Rcc box culvert methodology and designs including computer method

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Design of Box Culvert

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Rcc box culvert methodology and designs including computer method

  1. 1. 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 theIt 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 theof 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 profiledrainage works are required to be provided to allow at the location of the culvert. This Paper is devoted towater to pass across the embankment. The structures to box culverts constructed in reinforced concrete havingaccomplish such flow across the road are called culverts, one, two or three cells and varying cushion including nosmall and major bridges depending on their span which cushion. The main emphasis is on the methodology ofin turn depends on the discharge. The culvert cover upto design which naturally covers the type of loading as perwaterways of 6 m (IRC:5-19981) and can mainly be of relevant IRC Codes and their combination to producetwo types, namely, box or slab. The box is one which the worst effect for a safe structure. The IS:1893-1984²has its top and bottom slabs monolithically connected (Clause 6.1.3) provide that box culverts need not beto the vertical walls. In case of a slab culvert the top designed for earthquake forces, hence no earthquakeslab is supported over the vertical walls (abutments/ forces are considered. Although box of maximum threepiers) but has no monolithic connection between them. cells has been discussed but in practice a box culvert canA 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
  2. 2. 190 Sinha & Sharma onthe embankment and follow natural course of flow but for more number of lanes, a situation which occurs onthese are also provided to balance the water level on both widening of the road and frequently encountered forsides of embankment during floods, such culverts are road development, and whether the culvert designed fortermed as balancers (IRC:78-2000³), although there is no no cushion shall be safe for cushion loads which maydifference in the design. Sometimes the road alignment become a necessity at a future date due to change in roadmay cross a stream at an angle other than right angle, profile. If so, up to what height of cushion, the box needin such situation a skew culvert may be provided. For not be reconstructed. These shall be addressed in thisa 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 slabthe 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 mainFor a box culvert, the top slab is required to withstand advantage is, it can be placed at any elevation within thedead loads, live loads from moving traffic, earth pressure embankment with varying cushion which is not possibleon sidewalls, water pressure from inside, and pressure for other type of culverts. A multi cell box can cater foron the bottom slab besides self weight of the slab. The large discharge and can be accommodated within smallerstructure is designed like a rigid frame considering one height of embankment. It does not require separatemeter element and adopting moment distribution method elaborate foundation and can be placed on soft soil byfor obtaining final distributed moments on the basis of providing suitable base slab projection to reduce basethe relative stiffness of the slab and vertical walls. The pressure within the safe bearing capacity of foundationmethod is well known and does not need any elucidation. soil. Bearings are not needed. It is convenient to extendThe mid span moments are computed with free supported the existing culvert in the event of widening of theends 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 PRESSUREof loads and the member is designed for the maximummoment it may be subjected to. Also the shear force at The earth can exert pressure, minimum as active anda 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 (Terzaghi4the 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 fromfor lateral pressure on walls, effective width (run of the earth fill the pressure exerted by the earth shall tendculvert) for live loads and applicability of braking force to reach active state and thus be minimum. As to reachon box without cushion (or little cushion) for structural active state only a small movement is required whichdeformation 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 isaffect the design significantly and therefore, required to bound to reach active state. The wall thus can safely bebe assessed correctly for designing a safe structure. It is designed for active pressure of earth, with co-efficientcustomary to consider box a rigid frame and unit length applicable for active pressure. In case of an anchoredof box is taken for design by considering the effect of bulk head, the earth pressure on the anchor plate willall forces acting on this unit length (generally 1.0 m of tend to achieve passive state because the anchor platebox). While calculating weight of cushion on top slab, is dragged against earth and large displacement can besome designer take average height of earth fill coming allowed, one can consider passive co-efficient for theover full length of box including sloping side fill. This design of anchor, of course, some factor of safety need beis not correct and full height of cushion should be taken taken as required displacement to achieve passive stateat the worst section of the box (central portion) will before the bulk head gives way may not be practical. Inbe subjected to this load and the section needs to be cases where the structure is constructed before back filldesigned accordingly. earth is placed in position and the situation is such thatA question has been raised frequently whether culverts structure is not in a position to yield on either side, thedesigned for four lane divided carriageway are safe earth pressure shall reach a state at rest. In such situation Journal of the Indian Roads Congress, October-December 2009
