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Research ArticleSimplified Reliability Estimation for OptimumStrengthening Ratio of 30-Year-Old Double T-Beam RailwayBridge by NSM Techniques
Minkwan Ju1 Hongseob Oh2 and Jong-Wan Sun3
1 Department of Civil Engineering Kangwon National University 1 Joonang-ro Kangwon Samcheok 245-711 Republic of Korea2Department of Civil Engineering Gyeongnam National University of Science and Technology 150 Chilam-dong Jinju Gyeongnam660-758 Republic of Korea
3 Research Division G3Way Co Yangjae-dong Seocho Seoul 20-32 Republic of Korea
Correspondence should be addressed to Hongseob Oh opera69cholcom
Received 25 November 2013 Revised 3 March 2014 Accepted 4 March 2014 Published 11 May 2014
Academic Editor Ting-Hua Yi
Copyright copy 2014 Minkwan Ju et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
This study is to develop simplified reliability estimation for optimum strengthening ratio of T-beam railway bridge strengthenedby CFRP strip Until now strengthening design has been usually proceeded to satisfy the target load-carrying capacity by using thedeterministic parameter of nominal property for concrete or FRP For the optimum strengthening design however it is requiredthat reliability-based strengthening design should be applied to effectively determine the amount of strengthening material andmake sure of the safety of the structure As applying the reliability-based strengthening ratio more reliable strengthening designusing CFRP strip is possible as well as having a structural redundancy The reliability-based strengthening design methodologysuggested in this study is able to contribute the optimum strengthening design for a concrete structure strengthened by CFRP strip
1 Introduction
FHWA 2009 [1] reported that many existing reinforced con-crete bridges especially superstructures have consistentlyexperienced deteriorations with significant loss of load-carrying capacity As the national budget is decreased forthe new construction the repair and strengthening needshave beenmajor consideration inmaintenance field of infras-tructure In the last decade the conventional strengtheningmaterials have been replaced with fiber reinforced polymer(FRP) materials for strengthening of the deteriorated con-crete structures Among these FRP strengthening materialforms FRP laminate and sheet are widely applied on thesurface of the structure to be strengthened by the externallybonded reinforcing (EBR) technique For this strengtheninghowever the previous researches have raised several kinds ofproblems that the EBR technique cannot sufficiently transfertensile strength of the FRP materials to concrete memberdue to their premature debonding [2] Near surface mounted(NSM) strengthening technique has many advantages for
improving the structural capacity over a conventional ERBstrengthening less site installation work better bondingand structural performance and more effective mainte-nance point of view For these reasons many experimentalresearches have suggested that NSM-FRP strengthening isone of themost reliable strengthening techniques for concretestructures [3ndash5] Although EBR technique needs additionalexternal protection against either the fire attack or an unex-pected collision the NSM strengthening technique providesbetter protection in disaster situations than conventional EBR[6] methods
Also NSM using FRP strips has substantially betterbond resistance because it can be embedded in an adhesiveentirely within the narrow groove of the substrate concreteThis advantage of FRP strips for bonding performance waspreviously demonstrated by Soliman et al [7] In amonotonicload test theNSMCFRP strip demonstrated better anchoragethan the EBR CFRP strips [8 9]
Although many studies for FRP strengthening havebeen conducted previously there are few studies to suggest
Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 734016 10 pageshttpdxdoiorg1011552014734016
Figure 1 Standard train load in Korea (LS-18 LS-22)
the strengthening guideline such as a strengthening ratioby applying a probabilistic and reliability analysis Thisis important because of the uncertainty for material andstructural point of view on the FRP strengthening methodA parametric study of GFRP rebar for design factors suchas cross-sectional dimension GFRP and concrete strength[10] is conducted Another research is carried out a reli-ability assessment of an FRP-strengthened concrete beamby Chinese codes [11] A parametric study on the effects ofinfluencing factors on average reliability level shows that loadeffect ratio and concrete strength are the first two dominantinfluencing factors among all design variables For designconcepts the conventional ultimate strength design (USD)method is changed to limit state design after 2015 in KoreaTherefore safety and reliability for all structures will beregarded widely as well as the strengthening of concretestructures
This study aims to propose the reliability-based determi-nation procedure on the strengthening ratio of a deterioratedconcrete girder with CFRP strips which has advantages forthe full composite performance with concrete members Thetarget bridge in this study is a double T-beam railway bridgeoriginally designed by LS-18 (an old type of design load fora railway bridge in Korea) Therefore it is required that thetarget bridge should satisfy the present design load (LS-22)and enhance the design speed with the high speed era in thefuture In order to assess the optimal strengthening ratio forthe target bridge in this study the CFRP strip strengtheningmethod was analytically applied to the target bridge
NSM strengthening technique is more effective forenhancing flexural capacity of railway bridge in case vibrationof train traffic due to its superior bond performance Thegoal of this study was to calculate the reliability-basedstrengthening ratio of the concrete beams strengthened byNSM using CFRP strips by applying the reliability indexfor bridge design FE analysis on the deteriorated and thenstrengthened bridge was performed using the design railwayload in the Korea railway specification FEM analysis wasalso used to estimate the amount of steel reinforcements ofthe target bridge due to the absence of structural designinformation of this aged bridge To consider the structural
uncertainties of the strengthening method the probabilityand reliability analysis were performed with Monte Carlosimulation (MCS) Finally the reliability-based strengthen-ing ratio which satisfies the reliability index for the structuraldesign (120573 = 35) is estimated with the structural redundancyfor the target design strength Finally it is suggested thatthe strengthening procedure of the applied probabilistic andreliability approach is a reasonable strengthening designmethod
2 Estimation of the Unknown Property ofTarget Bridge
The target bridge is a simply supported railway bridge inKorea which was built for the design load of LS-18 in 1982 InDesign Specification of Railway ofKorea [15] standard designload is categorized as LS-18 restricted to 120 kmhr and LS-22for high speed railway as depicted in Figure 1 Actual speedand dynamic behavior on the LS-18 train weremonitored andanalyzed by [16]
Figures 2 and 3 show the typical cross-section andlongitudinal view of the RC T bridge
There are some recent diagnosis techniques [17ndash19] Forthis bridge conventional inspection method was appliedSome of deterioration defects such as cracks efflorescencesteel corrosion and concrete segregation were visualized byinspection Whereas the compressive strength of concrete is408MPa the strength of steel rebar is not verified from thefield inspection
To evaluate the requirement of strengthening amount aload-carrying capacity or flexural stiffness for the structuralcondition in service mode should be investigated Due tothe characteristics of this railway bridge dynamic tests forstructural evaluation were performed using in-field moni-toring data for the train loads passing the target point [16]with structural stiffness as the main indicator of structuralcondition For this acceleration data was monitored andcompared with an RC bridge with a similar span length andsize According to Hwang et al [16] the acceleration of thetarget bridge was shown to be over 04 g (1 g is 980 cms2 gal)
Mathematical Problems in Engineering 3
Waterproof mortar
540420350 1520 100 20
8020 2070 7080 80
260
1515
1025
135
95
CL
Figure 2 A cross-section of the target bridge (unit m)
B(T) Haseo-cheon
Centrifugalreinforced
concrete pileempty 300 times 900
FL
H middot W middot L = 10645
L middot W middot L = 10445
Mokpo direction
Centrifugalreinforced
concrete pileempty 400 times 1000
Daejeondirection
900 900 900 900122 122 1223956
250
140
300
120
90times4
(Southbound lane) 108 km 13
680 L
=3956
Figure 3 A longitudinal view of the target bridge
when the train passed In Europe it is recommended thatthe acceleration should be under 035 g for the preventionof turbulence on the railway in service [20 21] Thus high-level acceleration in service is considered proof of structuralperformance degradation and the appropriate strengtheningmeans to satisfy the serviceability limit are required Tosolve the vibration problem strengthening by FRP compositecan enhance the structural stiffness [22 23] For anotherstrengthening need structural condition was recorded asC-grade after an in-depth inspection conducted in 2003[24] During the bridgersquos 30 years of service time structuralmaterials such as concrete and steel reinforcement havepossibly deteriorated Therefore the target bridge should betreated with structural upgrade maintenance In this studyFRP strip strengthening of the deteriorated target bridge
is an effective strategy and the strengthening ratiomdashthemost significant factor for the strengthening designmdashwillbe suggested through a reliability analysis of material andstructural uncertainties using a reliability index
To assess the amount of adequate strengthening ratio tosatisfy the requirement the unknown reinforcement ratio ofsteel rebar should be reasonably estimated Structural analysison the target bridge without the steel rebar was initiallyperformed to calculate external flexuralmoment subjected byLS-18 design loadsThe structuralmodeling and analysis wereconducted by commercial FEA program [25] The bridgemodel was built by plate and solid elements the dead load likegravel rail was excepted Figure 4 shows the analysis resultsof external flexural moments for dead and live loads Thedesign load factors for dead and live loads were based on the
4 Mathematical Problems in Engineering
MIDASCivilPostprocessorBeam forceMoment-120574
179960e + 002
160096e + 002
122768e + 002
141032e + 002
103703e + 002
046392e + 001
655749e + 001
465107e + 001
274455e + 001
000000e + 000
minus106820e + 001
minus297452e + 001
Scale factor =40289E + 002
CB dead allMax 0Min 26File railroadUnit kNmiddotm
X minus0516Y minus0766Z 0383
View-directionDate 4132012
(a) Bending moment diagram for a factored dead loadMIDASCivilPostprocessorBeam forceMoment-120574
Scale factor =
Max 10Min 3File railroadUnit kNmiddotm
X minus0516Y minus0766Z 0383
View-direction
500095e + 002
514061e + 002
447227e + 002
300393e + 002
313559e + 002
246725e + 002
179891e + 002
112057e + 002
462233e + 001
000000e + 000
minus874446e + 001
minus154279e + 002
119743E + 002Ctall live all
Date 4132012
(b) Bending moment diagram for a factored live load
Figure 4 FE analyses for dead and live loads
design specification of railway of Korea and were 14 and 20respectively
The design flexural moment by FE analysis was calculatedas 7610 kNsdotm With this moment capacity the area of steelrebar can be estimated as 1718mm2 by the moment equi-librium equation for the rectangular beam with an effectivewidth of slab
3 Limit State Function and Safety Index
31 Limit State Function The conventional performancefunction for flexural capacity of the bridge cross-sectionconsists of 119877119863 and 119871 where 119877 is strength resistance or loadcarrying capacity119863 is dead load effect and119871 is live load effectincluding impact [26] For consideration of the limit state thelimit state model to express railway by Cho et al [27] wasadapted and followed as
119892 (sdot) = 119877 minus (119878119863+ 119878119871) (1)
where 119877 is structural resistance and 119878119863and 119878119871are dead and
live load effect respectively 119877 119878119863 and 119878
where 119877119899is estimated nominal strength of undamaged
structures (flexural moment or shear force) 119863119865is damage
coefficient 119873119877is uncertain parameter when 119877
119873and 119863
119865are
estimated119862119863and119862
119871are the effect factor of flexural moment
and shear force for dead and live loads 119863119899and 119871
119899are the
nominal dead and live loads respectively 119870119878is the response
ratio (CalculationMeasure) 119894 is the impact factor and 119873119863
and119873119871are the calibration factors of 119862
119863and 119862
119871 respectively
119873119877can be calculated by PsdotMsdotFsdotD P for uncertainties of
estimation for analytical modelM formaterial strength F forfabrication andD for damage factors In this study structural
Mathematical Problems in Engineering 5
h d2 d1
d998400
be
c
120576s120576f
120576998400c
120576cu
fsff
Cc
C998400s
085f998400c
1205731c
Figure 5 Compatibility diagram of strain and strength of the cross-section for strengthening
failure denotes the state when the theoretical flexural capacityis reached Failure occurs if the function119892 is less than or equalto zero
As depicted in Figure 5 the resistancemoment (119872119899) used
in this reliability analysis is calculated by (3) to (6) accordingto the recommendations from ACI Committee 440 [28] andBank [29] In this study the damage factor 119863
of concrete (41MPa) and 119887119890is effective width of rectangular
beam (1900mm) 119863119891means the damage factor assumed in
the reliability analysis (Table 4)In the case of failure mode of a concrete beam externally
bonded with CFRP materials except in a premature failurecase the following four failure modes are classified represen-tatively
(1) steel yielding and concrete compressive failure beforeCFRP rupture
(2) steel yielding and CFRP rupture after concrete com-pressive failure
(3) CFRP rupture and concrete compressive failurebefore steel yielding
(4) concrete compressive failure before steel yielding andCFRP rupture
Among the Cases 1sim4 Cases 3 and 4 are typicaloverstrengthening failure which leads to brittle failure ofstrengthening beams Cases 1 and 2 however would resultin ductile failure rather than that of Cases 3 and 4 For rea-sonable failure cases Case 1) is more suitable for preventingthe brittle failure because concrete compressive failure is lessbrittle than that of CFRP strip Balanced failure means thata strengthened concrete member fails simultaneously withconcrete compressive failure and CFRP rupture
Structural safety can be conveniently calculated withrespect to the reliability index 120573 as follows
120573 =120583119892
120590119892
(7)
The variables 120583119892and 120590
119892are the terms of the mean and stan-
dard deviation of the performance function 119892 respectivelyThe reliability index for flexural capacity after strengtheningis calculated based on the effective cross-section of the targetbridge with the amount of CFRP strip required to satisfy thestrength for NSM strengthening In this study the reliabilityindex is computed by the Rackwitz-Fiessler algorithm [30]
32 Computational Uncertainty Factors (119870119904) The computa-
tional uncertainties 119870119904 are adapted to be considered in pre-
