SIMPLIFIED MODEL FOR DESIGN RCC BOX CULVERTS BY
VOL. 13, NO. 22, NOVEMBER 2018ISSN 1819-6608ARPN Journal of Engineering and Applied Sciences 2006-2018 Asian Research Publishing Network (ARPN). All rights reserved.www.arpnjournals.comSIMPLIFIED MODEL FOR DESIGN RCC BOX CULVERTSBY STAAD.PROAbdul Kareem M. B. Al-ShammaaUniversity of Kufa, Faculty of Physical Planning, IraqE-Mail: abdulkareem.baqir@uokufa.edu.iqABSTRACTReinforced concrete box culvert consists of top slab, bottom slab and two vertical side walls built monolithicallywhich form a closed hollow rectangular or square single cell or multiple cells. Culverts are required to be used under earthembankment to construct and pass roads or railways at the moment for crossing of water from both sides of earthembankment. Current of great rivers and their tributaries in my country have encouraged me to go ahead to find simplifiedmethod for design box culvert. This research focuses on analysis and design of single cell by software “STAAD.Pro” on asegment in one meter length from culvert barrel to produce a plane structure like instead of space structure. The structureis subjected to various types of loads and supported by a bed of springs instead of soil interaction according to Winkler'smodeling. The author believes that he is able to create a method which is quick, accurate and optimal solution for designRCC box culvert. This paper was carried out using ACI-code 2011 with SI units.Keywords: box culvert, RCC culvert, single cell, soil interaction, spring stiffness.1. INTRODUCTIONTigris and Euphrates are two great rivers in Iraqhaving many tributaries which need to construct more boxculvert to facilitate the construction of roads and railwayspassing through water streams. A culvert is a crossdrainage structure having types such as box, pipe and RCCSolid Slab Culverts. RCC box culvert is the most commonand its structural components are top slab (called, deck),base slab (called, invert) and two vertical side walls (called, upright) built monolithically which form a closedhollow rectangular or square single cell or multiple cells.By reading and browsing a number of research papers,anyone can find many methods to analysis and design boxculvert such as finite element, moment distribution,genetic algorithms etc. Sometimes these methods usedmanual calculations or software. All of these methods arecorrect, but need more time and effort. So, this paper dealswith study of simplified method for design single cellRCC box culvert using software STAAD.ProV8iaccording to ACI-code 2011, after inserting modificationto the culvert structure.The Winkler's model was used to represent thestructure supported by a bed of springs instead of soilinteraction. The earliest use of these springs to representthe interaction between soil and foundation has beenattributed to Winkler (1876). In its classical form the,Winkler method assumes each spring is linear and actsindependently from the others, and that all the springshave the same stiffness 𝑘𝑠 . This representation has thedesired effect of increasing the bearing pressure beneaththe columns, and thus is a significant improvement overthe rigid method. However, it is still only a coarserepresentation of the true interaction between mats andsoil ( Hain and Lee, 1974, Horvath, 