  3. 3. Rcc Box Culvert- Methodology and Designs Including Computer Method 191the co-efficient of earth pressure shall be more than deformation can be assumed to be at rest/active pressurethe active condition. In case of box since it is confined as the earth pressure co-efficient has little over all effectwith earth from both sides the state of earth shall be at on the structural sizes of box members as already shownrest and a co-efficient more than the active pressure is in Table 1 and explained under sub para 2 above. Fornormally 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 positionto move/yield therefore the pressure shall be at rest. The 3 EFFECTIVE WIDTHvalue 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. Thistaken to be 0.333 for a soil having ф = 30º equivalent width plays a significant role as far as consideration ofto active condition by many authors in their books of live load in the design of culvert. Where however, theredesign. Some authors take this value = 0.5 for normal is large cushion the live load gets dispersed on a verysoil having ф = 30º. A typical box has been designed large area through the fill and the load per unit areakeeping all factors to be same for the two values of earth becomes less and does not remain significant for thepressure co-efficient. It is seen that these co-efficient design of box, particularly in comparison to the deadeven when taken differently have little effect on the load due to such large cushion. In case of dead load orover all design of the section. To bring out difference uniform surcharge load the effective width has no rolein more appreciable form the two designs are compared to play and such loads are to be taken over the entirein 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 withoutis marginal. However, box with cushion shows more cushion as the live load becomes the main load on thedifference. top slab and to evaluate its effects per unit run for designConsidering the situation typical to the box, it is close as a rigid frame, this load is required to be divided byto at rest condition and a co-efficient higher than active the effective width. As such evaluating effective widthpressure 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 variancethere is no point of difference in taking this value for as far as effective width is concerned and requiresculverts 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 effectivecushion, where the box is assumed to deform pressing width. Basically, it is the width of slab perpendicular toagainst the fill earth on one side and the pressure can be the span which is affected by the load placed on the topdifferent on two sides, at least it may tend to be active of slab. It shall be related to the area of slab expectedon the side the box is tilting away from the fill. In design to deform under load. It can be well imagined that thisthis difference of earth pressure on two sides of box is area of slab which may get affected will depend on hownot taken, as the pressure on the passive side, which the slab is supported whether in one direction or bothdepends on amount of deformation of culvert, can not directions and secondly on the condition of support thatbe 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 Journal of the Indian Roads Congress, October-December 2009
  4. 4. 192 Sinha & Sharma onslab is allowed to slide over support under the load as The live load moment and shear for the top slab can bein case of freely supported, and the same will reduce if obtained per unit run of box considering effective widththe slab is restrained from sliding and more the restraint for an assessed value of α. For the bottom slab the livethe less shall be the width. In this view the effective load shall disperse through the walls and such dispersedwidth 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 couldand shall reach maximum for slabs freely supported at be obtained on this basis and used in the analysis. Inends. Where support on one side is different than on other words the effect of live load on bottom slab shallthe other side the effective width should be obtained be as in case of large cushion for top slab explainedtaking this fact in consideration. The distance of the load under sub para 1. As far as walls are concerned thefrom the near support affects effective width, more the loads are uniform and pressure etc all are same per unitdistance 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 bewidth. All factors mentioned above need to be taken practical. The AASHTO also