dicting resistance The statistics for randomness are definedbased on analytical results or test results Some analytical andtest results are introduced by a literature review of previousresearch papers for reliability analysis [10] In this study itis assumed that statistics of the computational uncertaintyfactor in concrete crushing mode are effective to estimatethe strengthening ratio by reliability analysisThus from datafrom a total of 91 specimens 1061 of mean value and 009 ofstandard deviation resulted The following equation denotesthe computational uncertainties in this analysis
119870119904=119872119880exp
119872119880pre
(8)
33 Damage Factor Cho et al [31] have theoretically definedthat the damage factor is the ratio of stiffness for a non-damaged structure to a damaged structure For quantitative
6 Mathematical Problems in Engineering
Select the target structure forNSM strengthening
Constitute the limit state function
Calculate the external moment
Define of material and structural uncertainty
Calculate the resistance moment and perform reliability analysis
Determine the strengthening ratio of CFRP strip
Reassuming the CFRP
strengthening ratio
No
Yes
120573 = 35
Figure 6 A procedure for determining the reliability-based strengthening ratio of CFRP strip with a target reliability index of 35
approaches it can be calculated by using the ratio of powerof natural frequency for a damaged structure to that fora nondamaged structure In actual state however it is notasserted that this ratio can directly represent the degreeof damage Estimating the damage factor is hard to bedetermined without the plentiful history data so that thedamage factor in this study is assumed by previous research[29] Therefore the average of damage factor is ranged from06 to 09 anduncertainty of damage factor is considered from01 to 03 of coefficient of variation With this statistical datathe probability and reliability analysis are carried out and aresult of sensitive analysis for the variation of damage factoris discussed
4 Characteristics of Random Variables
For reliability analyses the statistics of random variables aredefined in advance There are three variables considered inthis analysis external load for dead and live ones materialstrength of concrete steel rebar and CFRP strip and designof cross-section
In the reliability analysis for structural safety it is essentialthat the load effect must be considered by combining thevariability of loads dead and live loads A related study wasconducted and suggested the load and resistance factors forRC concrete design [32] Table 1 shows the statistics of theload effect for dead and live load for reliability analysis [33]Among these mean value is the external moment resulting
from FE analysis to the target bridge and load factor is basedon the KR specification
The statistics of resistance-related variables such as 1198911015840119888 ℎ
and 119889 listed in Table 2 are adopted from Ellingwood [32]Also included in Table 2 are the statistics of the strength ofCFRP strip (119891fu) for Barros and Fortes [34] and of the width(119887) of T-beam for Oh et al [13] In the case of the nominalvalue of ℎ and 119889 the real dimension of the cross section inthe target bridge is used For steel rebar statistics from manyof tensile tests are summarized in Table 3 [35] As comparedwith Grade series by ASTM A 165 SD30 SD35 and SD40rebar considered in the reliability analysis showed relativelybetter coefficient of variation The probability distributionwas considered as normal type In this study statistics ofSD40 in Korea were adopted in reliability analysis
5 Reliability-Based Strengthening Ratio ofCFRP Strip
51 Target Safety Index in Reliability Analysis This studyis to calculate the reliability-based strengthening ratio ofCFRP strip to the existing railway bridge which has struc-tural uncertainties Therefore it is important to define howmuch structural safety should be acquired This is simplydetermined by using the reliability index or the target safetyfactor 120573 in the load and resistance analysis Previous studyhas shown that 120573 values of 25sim30 and 30sim35 were used
Mathematical Problems in Engineering 7
Table 1 Result of FEM analysis for external railway load
Probability distribution MeanNominal Mean COVa Load factorDead load Normal 105 1800 kNsdotm 01 14Live load Lognormal 100 5808 kNsdotm 02ndash04 20aCOV coefficient of variation
Table 2 Statistics of random design variables (I)
Design variable Nominal value Mean value Standard deviation Probability distribution119891119888
1015840 (MPa) 4134 4616 194 Normal119891fu (MPa)a mdash 2790 857 Normal119887 (mm)b 1900 119887 + 094 60 Normalℎ (mm)c 1250 ℎ minus 305 635 Normal119889 (mm)c 1200 119889 minus 470 1270 NormalaISO 527-3 (1997)[12] bOh et al (1993) [13] ccross-sectional dimension of the target bridge
Table 3 Statistics of random design variables (II)
MeanNominal COV Average strength Number of data Standard deviation Probability distributionSD 30a 120 0064 3600 822 2304 NormalSD 35a 113 0038 3955 80 1503 NormalSD 40a 109 0048 4360 773 2093 NormalGrade 40b 113 0116 3170 mdash 3672 NormalGrade 60b 112 0098 4725 mdash 4631 NormalaKS D 3504bASTM A 615 Standard Specification for Deformed and Plain Carbon Steel Bars for Concrete Reinforcement-AASHTO No M 31 [14]
for tension failure and compression failure respectively [36]Kulicki et al [37] proposed the target or code-specifiedreliability indices obtained from reliability analysis of a groupof 175 existing actual bridges designed by either ASD or LFDmethod and then suggested the range of values using the newload and resistance factors From this research AASHTOaltered the reliability index to 35 when either a higher levelof safety or taking more risk was appropriate [38] Accordingto the recent research [39] the target beta for beam is 35for flexural strength of RC beams constructed with lightweight and normal weight concrete In this study the targetreliability index is determined with 35 and a reliability-basedstrengthening ratio satisfying the probability index 120573 = 35will be calculated
52 Result of Reliability Analysis To evaluate the reliability-based strengthening ratio of the target bridge the probabilitydistribution between the external load and structural resis-tance from the limit state function was analyzed A safetymargin was used and 120573
119879= 35 of target reliability index was
specified by AASHTO [38] Figure 6 is a process to calculatestrengthening ratio of CFRP strip by reliability analysis witha reliability index of 35 FEM analysis should be conductedto determine the external moment for dead and live loadsStructural resistance is affected as when strengthening ratioof CFRP strip is variedTherefore iteration process is neededuntil safety margin of 35 of the strengthening bridge againstexternal load is acquired
0
00005
0001
00015
0002
00025
0003
00035
0004
00045
Prob
abili
ty d
ensit
y
0 500 1000 1500 2000 2500 3000Flexural moment (kNmiddotm)
Q(LS-18)Q(LS-22)R for LS-18Case1 (120588cfrp = 00001)
Figure 7 Probability distribution curves for external load andresistance
Figure 7 is the probability distribution curves for externalload and resistance resulted from the reliability analysisFor external loads the probability distribution of LS-22was additionally considered to investigate the how muchthe strengthening effect of CFRP strips can decrease theprobability of failure compared LS-22 design load 119876 meansthe external load and 119877 is for the resistance moment
8 Mathematical Problems in Engineering
Table 4 Sensitive analysis for damage factor standard deviation of damage factor and live load effect
Degree of sensitive for COV of Degree of sensitive for COV of live load factorDegree of sensitive for average value of
120588cf
rp
Df
Df
Figure 9 Sensitive analysis for COV and average value of 119863119891and
COV of live load factor
Strengthening effect is denoted as a case series FEM analysiswas performed to calculate the external moment for LS-18and LS-22 design railway load For probability distribution ofLS-22 which is the present design load of railway in Korea
probability characteristics for LS-18 were used in the sameway In order to acquire the reliability-based strengtheningratio for 120573
119879= 35 the range of probability parameters was
roughly considered then the final 5 cases for 120588cfrp from 00001to 000013 were analyzed Each probability distribution curveis illustrated in Figure 7 Figure 8 is the result of reliability-based strengthening ratio According to the result of thestrengthening effect by probability distribution the targetbridge strengthened by the CFRP strip strengthening ratioresulting from the reliability analysis could be sufficientlysafe against the LS-22 present design railway load As thestrengthening ratio of CFRP strip that could satisfy 120573
119879= 35
it was with 120588cfrp = 0000114
53 Sensitive Analysis for Three Important ParametersFigure 9 shows the result of sensitive analysis for three param-eters such as damage factor standard deviation of damagefactor and live load effect The CFRP strip strengtheningratio resulting from the reliability analysis is plotted withthree important parameters The purpose of this process isto identify how sensitively the strengthening ratio will beaffected when the three parameters are varied independentlyThe determination of the variation ranges of the parameterswas considered to simply but effectively apply the sensitivecharacteristics For live loads and damage factor there weresimilar degrees of sensitivity Variation of COV of damagefactor however was more sensitive than that of the otherparameters Itmight be concluded that COVof damage factorlargely affected to estimate the reliability-based strengtheningusing about the CFRP strip For more reliable estimation ofdamage factor many of structural diagnosis data should beanalyzed in future Table 4 summarizes the input parametersused in the sensitive analysis
6 Conclusions
This study suggested the reliability-based strengthening ratiofor 30-year-old railway bridge using CFRP strips Conclu-sions are as follows
(1) In previous strengthening schemes it has beenuncertain to determine how much the strengthen-ing effect should be required The methodology forthe reliability-based strengthening ratio can improve
Mathematical Problems in Engineering 9
these problems of the previous strengtheningmethodThe target reliability index for CFRP strip strengthen-ing is considered as 35 according to AASHTO spec-ification As using the reliability-based strengtheningratio in this studymore effective strengthening designto concrete structure having a specified strength-ening target as well as reflecting the structural andmaterial uncertainties is possible
(2) In the result of a sensitive analysis variation of COVfor damage factor mostly affected to the reliability-based strengthening ratio of CFRP strip Thereforedamage factor should be studied more properly onthe target bridge This may be possible by analyzingthe database for long-term safety inspection historyand its reasonable quantification Stabilization andnormalization processes of the damage factor are alsorequired
(3) One of the important factors for determining thesafety margin against the resistance is external loadeffect In order to improve the reliability-basedstrengthening ratio of CFRP strip in this study uncer-tainties for external load of a railway bridge should beanalytically and experimentally verified This can besolved by analyzing the acquired data from long-termmonitoring then the reliability of the strengtheningratio of CFRP strip will be promoted
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by Korea Institute of EnergyTechnology Evaluation and Planning (0000000015513) andResearch grant from Gyeongnam National University ofScience and Technology
References
[1] FHWA Bridge Programs NBI data 2009 httpwwwfhwadotgovbridgenbi
[2] ACI Committee 440 Guide for the Design and Constructionof Externally Bonded FRP Systems for Strengthening Con-crete Structures (ACI 4402R-08) American Concrete InstituteFarmington Hills Mich USA 2008
[3] J M de Sena Cruz and J A O De Barros ldquoBond between near-surface mounted carbon-fiber-reinforced polymer laminatestrips and concreterdquo Journal of Composites for Construction vol8 no 6 pp 519ndash527 2004
[4] T Hassan and S Rizkalla ldquoInvestigation of bond in concretestructures strengthened with near surface mounted carbonfiber reinforced polymer stripsrdquo Journal of Composites forConstruction vol 7 no 3 pp 248ndash257 2003
[5] S M Soliman E El-Salakawy and B Benmokrane ldquoFlexuralbehavior of concrete beams strengthened with near surfacemounted FRP barsrdquo in Proceedings of 4th International confer-ence on FRP composites in civil engineering (CICE rsquo08) 2008
[6] J P Firmo J R Correia and P Franca ldquoFire behaviour ofreinforced concrete beams strengthened with CFRP laminatesprotection systems with insulation of the anchorage zonesrdquoComposites Part B Engineering vol 43 no 3 pp 1545ndash15562012
[7] S M Soliman E El-Salakawy and B Benmokrane ldquoBondperformance of near-surface-mounted FRP barsrdquo Journal ofComposites for Construction vol 15 no 1 pp 103ndash111 2011
[8] THassan and S Rizkalla ldquoFlexural strengthening of prestressedbridge slabs with FRP systemsrdquo PCI Journal vol 47 no 1 pp76ndash93 2002
[9] J R Yost S P Gross and D W Dinehart ldquoNear surfacemounted CFRP reinforcement for structural retrofit of concreteflexural membersrdquo in Proceedings of the 4th InternationalConference on Advanced Composite Materials in Bridges andStructures Calgary Canada 2004
[10] Z He and F Qiu ldquoProbabilistic assessment on flexural capacityof GFRP-reinforced concrete beams designed by guideline ACI4401R-06rdquo Construction and Building Materials vol 25 no 4pp 1663ndash1670 2011
[11] Z He and L Jiang ldquoFlexural reliability assessment of FRP-strengthened reinforced concrete beams designed by ChineseCECS-146 Guidelinerdquo Pacific Science Review vol 9 no 1 pp123ndash133 2007
[12] International Organization for Standardization ldquoDetermina-tion of tensile properties-part 5 test conditions for unidirec-tional fibre reinforced plastic compositesrdquo ISO 527-5 Interna-tional Organization for Standardization Geneva Switzerland1997
[13] B H Oh C K Koh S W Baik H J Lee and S H HanldquoRealistic reliability analysis of reinforced concrete structuresrdquoJournal of Korea Society of Civil Engineering vol 13 no 2 pp121ndash133 1993 (Korean)
[14] Steel bars for concrete reinforcement KS D 3504 KoreanIndustrial Standards 2011 (Korean)
[15] KR Network Design Specification of Railway Railway BridgeKorea Rail Network Authority Seoul Republic of Korea 2004(Korean)
[16] S K Hwang J T Oh J S Lee et al Performance Enhancementof Railway System-Track amp Civil Development of the DesignSpecification for Improving Dynamic Characteristics of RailwayBridges Korea Railway Research Institute Seoul Republic ofKorea 2003 (Korean)
[17] H S Shang T H Yi and L S Yang ldquoExperimental studyon the compressive strength of big mobility concrete withnondestructive testing methodrdquo Advances in Materials Scienceand Engineering vol 2012 Article ID 345214 6 pages 2012
[18] TH YiHN Li andHM Sun ldquoMulti-stage structural damagediagnosis method based on ldquoenergy-damagerdquo theoryrdquo SmartStructures And Systems vol 12 no 3-4 pp 345ndash361 2013
[19] H S Shang T H Yi and X X Guo ldquoStudy on strength andultrasonic of air-entrained concrete and plain concrete in coldenvironmentrdquo Advances in Materials Science and Engineeringvol 2014 Article ID 706986 7 pages 2014
[20] Korea High Speed Rail Construction Authority (KHRC)ldquoBridge designmanual (BRDM)rdquo Technical Report KoreaHighSpeed Rail Construction Authority (KHRC) Pusan Public ofKorea 1995 (Korean)
