Analysis and Design of Prestressed Concrete Box Girder Bridge

Analysis and design of prestressed concrete box girder bridge Posted in Prestress Engineering, Engineering, Project Reports, Reports, Research Papers | Papers |

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By Miss.P.R. Bhivgade Abstract: –  – Bridge construction today has achieved a worldwide level of importance. Bridges are the key elements in any road network Use of box girder is gaining popularity in bridge engineering fraternity because of its better stability, serviceability, economy, aesthetic appearance and structural efficiency. The structural behavior of box girder is complicated, which is difficult to analyze in its actual conditions by conventional methods. In present study a two lane simply supported Box Girder 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 2000 14 Bridge Wizard and prestressed with parabolic tendons in which utilize full section. The various span/ depth ratio considered to get the proportioning depth 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. INTRODUCTION Prestress concrete is ideally suited for the construction of medium and long span bridges. Ever since the development of prestressed concrete by Freyssinet in the early 1930s, the material has found extensive application in the construction of long-span bridges, gradually replacing steel which needs costly maintenance due to the inherent disadvantage of corrosion under aggressive environment conditions. One of the most commonly used forms of  superstructure 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 or I-girder bridges are the most common example under this category and are very popular because of their simple geometry, low fabrication cost, easy erection or casting and smaller dead loads. In this paper study the India Road Loading considered for design of bridges, also factor which are important to decide the preliminary sizes of concrete box girders. Also considered the IRC:18-2000 for “Prestressed Concrete Road Bridges” and “Code of Practice for Prestressed Concrete ” Indian Standard. Analyze the Concrete Box Girder Road Bridg es for various spans, various depth and check the proportioning depth. depth. II. FORMULATION A. Loading L oading on Box Girder Bridge The 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 IRC 6:2000(Section II. But the common forces are considered to design the model are as follows:

 Dead Load(DL): The 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 any fixed loads supported by the member. The dead load can be estimated fairly accurately during design and can be controlled during construction and service. 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 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 need to 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 loading ii. IRC Class AA loading iii. IRC Class A loading iv. 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.

Other information regarding Live load combination as per IRC:6 2000 Clause No.207.1 Note No.4 B. Thickness of Web The 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 overall depth 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 Flange The 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 mm whichever is more. D. Thickness of Top Flange The minimum thickness of the deck slab including that at cantilever tips be 200 mm. For top and bottom flange having prestressing cables, the thickness of such flange shall not be less than 150 mm plus diameter of duct hole. E. Losses in Prestress While assessing the stresses in concrete and steel during tensioning operations and later in service, due regard shall be paid to all losses and variations in stress resulting from creep of concrete, shrinkage of concrete, relaxation of steel, the shortening (elastic deformation) of concrete at transfer, and friction and slip of anchorage.

In computing the losses in prestress when untensioned reinforcement is present, the effect of the tensile stresses developed by the untensioned reinforcement due to shrinkage and creep shall be considered. F. Calculation of Ultimate Strength Ultimate moment resistance of sections, under these two alternative conditions of failure shall be calculated by the following formulae and the smaller of  the two values shall be taken as the ultimate moment of resistance for design:

i. Failure by yield of steel (under-reinforced section) Mult = 0.9dbAsFp Where, As = the area of high tensile steel F p  = 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 a definite yield point. d b = 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 bdb2f ck  Where,  b = the width of rectangular section or web of beam f ck = 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 beams d = overall depth of the member fcp = compressive stress at centroidal axis due to prestress taken as positive. III. ANALYSIS AND DESIGN OF POST-TENSIONED DECK TYPE BOX-GIRDER BRIDGE A post- tensioned deck type Box – Girder Bridges 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

table no. 4.2. The Bridge analysis for different L/d ratio starting from 15 to 20 and different L/d ratio considered are as follows: Case 1 L/d= 19, d = 1.6 Case 2 L/d =18, d = 1.7 Case3 L/d = 17, d = 1.8 Case4 L/d= 16, d= 1.9 Case5 L/d= 15, d=2.0 Preliminary data Clear span = 30m Width of roadway = 7.5 m Overhang from face of girder = 1.2m Deck thickness = 0.2 m Bottom slab thickness = 0.2 m Girder thickness = 0.3 m The tendon profile is considered as parabolic in nature. As per IRC:18-2000 fck= 50 Mpa, fci = 0.8f ck  = 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 = 5700fck 1/2  = 40.30 kN/m2 fp = 1862 Mpa, n = 0.85, E = 2×105 Mpa

Validation of Resuts The bending moment, shear force and deflection result obtained by SAP 2000. The bending moment and shear force are calculated by considering different 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

Live Prestressing Load Force

Deflection (at 30.8 mm 25.2 midspan)

-14.36 mm

mm Table.2 Bending Moment(t.m)

Span   0.0L (m)

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 1105.23 1443.82 1650.26 1718.45 Table.3 Shear Force (t)

Span (m)

DL

0.0L

0.1L

0. 2L

0.3L 0. 4L

130.9 104.7 78.57 52.4

26.3

0.5L

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

Table.5 Calculation of Eccentricity

Eccentricity Prestressing (mm) Force (kN)

440

21617.96

548

19380.69

650

17655.06

731

16489.15

The eccentricity which give minimum  prestressing force (e) = 731mm

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

Span ^S ^C ^E ^ A ^F

^R Total

n

(m)