advocates dispersal forinto account while obtaining the effective width. bottom slab. Jaikrishna and O.P. Jain8 in his book hasThe IRC:21-20006 Clause 305.16 gives an equation considered dispersal of live load through walls forfor obtaining effective width for simply supported and bottom slab at 45°. However, the MORT&H7 Standardcontinuous 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 Highwayprovide if one of the support is continuous while other is Bridges 17th Edition 2002, provides at para 16.6.4.3simply supported. The Code is silent for other types of under RCC Box that “The width of top slab strip usedsupports such as fixed or partially fixed. Some designers for distribution of concentrated wheel loads may beuse this formula and factors for continuous slab is taken increased by twice the box height and used for thevalid for partially restrained support in a situation like distribution of loads to the bottom slab”. This confirmsbox 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 topgiven in sub para 3 above. Nevertheless, effective width slab shall not be practical when braking force effect isneed to be obtained in box type structure also to evaluate to be taken, which shall have to be for the same run ofaffected 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 FORCEconsidering varying value of α such as 2.6, 2.0, 1.0, 0.9, This is another area where opinion of the designers vary0.8 & 0 (Table 2). The moment and consequently the in two ways firstly, whether braking force caused bymain reinforcement varies significantly with value of α, moving loads shall deform the box structure and shouldthe 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 bewidth and, therefore, more moment and shear per unit taken to obtain force and moment per unit run of box. Oflength (run) of box, as all other dimensions are same course the braking force will affect the global stabilityreinforcement increases with decrease in value of α. It and change the base pressure to some extent. The IRCis further observed that MORT&H7 provision in their Code is silent as far as box is concerned. It will be instandard drawings for a similar culvert and situation falls order to neglect effect of braking force on box havingbetween α value 0 to 1.0. This also indicates that taking large cushion. In such situation the braking effect willvalue of α equivalent to that for continuous slab given be absorbed by the cushion itself and no force will bein 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 needmainly the top slab. Bottom slab due to dispersal through be taken. This height generally is taken to be 3 m. Thuswalls and box with cushion due to dispersal through fill no braking force for cushion height of 3 m and moreto even the top slab, are not affected much. and full braking force for no cushion, for intermediate Journal of the Indian Roads Congress, October-December 2009
  5. 5. Rcc Box Culvert- Methodology and Designs Including Computer Method 193Table 2 Shows Moment and Reinforcement for Different Values of α Keeping other Parameters Constant asgiven 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 shownheights of cushion the braking force can be interpolated. The box is considered a rigid frame for analysis andThere is no literature on this aspect and the Code is also design. The braking force can be taken to act on the topnot specific for box, however, IRC:6-200010 Clause junction of the box causing moment at fixed ends of both211.7 mentions that no effect be taken at 3 m below walls and the top and bottom slabs having zero fixed endbed block in case of bridge pear/abutment. Our further moments (IRC:6-200010 Clause 214.7). The momentdiscussions shall be on box without cushion as far as distribution is carried out and distributed moments arebraking force is concerned. obtained at supports. This moment shall be added to the maximum moment under different conditions for otherBraking force by the moving loads on top slab of box loads to get final design moments at supports. It mayhaving no cushion shall act on the box structure and be mentioned here that the mid span moments are notshall deform the box. The question is what length of box affected by braking force moments as the same beingcan be considered to share this braking force. In another zero at mid span even after distribution. Also brakingwords what effective width of box shall be taken to obtain force can act in either direction hence the momentbraking force per unit run of box. One way is to take the at junctions can reverse in sign and thus needs to beeffective width of box same as considered for vertical arithmetically added to moments due to vertical effecteffect of moving loads, discussed under para 3 above. of loads for the design.The arguments in favor of this is the same which holdsfor effective width for vertical deformation of top slab It is seen that box without cushion if designed ignoringunder moving loads. Vertical effect as well as braking braking force effect gives smaller thickness and veryeffect both are product of the same loads and can affect less reinforcement compared to the MORT&H7 standardthe same run of box. In absence of specific provision designs for similar culvert. In case of 2 m x 2 m box thein 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 Journal of the Indian Roads Congress, October-December 2009