[21] International Union of Railway UIC Code 776-1R Loads to BeConsidered in Railway Bridge Design International Union ofRailway Paris France 4th edition 1994
10 Mathematical Problems in Engineering
[22] M Abdessemed S Kenai A Bali and A Kibboua ldquoDynamicanalysis of a bridge repaired by CFRP experimental andnumerical modellingrdquoConstruction and BuildingMaterials vol25 no 3 pp 1270ndash1276 2011
[23] G Zanardo H Hao Y Xia and A J Deeks ldquoStiffness assess-ment through modal analysis of an RC slab bridge before andafter strengtheningrdquo Journal of Bridge Engineering vol 11 no 5pp 590ndash601 2006
[24] Korea Infrastructure Safety and Technology corporation(KISTEC) A Database of Maintenance History KoreaInfrastructure Safety and Technology corporation (KISTEC)Gyeonggi-do Republic of Korea 2003 (Korean)
[25] MIDAS IT MIDAS Civil Program Manual MIDAS ITGyeonggi Republic of Korea 2009
[26] S W Tabsh and A S Nowak ldquoReliability of highway girderbridgesrdquo Journal of Structural Engineering ASCE vol 117 no 8pp 2372ndash2388 1991
[27] H N Cho K H Kwak and S J Lee ldquoReliability-based safetyand capacity evaluation of high-speed railway bridgesrdquo Journalof Computational Structural Engineering Institute in KoreaCOSEIK vol 10 no 3 pp 133ndash143 1997 (Korean)
[28] ACI Committee 440 Guide for the Design and Constructionof Externally Bonded FRP Systems for Strengthening ConcreteStructures American Concrete Institute Farmington HillsMich USA 2008
[29] L C Bank Composites for Construction-Structural Design withFRP Materials John Wiley amp Sons New York NY USA 2006
[30] R Rackwitz and B Flessler ldquoStructural reliability under com-bined random load sequencesrdquo Computers and Structures vol9 no 5 pp 489ndash494 1978
[31] H N Cho H H Choi S Y Lee and J W Sun ldquoMethodologyfor reliability-based assessment of capacity-rating of plate girderrailway bridges using ambient measurement datardquo Journal ofKorea Society of Steel Construction vol 15 no 2 pp 187ndash1962003 (Korean)
[32] B Ellingwood Reliability Bases of Load and Resistance Factorsfor Reinforced Concrete Design National Bureau of StandardsBuilding Science Series 110 Washington DC USA 1978
[33] US Department of CommreceNational Bureau of StandardsldquoDevelopment of a probability based load criteria for Amer-ican National Standard A58rdquo NBS Special Publication 577US Department of CommreceNational Bureau of StandardsGaithersburg Md USA 1980
[34] J A O Barros and A S Fortes ldquoFlexural strengthening ofconcrete beamswithCFRP laminates bonded into slitsrdquoCementand Concrete Composites vol 27 no 4 pp 471ndash480 2005
[35] S H Kim H K Cho H W Bae and H S Park ldquoReliabilityevaluation of structures-a case of reinforced concrete buildingsunder dead live and wind loadsrdquo Technical Report KoreaInstitute of Construction Technology 1989 (Korean)
[36] J G MacGregor ldquoLoad and resistance factors for concretedesignrdquo Journal of the American Concrete Institute vol 80 no4 pp 279ndash287 1983
[37] J M Kulicki D R Mertz and W G Wassef ldquoLRFD Designof highway bridgesrdquo NHI Course 13061 Federal HighwayAdministration Washington DC USA 1994
[38] AASHTO Bridge Design Practice American Association ofState Highway and Transportation Officials Washington DCUSA 2011
[39] A S Nowak and A M Rakoczy ldquoReliability-based calibrationof design code for concrete structures (ACI 318)rdquo in Proceeding
of the Anais do 54 Congress Brasileiro do Concreto CBC2012-54CBC pp 1ndash12 2012
Figure 1 Standard train load in Korea (LS-18 LS-22)
the strengthening guideline such as a strengthening ratioby applying a probabilistic and reliability analysis Thisis important because of the uncertainty for material andstructural point of view on the FRP strengthening methodA parametric study of GFRP rebar for design factors suchas cross-sectional dimension GFRP and concrete strength[10] is conducted Another research is carried out a reli-ability assessment of an FRP-strengthened concrete beamby Chinese codes [11] A parametric study on the effects ofinfluencing factors on average reliability level shows that loadeffect ratio and concrete strength are the first two dominantinfluencing factors among all design variables For designconcepts the conventional ultimate strength design (USD)method is changed to limit state design after 2015 in KoreaTherefore safety and reliability for all structures will beregarded widely as well as the strengthening of concretestructures
This study aims to propose the reliability-based determi-nation procedure on the strengthening ratio of a deterioratedconcrete girder with CFRP strips which has advantages forthe full composite performance with concrete members Thetarget bridge in this study is a double T-beam railway bridgeoriginally designed by LS-18 (an old type of design load fora railway bridge in Korea) Therefore it is required that thetarget bridge should satisfy the present design load (LS-22)and enhance the design speed with the high speed era in thefuture In order to assess the optimal strengthening ratio forthe target bridge in this study the CFRP strip strengtheningmethod was analytically applied to the target bridge
NSM strengthening technique is more effective forenhancing flexural capacity of railway bridge in case vibrationof train traffic due to its superior bond performance Thegoal of this study was to calculate the reliability-basedstrengthening ratio of the concrete beams strengthened byNSM using CFRP strips by applying the reliability indexfor bridge design FE analysis on the deteriorated and thenstrengthened bridge was performed using the design railwayload in the Korea railway specification FEM analysis wasalso used to estimate the amount of steel reinforcements ofthe target bridge due to the absence of structural designinformation of this aged bridge To consider the structural
uncertainties of the strengthening method the probabilityand reliability analysis were performed with Monte Carlosimulation (MCS) Finally the reliability-based strengthen-ing ratio which satisfies the reliability index for the structuraldesign (120573 = 35) is estimated with the structural redundancyfor the target design strength Finally it is suggested thatthe strengthening procedure of the applied probabilistic andreliability approach is a reasonable strengthening designmethod
2 Estimation of the Unknown Property ofTarget Bridge
The target bridge is a simply supported railway bridge inKorea which was built for the design load of LS-18 in 1982 InDesign Specification of Railway ofKorea [15] standard designload is categorized as LS-18 restricted to 120 kmhr and LS-22for high speed railway as depicted in Figure 1 Actual speedand dynamic behavior on the LS-18 train weremonitored andanalyzed by [16]
Figures 2 and 3 show the typical cross-section andlongitudinal view of the RC T bridge
There are some recent diagnosis techniques [17ndash19] Forthis bridge conventional inspection method was appliedSome of deterioration defects such as cracks efflorescencesteel corrosion and concrete segregation were visualized byinspection Whereas the compressive strength of concrete is408MPa the strength of steel rebar is not verified from thefield inspection
To evaluate the requirement of strengthening amount aload-carrying capacity or flexural stiffness for the structuralcondition in service mode should be investigated Due tothe characteristics of this railway bridge dynamic tests forstructural evaluation were performed using in-field moni-toring data for the train loads passing the target point [16]with structural stiffness as the main indicator of structuralcondition For this acceleration data was monitored andcompared with an RC bridge with a similar span length andsize According to Hwang et al [16] the acceleration of thetarget bridge was shown to be over 04 g (1 g is 980 cms2 gal)
Mathematical Problems in Engineering 3
Waterproof mortar
540420350 1520 100 20
8020 2070 7080 80
260
1515
1025
135
95
CL
Figure 2 A cross-section of the target bridge (unit m)
B(T) Haseo-cheon
Centrifugalreinforced
concrete pileempty 300 times 900
FL
H middot W middot L = 10645
L middot W middot L = 10445
Mokpo direction
Centrifugalreinforced
concrete pileempty 400 times 1000
Daejeondirection
900 900 900 900122 122 1223956
250
140
300
120
90times4
(Southbound lane) 108 km 13
680 L
=3956
Figure 3 A longitudinal view of the target bridge
when the train passed In Europe it is recommended thatthe acceleration should be under 035 g for the preventionof turbulence on the railway in service [20 21] Thus high-level acceleration in service is considered proof of structuralperformance degradation and the appropriate strengtheningmeans to satisfy the serviceability limit are required Tosolve the vibration problem strengthening by FRP compositecan enhance the structural stiffness [22 23] For anotherstrengthening need structural condition was recorded asC-grade after an in-depth inspection conducted in 2003[24] During the bridgersquos 30 years of service time structuralmaterials such as concrete and steel reinforcement havepossibly deteriorated Therefore the target bridge should betreated with structural upgrade maintenance In this studyFRP strip strengthening of the deteriorated target bridge
is an effective strategy and the strengthening ratiomdashthemost significant factor for the strengthening designmdashwillbe suggested through a reliability analysis of material andstructural uncertainties using a reliability index
To assess the amount of adequate strengthening ratio tosatisfy the requirement the unknown reinforcement ratio ofsteel rebar should be reasonably estimated Structural analysison the target bridge without the steel rebar was initiallyperformed to calculate external flexuralmoment subjected byLS-18 design loadsThe structuralmodeling and analysis wereconducted by commercial FEA program [25] The bridgemodel was built by plate and solid elements the dead load likegravel rail was excepted Figure 4 shows the analysis resultsof external flexural moments for dead and live loads Thedesign load factors for dead and live loads were based on the
4 Mathematical Problems in Engineering
MIDASCivilPostprocessorBeam forceMoment-120574
179960e + 002
160096e + 002
122768e + 002
141032e + 002
103703e + 002
046392e + 001
655749e + 001
465107e + 001
274455e + 001
000000e + 000
minus106820e + 001
minus297452e + 001
Scale factor =40289E + 002
CB dead allMax 0Min 26File railroadUnit kNmiddotm
X minus0516Y minus0766Z 0383
View-directionDate 4132012
(a) Bending moment diagram for a factored dead loadMIDASCivilPostprocessorBeam forceMoment-120574
Scale factor =
Max 10Min 3File railroadUnit kNmiddotm
X minus0516Y minus0766Z 0383
View-direction
500095e + 002
514061e + 002
447227e + 002
300393e + 002
313559e + 002
246725e + 002
179891e + 002
112057e + 002
462233e + 001
000000e + 000
minus874446e + 001
minus154279e + 002
119743E + 002Ctall live all
Date 4132012
(b) Bending moment diagram for a factored live load
Figure 4 FE analyses for dead and live loads
design specification of railway of Korea and were 14 and 20respectively
The design flexural moment by FE analysis was calculatedas 7610 kNsdotm With this moment capacity the area of steelrebar can be estimated as 1718mm2 by the moment equi-librium equation for the rectangular beam with an effectivewidth of slab
3 Limit State Function and Safety Index
31 Limit State Function The conventional performancefunction for flexural capacity of the bridge cross-sectionconsists of 119877119863 and 119871 where 119877 is strength resistance or loadcarrying capacity119863 is dead load effect and119871 is live load effectincluding impact [26] For consideration of the limit state thelimit state model to express railway by Cho et al [27] wasadapted and followed as
119892 (sdot) = 119877 minus (119878119863+ 119878119871) (1)
where 119877 is structural resistance and 119878119863and 119878119871are dead and
live load effect respectively 119877 119878119863 and 119878
where 119877119899is estimated nominal strength of undamaged
structures (flexural moment or shear force) 119863119865is damage
coefficient 119873119877is uncertain parameter when 119877
119873and 119863
119865are
estimated119862119863and119862
119871are the effect factor of flexural moment
and shear force for dead and live loads 119863119899and 119871
119899are the
nominal dead and live loads respectively 119870119878is the response
ratio (CalculationMeasure) 119894 is the impact factor and 119873119863
and119873119871are the calibration factors of 119862
119863and 119862
119871 respectively
119873119877can be calculated by PsdotMsdotFsdotD P for uncertainties of
estimation for analytical modelM formaterial strength F forfabrication andD for damage factors In this study structural
Mathematical Problems in Engineering 5
h d2 d1
d998400
be
c
120576s120576f
120576998400c
120576cu
fsff
Cc
C998400s
085f998400c
1205731c
Figure 5 Compatibility diagram of strain and strength of the cross-section for strengthening
failure denotes the state when the theoretical flexural capacityis reached Failure occurs if the function119892 is less than or equalto zero
As depicted in Figure 5 the resistancemoment (119872119899) used
in this reliability analysis is calculated by (3) to (6) accordingto the recommendations from ACI Committee 440 [28] andBank [29] In this study the damage factor 119863
of concrete (41MPa) and 119887119890is effective width of rectangular
beam (1900mm) 119863119891means the damage factor assumed in
the reliability analysis (Table 4)In the case of failure mode of a concrete beam externally
bonded with CFRP materials except in a premature failurecase the following four failure modes are classified represen-tatively
(1) steel yielding and concrete compressive failure beforeCFRP rupture
(2) steel yielding and CFRP rupture after concrete com-pressive failure
(3) CFRP rupture and concrete compressive failurebefore steel yielding
(4) concrete compressive failure before steel yielding andCFRP rupture
Among the Cases 1sim4 Cases 3 and 4 are typicaloverstrengthening failure which leads to brittle failure ofstrengthening beams Cases 1 and 2 however would resultin ductile failure rather than that of Cases 3 and 4 For rea-sonable failure cases Case 1) is more suitable for preventingthe brittle failure because concrete compressive failure is lessbrittle than that of CFRP strip Balanced failure means thata strengthened concrete member fails simultaneously withconcrete compressive failure and CFRP rupture
Structural safety can be conveniently calculated withrespect to the reliability index 120573 as follows
120573 =120583119892
120590119892
(7)
The variables 120583119892and 120590
119892are the terms of the mean and stan-
dard deviation of the performance function 119892 respectivelyThe reliability index for flexural capacity after strengtheningis calculated based on the effective cross-section of the targetbridge with the amount of CFRP strip required to satisfy thestrength for NSM strengthening In this study the reliabilityindex is computed by the Rackwitz-Fiessler algorithm [30]
32 Computational Uncertainty Factors (119870119904) The computa-
tional uncertainties 119870119904 are adapted to be considered in pre-
dicting resistance The statistics for randomness are definedbased on analytical results or test results Some analytical andtest results are introduced by a literature review of previousresearch papers for reliability analysis [10] In this study itis assumed that statistics of the computational uncertaintyfactor in concrete crushing mode are effective to estimatethe strengthening ratio by reliability analysisThus from datafrom a total of 91 specimens 1061 of mean value and 009 ofstandard deviation resulted The following equation denotesthe computational uncertainties in this analysis
