Analysis and Design of Prestressed Concrete Box Girder Bridge
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8/29/2016
Analysis and design of prestressed concrete box girder bridge
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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 longspan 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 castinsitu slab. This type of superstructure is generally used for spans between 20 to 40 m. T or Igirder 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:182000 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, earthfills, wearing course, stayin 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.
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Analysis and design of prestressed concrete box girder bridge
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 (underreinforced 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 POSTTENSIONED DECK TYPE BOXGIRDER 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: 62000 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 http://www.engineeringcivil.com/analysisanddesignofprestressedconcreteboxgirderbridge.html
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Analysis and design of prestressed concrete box girder bridge
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:182000 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:13431980 Ec = 5700fck1/2 = 40.30 kN/m2 fp = 1862 Mpa, n = 0.85, E = 2×105 Mpa
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Analysis and design of prestressed concrete box girder bridge
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 0.0L (m)
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
Table.5 Calculation of Eccentricity http://www.engineeringcivil.com/analysisanddesignofprestressedconcreteboxgirderbridge.html
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Analysis and design of prestressed concrete box girder bridge
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:13431980) Span (m)
^S ^C ^E ^A ^F ^R Total
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
2.6 2.4 39
22
90 155.8 0.91
0.2L 0.3L
8E 05
90
n
0.95
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 (1Losses) = 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
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Analysis and design of prestressed concrete box girder bridge
Compressive Stress at Transfer = 6.66
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