  6. 6. 194 Sinha & Sharma onlesser thickness and reinforcements. In case of box of The IRC:6-200010, Code Clause 211.7 specifies thatsize 6 m x 6 m the braking force effect if not taken gives for calculating pressure on the bearings and on thelesser moment say around 30% less (Table 3). That is for top surface of the bed blocks, full value of appropriatelarger 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 appropriatebraking force effect has to be taken in design. When, impact percentage shall be multiplied by the factor givenhowever, 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, proportionatelybraking 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 structure5 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 thedeck slab (top slab). The impact depends on the class The AASHTO9 at para 3.8.1.2 specifies that impactand type of load. The IRC:6-2000 Code gives formula to shall not be included for culverts having 1m or moreobtain impact factor for different kind of loads by which cover. This, however, will be on lower side comparedthe 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 impactsubjected to impact is required to be designed for live on top slab without cushion and zero impact for 3mloads including such impact loads. Any such impact is cushion and interpolating impact load for intermediatenot supposed to act on box with cushion. Hence no such height of cushion is on conservative side and can beimpact factor shall be considered for box with cushion. safely adopted.The impact by its very nature is not supposed to act atlower depth and no impact is considered for the bottom 6 SHEAR STRESSslab of the box. It does not affect the vertical walls of The box is designed for maximum moment for itsthe box and not considered in the design. concrete section and reinforcements. It is checked forTable 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 Journal of the Indian Roads Congress, October-December 2009
  7. 7. Rcc Box Culvert- Methodology and Designs Including Computer Method 195shear at the critical section and if it exceeds permissible away from the face of wall, the distance where theshear stress for the size of section; mix of concrete and shear force becomes equal to shear capacity of sectionpercentage of reinforcements, the section has to be (without shear reinforcement) is obtained. The shearincreased to bring shear stress within the permissible reinforcement shall be provided up to this distance onlimit. Alternatively, the reinforcement can be increased both sides of box from near wall. The design at annexureto 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. Themay have to be adopted in situation where thickness box can be designed for maximum shear and checked forof slab cannot be increased due to certain restrictions. bending, particularly where shear is expected to governThe top and bottom slabs are needed to be checked the design as for box having large cushion. However, thefor shear. The vertical walls carry much less loads and tension reinforcement has to be provided for the bendingshall be normally safe in shear, therefore, there is no moment in any case.need to check in shear. To make safe in shear one orany combination of increasing size, increasing tensionreinforcement and/or providing shear stirrups can be 7 DISTRIBUTION REINFORCEMENTSadopted. The Code IRC:21-20006, in Clause 305.18 providesIt is important to note that IRC:21-20006 under Clause for distribution reinforcements. The distribution304.7.1 has given table 12B. Permissible shear stress in reinforcement shall be such as to produce a resistingConcrete for checking section for shear stress. The values moment in direction perpendicular to the span equalgiven here have been drastically reduced compared to to 0.3 times the moment due to concentrated live loadssimilar provision in previous Codes and practices. It is plus 0.2 times the moment due to other loads such asobserved 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 loadsCritical 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 thesedepth is the distance of center of tension reinforcement two moments to apply above provision of the Codefrom the extreme compression face. Where, however, to calculate distribution reinforcements. To make ithaunch is provided, an extra depth due to haunch within convenient and easy a combined factor for both thea slope of 1V:3H can be considered to increase the loads, based on weighted average in proportion of theireffective 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 providedsection. However, for shear stress at the critical section, in Annexure.the effective depth only without effect of haunch betaken. 8 LOAD CASES FOR DESIGNIn situation when the section is required to be provided Mainly three load cases govern the design. These arewith 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 boxcapacity of the section based on permissible shear stress, and superimposed surcharge load on earth fill.which is based on percentage of tension reinforcementand concrete mix, is obtained. Shear capacity of b) Box inside full with water, live load surcharge onsection is deducted from the shear force obtained at top slab and superimposed surcharge load on earthcritical section and shear reinforcement is calculated fill.for the balance shear force and accordingly provided c) Box inside full with water, live load surcharge onin addition to other steel. It is obvious that such shear top slab and no superimposed surcharge on earthreinforcement shall be required for the whole length of fill.box but the distance along the span from the face of wallup to which these shear reinforcement is to be provided The above mentioned load cases are to be examined forshall have to be calculated. As the shear is reducing box with cushion and without cushion. In case of box Journal of the Indian Roads Congress, October-December 2009