1983, Coduto, 2001).2. EXPERIMANTAL PROCEDURETo know the details of the study, the structuralanalysis and design will be focused on the culvert that hasthe following characteristics:A. Geometry Total length of culvert is equal 15 meters. Segment inone meter length will be taken to perform the analysisand design so that considers the structure as a planeinstead of space structure. Depending on the discharge data every ten years, thehighest level of water in front of the culvert is onemeter. Choose, squire section single cell withdimensions(2x2 𝑐/𝑐)meters.Precisely,thedimensions can be chosen from the equation Q10 V A. Thickness of all components will be chosen equal to400mm, as a condition that not less than sixth ofdimensions. So, D 2 0.4 2.4m.B. Loads analysisAfter the verification and collection of the fielddata, the worst case of loading that applied to the culvertbarrel will be calculated.The Loads that applied to the deck are: Due to earth embankment,𝑊1 (1)8 111 3 18 46.6kN/m211Due to live loads,𝑊1 𝐿1 𝐿21 𝑑 𝛾𝑒 2𝐿2𝜔 𝐿1𝐿220 8𝑊2 14.5kN/m11𝑊2 (2)8823
VOL. 13, NO. 22, NOVEMBER 2018ISSN 1819-6608ARPN Journal of Engineering and Applied Sciences 2006-2018 Asian Research Publishing Network (ARPN). All rights reserved.www.arpnjournals.com Due to wheel loads as shown in Figure-1,2P[2(a d) x]d2(70)W3 13kN/m[2(0.6 3) 1.8](2)W3 (3)Summary of loads that applied to the uprights,𝑒𝑢 25.2 6.7 32 kN/mThe Loads that applied to the invert due to waterpressureare,Ww γw water height 10(1) 10kN/m.C. Input fileTo provide the simplified culvert model which issuggested as shown in fig.3, the following well beconsidered:a) Invert member well be divided in to four memberseach 0.5m to induce springs at the ends of eachmember to create bed springs as that Winkler hasdenoted.b) (Bowles, 1996) has suggested the following forapproximating soil stiffness K s ,Summary of loads that applied to the deck,Wu 46.6 14.5 13 74.1 kN/mK s 40(S. F)qa kN/m3 (7) K s 40(2)(80) 6400 kN/m3Figure-1.Dispersion of wheel loads.The loads that applied to the uprights accordingto diagram shown in Figure-2 are: Due to earth pressure,For the inner support at intermediate nodes ofinvert member,KFY will be calculated equal to,KFY 6400(0.5*1.00) 3200kN/m,While for the outer supports,KFY 6400(0.25*1.00) 1600kN/m. The input file content the following date,1 sin (4)1 sin 1 sin30 1𝐾𝑎 1 sin30 3at top outer edge of the culvert section,e1 γe . d. K a , while at bottom,e2 γe . (d D). K a . Easily, pressure can be consideredas uniform distributed and its amount,𝐾𝑎 𝐷𝑒 γe . (𝑑 ) . K a22.4 1𝑒 18 (3 ) 25.2kN/m2 3 Due to surcharge of live loads,𝑒𝑠 𝜔. K a1𝑒𝑠 20 ( ) 6.7 kN/m3Figure-2. Pressure diagram on uprights.(5)(6)Figure-3. The simplified model .STAAD PLANE . analysis and design of the culvertSTART JOB INFORMATIONENGINEER DATE 31-Jan-18END JOB INFORMATIONINPUT WIDTH 79UNIT METER KNJOINT COORDINATES1 0 0 0; 2 2 0 0; 3 2 2 0; 4 0 2 0; 5 0.5 0 0; 6 1 0 0; 7 1.5 00;MEMBER INCIDENCES1 1 5; 2 2 3; 3 3 4; 4 4 1; 5 5 6; 6 6 7; 7 7 2;DEFINE MATERIAL STARTISOTROPIC CONCRETE8824
