ISSN 2319-8885

Vol.06,Issue.09
March-2017,
Pages:1729-1734
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A Study on Analysis and Design of Prestressed Concrete Girder Bridge

Using Finite Element Method
MD. MAHABOOB SUBHANI1, KAVIN RAJ. P2
1
PG Scholar, Dept of Civil Engineering, Nalanda Institute of Technology, Kantepudi, Guntur (Dt), AP, India.
2
Professor, Dept of Civil Engineering, Nalanda Institute of Technology, Kantepudi, Guntur (Dt), AP, India.

Abstract: Bridge construction nowadays has achieved a worldwide level of importance. Bridges square measure the key parts in
any road network and use of prestress beam sort bridges gaining quality in bridge engineering fraternity attributable to its higher
stability, utility, economy, aesthetic look and structural potency. During this thesis analysis and style of prestressed concrete
bridges (Deck block, T-Girder and Box Girder) square measure dole out exploitation. The unified concrete code printed by the
Indian Road Congress in Nov 2011 combining the code for concrete and prestressed concrete structures represents a replacement
generation code, that is considerably totally different as compared to previous codes and recent codes is supported limit state
theory whereas the previous codes were supported operating stress style philosophy.

Keywords: Prestress, Deck slab, T-slab, Box Girder, IRC.

I. INTRODUCTION position of bridge floor relative to structure as a deck, trough,

Bridges square measure outlined as structures that square half-trough or bridge. consistent with span length as waste
measure provided a passage over a niche while not closing pipe (less than 8m), minor bridge (8m to 30m) or long span
manner to a lower place. They will be required for a passage bridge.
of railway, roadway, path and even for carriage of fluid,
bridge website ought to be therefore chosen that it offers most II. BASIC CONCEPTION OF PRESTRESSING
business and social edges, efficiency, effectiveness and Prestressing is that the application of Associate in Nursing
equality. Bridges square measure nation’s lifelines and initial load on a structure, to modify it to counteract the
backbones within the event of war. Bridges symbolize ideals stresses arising from resultant masses throughout its service
and aspirations of humanity. They span barriers that divide, amount. Prestressing has been practiced from precedent days
bring individuals, communities and nations into nearer the behavior of spokes of the bicycle once it's loaded, is
proximity. They shorten distances, speed transportation and additionally example of prestressing. Prestressed concrete is
facilitate commerce. Bridges square measure symbols of essentially a concrete within which internal stresses of an
humanity’s heroic struggle towards mastery of forces of acceptable magnitude and distribution square measure
nature and these square measure silent monuments of introduced so the stresses ensuing from external masses
mankind’s never-say-die can to realize it. Bridge construction square measure counteracted to desired degree. In concrete
constitutes Associate in nursing importance part in members, the prestress is usually the steel reinforcement. The
communication and is a vital think about progress of minimum grade of concrete in prestressing technique is M40
civilization, bridges stand as tributes to the work of civil for pre tensioning and M35 for post tensioning. The
engineers. enduringness of concrete is barely 8-14% of its compressive
strength of concrete. One of the foremost unremarkably used
A. Classification of Bridges varieties of structure in concrete bridges is formed girders
Bridges square measure classified supported totally with cast-in-situ block. This sort of structure is mostly used
different criteria as follows consistent with perform as conduit for spans between twenty to forty m. Majority of prestress
(canal over a river), bridge (road or railways depression, concrete bridges, created in Asian nation square measure post
Pedestrian, highway, railway, road-cum-rail or pipe Line tension sort. The span to depth magnitude relation is
Bridge. consistent with material of construction of super sometimes unbroken as twenty for merely supported spans
Structure as timber, masonry, iron, steel, concrete, prestress and twenty five for continuous spans. The beam spacing of
concrete, composite or metallic element bridge. Consistent two to three. The deck block overhang ought to be provided
with kind or style of super structure as block, beam, truss, pro re nata to produce the fascinating aesthetic result and to
arch, bridge. Consistent with inhume span relation as cut back transfer moments. Differing kinds of beam bridges
straightforward, continuous and span. Consistent with as shown in Fig.1.

Copyright @ 2017 IJSETR. All rights reserved.

