Analysis and Design of Prestressed Concrete Box Girder Bridge

Posted in Prestress Engineering, Project Reports, Research Papers | Email This Post |

ByMiss.P.R. Bhivgade

Abstract:- Bridge construction today has achieved a worldwide level of importance. Bridges are thekey elements in any road network Use of box girder is gaining popularity in bridge engineeringfraternity because of its better stability, serviceability, economy, aesthetic appearance and structuralefficiency. The structural behavior of box girder is complicated, which is difficult to analyze in itsactual conditions by conventional methods. In present study a two lane simply supported BoxGirder Bridge made up of prestressed concrete which is analysis for moving loads as per Indian

Road Congress (IRC:6) recommendations, Prestressed Code (IS: 1343) and also as per IRC: 18 specifications. The analyzed of box girder using SAP 200014 Bridge Wizard and prestressed with parabolic tendons in which utilize full section. The various span/ depth ratio considered to get the proportioningdepth at which stresses criteria and deflection criteria get satisfied.

Keywords: Concrete Box Girder Bridge, Prestress Force, Eccentricity, Prestress Losses, Reinforcement, Flexure strength, shear strength, SAP Model.

I. INTRODUCTIONPrestress concrete is ideally suited for the construction of medium and long span bridges. Ever since the development of prestressed concrete byFreyssinet in the early 1930s, the material has found extensive application in the construction of long-span bridges, gradually replacing steel which needscostly maintenance due to the inherent disadvantage of corrosion under aggressive environment conditions. One of the most commonly used forms ofsuperstructure in concrete bridges is precast girders with cast-in-situ slab. This type of superstructure is generally used for spans between 20 to 40 m. T orI-girder bridges are the most common example under this category and are very popular because of their simple geometry, low fabrication cost, easyerection or casting and smaller dead loads. In this paper study the India Road Loading considered for design of bridges, also factor which are important todecide the preliminary sizes of concrete box girders. Also considered the IRC:18-2000 for “Prestressed Concrete Road Bridges” and “Code of Practicefor Prestressed Concrete ” Indian Standard. Analyze the Concrete Box Girder Road Bridges for various spans, various depth and check the proportioningdepth.

II. FORMULATIONA. Loading on Box Girder BridgeThe various type of loads, forces and stresses to be considered in the analysis and design of the various components of the bridge are given in IRC6:2000(Section II. But the common forces are considered to design the model are as follows:

Dead Load(DL): The dead load carried by the girder or the member consists of its own weight and the portions of the weight of the superstructure and anyfixed loads supported by the member. The dead load can be estimated fairly accurately during design and can be controlled during construction andservice.

Superimposed Dead Load (SIDL): The weight of superimposed dead load includes footpaths, earth-fills, wearing course, stay-in -place forms, ballast,water-proofing, signs, architectural ornamentation, pipes, conduits, cables and any other immovable appurtenances installed on the structure.

Live Load(LL): Live loads are those caused by vehicles which pass over the bridge and are transient in nature. These loads cannot be estimated precisely,and the designer has very little control over them once the bridge is opened to traffic. However, hypothetical loadings which are reasonably realistic needto be evolved and specified to serve as design criteria. There are four types of standard loadings for which road bridges are designed.i. IRC Class 70R loadingii. IRC Class AA loadingiii. IRC Class A loadingiv. IRC Class B loading

The model is design by considering IRC Class A loading, which is normally adopted on all roads on which permanent bridges and culverts are constructed.Total load is 554, the Fig.1 show the complete details of Class A.

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Other information regarding Live load combination as per IRC:6 2000 Clause No.207.1 Note No.4

B. Thickness of WebThe thickness of the web shall not be less than d/36 plus twice the clear cover to the reinforcement plus diameter of the duct hole where‘d’ is the overalldepth of the box girder measured from the top of the deck slab to the bottom of the soffit or 200 mm plus the diameter of duct holes, whichever is greater.

C. Thickness of Bottom FlangeThe thickness of the bottom flange of box girder shall be not less than 1/20th of the clear web spacing at the junction with bottom flange or 200 mmwhichever is more.

D. Thickness of Top FlangeThe minimum thickness of the deck slab including that at cantilever tips be 200 mm. For top and bottom flange having prestressing cables, the thickness ofsuch flange shall not be less than 150 mm plus diameter of duct hole.

E. Losses in PrestressWhile assessing the stresses in concrete and steel during tensioning operations and later in service, due regard shall be paid to all losses and variations instress resulting from creep of concrete, shrinkage of concrete, relaxation of steel, the shortening (elastic deformation) of concrete at transfer, and frictionand slip of anchorage.