0.0L

0.0 0.0 0.0

0.0

90

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

8E05

90

0.95

2.6 2.4 26 36.7 90 157.7 0.91

0.4L

2.7 2.5 2 0 54.3 90 169.0 0.9

0.5L

9.1 8.3 1 6 171

90 294.0 0.85

Where, ^S = Shrinkage ^C= Creep ^E = Shortening of concrete ^A = Slip in anchorage ^F = Friction ^R = Relaxation n= Efficiency After Losses, effective Prestressing Force (P) = P (1-Losses) = 14011.51 kN Table.7 Calculation of Stresses at top and bottom fibre

At Transfer Span (m)

At Service Load

Top Fibre

Bottom fibre

Top fibre

Bottom Fibre

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 at Transfer = 6.66 < 0.5 fcj = 20 mpa Service = 8.367 < 0.33 fck = 16.5 mpa Tensile stress at Initial Stage = 2.979 < 3mpa (As per IS:1343 – 1980) Working Stage = No tensile stress Table.8 Calculation of Ultimate Flexure Strength

Failure by Failure by Ultimate Moment crushing Span yielding of  Mu = (1.5DL +2.5 of  (m) steel LL) (kN.m) concrete (kN.m) (kN.m)

0.0L

0.00

0.1L

11574.43

0.2L

20394.85

340578.53 5970560

0.3L

26598.28

0.4L

30402.45

0.5L

31654.88

Table.9 Calculation of Ultimate Shear strength

Span (m)

Ultimate Shear Balance Spacing Moment capacity Shear (mm) Vu = Vcw (kN) (1.5DL (kN) +2.5 LL) (kN.m)

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 Bridge P =14011.51 kN, d = 1350 mm, bw = 200 mm Assume 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 kN Using 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 Reinforcement As 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 Slab Using M30 grade concrete and Fe415 Total moment due to DL+SIDL+LL = 1427.0 kN.m Depth required = 150.4 < 250 mm Main Reinforcement

Ast = 3192.6824 mm /2 Providing 16mmØ bars dia 100 mm c/c Design of Transverse Reinforcement M = 0.3ML + 0.2(MDL + MSIDL) M = 324 kN.m Ast = 724.74 mm/2 Providing 12 mm dia bars @ 160 mm c/c

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

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

Deflection Prestress Eccentricity Span/Depth Force (mm) (kN)

DL +LL DL –  Prestress Prestress Force Force

1.6

16.48

731

11.2

36.4

1.7

15.66

777

11.4

33.6

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

Stress at mid span (N/mm2)

Eccen Span/ Depth

Prestress Tricity Force (tonne)

(mm)

At Transfer

At 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. CONCLUSION This paper gives basic principles for portioning of concrete box girder to help designer to start with project. Box girder shows better resistance to the torsion of superstructure. The various trail of L/d ratio are carried out for Box Girder Bridges, deflection and stress criteria satisfied the well within  permissible limits. As the depth increases, the prestressing force decreases and the no. of cables decrease. Because of prestressing the more strength of  concrete is utilized and also well governs serviceability. VI. REFERENCES 1. IRC: 18 – 2000 “ DESIGN CRITERIA FOR PRESTRESSED CONCRETE ROAD BRIDGES (POST – TENSIONED CONCRETE)” THE INDIAN ROADS 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 BRIDGE ENGINEERING / FEBRUARY 1999 5. Ferhat Akgul and Dan M. Frangopol “Lifetime Performance Analysis of Existing Prestressed Concrete Bridge Superstructures” JOURNAL OF STRUCTURAL ENGINEERING © ASCE / DECEMBER 2004 6. James H. Loper,1 Eugene L. Marquis,2 Members and Edward J. Rhomberg Fellow. “PRECAST PRESTRESSED LONG-SPAN BRIDGES” JOURNAL OF STRUCTURAL ENGINEERING © ASCE 7. John R. Fowler, P.Eng, Bob Stofko, P.Eng. “Precast Options for Bridge Superstructure Design” Economical and Social Linkages Session of the 2007 Annual 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 box   girder 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 concrete box girder. More Entries :

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Which type of multiple-cell box girder is better, cells connected by top flanges or cells connected both by top and bottom flanges? Why does the presence of tension reinforcement lead to increasing deflection in concrete structures? What are the functions of different reinforcement in a typical pile cap? Plate Girder In Buildings What 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-span construction, why is a length of about 1.25L bridge segment is constructed in the first phase of 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  this design as I intend to use it in near future.Thanks and regards Engr. Hameed A Sheikh Reply Link Quote Yoseph 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 documents I develop my knowledge for the future. Thanks for your cooperation. Eng. Yoseph Asrat. Reply Link Quote Sharma RL September 6, 2013 at 11:10 am I find it very interesting and knowledgeable. Kindly send more information,Excel sheets and other relevant details Thanks Sharma RL Reply Link Quote SHOAIB AHMED December 10, 2014 at 8:48 pm 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  this design as I intend to use it in near future.Thanks and regards Engr. SHOAIB AHMED Reply Link Quote  Md.Nurul Amin February 24, 2015 at 11:56 am It is very useful information for design engineers especially Bridge Design engineer.It will be more helpful if the the Excel sheets for this design is attached.With thanks and regards Engr. Md.Nurul Amin Reply Link Quote Post a comment  Name Email Website

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