119870119904=119872119880exp
119872119880pre
(8)
33 Damage Factor Cho et al [31] have theoretically definedthat the damage factor is the ratio of stiffness for a non-damaged structure to a damaged structure For quantitative
6 Mathematical Problems in Engineering
Select the target structure forNSM strengthening
Constitute the limit state function
Calculate the external moment
Define of material and structural uncertainty
Calculate the resistance moment and perform reliability analysis
Determine the strengthening ratio of CFRP strip
Reassuming the CFRP
strengthening ratio
No
Yes
120573 = 35
Figure 6 A procedure for determining the reliability-based strengthening ratio of CFRP strip with a target reliability index of 35
approaches it can be calculated by using the ratio of powerof natural frequency for a damaged structure to that fora nondamaged structure In actual state however it is notasserted that this ratio can directly represent the degreeof damage Estimating the damage factor is hard to bedetermined without the plentiful history data so that thedamage factor in this study is assumed by previous research[29] Therefore the average of damage factor is ranged from06 to 09 anduncertainty of damage factor is considered from01 to 03 of coefficient of variation With this statistical datathe probability and reliability analysis are carried out and aresult of sensitive analysis for the variation of damage factoris discussed
4 Characteristics of Random Variables
For reliability analyses the statistics of random variables aredefined in advance There are three variables considered inthis analysis external load for dead and live ones materialstrength of concrete steel rebar and CFRP strip and designof cross-section
In the reliability analysis for structural safety it is essentialthat the load effect must be considered by combining thevariability of loads dead and live loads A related study wasconducted and suggested the load and resistance factors forRC concrete design [32] Table 1 shows the statistics of theload effect for dead and live load for reliability analysis [33]Among these mean value is the external moment resulting
from FE analysis to the target bridge and load factor is basedon the KR specification
The statistics of resistance-related variables such as 1198911015840119888 ℎ
and 119889 listed in Table 2 are adopted from Ellingwood [32]Also included in Table 2 are the statistics of the strength ofCFRP strip (119891fu) for Barros and Fortes [34] and of the width(119887) of T-beam for Oh et al [13] In the case of the nominalvalue of ℎ and 119889 the real dimension of the cross section inthe target bridge is used For steel rebar statistics from manyof tensile tests are summarized in Table 3 [35] As comparedwith Grade series by ASTM A 165 SD30 SD35 and SD40rebar considered in the reliability analysis showed relativelybetter coefficient of variation The probability distributionwas considered as normal type In this study statistics ofSD40 in Korea were adopted in reliability analysis
5 Reliability-Based Strengthening Ratio ofCFRP Strip
51 Target Safety Index in Reliability Analysis This studyis to calculate the reliability-based strengthening ratio ofCFRP strip to the existing railway bridge which has struc-tural uncertainties Therefore it is important to define howmuch structural safety should be acquired This is simplydetermined by using the reliability index or the target safetyfactor 120573 in the load and resistance analysis Previous studyhas shown that 120573 values of 25sim30 and 30sim35 were used
Mathematical Problems in Engineering 7
Table 1 Result of FEM analysis for external railway load
Probability distribution MeanNominal Mean COVa Load factorDead load Normal 105 1800 kNsdotm 01 14Live load Lognormal 100 5808 kNsdotm 02ndash04 20aCOV coefficient of variation
Table 2 Statistics of random design variables (I)
Design variable Nominal value Mean value Standard deviation Probability distribution119891119888
1015840 (MPa) 4134 4616 194 Normal119891fu (MPa)a mdash 2790 857 Normal119887 (mm)b 1900 119887 + 094 60 Normalℎ (mm)c 1250 ℎ minus 305 635 Normal119889 (mm)c 1200 119889 minus 470 1270 NormalaISO 527-3 (1997)[12] bOh et al (1993) [13] ccross-sectional dimension of the target bridge
Table 3 Statistics of random design variables (II)
MeanNominal COV Average strength Number of data Standard deviation Probability distributionSD 30a 120 0064 3600 822 2304 NormalSD 35a 113 0038 3955 80 1503 NormalSD 40a 109 0048 4360 773 2093 NormalGrade 40b 113 0116 3170 mdash 3672 NormalGrade 60b 112 0098 4725 mdash 4631 NormalaKS D 3504bASTM A 615 Standard Specification for Deformed and Plain Carbon Steel Bars for Concrete Reinforcement-AASHTO No M 31 [14]
for tension failure and compression failure respectively [36]Kulicki et al [37] proposed the target or code-specifiedreliability indices obtained from reliability analysis of a groupof 175 existing actual bridges designed by either ASD or LFDmethod and then suggested the range of values using the newload and resistance factors From this research AASHTOaltered the reliability index to 35 when either a higher levelof safety or taking more risk was appropriate [38] Accordingto the recent research [39] the target beta for beam is 35for flexural strength of RC beams constructed with lightweight and normal weight concrete In this study the targetreliability index is determined with 35 and a reliability-basedstrengthening ratio satisfying the probability index 120573 = 35will be calculated
52 Result of Reliability Analysis To evaluate the reliability-based strengthening ratio of the target bridge the probabilitydistribution between the external load and structural resis-tance from the limit state function was analyzed A safetymargin was used and 120573
119879= 35 of target reliability index was
specified by AASHTO [38] Figure 6 is a process to calculatestrengthening ratio of CFRP strip by reliability analysis witha reliability index of 35 FEM analysis should be conductedto determine the external moment for dead and live loadsStructural resistance is affected as when strengthening ratioof CFRP strip is variedTherefore iteration process is neededuntil safety margin of 35 of the strengthening bridge againstexternal load is acquired
0
00005
0001
00015
0002
00025
0003
00035
0004
00045
Prob
abili
ty d
ensit
y
0 500 1000 1500 2000 2500 3000Flexural moment (kNmiddotm)
Q(LS-18)Q(LS-22)R for LS-18Case1 (120588cfrp = 00001)
Figure 7 Probability distribution curves for external load andresistance
Figure 7 is the probability distribution curves for externalload and resistance resulted from the reliability analysisFor external loads the probability distribution of LS-22was additionally considered to investigate the how muchthe strengthening effect of CFRP strips can decrease theprobability of failure compared LS-22 design load 119876 meansthe external load and 119877 is for the resistance moment
8 Mathematical Problems in Engineering
Table 4 Sensitive analysis for damage factor standard deviation of damage factor and live load effect
Degree of sensitive for COV of Degree of sensitive for COV of live load factorDegree of sensitive for average value of
120588cf
rp
Df
Df
Figure 9 Sensitive analysis for COV and average value of 119863119891and
COV of live load factor
Strengthening effect is denoted as a case series FEM analysiswas performed to calculate the external moment for LS-18and LS-22 design railway load For probability distribution ofLS-22 which is the present design load of railway in Korea
probability characteristics for LS-18 were used in the sameway In order to acquire the reliability-based strengtheningratio for 120573
119879= 35 the range of probability parameters was
roughly considered then the final 5 cases for 120588cfrp from 00001to 000013 were analyzed Each probability distribution curveis illustrated in Figure 7 Figure 8 is the result of reliability-based strengthening ratio According to the result of thestrengthening effect by probability distribution the targetbridge strengthened by the CFRP strip strengthening ratioresulting from the reliability analysis could be sufficientlysafe against the LS-22 present design railway load As thestrengthening ratio of CFRP strip that could satisfy 120573
119879= 35
it was with 120588cfrp = 0000114
53 Sensitive Analysis for Three Important ParametersFigure 9 shows the result of sensitive analysis for three param-eters such as damage factor standard deviation of damagefactor and live load effect The CFRP strip strengtheningratio resulting from the reliability analysis is plotted withthree important parameters The purpose of this process isto identify how sensitively the strengthening ratio will beaffected when the three parameters are varied independentlyThe determination of the variation ranges of the parameterswas considered to simply but effectively apply the sensitivecharacteristics For live loads and damage factor there weresimilar degrees of sensitivity Variation of COV of damagefactor however was more sensitive than that of the otherparameters Itmight be concluded that COVof damage factorlargely affected to estimate the reliability-based strengtheningusing about the CFRP strip For more reliable estimation ofdamage factor many of structural diagnosis data should beanalyzed in future Table 4 summarizes the input parametersused in the sensitive analysis
6 Conclusions
This study suggested the reliability-based strengthening ratiofor 30-year-old railway bridge using CFRP strips Conclu-sions are as follows
(1) In previous strengthening schemes it has beenuncertain to determine how much the strengthen-ing effect should be required The methodology forthe reliability-based strengthening ratio can improve
Mathematical Problems in Engineering 9
these problems of the previous strengtheningmethodThe target reliability index for CFRP strip strengthen-ing is considered as 35 according to AASHTO spec-ification As using the reliability-based strengtheningratio in this studymore effective strengthening designto concrete structure having a specified strength-ening target as well as reflecting the structural andmaterial uncertainties is possible
(2) In the result of a sensitive analysis variation of COVfor damage factor mostly affected to the reliability-based strengthening ratio of CFRP strip Thereforedamage factor should be studied more properly onthe target bridge This may be possible by analyzingthe database for long-term safety inspection historyand its reasonable quantification Stabilization andnormalization processes of the damage factor are alsorequired
(3) One of the important factors for determining thesafety margin against the resistance is external loadeffect In order to improve the reliability-basedstrengthening ratio of CFRP strip in this study uncer-tainties for external load of a railway bridge should beanalytically and experimentally verified This can besolved by analyzing the acquired data from long-termmonitoring then the reliability of the strengtheningratio of CFRP strip will be promoted
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by Korea Institute of EnergyTechnology Evaluation and Planning (0000000015513) andResearch grant from Gyeongnam National University ofScience and Technology
References
[1] FHWA Bridge Programs NBI data 2009 httpwwwfhwadotgovbridgenbi
[2] ACI Committee 440 Guide for the Design and Constructionof Externally Bonded FRP Systems for Strengthening Con-crete Structures (ACI 4402R-08) American Concrete InstituteFarmington Hills Mich USA 2008
[3] J M de Sena Cruz and J A O De Barros ldquoBond between near-surface mounted carbon-fiber-reinforced polymer laminatestrips and concreterdquo Journal of Composites for Construction vol8 no 6 pp 519ndash527 2004
[4] T Hassan and S Rizkalla ldquoInvestigation of bond in concretestructures strengthened with near surface mounted carbonfiber reinforced polymer stripsrdquo Journal of Composites forConstruction vol 7 no 3 pp 248ndash257 2003
[5] S M Soliman E El-Salakawy and B Benmokrane ldquoFlexuralbehavior of concrete beams strengthened with near surfacemounted FRP barsrdquo in Proceedings of 4th International confer-ence on FRP composites in civil engineering (CICE rsquo08) 2008
[6] J P Firmo J R Correia and P Franca ldquoFire behaviour ofreinforced concrete beams strengthened with CFRP laminatesprotection systems with insulation of the anchorage zonesrdquoComposites Part B Engineering vol 43 no 3 pp 1545ndash15562012
[7] S M Soliman E El-Salakawy and B Benmokrane ldquoBondperformance of near-surface-mounted FRP barsrdquo Journal ofComposites for Construction vol 15 no 1 pp 103ndash111 2011
[8] THassan and S Rizkalla ldquoFlexural strengthening of prestressedbridge slabs with FRP systemsrdquo PCI Journal vol 47 no 1 pp76ndash93 2002
[9] J R Yost S P Gross and D W Dinehart ldquoNear surfacemounted CFRP reinforcement for structural retrofit of concreteflexural membersrdquo in Proceedings of the 4th InternationalConference on Advanced Composite Materials in Bridges andStructures Calgary Canada 2004
[10] Z He and F Qiu ldquoProbabilistic assessment on flexural capacityof GFRP-reinforced concrete beams designed by guideline ACI4401R-06rdquo Construction and Building Materials vol 25 no 4pp 1663ndash1670 2011
[11] Z He and L Jiang ldquoFlexural reliability assessment of FRP-strengthened reinforced concrete beams designed by ChineseCECS-146 Guidelinerdquo Pacific Science Review vol 9 no 1 pp123ndash133 2007
[12] International Organization for Standardization ldquoDetermina-tion of tensile properties-part 5 test conditions for unidirec-tional fibre reinforced plastic compositesrdquo ISO 527-5 Interna-tional Organization for Standardization Geneva Switzerland1997
[13] B H Oh C K Koh S W Baik H J Lee and S H HanldquoRealistic reliability analysis of reinforced concrete structuresrdquoJournal of Korea Society of Civil Engineering vol 13 no 2 pp121ndash133 1993 (Korean)
[14] Steel bars for concrete reinforcement KS D 3504 KoreanIndustrial Standards 2011 (Korean)
[15] KR Network Design Specification of Railway Railway BridgeKorea Rail Network Authority Seoul Republic of Korea 2004(Korean)
[16] S K Hwang J T Oh J S Lee et al Performance Enhancementof Railway System-Track amp Civil Development of the DesignSpecification for Improving Dynamic Characteristics of RailwayBridges Korea Railway Research Institute Seoul Republic ofKorea 2003 (Korean)
[17] H S Shang T H Yi and L S Yang ldquoExperimental studyon the compressive strength of big mobility concrete withnondestructive testing methodrdquo Advances in Materials Scienceand Engineering vol 2012 Article ID 345214 6 pages 2012
[18] TH YiHN Li andHM Sun ldquoMulti-stage structural damagediagnosis method based on ldquoenergy-damagerdquo theoryrdquo SmartStructures And Systems vol 12 no 3-4 pp 345ndash361 2013
[19] H S Shang T H Yi and X X Guo ldquoStudy on strength andultrasonic of air-entrained concrete and plain concrete in coldenvironmentrdquo Advances in Materials Science and Engineeringvol 2014 Article ID 706986 7 pages 2014
[20] Korea High Speed Rail Construction Authority (KHRC)ldquoBridge designmanual (BRDM)rdquo Technical Report KoreaHighSpeed Rail Construction Authority (KHRC) Pusan Public ofKorea 1995 (Korean)
[21] International Union of Railway UIC Code 776-1R Loads to BeConsidered in Railway Bridge Design International Union ofRailway Paris France 4th edition 1994
10 Mathematical Problems in Engineering
[22] M Abdessemed S Kenai A Bali and A Kibboua ldquoDynamicanalysis of a bridge repaired by CFRP experimental andnumerical modellingrdquoConstruction and BuildingMaterials vol25 no 3 pp 1270ndash1276 2011