 MD. MAHABOOB SUBHANI, KAVIN RAJ. P
III. FINITE PART METHODOLOGY A. Description Of Model
The finite part methodology may be a technique for Loading on beam Bridge: The various style of masses,
analyzing sophisticated structure by status cutting up the time forces and stresses to be thought of within the analysis and
of the example into variety of little parts that square measure style of the varied elements of the bridges square measure
connected at separate joints known as nodes. for every part, given in IRC 6.
approximate stiffness equation square measure derived
relating the displacements Analysis and style of Prestressed Thickness of Web: The thickness of the online shall not be
beam Bridge by IRC: 112-2011 of the nodes to the node but d/36 and doubly the clear cowl to the reinforcement and
forces between parts and, within the same manner that slope diameter of the duct hole where’d‟ is that the overall depth of
defection equations will be solved for joints during a the beam measured from the highest of the deck block to rock
continuous beam, Associate in Nursing computing device is bottom of the side or two hundred millimeter and the diameter
employed to solved the terribly sizable amount of equation of duct holes, whichever is larger.
that relate node forces and displacements.
Thickness of Bottom Flange: The thickness of rock bottom
IV. IRC RECOMMENDATIONS ON style OF BRIDGES projection of beam shall be not but 1/20 th of the clear
The first and major step in any bridge analysis is choice of internet spacing at the junction with bottom projection or two
style of loading, they're loading, live load, impact result, wind hundred millimeter whichever is a lot of.
load, longitudinal force attributable to rubbing effort of
vehicles, longitudinal force attributable to braking of car, Thickness of prime Flange: The minimum thickness of the
seismic effects, earth pressure, vehicle collision forces etc. deck block together with that at cantilever tips be two
Out of those masses load plays a significant role. hundred millimeter. For prime and bottom projection having
prestressing cables, the thickness of such projection shall not
Vehicle Live Loads: Vehicle live masses square measure be but a hundred and fifty millimeter and diameter of duct
classified supported their configuration and intensity as IRC hole.
category 70R, IRC category AA (tracked and wheeled type),
IRC category A and IRC category B loading. Losses in Prestress: While assessing the stresses in concrete
and steel throughout tensioning operations and later in
Load Combinations: All crucial loading stages shall be commission, due regard shall be paid to any or all losses and
investigated. The stages explicit below At the stage of variations in stress ensuing from creep of concrete, shrinkage
prestressing construction stages together with temporary of concrete, relaxation of steel, the shortening (elastic
loading, transport, handling and erection or any occasional deformation) of concrete at transfer, and friction and slip of
masses that will occur throughout launching of girders style anchorage.
masses consistent with IRC:6 that features service loading,
prestress with full losses and repair loading, load and Calculation of final Strength: Ultimate moment resistance
prestress with full losses For the mixture of masses with of sections, below these 2 various conditions of failure shall
differential gradient effects, most fifty per cent load shall be be calculated by the subsequent formulae and therefore the
thought of final strength: A prestressed concrete members smaller of the 2 values shall be taken because the final
checked for failure conditions at Associate in Nursing final moment of resistance for style.
load of  Failure by Yield of Steel Mult = 0.9 db As Fp
 1.25 G + two SG + two.5 Q---under moderate conditions  Failure by Crushing of Concrete Mult = 0.176 b db2
 1.5 G + two SG + two.5 Q--- below severe exposure fck (5.1)
conditions. For sections, wherever the loading causes
effects opposite to those of live masses shall be checked VI. ANALYSIS AND STYLE OF POST TENSIONED
for G + SG + 2.5 Q. DECK SORT BEAM BRIDGE
A post tensioned deck sort beam bridge of clear span
Calculation of Final Strength: There square measure 2 thirty m and dimension of road is seven.5 m is taken into
conditions of failure at that strength ought to be calculated account for the analysis. Live masses square measure taken as
and minimum of those shall be thought of for style. They are per IRC:6. Cross section of beam is shown in Figure six.1 and
 Failure by yield of steel Mult = 0.9 db As fp (2.1) mathematical modeling is finished exploitation SAP2000 and
 Failure by crushing of concrete Mult = 0.176 b db2 fck is shown in Figure five.3. The overhang face of the beam is
one.2 m and deck block thickness is zero.25 m. Bottom block
V. ANALYSIS OF BEAM BRIDGES thickness is zero.25 m and beam thickness is zero.35 m.
The strategies for the analysis of beam bridges square Material properties used square measure M50 grade of
measure as follows straightforward line analysis or beam concrete and Fe415 grade steel. The connective tissue profile
analysis Grillage analysis BEF Analysis (Beams on elastic thought of is parabolic in nature. The Bridge analysis {for
foundation) area frame analysis Finite part methodology. For totally different for various} span to depth magnitude
study of beam bridges finite part methodology is a lot of relations (L/d) ratio ranging from fifteen to nineteen and
correct methodology. different span to depth ratios (L/d) square measure thought of
as follows.