In computing the losses in prestress when untensioned reinforcement is present, the effect of the tensile stresses developed by the untensionedreinforcement due to shrinkage and creep shall be considered.

F. Calculation of Ultimate StrengthUltimate moment resistance of sections, under these two alternative conditions of failure shall be calculated by the following formulae and the smaller ofthe two values shall be taken as the ultimate moment of resistance for design:

i. Failure by yield of steel (under-reinforced section)Mult = 0.9dbAsFpWhere,As = the area of high tensile steelFp = the ultimate tensile strength for steel without definite yield point or yield stress or stress at 4 per centelongation whichever is higher for steel with adefinite yield point.db = the depth of the beam from the maximum compression edge to the centre of gravity of the steel tendons.

ii. Failure by crushing concrete

Mult = 0.176 bdb2fck

Where,b = the width of rectangular section or web of beamfck= characteristics strength of concrete

G. Calculation of Section un- cracked in flexure

b = width in the case of rectangular member and width of the rib in the case of T, I and L beamsd = overall depth of the memberfcp = compressive stress at centroidal axis due to prestress taken as positive.

III. ANALYSIS AND DESIGN OF POST-TENSIONED DECK TYPE BOX-GIRDER BRIDGEA post- tensioned deck type Box – GirderBridges of clear span 30m and width of roadway is 7.5m. Assume Live Load as per IRC: 6-2000 vehicle is passing over deck given in chapter 4 and tableno. 4.2. The Bridge analysis for different L/d ratio starting from 15 to 20 and different L/d ratio considered are as follows:


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Case 1 L/d= 19, d = 1.6Case 2 L/d =18, d = 1.7Case3 L/d = 17, d = 1.8Case4 L/d= 16, d= 1.9Case5 L/d= 15, d=2.0

Preliminary dataClear span = 30mWidth of roadway = 7.5 mOverhang from face of girder = 1.2mDeck thickness = 0.2 mBottom slab thickness = 0.2 mGirder thickness = 0.3 m

The tendon profile is considered as parabolic in nature.As per IRC:18-2000fck= 50 Mpa, fci = 0.8fck = 40 Mpa,fct = 0.5fci = 20 Mpa, fcw = 0.33fck = 16.5 Mpa ft = 1/10fct = 2.0 Mpa, ftw = 0

As per IS:1343-1980

Ec = 5700fck1/2 = 40.30 kN/m2

fp = 1862 Mpa, n = 0.85, E = 2×105 Mpa


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Validation of ResutsThe bending moment, shear force and deflection result obtained by SAP 2000. The bending moment and shear force are calculated by consideringdifferent loading condition such as dead load, live load and superimposed load. Same as deflection calculated. This results are the Case:1.

Table.1 Deflection

Load Case DL +SIDL

LiveLoad

PrestressingForce

Deflection (atmidspan) 30.8 mm 25.2

mm

-14.36 mm

Table.2 Bending Moment(t.m)

Span(m)

0.0L 0.1L 0.2L 0.3L 0.4L 0.5L

DL 0.00 353.56 628.56 824.98 942.84 982.12

LL 0.00 218.76 381.63 494.10 564.85 587.82

SIDL 0.00 53.46 95.04 124.74 142.56 148.50

Total 0.00 625.78 1105.231443.821650.261718.45

Table.3 Shear Force (t)

Span(m)

0.0L 0.1L 0.2L 0.3L 0.4L 0.5L

DL 130.9 104.7 78.57 52.4 26.3 0.0

LL 32.92 23.29 14.27 7.42 2.62 0.0

SIDL 19.80 15.84 11.88 7.92 3.90 0.0

Total 183.6 143.9 104.7 67.7 32.8 0.0

Table.4 Calculation of Prestress Force


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Table.5 Calculation of Eccentricity

Eccentricity(mm)

PrestressingForce (kN)

The eccentricitywhich giveminimum

prestressing force(e) = 731mm440 21617.96

548 19380.69

650 17655.06

731 16489.15

Table.6 Calculation of Prestress Losses(As per IS:1343-1980)

