# Analysis and design of prestressed concrete box girder bridge

**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 Bridges for various spans, various depth and check the proportioning depth.

**II. FORMULATION
A. Loading 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 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 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

Fp = 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.

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 beam

fck= 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 = 0.8fck = 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

**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.

Load Case

DL + SIDL

Live Load

Prestressing Force

Deflection (at midspan)

30.8 mm

25.2

mm

-14.36 mm

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

1105.23

1443.82

1650.26

1718.45

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

Eccentricity (mm)

Prestressing Force (kN)

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

440

21617.96

548

19380.69

650

17655.06

731

16489.15

(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

^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

Span (m)

At Transfer

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

Span (m)

Ultimate Moment Mu = (1.5DL +2.5 LL) (kN.m)

Failure by yielding of steel (kN.m)

Failure by crushing of concrete (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

Span (m)

Ultimate Moment Vu = (1.5DL +2.5 LL) (kN.m)

Shear capacity Vcw (kN)

Balance Shear (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 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.

Span/Depth

Prestress Force (kN)

Eccentricity (mm)

Deflection

DL-Prestress Force

DL +LL –Prestress 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

Span/

Depth

Prestress Force

(tonne)

Eccen

Tricity

(mm)

Stress at mid span (N/mm2)

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.*

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