  8. 8. 196 Sinha & Sharma onwithout cushion live load surcharge shall straightway be of Soil for Vehicular Loading. Table 3.11.6.4-1 and Tableconsidered to act on the top slab, of course with dispersal 3.11.6.4-2 give height of earth fill for Equivalent Heightthrough wearing coat and slab thickness as applicable. of Soil for Vehicular Loading. This is in conformityIn case of box with cushion the live load surcharge with varying live load surcharge explained in sub parais 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 BOXgenerally 70R(T) vehicle, with due restrictions due to Based on the above discussions and clarificationsseveral wheels placed simultaneously. One question design of a typical box covering all above mentionedarises that with increase in cushion height, live load points are presented as Annexure. The box of 3 m x 3 mintensity 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 maximumwhich of the two that is the actual dispersed live loador superimposed load equivalent to 1.2 m height of fill design moments. The box has also been checked inwhich 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 andobtain this load and no live load can be expected higher without cushion have been given. Basically, there isthan 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 byis natural compared to taking superimposed surcharge moment distribution considering all the cells togetherload equivalent to 1.2 m of fill at a constant rate for all for different combination of loading and design ofcushion heights. Further the superimposed live load section accomplished for final bending moments for thatequivalent to 1.2 m of fill is a very general provision member. Shear force and resulting shear stress have toand shall be adopted where it is not practical to obtain be checked for members independently as done in caseactual live load more accurately as in case of earth of single cell. A drawing furnishing details of the boxretaining structures. based on detailed design and general arrangement forAASHTO9 provides varying superimposed surcharge site of work as usually required for construction has alsoload 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 Journal of the Indian Roads Congress, October-December 2009
  9. 9. Rcc Box Culvert- Methodology and Designs Including Computer Method 197The design of the single cell box of size 3 m x 3 m with little influence on the design of box particularly5 m cushion have also been done by using STAAD. Pro without cushion.computer software and moment and shear as obtainedare 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 inthey compare well. The design of box can, therefore, IRC:21-2000 corresponding to α for continuousbe carried out by STAAD. Pro as well. Input data sheet, slab shall not be correct. It is likely to providebending moment diagram and shear force diagram as design moments and shear on lower side henceobtained 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 requiredand shear values for relevant members which runs innumber of pages, is not given in the Paper as it will add to to be considered particularly for smaller spanthe length without serving much purpose. The STAAD. culverts. Further for distribution of braking forcePro 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 distributedBox with cushion : Annex B over the whole length of box (not restricted within the effective width) the design shall be unsafe.Design of box withcushion 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 (particularlyfor construction purposes : Annex D for box without cushion) and braking force. As regards bottom slab and top and bottom slabs of10 CONCLUSIONS box with cushion due to dispersal of loads either through walls or through fills effective width losesi) 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 casesii) 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 casesiii) 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 bringvi) 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 Jetendravii) 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 formattingviii) Small variation in co-efficient of earth pressure has and typing. Journal of the Indian Roads Congress, October-December 2009
  10. 10. 198 Sinha & Sharma onREFERENCES 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., Roorkee3. 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 Specifications4. 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 of5. 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 Concrete6. IRC:21-2000, “Standard Specifications and Code of Structures”, Dhanpat Rai Publishing Company, Tenth Practice for Road Bridges”, Section III. Edition, 1985. Journal of the Indian Roads Congress, October-December 2009