[23] G Zanardo H Hao Y Xia and A J Deeks ldquoStiffness assess-ment through modal analysis of an RC slab bridge before andafter strengtheningrdquo Journal of Bridge Engineering vol 11 no 5pp 590ndash601 2006
[24] Korea Infrastructure Safety and Technology corporation(KISTEC) A Database of Maintenance History KoreaInfrastructure Safety and Technology corporation (KISTEC)Gyeonggi-do Republic of Korea 2003 (Korean)
[25] MIDAS IT MIDAS Civil Program Manual MIDAS ITGyeonggi Republic of Korea 2009
[26] S W Tabsh and A S Nowak ldquoReliability of highway girderbridgesrdquo Journal of Structural Engineering ASCE vol 117 no 8pp 2372ndash2388 1991
[27] H N Cho K H Kwak and S J Lee ldquoReliability-based safetyand capacity evaluation of high-speed railway bridgesrdquo Journalof Computational Structural Engineering Institute in KoreaCOSEIK vol 10 no 3 pp 133ndash143 1997 (Korean)
[28] ACI Committee 440 Guide for the Design and Constructionof Externally Bonded FRP Systems for Strengthening ConcreteStructures American Concrete Institute Farmington HillsMich USA 2008
[29] L C Bank Composites for Construction-Structural Design withFRP Materials John Wiley amp Sons New York NY USA 2006
[30] R Rackwitz and B Flessler ldquoStructural reliability under com-bined random load sequencesrdquo Computers and Structures vol9 no 5 pp 489ndash494 1978
[31] H N Cho H H Choi S Y Lee and J W Sun ldquoMethodologyfor reliability-based assessment of capacity-rating of plate girderrailway bridges using ambient measurement datardquo Journal ofKorea Society of Steel Construction vol 15 no 2 pp 187ndash1962003 (Korean)
[32] B Ellingwood Reliability Bases of Load and Resistance Factorsfor Reinforced Concrete Design National Bureau of StandardsBuilding Science Series 110 Washington DC USA 1978
[33] US Department of CommreceNational Bureau of StandardsldquoDevelopment of a probability based load criteria for Amer-ican National Standard A58rdquo NBS Special Publication 577US Department of CommreceNational Bureau of StandardsGaithersburg Md USA 1980
[34] J A O Barros and A S Fortes ldquoFlexural strengthening ofconcrete beamswithCFRP laminates bonded into slitsrdquoCementand Concrete Composites vol 27 no 4 pp 471ndash480 2005
[35] S H Kim H K Cho H W Bae and H S Park ldquoReliabilityevaluation of structures-a case of reinforced concrete buildingsunder dead live and wind loadsrdquo Technical Report KoreaInstitute of Construction Technology 1989 (Korean)
[36] J G MacGregor ldquoLoad and resistance factors for concretedesignrdquo Journal of the American Concrete Institute vol 80 no4 pp 279ndash287 1983
[37] J M Kulicki D R Mertz and W G Wassef ldquoLRFD Designof highway bridgesrdquo NHI Course 13061 Federal HighwayAdministration Washington DC USA 1994
[38] AASHTO Bridge Design Practice American Association ofState Highway and Transportation Officials Washington DCUSA 2011
[39] A S Nowak and A M Rakoczy ldquoReliability-based calibrationof design code for concrete structures (ACI 318)rdquo in Proceeding
of the Anais do 54 Congress Brasileiro do Concreto CBC2012-54CBC pp 1ndash12 2012
Figure 2 A cross-section of the target bridge (unit m)
B(T) Haseo-cheon
Centrifugalreinforced
concrete pileempty 300 times 900
FL
H middot W middot L = 10645
L middot W middot L = 10445
Mokpo direction
Centrifugalreinforced
concrete pileempty 400 times 1000
Daejeondirection
900 900 900 900122 122 1223956
250
140
300
120
90times4
(Southbound lane) 108 km 13
680 L
=3956
Figure 3 A longitudinal view of the target bridge
when the train passed In Europe it is recommended thatthe acceleration should be under 035 g for the preventionof turbulence on the railway in service [20 21] Thus high-level acceleration in service is considered proof of structuralperformance degradation and the appropriate strengtheningmeans to satisfy the serviceability limit are required Tosolve the vibration problem strengthening by FRP compositecan enhance the structural stiffness [22 23] For anotherstrengthening need structural condition was recorded asC-grade after an in-depth inspection conducted in 2003[24] During the bridgersquos 30 years of service time structuralmaterials such as concrete and steel reinforcement havepossibly deteriorated Therefore the target bridge should betreated with structural upgrade maintenance In this studyFRP strip strengthening of the deteriorated target bridge
is an effective strategy and the strengthening ratiomdashthemost significant factor for the strengthening designmdashwillbe suggested through a reliability analysis of material andstructural uncertainties using a reliability index
To assess the amount of adequate strengthening ratio tosatisfy the requirement the unknown reinforcement ratio ofsteel rebar should be reasonably estimated Structural analysison the target bridge without the steel rebar was initiallyperformed to calculate external flexuralmoment subjected byLS-18 design loadsThe structuralmodeling and analysis wereconducted by commercial FEA program [25] The bridgemodel was built by plate and solid elements the dead load likegravel rail was excepted Figure 4 shows the analysis resultsof external flexural moments for dead and live loads Thedesign load factors for dead and live loads were based on the
4 Mathematical Problems in Engineering
MIDASCivilPostprocessorBeam forceMoment-120574
179960e + 002
160096e + 002
122768e + 002
141032e + 002
103703e + 002
046392e + 001
655749e + 001
465107e + 001
274455e + 001
000000e + 000
minus106820e + 001
minus297452e + 001
Scale factor =40289E + 002
CB dead allMax 0Min 26File railroadUnit kNmiddotm
X minus0516Y minus0766Z 0383
View-directionDate 4132012
(a) Bending moment diagram for a factored dead loadMIDASCivilPostprocessorBeam forceMoment-120574
Scale factor =
Max 10Min 3File railroadUnit kNmiddotm
X minus0516Y minus0766Z 0383
View-direction
500095e + 002
514061e + 002
447227e + 002
300393e + 002
313559e + 002
246725e + 002
179891e + 002
112057e + 002
462233e + 001
000000e + 000
minus874446e + 001
minus154279e + 002
119743E + 002Ctall live all
Date 4132012
(b) Bending moment diagram for a factored live load
Figure 4 FE analyses for dead and live loads
design specification of railway of Korea and were 14 and 20respectively
The design flexural moment by FE analysis was calculatedas 7610 kNsdotm With this moment capacity the area of steelrebar can be estimated as 1718mm2 by the moment equi-librium equation for the rectangular beam with an effectivewidth of slab
3 Limit State Function and Safety Index
31 Limit State Function The conventional performancefunction for flexural capacity of the bridge cross-sectionconsists of 119877119863 and 119871 where 119877 is strength resistance or loadcarrying capacity119863 is dead load effect and119871 is live load effectincluding impact [26] For consideration of the limit state thelimit state model to express railway by Cho et al [27] wasadapted and followed as
119892 (sdot) = 119877 minus (119878119863+ 119878119871) (1)
where 119877 is structural resistance and 119878119863and 119878119871are dead and
live load effect respectively 119877 119878119863 and 119878
where 119877119899is estimated nominal strength of undamaged
structures (flexural moment or shear force) 119863119865is damage
coefficient 119873119877is uncertain parameter when 119877
119873and 119863
119865are
estimated119862119863and119862
119871are the effect factor of flexural moment
and shear force for dead and live loads 119863119899and 119871
119899are the
nominal dead and live loads respectively 119870119878is the response
ratio (CalculationMeasure) 119894 is the impact factor and 119873119863
and119873119871are the calibration factors of 119862
119863and 119862
119871 respectively
119873119877can be calculated by PsdotMsdotFsdotD P for uncertainties of
estimation for analytical modelM formaterial strength F forfabrication andD for damage factors In this study structural
Mathematical Problems in Engineering 5
h d2 d1
d998400
be
c
120576s120576f
120576998400c
120576cu
fsff
Cc
C998400s
085f998400c
1205731c
Figure 5 Compatibility diagram of strain and strength of the cross-section for strengthening
failure denotes the state when the theoretical flexural capacityis reached Failure occurs if the function119892 is less than or equalto zero
As depicted in Figure 5 the resistancemoment (119872119899) used
in this reliability analysis is calculated by (3) to (6) accordingto the recommendations from ACI Committee 440 [28] andBank [29] In this study the damage factor 119863
of concrete (41MPa) and 119887119890is effective width of rectangular
beam (1900mm) 119863119891means the damage factor assumed in
the reliability analysis (Table 4)In the case of failure mode of a concrete beam externally
bonded with CFRP materials except in a premature failurecase the following four failure modes are classified represen-tatively
(1) steel yielding and concrete compressive failure beforeCFRP rupture
(2) steel yielding and CFRP rupture after concrete com-pressive failure
(3) CFRP rupture and concrete compressive failurebefore steel yielding
(4) concrete compressive failure before steel yielding andCFRP rupture
Among the Cases 1sim4 Cases 3 and 4 are typicaloverstrengthening failure which leads to brittle failure ofstrengthening beams Cases 1 and 2 however would resultin ductile failure rather than that of Cases 3 and 4 For rea-sonable failure cases Case 1) is more suitable for preventingthe brittle failure because concrete compressive failure is lessbrittle than that of CFRP strip Balanced failure means thata strengthened concrete member fails simultaneously withconcrete compressive failure and CFRP rupture
Structural safety can be conveniently calculated withrespect to the reliability index 120573 as follows
120573 =120583119892
120590119892
(7)
The variables 120583119892and 120590
119892are the terms of the mean and stan-
dard deviation of the performance function 119892 respectivelyThe reliability index for flexural capacity after strengtheningis calculated based on the effective cross-section of the targetbridge with the amount of CFRP strip required to satisfy thestrength for NSM strengthening In this study the reliabilityindex is computed by the Rackwitz-Fiessler algorithm [30]
32 Computational Uncertainty Factors (119870119904) The computa-
tional uncertainties 119870119904 are adapted to be considered in pre-
dicting resistance The statistics for randomness are definedbased on analytical results or test results Some analytical andtest results are introduced by a literature review of previousresearch papers for reliability analysis [10] In this study itis assumed that statistics of the computational uncertaintyfactor in concrete crushing mode are effective to estimatethe strengthening ratio by reliability analysisThus from datafrom a total of 91 specimens 1061 of mean value and 009 ofstandard deviation resulted The following equation denotesthe computational uncertainties in this analysis
119870119904=119872119880exp
119872119880pre
(8)
33 Damage Factor Cho et al [31] have theoretically definedthat the damage factor is the ratio of stiffness for a non-damaged structure to a damaged structure For quantitative
6 Mathematical Problems in Engineering
Select the target structure forNSM strengthening
Constitute the limit state function
Calculate the external moment
Define of material and structural uncertainty
Calculate the resistance moment and perform reliability analysis
Determine the strengthening ratio of CFRP strip
Reassuming the CFRP
strengthening ratio
No
Yes
120573 = 35
Figure 6 A procedure for determining the reliability-based strengthening ratio of CFRP strip with a target reliability index of 35
approaches it can be calculated by using the ratio of powerof natural frequency for a damaged structure to that fora nondamaged structure In actual state however it is notasserted that this ratio can directly represent the degreeof damage Estimating the damage factor is hard to bedetermined without the plentiful history data so that thedamage factor in this study is assumed by previous research[29] Therefore the average of damage factor is ranged from06 to 09 anduncertainty of damage factor is considered from01 to 03 of coefficient of variation With this statistical datathe probability and reliability analysis are carried out and aresult of sensitive analysis for the variation of damage factoris discussed
4 Characteristics of Random Variables
For reliability analyses the statistics of random variables aredefined in advance There are three variables considered inthis analysis external load for dead and live ones materialstrength of concrete steel rebar and CFRP strip and designof cross-section
In the reliability analysis for structural safety it is essentialthat the load effect must be considered by combining thevariability of loads dead and live loads A related study wasconducted and suggested the load and resistance factors forRC concrete design [32] Table 1 shows the statistics of theload effect for dead and live load for reliability analysis [33]Among these mean value is the external moment resulting
from FE analysis to the target bridge and load factor is basedon the KR specification
The statistics of resistance-related variables such as 1198911015840119888 ℎ
and 119889 listed in Table 2 are adopted from Ellingwood [32]Also included in Table 2 are the statistics of the strength ofCFRP strip (119891fu) for Barros and Fortes [34] and of the width(119887) of T-beam for Oh et al [13] In the case of the nominalvalue of ℎ and 119889 the real dimension of the cross section inthe target bridge is used For steel rebar statistics from manyof tensile tests are summarized in Table 3 [35] As comparedwith Grade series by ASTM A 165 SD30 SD35 and SD40rebar considered in the reliability analysis showed relativelybetter coefficient of variation The probability distributionwas considered as normal type In this study statistics ofSD40 in Korea were adopted in reliability analysis
5 Reliability-Based Strengthening Ratio ofCFRP Strip
51 Target Safety Index in Reliability Analysis This studyis to calculate the reliability-based strengthening ratio ofCFRP strip to the existing railway bridge which has struc-tural uncertainties Therefore it is important to define howmuch structural safety should be acquired This is simplydetermined by using the reliability index or the target safetyfactor 120573 in the load and resistance analysis Previous studyhas shown that 120573 values of 25sim30 and 30sim35 were used
Mathematical Problems in Engineering 7
Table 1 Result of FEM analysis for external railway load
Probability distribution MeanNominal Mean COVa Load factorDead load Normal 105 1800 kNsdotm 01 14Live load Lognormal 100 5808 kNsdotm 02ndash04 20aCOV coefficient of variation
Table 2 Statistics of random design variables (I)
Design variable Nominal value Mean value Standard deviation Probability distribution119891119888
1015840 (MPa) 4134 4616 194 Normal119891fu (MPa)a mdash 2790 857 Normal119887 (mm)b 1900 119887 + 094 60 Normalℎ (mm)c 1250 ℎ minus 305 635 Normal119889 (mm)c 1200 119889 minus 470 1270 NormalaISO 527-3 (1997)[12] bOh et al (1993) [13] ccross-sectional dimension of the target bridge
Table 3 Statistics of random design variables (II)
MeanNominal COV Average strength Number of data Standard deviation Probability distributionSD 30a 120 0064 3600 822 2304 NormalSD 35a 113 0038 3955 80 1503 NormalSD 40a 109 0048 4360 773 2093 NormalGrade 40b 113 0116 3170 mdash 3672 NormalGrade 60b 112 0098 4725 mdash 4631 NormalaKS D 3504bASTM A 615 Standard Specification for Deformed and Plain Carbon Steel Bars for Concrete Reinforcement-AASHTO No M 31 [14]