International Journal of Scientific Engineering and Technology Research

Volume.06, IssueNo.09, March-2017, Pages: 1729-1734
 A Study on Analysis and Design of Prestressed Concrete Girder Bridge Using Finite Element Method
Case1 L/d= fifteen, d= 2.0 The description of facet face reinforcement as shown in
Figure 6.4 and cross sectional description as shown in
Case2 L/d=16, d= 1.9
C. Comparison of Results for Numerous Spans to Depth
Case3 L/d=17, d= 1.8 Magnitude Relation
The comparison of prestress force, deflection and stresses
Case4 L/d= eighteen, d= 1.7 values square measure obtained for numerous span/depth
ratios for Beam Bridge as shown in TableI.
Case5 L/d= nineteen, d= 1.

A. Mathematical Modeling
The mathematical model of a beam bridge having a span
of 30 m is shown in Figure6.2. Fig6.2. Modeling of beam
Bridge The connective tissue profile thought of for the
planning of post tensioned beam bridge is parabolic and
Mathematical model is shown in Figure six.3

B. Validation of Results
The bending moment, shear force and deflection results
square measure obtained by exploitation SAP2000. The
bending Moment and shear force square measure obtained by
Fig.1. Behavior of RC member with and without pre-
considering totally different loading conditions consisting of
stressing.
dead Load, super obligatory loading and load. The results
square measure shown below for case one. The variation of
bending moment and shear force on the length up to middle
span is shown in Tables 6.1 and 6.2. Provide twelve
millimeter diameter bars @ a hundred millimeter c/c in
horizontal direction and in vertical direction additionally same
reinforcement provided up to 750 millimeter in longitudinal
direction and same reinforcement to alternative internet
additionally.

Side Face Reinforcement

Ast = 315 mm2

Provide 6-12 millimeter diameter on every face of internet.

Design of Deck block

Bending moment = 2219 kNm

Depth required= 201 millimeter

Depth provided= 250 millimeter safe.

Main Reinforcement

Sat = 4256 mm2

Providing sixteen millimeter diameter bars a hundred

millimeter c/c

Design of transversal Reinforcement

M = 0.3 ML + 0.2 (MDL + MSIDL) M = 503 kNm

Ast = 1235 mm2

Providing twelve millimeter diameter bars @ one hundred 60 Fig.2. 9 Noded Hexahedron, 10 Noded tetrahedron, 20
millimeter c/c Noded Curved solid.

International Journal of Scientific Engineering and Technology Research

Volume.06, IssueNo.09, March-2017, Pages: 1729-1734
 MD. MAHABOOB SUBHANI, KAVIN RAJ. P

Fig.6. Tendon profile.

TABLE I: Check for Deflection

Maximum permissible deflection according to IS: 1343-

1980, Deflection due to self weight + prestress + live load =
span / 350 or 20 mm, whichever is less Permissible
deflection = minimum of (86 or 20) =20 mm > 18 mm
Hence safe.
TABLE II: Bending Moment Variation Along Span (tm)
Fig.3. 3 Noded Triangle, 4 Noded Quadrilateral, 6 Noded
Triangle, 8 Noded Quadrilateral.

