.42 22.23 XINC 0.5

*TYPE 5 1.5 8.42 20.43 XINC 0.5

*TYPE 6 1.5 8.42 22.23 XINC 0.5

*TYPE 5 1.5 8.42 20.43 XINC 0.5

*TYPE 6 1.5 8.42 22.23 XINC 0.5

*TYPE 5 1.5 8.42 20.43 XINC 0.5

*TYPE 6 1.5 8.42 22.23 XINC 0.5

*TYPE 5 1.5 8.42 20.43 XINC 0.5

*TYPE 6 1.5 8.42 22.23 XINC 0.5


*TYPE 5 6.01 8.42 20.43 XINC 0.5

*TYPE 6 6.01 8.42 22.23 XINC 0.5

*TYPE 5 6.01 8.42 20.43 XINC 0.5

*TYPE 6 6.01 8.42 22.23 XINC 0.5

*TYPE 5 6.01 8.42 20.43 XINC 0.5

*TYPE 6 6.01 8.42 22.23 XINC 0.5

*TYPE 5 6.01 8.42 20.43 XINC 0.5

*TYPE 6 6.01 8.42 22.23 XINC 0.5

*TYPE 5 6.01 8.42 20.43 XINC 0.5

*TYPE 6 6.01 8.42 22.23 XINC 0.5


*TYPE 5 7 8.42 20.43 XINC 0.5

*TYPE 6 7 8.42 22.23 XINC 0.5

*TYPE 5 7 8.42 20.43 XINC 0.5

*TYPE 6 7 8.42 22.23 XINC 0.5

*TYPE 5 7 8.42 20.43 XINC 0.5

*TYPE 6 7 8.42 22.23 XINC 0.5

*TYPE 5 7 8.42 20.43 XINC 0.5



*TYPE 6 7 8.42 22.23 XINC 0.5

*TYPE 5 7 8.42 20.43 XINC 0.5

*TYPE 6 7 8.42 22.23 XINC 0.5

PERFORM ANALYSIS

PRINT SUPPORT REACTION

PERFORM ANALYSIS

PRINT MAXFORCE ENVELOPE LIST 85 TO 162

247 TO 324

PRINT MAXFORCE ENVELOPE LIST 397 TO 500

START CONCRETE DESIGN

Fig. 1 Model of box showing nodes and members

CODE INDIAN

FC 25000 ALL

CLEAR 0.05 MEMB 163 TO 500

CLEAR 0.075 MEMB 1 TO 162

FYMAIN 415000 ALL

FYSEC 415000 ALL

DESIGN BEAM 1 TO 500

END CONCRETE DESIGN

FINISH



Table 1 Beam End Force Summary

Beam Node L/C Axial Shear Torsion Bending

Fx (kN) Fy (kN) Fz (kN) Mx

(kNm)

My

(kNm)

Mz

(kNm)

Max Fx 473 1 1: 85 294.174 -217.946 0.004 0.000 -0.002 -155.240

Min Fx 163 1 1: 92 -0.004 0.091 -0.025 -0.005 0.021 0.075

Max Fy 283 1 1: 98 181.746 294.014 0.002 -0.001 -0.000 136.419

Min Fy 264 1 1: 172 181.859 -294.142 -0.070 0.004 0.016 136.647

Max Fz 397 1 1: 1 147.825 109.156 5.118 -0.007 -5.533 77.873

Min Fz 445 1 1: 13 147.845 109.162 -5.131 0.009 5.543 77.880

Max

Mx

162 1 1: 78 0.000 142.375 0.000 0.718 0.000 3.481

Min Mx 90 1 1: 66 0.000 142.354 0.000 -0.724 0.000 3.477

Max

My

445 1 1: 13 147.845 109.162 -5.131 0.009 5.543 77.880

Min My 397 1 1: 1 147.825 109.156 5.118 -0.007 -5.533 77.873

Max Mz 405 1 1: 3 293.940 218.072 -0.640 0.030 0.082 155.434

Min Mz 97 1 1: 3 0.000 -284.032 0.000 0.056 0.000 -155.434

Refer Fig. 2

WIDTH OF MEMBERS 97 to 102,405 TO 408,489 TO 492,259 TO 264 = 1.642 m

B.M. PER M RUN AT CORNERS OF TOP SLAB IN MEMBERS 259,264,408 AND 492 = 136.369/1.642 =

83.05 kNm

B.M. PER M RUN AT CORNERS OF BOTTOM SLAB IN MEMBERS 97, 102, 405 AND 489 =

155.434/1.642=94.66 kNm

B.M. PER M RUN AT MID POINT OF TOP SLAB AT JOINT OF MEMBERS 261 AND 262 = 114.918/1.642

= 69.99 kNm

B.M. PER M RUN AT MID POINT OF BOTTOM SLAB AT JOINT OF MEMBERS 99 AND 100 =

134.148/1.642 = 81.70 kNm

B.M. PER M RUN AT MID POINT OF SIDE SLAB AT JOINT OF MEMBERS 406-407 AND 490-491 =

25/1.642 = 15.22 kNm

Refer Fig. 3

SHEAR FORCE DIAGRAM

WIDTH OF MEMBERS 121 to 126,421 to 424,283 TO 288,473 TO 476 = 1.642 m

S.F. PER M RUN AT EFFECTIVE DISTANCE 0.622 m FROM CENTER OF SUPPORT IN TOP SLAB IN

MEMEBR 284=97.972*1.088/(1.642*.57) = 113.88 kN

S.F. PER M RUN AT EFFECTIVE DISTANCE 0.597 m FROM CENTER OF SUPPORT IN BOTTOM

SLAB IN MEMBER 122

=168.253 /(1.642) = 102.46 kN



S.F. PER M RUN AT EFFECTIVE DISTANCE 0.622 m FROM CENTER OF SUPPORT IN SIDE SLAB IN

MEMEBR 424 =98.004*1.088/(1.642*.855) = 75.95 kN

S.F. PER M RUN AT EFFECTIVE DISTANCE 0.622 m FROM CENTER OF SUPPORT IN SIDE SLAB IN

MEMEBR 421

=101.89*1.088 (1.642*.855) = 78.96 kN

Fig. 2 Bending Moment Diagram

(Value are for element length of 1.642 m)

Fig. 3 Shear Force Diagram

(Value are for element length of 1.642 m)

RCC Box Culvert Methodology and Designs

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Transcript of RCC Box Culvert Methodology and Designs