for tension failure and compression failure respectively [36]Kulicki et al [37] proposed the target or code-specifiedreliability indices obtained from reliability analysis of a groupof 175 existing actual bridges designed by either ASD or LFDmethod and then suggested the range of values using the newload and resistance factors From this research AASHTOaltered the reliability index to 35 when either a higher levelof safety or taking more risk was appropriate [38] Accordingto the recent research [39] the target beta for beam is 35for flexural strength of RC beams constructed with lightweight and normal weight concrete In this study the targetreliability index is determined with 35 and a reliability-basedstrengthening ratio satisfying the probability index 120573 = 35will be calculated
52 Result of Reliability Analysis To evaluate the reliability-based strengthening ratio of the target bridge the probabilitydistribution between the external load and structural resis-tance from the limit state function was analyzed A safetymargin was used and 120573
119879= 35 of target reliability index was
specified by AASHTO [38] Figure 6 is a process to calculatestrengthening ratio of CFRP strip by reliability analysis witha reliability index of 35 FEM analysis should be conductedto determine the external moment for dead and live loadsStructural resistance is affected as when strengthening ratioof CFRP strip is variedTherefore iteration process is neededuntil safety margin of 35 of the strengthening bridge againstexternal load is acquired
0
00005
0001
00015
0002
00025
0003
00035
0004
00045
Prob
abili
ty d
ensit
y
0 500 1000 1500 2000 2500 3000Flexural moment (kNmiddotm)
Q(LS-18)Q(LS-22)R for LS-18Case1 (120588cfrp = 00001)
Figure 7 Probability distribution curves for external load andresistance
Figure 7 is the probability distribution curves for externalload and resistance resulted from the reliability analysisFor external loads the probability distribution of LS-22was additionally considered to investigate the how muchthe strengthening effect of CFRP strips can decrease theprobability of failure compared LS-22 design load 119876 meansthe external load and 119877 is for the resistance moment
8 Mathematical Problems in Engineering
Table 4 Sensitive analysis for damage factor standard deviation of damage factor and live load effect
Degree of sensitive for COV of Degree of sensitive for COV of live load factorDegree of sensitive for average value of
120588cf
rp
Df
Df
Figure 9 Sensitive analysis for COV and average value of 119863119891and
COV of live load factor
Strengthening effect is denoted as a case series FEM analysiswas performed to calculate the external moment for LS-18and LS-22 design railway load For probability distribution ofLS-22 which is the present design load of railway in Korea
probability characteristics for LS-18 were used in the sameway In order to acquire the reliability-based strengtheningratio for 120573
119879= 35 the range of probability parameters was
roughly considered then the final 5 cases for 120588cfrp from 00001to 000013 were analyzed Each probability distribution curveis illustrated in Figure 7 Figure 8 is the result of reliability-based strengthening ratio According to the result of thestrengthening effect by probability distribution the targetbridge strengthened by the CFRP strip strengthening ratioresulting from the reliability analysis could be sufficientlysafe against the LS-22 present design railway load As thestrengthening ratio of CFRP strip that could satisfy 120573
119879= 35
it was with 120588cfrp = 0000114
53 Sensitive Analysis for Three Important ParametersFigure 9 shows the result of sensitive analysis for three param-eters such as damage factor standard deviation of damagefactor and live load effect The CFRP strip strengtheningratio resulting from the reliability analysis is plotted withthree important parameters The purpose of this process isto identify how sensitively the strengthening ratio will beaffected when the three parameters are varied independentlyThe determination of the variation ranges of the parameterswas considered to simply but effectively apply the sensitivecharacteristics For live loads and damage factor there weresimilar degrees of sensitivity Variation of COV of damagefactor however was more sensitive than that of the otherparameters Itmight be concluded that COVof damage factorlargely affected to estimate the reliability-based strengtheningusing about the CFRP strip For more reliable estimation ofdamage factor many of structural diagnosis data should beanalyzed in future Table 4 summarizes the input parametersused in the sensitive analysis
6 Conclusions
This study suggested the reliability-based strengthening ratiofor 30-year-old railway bridge using CFRP strips Conclu-sions are as follows
(1) In previous strengthening schemes it has beenuncertain to determine how much the strengthen-ing effect should be required The methodology forthe reliability-based strengthening ratio can improve
Mathematical Problems in Engineering 9
these problems of the previous strengtheningmethodThe target reliability index for CFRP strip strengthen-ing is considered as 35 according to AASHTO spec-ification As using the reliability-based strengtheningratio in this studymore effective strengthening designto concrete structure having a specified strength-ening target as well as reflecting the structural andmaterial uncertainties is possible
(2) In the result of a sensitive analysis variation of COVfor damage factor mostly affected to the reliability-based strengthening ratio of CFRP strip Thereforedamage factor should be studied more properly onthe target bridge This may be possible by analyzingthe database for long-term safety inspection historyand its reasonable quantification Stabilization andnormalization processes of the damage factor are alsorequired
(3) One of the important factors for determining thesafety margin against the resistance is external loadeffect In order to improve the reliability-basedstrengthening ratio of CFRP strip in this study uncer-tainties for external load of a railway bridge should beanalytically and experimentally verified This can besolved by analyzing the acquired data from long-termmonitoring then the reliability of the strengtheningratio of CFRP strip will be promoted
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by Korea Institute of EnergyTechnology Evaluation and Planning (0000000015513) andResearch grant from Gyeongnam National University ofScience and Technology
References
[1] FHWA Bridge Programs NBI data 2009 httpwwwfhwadotgovbridgenbi
[2] ACI Committee 440 Guide for the Design and Constructionof Externally Bonded FRP Systems for Strengthening Con-crete Structures (ACI 4402R-08) American Concrete InstituteFarmington Hills Mich USA 2008
[3] J M de Sena Cruz and J A O De Barros ldquoBond between near-surface mounted carbon-fiber-reinforced polymer laminatestrips and concreterdquo Journal of Composites for Construction vol8 no 6 pp 519ndash527 2004
[4] T Hassan and S Rizkalla ldquoInvestigation of bond in concretestructures strengthened with near surface mounted carbonfiber reinforced polymer stripsrdquo Journal of Composites forConstruction vol 7 no 3 pp 248ndash257 2003
[5] S M Soliman E El-Salakawy and B Benmokrane ldquoFlexuralbehavior of concrete beams strengthened with near surfacemounted FRP barsrdquo in Proceedings of 4th International confer-ence on FRP composites in civil engineering (CICE rsquo08) 2008
[6] J P Firmo J R Correia and P Franca ldquoFire behaviour ofreinforced concrete beams strengthened with CFRP laminatesprotection systems with insulation of the anchorage zonesrdquoComposites Part B Engineering vol 43 no 3 pp 1545ndash15562012
[7] S M Soliman E El-Salakawy and B Benmokrane ldquoBondperformance of near-surface-mounted FRP barsrdquo Journal ofComposites for Construction vol 15 no 1 pp 103ndash111 2011
[8] THassan and S Rizkalla ldquoFlexural strengthening of prestressedbridge slabs with FRP systemsrdquo PCI Journal vol 47 no 1 pp76ndash93 2002
[9] J R Yost S P Gross and D W Dinehart ldquoNear surfacemounted CFRP reinforcement for structural retrofit of concreteflexural membersrdquo in Proceedings of the 4th InternationalConference on Advanced Composite Materials in Bridges andStructures Calgary Canada 2004
[10] Z He and F Qiu ldquoProbabilistic assessment on flexural capacityof GFRP-reinforced concrete beams designed by guideline ACI4401R-06rdquo Construction and Building Materials vol 25 no 4pp 1663ndash1670 2011
[11] Z He and L Jiang ldquoFlexural reliability assessment of FRP-strengthened reinforced concrete beams designed by ChineseCECS-146 Guidelinerdquo Pacific Science Review vol 9 no 1 pp123ndash133 2007
[12] International Organization for Standardization ldquoDetermina-tion of tensile properties-part 5 test conditions for unidirec-tional fibre reinforced plastic compositesrdquo ISO 527-5 Interna-tional Organization for Standardization Geneva Switzerland1997
[13] B H Oh C K Koh S W Baik H J Lee and S H HanldquoRealistic reliability analysis of reinforced concrete structuresrdquoJournal of Korea Society of Civil Engineering vol 13 no 2 pp121ndash133 1993 (Korean)
[14] Steel bars for concrete reinforcement KS D 3504 KoreanIndustrial Standards 2011 (Korean)
[15] KR Network Design Specification of Railway Railway BridgeKorea Rail Network Authority Seoul Republic of Korea 2004(Korean)
[16] S K Hwang J T Oh J S Lee et al Performance Enhancementof Railway System-Track amp Civil Development of the DesignSpecification for Improving Dynamic Characteristics of RailwayBridges Korea Railway Research Institute Seoul Republic ofKorea 2003 (Korean)
[17] H S Shang T H Yi and L S Yang ldquoExperimental studyon the compressive strength of big mobility concrete withnondestructive testing methodrdquo Advances in Materials Scienceand Engineering vol 2012 Article ID 345214 6 pages 2012
[18] TH YiHN Li andHM Sun ldquoMulti-stage structural damagediagnosis method based on ldquoenergy-damagerdquo theoryrdquo SmartStructures And Systems vol 12 no 3-4 pp 345ndash361 2013
[19] H S Shang T H Yi and X X Guo ldquoStudy on strength andultrasonic of air-entrained concrete and plain concrete in coldenvironmentrdquo Advances in Materials Science and Engineeringvol 2014 Article ID 706986 7 pages 2014
[20] Korea High Speed Rail Construction Authority (KHRC)ldquoBridge designmanual (BRDM)rdquo Technical Report KoreaHighSpeed Rail Construction Authority (KHRC) Pusan Public ofKorea 1995 (Korean)
[21] International Union of Railway UIC Code 776-1R Loads to BeConsidered in Railway Bridge Design International Union ofRailway Paris France 4th edition 1994
10 Mathematical Problems in Engineering
[22] M Abdessemed S Kenai A Bali and A Kibboua ldquoDynamicanalysis of a bridge repaired by CFRP experimental andnumerical modellingrdquoConstruction and BuildingMaterials vol25 no 3 pp 1270ndash1276 2011
[23] G Zanardo H Hao Y Xia and A J Deeks ldquoStiffness assess-ment through modal analysis of an RC slab bridge before andafter strengtheningrdquo Journal of Bridge Engineering vol 11 no 5pp 590ndash601 2006
[24] Korea Infrastructure Safety and Technology corporation(KISTEC) A Database of Maintenance History KoreaInfrastructure Safety and Technology corporation (KISTEC)Gyeonggi-do Republic of Korea 2003 (Korean)
[25] MIDAS IT MIDAS Civil Program Manual MIDAS ITGyeonggi Republic of Korea 2009
[26] S W Tabsh and A S Nowak ldquoReliability of highway girderbridgesrdquo Journal of Structural Engineering ASCE vol 117 no 8pp 2372ndash2388 1991
[27] H N Cho K H Kwak and S J Lee ldquoReliability-based safetyand capacity evaluation of high-speed railway bridgesrdquo Journalof Computational Structural Engineering Institute in KoreaCOSEIK vol 10 no 3 pp 133ndash143 1997 (Korean)
[28] ACI Committee 440 Guide for the Design and Constructionof Externally Bonded FRP Systems for Strengthening ConcreteStructures American Concrete Institute Farmington HillsMich USA 2008
[29] L C Bank Composites for Construction-Structural Design withFRP Materials John Wiley amp Sons New York NY USA 2006
[30] R Rackwitz and B Flessler ldquoStructural reliability under com-bined random load sequencesrdquo Computers and Structures vol9 no 5 pp 489ndash494 1978
[31] H N Cho H H Choi S Y Lee and J W Sun ldquoMethodologyfor reliability-based assessment of capacity-rating of plate girderrailway bridges using ambient measurement datardquo Journal ofKorea Society of Steel Construction vol 15 no 2 pp 187ndash1962003 (Korean)
[32] B Ellingwood Reliability Bases of Load and Resistance Factorsfor Reinforced Concrete Design National Bureau of StandardsBuilding Science Series 110 Washington DC USA 1978
[33] US Department of CommreceNational Bureau of StandardsldquoDevelopment of a probability based load criteria for Amer-ican National Standard A58rdquo NBS Special Publication 577US Department of CommreceNational Bureau of StandardsGaithersburg Md USA 1980
[34] J A O Barros and A S Fortes ldquoFlexural strengthening ofconcrete beamswithCFRP laminates bonded into slitsrdquoCementand Concrete Composites vol 27 no 4 pp 471ndash480 2005
[35] S H Kim H K Cho H W Bae and H S Park ldquoReliabilityevaluation of structures-a case of reinforced concrete buildingsunder dead live and wind loadsrdquo Technical Report KoreaInstitute of Construction Technology 1989 (Korean)
[36] J G MacGregor ldquoLoad and resistance factors for concretedesignrdquo Journal of the American Concrete Institute vol 80 no4 pp 279ndash287 1983
[37] J M Kulicki D R Mertz and W G Wassef ldquoLRFD Designof highway bridgesrdquo NHI Course 13061 Federal HighwayAdministration Washington DC USA 1994
[38] AASHTO Bridge Design Practice American Association ofState Highway and Transportation Officials Washington DCUSA 2011
[39] A S Nowak and A M Rakoczy ldquoReliability-based calibrationof design code for concrete structures (ACI 318)rdquo in Proceeding
of the Anais do 54 Congress Brasileiro do Concreto CBC2012-54CBC pp 1ndash12 2012
(a) Bending moment diagram for a factored dead loadMIDASCivilPostprocessorBeam forceMoment-120574
Scale factor =
Max 10Min 3File railroadUnit kNmiddotm
X minus0516Y minus0766Z 0383
View-direction
500095e + 002
514061e + 002
447227e + 002
300393e + 002
313559e + 002
246725e + 002
179891e + 002
112057e + 002
462233e + 001
000000e + 000
minus874446e + 001
minus154279e + 002
119743E + 002Ctall live all
Date 4132012
(b) Bending moment diagram for a factored live load
Figure 4 FE analyses for dead and live loads
design specification of railway of Korea and were 14 and 20respectively
The design flexural moment by FE analysis was calculatedas 7610 kNsdotm With this moment capacity the area of steelrebar can be estimated as 1718mm2 by the moment equi-librium equation for the rectangular beam with an effectivewidth of slab
3 Limit State Function and Safety Index
31 Limit State Function The conventional performancefunction for flexural capacity of the bridge cross-sectionconsists of 119877119863 and 119871 where 119877 is strength resistance or loadcarrying capacity119863 is dead load effect and119871 is live load effectincluding impact [26] For consideration of the limit state thelimit state model to express railway by Cho et al [27] wasadapted and followed as
119892 (sdot) = 119877 minus (119878119863+ 119878119871) (1)
where 119877 is structural resistance and 119878119863and 119878119871are dead and
live load effect respectively 119877 119878119863 and 119878
where 119877119899is estimated nominal strength of undamaged
structures (flexural moment or shear force) 119863119865is damage
coefficient 119873119877is uncertain parameter when 119877
119873and 119863
119865are