VOL. 13, NO. 22, NOVEMBER 2018ISSN 1819-6608ARPN Journal of Engineering and Applied Sciences 2006-2018 Asian Research Publishing Network (ARPN). All rights reserved.www.arpnjournals.comE 2.17185e 007POISSON 0.17DENSITY 23.5616ALPHA 1e-005DAMP 0.05TYPE CONCRETESTRENGTH FCU 27579END DEFINE MATERIALMEMBER PROPERTY AMERICAN1 TO 7 PRIS YD 0.4 ZD 1CONSTANTSMATERIAL CONCRETE ALLSUPPORTS1 2 FIXED BUT MZ KFY 16005 TO 7 FIXED BUT MZ KFY 3200LOAD 1 LOADTYPE None TITLE LOAD CASE 1SELFWEIGHT Y -1MEMBER LOAD1 5 TO 7 UNI GY -103 UNI GY -71.14 UNI GX 25.22 UNI GX -25.2PERFORM ANALYSISPRINT ANALYSIS RESULTSSTART CONCRETE DESIGNCODE ACIUNIT MMS NEWTONFYMAIN 350 ALLFC 25 ALLCLS 75 ALLCLB 75 ALLCLT 75 ALLMAXMAIN 20 ALLMINSEC 6 ALLDESIGN BEAM 1 TO 7END CONCRETE DESIGNFINISHD. Output fileFrom Figure-4 till Figure-7 are drawn for wholestructure by STAAD. Pro except of fig. 8. As a result ofSTAAD. Pro has no facility to draw main reinforcementdetails for whole structure, the author is drawn Figure-8according to the data of the outputs.Figure-4. Displacement diagram, drawn by STAAD.Pro.Figure-5. Actions and reactions, draw by STAAD.Pro.Figure-6. Bending moment diagram, draw bySTAAD.Pro.8825
VOL. 13, NO. 22, NOVEMBER 2018ISSN 1819-6608ARPN Journal of Engineering and Applied Sciences 2006-2018 Asian Research Publishing Network (ARPN). All rights reserved.www.arpnjournals.comcalculated by the users according to ACI.Code asfollow,for deck and invert,𝐴𝑠,𝑚𝑖𝑛 0.002(400)(1000) 800mm2 ,for uprights,𝐴𝑠,𝑚𝑖𝑛 0.0025(400)(1000) 1000mm2 . Reinforcement ratio (𝜌) for maximum bendingmoment is less than the minimum (𝜌𝑚𝑖𝑛 ).Therefore, STAAD.Pro calculates an equalreinforcement area from (𝜌𝑚𝑖𝑛 ) for all effectivesections. As mentioned in ACI.Code,Max. bending moment 𝑀𝑢 29.55kN. m .Figure-7. Shear force diagram, draw by STAAD. Pro.𝜌 𝜌Figure-8. Reinforcement details, draw by the author.3. RESULTS AND DISCUSIONS Several methods have been tackled in the analysis anddesign of RCC box culverts for researchers in thisfield. By comparing this simplified method with theprevious methods, there is no noticeable difference inthe values and shape of the bending moment andshear force diagrams. Spacing between the springs is installed by trial anderror method till a logical space was reached. Closerof spacing means more accurate values that areobtained for the outputs, especially that for invertmembers. Symmetry of section properties and loads applied tothe culvert barrel, causes that Joint displacement,support reactions, bending moment and shear forcediagrams are symmetrical also. STAAD.Pro provided main reinforcement withoutsecondary. Area of secondary reinforcement𝐴𝑠,𝑚𝑖𝑛 forresistance shrinkage and temperature stresses must be2.36Mu𝑓𝑐′[1 1 ]0.9b(effective depth)2 𝑓𝑐′1.18𝑓𝑦2.36(29.55 106 )25[1 1 ]0.9(1000)(400 75)2 (25)1.18(350)𝜌 0.0009 25 𝑓𝑐′ 0.00357,𝜌𝑚𝑖𝑛 4𝑓𝑦 4(350)1.4 𝑠𝑡ℎ𝑎𝑛 0.004𝑓𝑦350So, use 𝜌𝑚𝑖𝑛 0.004,and the main reinforcement area (As )is,As 0.004(1000)(450 75) 1300mm2 ,use 12 12/m′ , as shown in Figure-8.(8)4. CONCLUSIONSBased on the results of this study, the followingconclusions are drawn:This study focuses on reinforcement concrete boxculvert having single cell so that space structure for culvertbarrel transformed to the plane structure represent segmentof one meter length.Plane structure is subjected to the various type ofloads and supported on bed springs equivalent to the soilinteraction according to Winkler's model.Closer of spacing between springs, mean more accuratevalues that can be obtained for outputs of STAAD.Prosuch as bending moments, shear forces and supportreactions.Finally, the author believes that he is able tocreate a simplified method which is quick, accurate andoptimal solution for design RCC box culvert by using SIunits, ACI-Code 2011 and software STAAD.Pro.NOTATION AND DEFINITIONSQ10VADrate of discharge each 10 years, m3 /sec.flow velocity 0f water, m/sec.cross sectional area, m2 .outer dimensions of culvert section, m.8826