  11. 11. Rcc Box Culvert- Methodology and Designs Including Computer Method 199 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 Slab2.1.1 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 m2.1.2 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 Journal of the Indian Roads Congress, October-December 2009
  12. 12. 200 Sinha & Sharma onNote : Taking reduction for simultaneous additional lane1) 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 Wall3) 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 on4) 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/m²Impact factor for 70R(T) shall be 25 % as per Clause211.3 (a) (i) of IRC:6-2000Load 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/m²2.2 Bottom Slab Earth Pressure at base due to earth fill = 18 x 3.42 x 0.5 = 30.78 kN/m²2.2.1 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/m²2.2.2 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. Journal of the Indian Roads Congress, October-December 2009
  13. 13. Rcc Box Culvert- Methodology and Designs Including Computer Method 201 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 = 10.532.4.1 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 Load = 37.91 kN/m² Total F.E.M at base = 28.53 kN.m2.4.2 Live Load Mid span moment due to dead load There is no live load except coming from top slab without impact = 21 kN/m² = = 22.52.4.3 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 = 15.793 MOMENT CALCULATION Total Mid Span Moment = 38.29 kN.m3.1 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 Total Mid Span Moment = 157.96 kN.m Mid span moment due to dead load 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 Journal of the Indian Roads Congress, October-December 2009
  14. 14. 202 Sinha & Sharma on3.3.3 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 Journal of the Indian Roads Congress, October-December 2009
  15. 15. Rcc Box Culvert- Methodology and Designs Including Computer Method 203 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 = (-) 31.576 BRAKING FORCE The moments at top and bottom slab ends shall all6.1 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 Journal of the Indian Roads Congress, October-December 2009
  16. 16. 204 Sinha & Sharma on 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 841.8 483.47.2 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 from7.3 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) Journal of the Indian Roads Congress, October-December 2009
  17. 17. Rcc Box Culvert- Methodology and Designs Including Computer Method 205 ANNEX B (Para 2) RCC BOX CULVERT, DESIGNATION: [1/3 x 3/5]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/m²2.1 Top Slab Total load = 115.83 kN/m²2.1.1 Dead Load Live Loada) Cushion = 5 x 18 = 90 kN/m² Load from top slab without impact = 4.52 kN/m²b) Self weight of top slab = 0.42 x 24 =10.08 kN/m² Note: Some designers take further dispersal of livec) Total = 100.08 kN/m² load from top slab. Although further dispersal through2.1.2 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) Journal of the Indian Roads Congress, October-December 2009
  18. 18. 206 Sinha & Sharma on 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 Total Load = 125.91 kN/m²Case 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 Mid span moment due to dead load = 115.83 x 3.42 x 3.42/8 = 169.35 Mid span moment due to live load = 6.61 Total Mid Span Moment = 175.96 kN.m 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 Total F.E.M at top = 66.39 kN.m 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 Mid span moment due to dead load 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 Journal of the Indian Roads Congress, October-December 2009
  19. 19. Rcc Box Culvert- Methodology and Designs Including Computer Method 207 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 CUSHION3.3.2 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 Total F.E.M at top = 59.72 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 Mid span moment due to dead 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 Journal of the Indian Roads Congress, October-December 2009
  20. 20. 208 Sinha & Sharma on 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 = (-) 4.296 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 2236.1 Top Slab Check for Shear Maximum moment support/mid span = 83.0 kN.m Depth required = Journal of the Indian Roads Congress, October-December 2009
  21. 21. Rcc Box Culvert- Methodology and Designs Including Computer Method 209 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 Journal of the Indian Roads Congress, October-December 2009
  22. 22. 210 Sinha & Sharma on ANNEX C (Para 9) RCC BOX CULVERT, DESIGNATION: [1/3 x 3/5] STAAD. Pro : Structural Analysis and Design SoftwareSTAAD SPACESTART JOB INFORMATIONENGINEER DATE 17-Dec-08END JOB INFORMATIONINPUT WIDTH 79* ANALYSIS FOR LIVE LOAD**BOTTOM SLAB*LONGITUDINAL MEMBER* TRANSVERSE MEMBER*TOP SLAB*LONGITUDINAL MEMBER* TRANSVERSE MEMBER* VERTICAL WALL*UNIT METER kNJOINT COORDINATES1 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; Journal of the Indian Roads Congress, October-December 2009

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