estimated119862119863and119862
119871are the effect factor of flexural moment
and shear force for dead and live loads 119863119899and 119871
119899are the
nominal dead and live loads respectively 119870119878is the response
ratio (CalculationMeasure) 119894 is the impact factor and 119873119863
and119873119871are the calibration factors of 119862
119863and 119862
119871 respectively
119873119877can be calculated by PsdotMsdotFsdotD P for uncertainties of
estimation for analytical modelM formaterial strength F forfabrication andD for damage factors In this study structural
Mathematical Problems in Engineering 5
h d2 d1
d998400
be
c
120576s120576f
120576998400c
120576cu
fsff
Cc
C998400s
085f998400c
1205731c
Figure 5 Compatibility diagram of strain and strength of the cross-section for strengthening
failure denotes the state when the theoretical flexural capacityis reached Failure occurs if the function119892 is less than or equalto zero
As depicted in Figure 5 the resistancemoment (119872119899) used
in this reliability analysis is calculated by (3) to (6) accordingto the recommendations from ACI Committee 440 [28] andBank [29] In this study the damage factor 119863
of concrete (41MPa) and 119887119890is effective width of rectangular
beam (1900mm) 119863119891means the damage factor assumed in
the reliability analysis (Table 4)In the case of failure mode of a concrete beam externally
bonded with CFRP materials except in a premature failurecase the following four failure modes are classified represen-tatively
(1) steel yielding and concrete compressive failure beforeCFRP rupture
(2) steel yielding and CFRP rupture after concrete com-pressive failure
(3) CFRP rupture and concrete compressive failurebefore steel yielding
(4) concrete compressive failure before steel yielding andCFRP rupture
Among the Cases 1sim4 Cases 3 and 4 are typicaloverstrengthening failure which leads to brittle failure ofstrengthening beams Cases 1 and 2 however would resultin ductile failure rather than that of Cases 3 and 4 For rea-sonable failure cases Case 1) is more suitable for preventingthe brittle failure because concrete compressive failure is lessbrittle than that of CFRP strip Balanced failure means thata strengthened concrete member fails simultaneously withconcrete compressive failure and CFRP rupture
Structural safety can be conveniently calculated withrespect to the reliability index 120573 as follows
120573 =120583119892
120590119892
(7)
The variables 120583119892and 120590
119892are the terms of the mean and stan-
dard deviation of the performance function 119892 respectivelyThe reliability index for flexural capacity after strengtheningis calculated based on the effective cross-section of the targetbridge with the amount of CFRP strip required to satisfy thestrength for NSM strengthening In this study the reliabilityindex is computed by the Rackwitz-Fiessler algorithm [30]
32 Computational Uncertainty Factors (119870119904) The computa-
tional uncertainties 119870119904 are adapted to be considered in pre-
dicting resistance The statistics for randomness are definedbased on analytical results or test results Some analytical andtest results are introduced by a literature review of previousresearch papers for reliability analysis [10] In this study itis assumed that statistics of the computational uncertaintyfactor in concrete crushing mode are effective to estimatethe strengthening ratio by reliability analysisThus from datafrom a total of 91 specimens 1061 of mean value and 009 ofstandard deviation resulted The following equation denotesthe computational uncertainties in this analysis
119870119904=119872119880exp
119872119880pre
(8)
33 Damage Factor Cho et al [31] have theoretically definedthat the damage factor is the ratio of stiffness for a non-damaged structure to a damaged structure For quantitative
6 Mathematical Problems in Engineering
Select the target structure forNSM strengthening
Constitute the limit state function
Calculate the external moment
Define of material and structural uncertainty
Calculate the resistance moment and perform reliability analysis
Determine the strengthening ratio of CFRP strip
Reassuming the CFRP
strengthening ratio
No
Yes
120573 = 35
Figure 6 A procedure for determining the reliability-based strengthening ratio of CFRP strip with a target reliability index of 35
approaches it can be calculated by using the ratio of powerof natural frequency for a damaged structure to that fora nondamaged structure In actual state however it is notasserted that this ratio can directly represent the degreeof damage Estimating the damage factor is hard to bedetermined without the plentiful history data so that thedamage factor in this study is assumed by previous research[29] Therefore the average of damage factor is ranged from06 to 09 anduncertainty of damage factor is considered from01 to 03 of coefficient of variation With this statistical datathe probability and reliability analysis are carried out and aresult of sensitive analysis for the variation of damage factoris discussed
4 Characteristics of Random Variables
For reliability analyses the statistics of random variables aredefined in advance There are three variables considered inthis analysis external load for dead and live ones materialstrength of concrete steel rebar and CFRP strip and designof cross-section
In the reliability analysis for structural safety it is essentialthat the load effect must be considered by combining thevariability of loads dead and live loads A related study wasconducted and suggested the load and resistance factors forRC concrete design [32] Table 1 shows the statistics of theload effect for dead and live load for reliability analysis [33]Among these mean value is the external moment resulting
from FE analysis to the target bridge and load factor is basedon the KR specification
The statistics of resistance-related variables such as 1198911015840119888 ℎ
and 119889 listed in Table 2 are adopted from Ellingwood [32]Also included in Table 2 are the statistics of the strength ofCFRP strip (119891fu) for Barros and Fortes [34] and of the width(119887) of T-beam for Oh et al [13] In the case of the nominalvalue of ℎ and 119889 the real dimension of the cross section inthe target bridge is used For steel rebar statistics from manyof tensile tests are summarized in Table 3 [35] As comparedwith Grade series by ASTM A 165 SD30 SD35 and SD40rebar considered in the reliability analysis showed relativelybetter coefficient of variation The probability distributionwas considered as normal type In this study statistics ofSD40 in Korea were adopted in reliability analysis
5 Reliability-Based Strengthening Ratio ofCFRP Strip
51 Target Safety Index in Reliability Analysis This studyis to calculate the reliability-based strengthening ratio ofCFRP strip to the existing railway bridge which has struc-tural uncertainties Therefore it is important to define howmuch structural safety should be acquired This is simplydetermined by using the reliability index or the target safetyfactor 120573 in the load and resistance analysis Previous studyhas shown that 120573 values of 25sim30 and 30sim35 were used
Mathematical Problems in Engineering 7
Table 1 Result of FEM analysis for external railway load
Probability distribution MeanNominal Mean COVa Load factorDead load Normal 105 1800 kNsdotm 01 14Live load Lognormal 100 5808 kNsdotm 02ndash04 20aCOV coefficient of variation
Table 2 Statistics of random design variables (I)
Design variable Nominal value Mean value Standard deviation Probability distribution119891119888
1015840 (MPa) 4134 4616 194 Normal119891fu (MPa)a mdash 2790 857 Normal119887 (mm)b 1900 119887 + 094 60 Normalℎ (mm)c 1250 ℎ minus 305 635 Normal119889 (mm)c 1200 119889 minus 470 1270 NormalaISO 527-3 (1997)[12] bOh et al (1993) [13] ccross-sectional dimension of the target bridge
Table 3 Statistics of random design variables (II)
MeanNominal COV Average strength Number of data Standard deviation Probability distributionSD 30a 120 0064 3600 822 2304 NormalSD 35a 113 0038 3955 80 1503 NormalSD 40a 109 0048 4360 773 2093 NormalGrade 40b 113 0116 3170 mdash 3672 NormalGrade 60b 112 0098 4725 mdash 4631 NormalaKS D 3504bASTM A 615 Standard Specification for Deformed and Plain Carbon Steel Bars for Concrete Reinforcement-AASHTO No M 31 [14]
for tension failure and compression failure respectively [36]Kulicki et al [37] proposed the target or code-specifiedreliability indices obtained from reliability analysis of a groupof 175 existing actual bridges designed by either ASD or LFDmethod and then suggested the range of values using the newload and resistance factors From this research AASHTOaltered the reliability index to 35 when either a higher levelof safety or taking more risk was appropriate [38] Accordingto the recent research [39] the target beta for beam is 35for flexural strength of RC beams constructed with lightweight and normal weight concrete In this study the targetreliability index is determined with 35 and a reliability-basedstrengthening ratio satisfying the probability index 120573 = 35will be calculated
52 Result of Reliability Analysis To evaluate the reliability-based strengthening ratio of the target bridge the probabilitydistribution between the external load and structural resis-tance from the limit state function was analyzed A safetymargin was used and 120573
119879= 35 of target reliability index was
specified by AASHTO [38] Figure 6 is a process to calculatestrengthening ratio of CFRP strip by reliability analysis witha reliability index of 35 FEM analysis should be conductedto determine the external moment for dead and live loadsStructural resistance is affected as when strengthening ratioof CFRP strip is variedTherefore iteration process is neededuntil safety margin of 35 of the strengthening bridge againstexternal load is acquired
0
00005
0001
00015
0002
00025
0003
00035
0004
00045
Prob
abili
ty d
ensit
y
0 500 1000 1500 2000 2500 3000Flexural moment (kNmiddotm)
Q(LS-18)Q(LS-22)R for LS-18Case1 (120588cfrp = 00001)
Figure 7 Probability distribution curves for external load andresistance
Figure 7 is the probability distribution curves for externalload and resistance resulted from the reliability analysisFor external loads the probability distribution of LS-22was additionally considered to investigate the how muchthe strengthening effect of CFRP strips can decrease theprobability of failure compared LS-22 design load 119876 meansthe external load and 119877 is for the resistance moment
8 Mathematical Problems in Engineering
Table 4 Sensitive analysis for damage factor standard deviation of damage factor and live load effect
Degree of sensitive for COV of Degree of sensitive for COV of live load factorDegree of sensitive for average value of
120588cf
rp
Df
Df
Figure 9 Sensitive analysis for COV and average value of 119863119891and
COV of live load factor
Strengthening effect is denoted as a case series FEM analysiswas performed to calculate the external moment for LS-18and LS-22 design railway load For probability distribution ofLS-22 which is the present design load of railway in Korea
probability characteristics for LS-18 were used in the sameway In order to acquire the reliability-based strengtheningratio for 120573
119879= 35 the range of probability parameters was
roughly considered then the final 5 cases for 120588cfrp from 00001to 000013 were analyzed Each probability distribution curveis illustrated in Figure 7 Figure 8 is the result of reliability-based strengthening ratio According to the result of thestrengthening effect by probability distribution the targetbridge strengthened by the CFRP strip strengthening ratioresulting from the reliability analysis could be sufficientlysafe against the LS-22 present design railway load As thestrengthening ratio of CFRP strip that could satisfy 120573
119879= 35
it was with 120588cfrp = 0000114
53 Sensitive Analysis for Three Important ParametersFigure 9 shows the result of sensitive analysis for three param-eters such as damage factor standard deviation of damagefactor and live load effect The CFRP strip strengtheningratio resulting from the reliability analysis is plotted withthree important parameters The purpose of this process isto identify how sensitively the strengthening ratio will beaffected when the three parameters are varied independentlyThe determination of the variation ranges of the parameterswas considered to simply but effectively apply the sensitivecharacteristics For live loads and damage factor there weresimilar degrees of sensitivity Variation of COV of damagefactor however was more sensitive than that of the otherparameters Itmight be concluded that COVof damage factorlargely affected to estimate the reliability-based strengtheningusing about the CFRP strip For more reliable estimation ofdamage factor many of structural diagnosis data should beanalyzed in future Table 4 summarizes the input parametersused in the sensitive analysis
6 Conclusions
This study suggested the reliability-based strengthening ratiofor 30-year-old railway bridge using CFRP strips Conclu-sions are as follows
(1) In previous strengthening schemes it has beenuncertain to determine how much the strengthen-ing effect should be required The methodology forthe reliability-based strengthening ratio can improve
Mathematical Problems in Engineering 9
these problems of the previous strengtheningmethodThe target reliability index for CFRP strip strengthen-ing is considered as 35 according to AASHTO spec-ification As using the reliability-based strengtheningratio in this studymore effective strengthening designto concrete structure having a specified strength-ening target as well as reflecting the structural andmaterial uncertainties is possible
(2) In the result of a sensitive analysis variation of COVfor damage factor mostly affected to the reliability-based strengthening ratio of CFRP strip Thereforedamage factor should be studied more properly onthe target bridge This may be possible by analyzingthe database for long-term safety inspection historyand its reasonable quantification Stabilization andnormalization processes of the damage factor are alsorequired
(3) One of the important factors for determining thesafety margin against the resistance is external loadeffect In order to improve the reliability-basedstrengthening ratio of CFRP strip in this study uncer-tainties for external load of a railway bridge should beanalytically and experimentally verified This can besolved by analyzing the acquired data from long-termmonitoring then the reliability of the strengtheningratio of CFRP strip will be promoted
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by Korea Institute of EnergyTechnology Evaluation and Planning (0000000015513) andResearch grant from Gyeongnam National University ofScience and Technology
References
[1] FHWA Bridge Programs NBI data 2009 httpwwwfhwadotgovbridgenbi
[2] ACI Committee 440 Guide for the Design and Constructionof Externally Bonded FRP Systems for Strengthening Con-crete Structures (ACI 4402R-08) American Concrete InstituteFarmington Hills Mich USA 2008
[3] J M de Sena Cruz and J A O De Barros ldquoBond between near-surface mounted carbon-fiber-reinforced polymer laminatestrips and concreterdquo Journal of Composites for Construction vol8 no 6 pp 519ndash527 2004
[4] T Hassan and S Rizkalla ldquoInvestigation of bond in concretestructures strengthened with near surface mounted carbonfiber reinforced polymer stripsrdquo Journal of Composites forConstruction vol 7 no 3 pp 248ndash257 2003
[5] S M Soliman E El-Salakawy and B Benmokrane ldquoFlexuralbehavior of concrete beams strengthened with near surfacemounted FRP barsrdquo in Proceedings of 4th International confer-ence on FRP composites in civil engineering (CICE rsquo08) 2008