VOL. 13, NO. 22, NOVEMBER 2018ISSN 1819-6608ARPN Journal of Engineering and Applied Sciences 2006-2018 Asian Research Publishing Network (ARPN). All rights reserved.www.arpnjournals.comdL1depth of earth embankment, 3m.width of road or width of top earth embankment,8m.L2width of the base earth embankment or effectivewidth of dispersed loads, as a result of assume thatthe angle of dispersion and side slope of earthembankment is the same and equal to 2:1. So, L2 inboth cases is equal to L2 d L1 11m.𝛾𝑒density of wet soils, kN/m3 .𝜔distributed live load, kN/m2 .Pconcentrated wheel loads. According to AASHTOthe load of vehicles (HS20-44) is equal to(16000Ib 70kN ) and the distance between twowheels centers, (6ft 1.8m).awidth of double wheel, (2ft 0.60m). angle of soil friction, for sandy soil taken 30 .𝛾𝑤density of water, kN/m3 .qaallowable bearing capacity for the soil, kN/m2 .S.Fsafety factor depend on type of soil. For sandy soiltaken 2.KFY spring stiffness for supports as denoted bySTAAD.Pro, kN/m.𝑓𝑐′ specified compressive strength of concrete, MPa.𝑓𝑦 specified yield strength of steel, MPa.bwidth of concrete section, mm.[9] Wang C., Salmon C.G. and Pincheira J.A.2007.Reinforced Concrete Design, 7th Edition, Wiley,USA.pp. 581-592.[10] Hassoun M. N. and Al-Manaseer A. 2008.StructuralConcrete Theoryand Design, 4th Edition. Wiley, USA.pp. 581-592.[11] Nilson, A.H., Darwin, D., and Dolan, C.W., Design ofConcrete Structures, 14th Edition, McGraw-Hill, USA,2010. pp. 300-320.[12] Davis, C.V. 1990.Hand Book of Applied Hydraulics.McGraw-Hill, USA.[13] Abdulkareem M.B. Al-Shamma. 2014. NovelFlowchart for Design of Concrete Rectangular Beams.IJSER. 5: 231-233.[14] Abdulkareem M.B. Al-Shammaa. 2014. Create ShearStair for Reinforcement of Concrete Beams. IJ RET.3(1): 412-414.REFERENCES[1] 2011.ACICommittee318.BuildingCodeRequirements for Reinforced Concrete (ACI 318-11),American Concrete Institute, Detroit, USA.[2] Bowles, J. E, P.E., S.E. 1996.Foundation Analysis andDesign, Fifth Edition, McGraw-Hill, USA. pp. 503506.[3] Coduto, D.P. 2001.Foundation Design Principles andPractices, second edition, Prentice-Hall, New Jersey,USA. pp. 358.[4] Komal S.Kattimani, R.Shreedhar. 2013. ParametricStudies of Box Culverts", IJRES.1(1): 58-65.[5] Siva Rama Krishna, Ch. Hanumantha Rao. 2017.Study on Box Culvert Soil Interaction. IJCIET. 8(1):734-738[6] Abdul-Hassan K. Al. Shukur1, Mohammed Abbas Al.Jumaili2, Hawraa Ali Hussein3. 2014. OptimalDesign of Reinforced Concrete Box Culvert by UsingGenetic Algorithms Method. IJSER. 5(1): 1890-1898.[7] PAUL TOM P. 2014. Analysis and Design of Bridgeand Culvert.M. Eng. Thesis, National Institute ofCnology, Karnataka, Surathkal, Mangalore, India.[8] Sujata Shreedhar1, R.Shreedhar2.Design coefficientsfor single and two cell box culvert. IJCSER.3(3):475-494.8827
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