Span

(m)^S ^C ^E ^A ^F ^R Total n

0.0L

8E-05

0.0 0.0 0.0 0.0 90 90 0.95

0.1L 2.6 2.3 78 9.7 90 182.6 0.9

0.2L 2.6 2.4 39 22 90 155.8 0.91

0.3L 2.6 2.4 26 36.7 90 157.7 0.91

0.4L 2.7 2.5 20 54.3 90 169.0 0.9

0.5L 9.1 8.3 16 171 90 294.0 0.85

Where,^S = Shrinkage^C= Creep


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^E = Shortening of concrete^A = Slip in anchorage^F = Friction^R = Relaxationn= EfficiencyAfter Losses, effective Prestressing Force(P) = P (1-Losses) = 14011.51 kN

Table.7 Calculation of Stresses at top and bottom fibre

Span(m)

At Transfer At Service Load

TopFibre

Bottomfibre

Topfibre

BottomFibre

0.0L 4.16 4.16 4.16 4.16

0.1L 2.98 5.48 6.35 0.00

0.2L 1.91 6.67 8.37 0.00

0.3L 2.112 6.44 7.46 0.00

0.4L 2.24 6.29 6.88 0.00

0.5L 3.00 6.24 6.42 0.00

Compressive Stress atTransfer = 6.66 < 0.5 fcj = 20 mpaService = 8.367 < 0.33 fck = 16.5 mpa

Tensile stress atInitial Stage = 2.979 < 3mpa

(As per IS:1343 – 1980)Working Stage = No tensile stress

Table.8 Calculation of Ultimate Flexure Strength

Span(m)

Ultimate MomentMu = (1.5DL +2.5

LL) (kN.m)

Failure byyielding of

steel(kN.m)

Failure bycrushing

ofconcrete(kN.m)

0.0L 0.00

340578.53 5970560

0.1L 11574.43

0.2L 20394.85

0.3L 26598.28

0.4L 30402.45

0.5L 31654.88

Table.9 Calculation of Ultimate Shear strength


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Span(m)

UltimateMoment

Vu =(1.5DL

+2.5 LL)(kN.m)

Shearcapacity

Vcw(kN)

BalanceShear(kN)

Spacing(mm)

0.0L 3084.27 363.85 2720.43 55

0.1L 2391.35 419.97 1971.38 75

0.2L 1713.50 432.54 1280.96 100

0.3L 1089.90 470.56 619.34 200

0.4L 517.85 492.95 24.90 300

0.5L 0.00 0.00 0.00 0

Design of Reinforcement in Box Girder BridgeP =14011.51 kN, d = 1350 mm, bw = 200 mmAssume 150 mm wide and 150 mm deep distribution plate, located concentrically at centre.ypo /y0 = 75/150 = 0.5 ,As per IRC:18-2000, From table value of Fbst/ Pk = 0.17 and Fbst = 452.753 kNUsing 12 mm diameter links, area of steel links are,

Ast = 1254 mm/2

Providing 24 bars of 12 mm dia, 750mm also bar of 12 mm dia @ 110 mm c/c horizontally to form mesh.

Side Face ReinforcementAs per clause 18.6.3.3 of IS:1343-1980

Ast = 0.05 x 1350 x 300/100 = 202.5 mm/2

Provide 6 – 12 mm dia on each face of web

Design of Deck SlabUsing M30 grade concrete and Fe415Total moment due to DL+SIDL+LL = 1427.0 kN.mDepth required = 150.4 < 250 mm

Main Reinforcement

Ast = 3192.6824 mm/2

Providing 16mmØ bars dia 100 mm c/cDesign of Transverse ReinforcementM = 0.3ML + 0.2(MDL + MSIDL)M = 324 kN.m

Ast = 724.74 mm/2

Providing 12 mm dia bars @ 160 mm c/c


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IV. COMPARSION OF RESULT FOR VARIOUS SPAN/ DEPTH RATIOThe comparison of prestress force, deflection and stresses values are obtained for various span/depth ratio ( table no. 10 & 11) for box girder bridge. Thevalues are calculated as per IS:1343-1980.

Table.10 Comparison of Deflection for various span/depth ratio.