TABLE III: Shear Variation Along Span (kN)

Moment due to DL+SIDL (Mg) = 1631 tm Total Maximum

moment (Mt) = 2219 tm

Initial Stresses:
fck = 50 MPa fci= 40 MPa
Fig.4. Cross Section of Box-Girder. fct= 20 MPa fcw = 16.5 MPa ftt= 2 MPa
ftw = 0 MPa fbr= 16 MPa
Loss ratio= 0.8
The variation of prestress force, eccentricity and number of
cables with respect to span to depth ratios are summarized in
Table6.3

TABLE IV: Calculation of Prestress Force and

Eccentricity

Fig.5. Modeling of box girder bridge.

International Journal of Scientific Engineering and Technology Research

Volume.06, IssueNo.09, March-2017, Pages: 1729-1734
 A Study on Analysis and Design of Prestressed Concrete Girder Bridge Using Finite Element Method
The following checks are performed for the above mentioned
case1.

D. Check for Section Modulus

Required section modulus Zreq = 571 x 106 mm3 Provided
section modulus Zpro =341 x 108 mm3 Zpro> Zreq, Hence the
section provided is adequate. Check for Stresses:
At transfer stage

Stress at top = 1.52 MPa < fct Stress at bottom = 0.87 MPa <
ftt At working stage

Stress at top = 1.4 MPa < fcw

TABLE V: Comparison of Prestress Force And

Deflection For Various Span To Depth Ratio
Fig.8.Cross sectional view (all dimensions are in mm).

VII. CONCLUSION
From the analysis and style of post tensioned beam bridge
for numerous span to depth ratios the subsequent observations
square measure created. the varied span to depth magnitude
relation square measure taken for the analysis of beam
bridges, and for all the cases, deflection and stresses square
measure inside the permissible limits. because the depth of
TABLEVI: Comparison Of Stresses For Various beam decreases, the prestressing force decreases and no of
Span/ Depth Ratio cables decreases. attributable to prestressing, a lot of strength
of concrete is used and additionally well governs utility. New
code (IRC:112) needs inflated protect pre tensioned strands
furthermore as post tensioned ducts, which can cause inflated
thickness of webs and deck block / side slabs for PSC girders
/ PSC beam bridges. For a similar cross section and same
applied moment, steel distinction is kind of noticeable
compare to WSM, LSM consumes less steel than WSM and
its higher to alter grade of steel rather increasing grade of
concrete for a lot of makeup steel distinction.

VIII. REFERENCES
[1] Kenneth W. Shushkewich (July-1998), Approximate
Analysis of Concrete Box Girder Bridges, ASCE, Journal of
Bridge Engineering, Vol.114, No.7, Pg. 1644-1657
[2] Khaled M. Sennah, John B. Kennedy ( march-2002 ),
Littrature Review in Analysis of Box Girder Bridges, ASCE,
Journal of Bridge Engineering, Vol 7, No.2, Pg 134-143
[3] W. Y. Li, L. G. Tham, Y. K. Cheung, (June1998), Curved
Box Girder Bridges, ASCE, Journal of Bridge Engineering,
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[4] Ricardo Gaspar, Fernando Reboucas Stucchi, (September-
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[5] Ayman M. Okeil, Sherif El Tawil, (September-2004),
Warping Stresses in Curved Box Girder Bridges: Case study,
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[6] Babu Kurian, Devdas Menon, (July-2007), Estimation of
Collapse Load of Single-cell Concrete Box-Girder Bridges,
ASCE, Journal of Bridge Engineering, Vol.12, No.4, Pg. 518-
526 .
Fig.7. Side face reinforcement detailing.

International Journal of Scientific Engineering and Technology Research

Volume.06, IssueNo.09, March-2017, Pages: 1729-1734
 MD. MAHABOOB SUBHANI, KAVIN RAJ. P
[7] Shi-Jun Zhou, (December-2011), Shear Lag Analysis in
Prestressed Concrete Box Girders, ASCE, Journal of Bridge
Engineering, Vol.16, No.4, Pg. 500-512 159-167.
[8] Robert K. Dowell, Timothy P. Johnson, (September-
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[9] Imad Eldin Khalafalla, Khaled M. Sennah, (July-2014),
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Member & Ductile Detailing for Seismic.

International Journal of Scientific Engineering and Technology Research

Volume.06, IssueNo.09, March-2017, Pages: 1729-1734