Span/DepthPrestress

Force(kN)

Eccentricity(mm)

Deflection

DL-PrestressForce

DL +LL–Prestress

Force

1.6 16.48 731 11.2 36.4

1.7 15.66 777 11.4 33.6


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1.8 14.83 829 9 30

1.9 14.02 886 6.6 26.6

2.0 13.20 950 5.6 25.3

Note: All dimension in tonnes and mm.• Permissible (DL-Prestress Force) = 12 mm• Permissible (DL-LL-Prestress Force)= 85.7 mm

Table.11 Comparison of stress for various span/depth ratio

Span/

Depth

PrestressForce

(tonne)

Eccen

Tricity

(mm)

Stress at mid span

(N/mm2)

At TransferAt

Working

Top Bottom Top

1.6 16.48 731 3.0 4.1 6.74

1.7 15.66 777 2.8 3.8 6.33

1.8 14.83 829 2.6 3.6 5.91

1.9 14.02 886 2.4 3.4 5.48

2.0 13.20 950 2.2 3.2 5.08

Note: Stress at mid span at working bottom = 0

V. CONCLUSIONThis paper gives basic principles for portioning of concrete box girder to help designer to start with project. Box girder shows better resistance to thetorsion of superstructure. The various trail of L/d ratio are carried out for Box Girder Bridges, deflection and stress criteria satisfied the well withinpermissible limits. As the depth increases, the prestressing force decreases and the no. of cables decrease. Because of prestressing the more strength ofconcrete is utilized and also well governs serviceability.

VI. REFERENCES1. IRC: 18 – 2000 “ DESIGN CRITERIA FOR PRESTRESSED CONCRETE ROAD BRIDGES (POST – TENSIONED CONCRETE)” THE INDIANROADS CONGRESS.2. IRC: 6- 2000 “STANDARD SPECIFICATIONS AND CODE OF PRACTICE FOR ROAD BRIDGES”THE ROAD CONGRESS.3. IS: 1343 – 1980 “ CODE OF PRACTICE FOR PRESTRESSED CONCRETE” INDIAN STANDARD.4. Andre Picard and Bruno Massicotte, Member “SERVICEABILITY DESIGN OF PRESTRESSED CONCRETE BRIDGES” JOURNAL OF BRIDGEENGINEERING / FEBRUARY 19995. Ferhat Akgul and Dan M. Frangopol “Lifetime Performance Analysis of Existing Prestressed Concrete Bridge Superstructures” JOURNAL OFSTRUCTURAL ENGINEERING © ASCE / DECEMBER 20046. James H. Loper,1 Eugene L. Marquis,2 Members and Edward J. Rhomberg Fellow. “PRECAST PRESTRESSED LONG-SPAN BRIDGES” JOURNALOF STRUCTURAL ENGINEERING © ASCE7. John R. Fowler, P.Eng, Bob Stofko, P.Eng. “Precast Options for Bridge Superstructure Design” Economical and Social Linkages Session of the 2007Annual Conference of the Transportation Association of Canada Saskatoon, Saskatchewan.8. Krishna Raju “DESIGN OF BRIDGES” OXFORD & IBH PUBLISHING CO. PVT. LTD.9. Prof. Dr.-Ing. G. Rombach “Concepts for prestressed concrete bridges Segmental box girder bridges with external prestressing” Technical University,Hamburg-Harburg, Germany.10. Tushar V. Ugale, Bhavesh A. Patel and H. V. Mojidra (2006).

We at engineeringcivil.com are thankful to Er. Priyanka Bhivgade for submitting her research on “Analysis and design of prestressed concrete boxgirder bridge” to us. We are hopeful that this will be of great use to all civil engineers who are willing to understand the design of prestressed concretebox girder.

More Entries :


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How do engineer determine the number of cells for concrete box girder bridges?Which type of multiple-cell box girder is better, cells connected by top flanges or cellsconnected both by top and bottom flanges?Why does the presence of tension reinforcement lead to increasing deflection in concretestructures?What are the functions of different reinforcement in a typical pile cap?Plate Girder In BuildingsWhat are the limitations of grillage analysis?What is the effect of shear lag in a typical box-girder bridge?In the construction of a two-span bridge (span length = L) by using span-by-spanconstruction, why is a length of about 1.25L bridge segment is constructed in the first phaseof construction?

Comments

Hameed Ajmal Sheikh May 7, 2013 at 12:47 am

It is very useful information for design engineers especially Bridge Design engineer.I shall be thankful if you could send me the Excel sheets for thisdesign as I intend to use it in near future.Thanks and regardsEngr. Hameed A Sheikh

Reply Link QuoteYoseph Asrat July 9, 2013 at 5:19 am

I got more information from the documents about bridge design.If u send me more other information about bridge design or other related documentsI develop my knowledge for the future. Thanks for your cooperation.

Eng. Yoseph Asrat.

Reply Link QuoteSharma RL September 6, 2013 at 11:10 am

I find it very interesting and knowledgeable.Kindly send more information,Excel sheets and other relevant detailsThanksSharma RL

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Analysis and Design of Prestressed Concrete Box Girder Bridge

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