[6] J P Firmo J R Correia and P Franca ldquoFire behaviour ofreinforced concrete beams strengthened with CFRP laminatesprotection systems with insulation of the anchorage zonesrdquoComposites Part B Engineering vol 43 no 3 pp 1545ndash15562012
[7] S M Soliman E El-Salakawy and B Benmokrane ldquoBondperformance of near-surface-mounted FRP barsrdquo Journal ofComposites for Construction vol 15 no 1 pp 103ndash111 2011
[8] THassan and S Rizkalla ldquoFlexural strengthening of prestressedbridge slabs with FRP systemsrdquo PCI Journal vol 47 no 1 pp76ndash93 2002
[9] J R Yost S P Gross and D W Dinehart ldquoNear surfacemounted CFRP reinforcement for structural retrofit of concreteflexural membersrdquo in Proceedings of the 4th InternationalConference on Advanced Composite Materials in Bridges andStructures Calgary Canada 2004
[10] Z He and F Qiu ldquoProbabilistic assessment on flexural capacityof GFRP-reinforced concrete beams designed by guideline ACI4401R-06rdquo Construction and Building Materials vol 25 no 4pp 1663ndash1670 2011
[11] Z He and L Jiang ldquoFlexural reliability assessment of FRP-strengthened reinforced concrete beams designed by ChineseCECS-146 Guidelinerdquo Pacific Science Review vol 9 no 1 pp123ndash133 2007
[12] International Organization for Standardization ldquoDetermina-tion of tensile properties-part 5 test conditions for unidirec-tional fibre reinforced plastic compositesrdquo ISO 527-5 Interna-tional Organization for Standardization Geneva Switzerland1997
[13] B H Oh C K Koh S W Baik H J Lee and S H HanldquoRealistic reliability analysis of reinforced concrete structuresrdquoJournal of Korea Society of Civil Engineering vol 13 no 2 pp121ndash133 1993 (Korean)
[14] Steel bars for concrete reinforcement KS D 3504 KoreanIndustrial Standards 2011 (Korean)
[15] KR Network Design Specification of Railway Railway BridgeKorea Rail Network Authority Seoul Republic of Korea 2004(Korean)
[16] S K Hwang J T Oh J S Lee et al Performance Enhancementof Railway System-Track amp Civil Development of the DesignSpecification for Improving Dynamic Characteristics of RailwayBridges Korea Railway Research Institute Seoul Republic ofKorea 2003 (Korean)
[17] H S Shang T H Yi and L S Yang ldquoExperimental studyon the compressive strength of big mobility concrete withnondestructive testing methodrdquo Advances in Materials Scienceand Engineering vol 2012 Article ID 345214 6 pages 2012
[18] TH YiHN Li andHM Sun ldquoMulti-stage structural damagediagnosis method based on ldquoenergy-damagerdquo theoryrdquo SmartStructures And Systems vol 12 no 3-4 pp 345ndash361 2013
[19] H S Shang T H Yi and X X Guo ldquoStudy on strength andultrasonic of air-entrained concrete and plain concrete in coldenvironmentrdquo Advances in Materials Science and Engineeringvol 2014 Article ID 706986 7 pages 2014
[20] Korea High Speed Rail Construction Authority (KHRC)ldquoBridge designmanual (BRDM)rdquo Technical Report KoreaHighSpeed Rail Construction Authority (KHRC) Pusan Public ofKorea 1995 (Korean)
[21] International Union of Railway UIC Code 776-1R Loads to BeConsidered in Railway Bridge Design International Union ofRailway Paris France 4th edition 1994
10 Mathematical Problems in Engineering
[22] M Abdessemed S Kenai A Bali and A Kibboua ldquoDynamicanalysis of a bridge repaired by CFRP experimental andnumerical modellingrdquoConstruction and BuildingMaterials vol25 no 3 pp 1270ndash1276 2011
[23] G Zanardo H Hao Y Xia and A J Deeks ldquoStiffness assess-ment through modal analysis of an RC slab bridge before andafter strengtheningrdquo Journal of Bridge Engineering vol 11 no 5pp 590ndash601 2006
[24] Korea Infrastructure Safety and Technology corporation(KISTEC) A Database of Maintenance History KoreaInfrastructure Safety and Technology corporation (KISTEC)Gyeonggi-do Republic of Korea 2003 (Korean)
[25] MIDAS IT MIDAS Civil Program Manual MIDAS ITGyeonggi Republic of Korea 2009
[26] S W Tabsh and A S Nowak ldquoReliability of highway girderbridgesrdquo Journal of Structural Engineering ASCE vol 117 no 8pp 2372ndash2388 1991
[27] H N Cho K H Kwak and S J Lee ldquoReliability-based safetyand capacity evaluation of high-speed railway bridgesrdquo Journalof Computational Structural Engineering Institute in KoreaCOSEIK vol 10 no 3 pp 133ndash143 1997 (Korean)
[28] ACI Committee 440 Guide for the Design and Constructionof Externally Bonded FRP Systems for Strengthening ConcreteStructures American Concrete Institute Farmington HillsMich USA 2008
[29] L C Bank Composites for Construction-Structural Design withFRP Materials John Wiley amp Sons New York NY USA 2006
[30] R Rackwitz and B Flessler ldquoStructural reliability under com-bined random load sequencesrdquo Computers and Structures vol9 no 5 pp 489ndash494 1978
[31] H N Cho H H Choi S Y Lee and J W Sun ldquoMethodologyfor reliability-based assessment of capacity-rating of plate girderrailway bridges using ambient measurement datardquo Journal ofKorea Society of Steel Construction vol 15 no 2 pp 187ndash1962003 (Korean)
[32] B Ellingwood Reliability Bases of Load and Resistance Factorsfor Reinforced Concrete Design National Bureau of StandardsBuilding Science Series 110 Washington DC USA 1978
[33] US Department of CommreceNational Bureau of StandardsldquoDevelopment of a probability based load criteria for Amer-ican National Standard A58rdquo NBS Special Publication 577US Department of CommreceNational Bureau of StandardsGaithersburg Md USA 1980
[34] J A O Barros and A S Fortes ldquoFlexural strengthening ofconcrete beamswithCFRP laminates bonded into slitsrdquoCementand Concrete Composites vol 27 no 4 pp 471ndash480 2005
[35] S H Kim H K Cho H W Bae and H S Park ldquoReliabilityevaluation of structures-a case of reinforced concrete buildingsunder dead live and wind loadsrdquo Technical Report KoreaInstitute of Construction Technology 1989 (Korean)
[36] J G MacGregor ldquoLoad and resistance factors for concretedesignrdquo Journal of the American Concrete Institute vol 80 no4 pp 279ndash287 1983
[37] J M Kulicki D R Mertz and W G Wassef ldquoLRFD Designof highway bridgesrdquo NHI Course 13061 Federal HighwayAdministration Washington DC USA 1994
[38] AASHTO Bridge Design Practice American Association ofState Highway and Transportation Officials Washington DCUSA 2011
[39] A S Nowak and A M Rakoczy ldquoReliability-based calibrationof design code for concrete structures (ACI 318)rdquo in Proceeding
of the Anais do 54 Congress Brasileiro do Concreto CBC2012-54CBC pp 1ndash12 2012
Figure 5 Compatibility diagram of strain and strength of the cross-section for strengthening
failure denotes the state when the theoretical flexural capacityis reached Failure occurs if the function119892 is less than or equalto zero
As depicted in Figure 5 the resistancemoment (119872119899) used
in this reliability analysis is calculated by (3) to (6) accordingto the recommendations from ACI Committee 440 [28] andBank [29] In this study the damage factor 119863
of concrete (41MPa) and 119887119890is effective width of rectangular
beam (1900mm) 119863119891means the damage factor assumed in
the reliability analysis (Table 4)In the case of failure mode of a concrete beam externally
bonded with CFRP materials except in a premature failurecase the following four failure modes are classified represen-tatively
(1) steel yielding and concrete compressive failure beforeCFRP rupture
(2) steel yielding and CFRP rupture after concrete com-pressive failure
(3) CFRP rupture and concrete compressive failurebefore steel yielding
(4) concrete compressive failure before steel yielding andCFRP rupture
Among the Cases 1sim4 Cases 3 and 4 are typicaloverstrengthening failure which leads to brittle failure ofstrengthening beams Cases 1 and 2 however would resultin ductile failure rather than that of Cases 3 and 4 For rea-sonable failure cases Case 1) is more suitable for preventingthe brittle failure because concrete compressive failure is lessbrittle than that of CFRP strip Balanced failure means thata strengthened concrete member fails simultaneously withconcrete compressive failure and CFRP rupture
Structural safety can be conveniently calculated withrespect to the reliability index 120573 as follows
120573 =120583119892
120590119892
(7)
The variables 120583119892and 120590
119892are the terms of the mean and stan-
dard deviation of the performance function 119892 respectivelyThe reliability index for flexural capacity after strengtheningis calculated based on the effective cross-section of the targetbridge with the amount of CFRP strip required to satisfy thestrength for NSM strengthening In this study the reliabilityindex is computed by the Rackwitz-Fiessler algorithm [30]
32 Computational Uncertainty Factors (119870119904) The computa-
tional uncertainties 119870119904 are adapted to be considered in pre-
dicting resistance The statistics for randomness are definedbased on analytical results or test results Some analytical andtest results are introduced by a literature review of previousresearch papers for reliability analysis [10] In this study itis assumed that statistics of the computational uncertaintyfactor in concrete crushing mode are effective to estimatethe strengthening ratio by reliability analysisThus from datafrom a total of 91 specimens 1061 of mean value and 009 ofstandard deviation resulted The following equation denotesthe computational uncertainties in this analysis
119870119904=119872119880exp
119872119880pre
(8)
33 Damage Factor Cho et al [31] have theoretically definedthat the damage factor is the ratio of stiffness for a non-damaged structure to a damaged structure For quantitative
6 Mathematical Problems in Engineering
Select the target structure forNSM strengthening
Constitute the limit state function
Calculate the external moment
Define of material and structural uncertainty
Calculate the resistance moment and perform reliability analysis
Determine the strengthening ratio of CFRP strip
Reassuming the CFRP
strengthening ratio
No
Yes
120573 = 35
Figure 6 A procedure for determining the reliability-based strengthening ratio of CFRP strip with a target reliability index of 35
approaches it can be calculated by using the ratio of powerof natural frequency for a damaged structure to that fora nondamaged structure In actual state however it is notasserted that this ratio can directly represent the degreeof damage Estimating the damage factor is hard to bedetermined without the plentiful history data so that thedamage factor in this study is assumed by previous research[29] Therefore the average of damage factor is ranged from06 to 09 anduncertainty of damage factor is considered from01 to 03 of coefficient of variation With this statistical datathe probability and reliability analysis are carried out and aresult of sensitive analysis for the variation of damage factoris discussed
4 Characteristics of Random Variables
For reliability analyses the statistics of random variables aredefined in advance There are three variables considered inthis analysis external load for dead and live ones materialstrength of concrete steel rebar and CFRP strip and designof cross-section
In the reliability analysis for structural safety it is essentialthat the load effect must be considered by combining thevariability of loads dead and live loads A related study wasconducted and suggested the load and resistance factors forRC concrete design [32] Table 1 shows the statistics of theload effect for dead and live load for reliability analysis [33]Among these mean value is the external moment resulting
from FE analysis to the target bridge and load factor is basedon the KR specification
The statistics of resistance-related variables such as 1198911015840119888 ℎ
and 119889 listed in Table 2 are adopted from Ellingwood [32]Also included in Table 2 are the statistics of the strength ofCFRP strip (119891fu) for Barros and Fortes [34] and of the width(119887) of T-beam for Oh et al [13] In the case of the nominalvalue of ℎ and 119889 the real dimension of the cross section inthe target bridge is used For steel rebar statistics from manyof tensile tests are summarized in Table 3 [35] As comparedwith Grade series by ASTM A 165 SD30 SD35 and SD40rebar considered in the reliability analysis showed relativelybetter coefficient of variation The probability distributionwas considered as normal type In this study statistics ofSD40 in Korea were adopted in reliability analysis
5 Reliability-Based Strengthening Ratio ofCFRP Strip
51 Target Safety Index in Reliability Analysis This studyis to calculate the reliability-based strengthening ratio ofCFRP strip to the existing railway bridge which has struc-tural uncertainties Therefore it is important to define howmuch structural safety should be acquired This is simplydetermined by using the reliability index or the target safetyfactor 120573 in the load and resistance analysis Previous studyhas shown that 120573 values of 25sim30 and 30sim35 were used
Mathematical Problems in Engineering 7
Table 1 Result of FEM analysis for external railway load
Probability distribution MeanNominal Mean COVa Load factorDead load Normal 105 1800 kNsdotm 01 14Live load Lognormal 100 5808 kNsdotm 02ndash04 20aCOV coefficient of variation
Table 2 Statistics of random design variables (I)
Design variable Nominal value Mean value Standard deviation Probability distribution119891119888
1015840 (MPa) 4134 4616 194 Normal119891fu (MPa)a mdash 2790 857 Normal119887 (mm)b 1900 119887 + 094 60 Normalℎ (mm)c 1250 ℎ minus 305 635 Normal119889 (mm)c 1200 119889 minus 470 1270 NormalaISO 527-3 (1997)[12] bOh et al (1993) [13] ccross-sectional dimension of the target bridge
Table 3 Statistics of random design variables (II)
MeanNominal COV Average strength Number of data Standard deviation Probability distributionSD 30a 120 0064 3600 822 2304 NormalSD 35a 113 0038 3955 80 1503 NormalSD 40a 109 0048 4360 773 2093 NormalGrade 40b 113 0116 3170 mdash 3672 NormalGrade 60b 112 0098 4725 mdash 4631 NormalaKS D 3504bASTM A 615 Standard Specification for Deformed and Plain Carbon Steel Bars for Concrete Reinforcement-AASHTO No M 31 [14]
for tension failure and compression failure respectively [36]Kulicki et al [37] proposed the target or code-specifiedreliability indices obtained from reliability analysis of a groupof 175 existing actual bridges designed by either ASD or LFDmethod and then suggested the range of values using the newload and resistance factors From this research AASHTOaltered the reliability index to 35 when either a higher levelof safety or taking more risk was appropriate [38] Accordingto the recent research [39] the target beta for beam is 35for flexural strength of RC beams constructed with lightweight and normal weight concrete In this study the targetreliability index is determined with 35 and a reliability-basedstrengthening ratio satisfying the probability index 120573 = 35will be calculated
52 Result of Reliability Analysis To evaluate the reliability-based strengthening ratio of the target bridge the probabilitydistribution between the external load and structural resis-tance from the limit state function was analyzed A safetymargin was used and 120573
119879= 35 of target reliability index was
specified by AASHTO [38] Figure 6 is a process to calculatestrengthening ratio of CFRP strip by reliability analysis witha reliability index of 35 FEM analysis should be conductedto determine the external moment for dead and live loadsStructural resistance is affected as when strengthening ratioof CFRP strip is variedTherefore iteration process is neededuntil safety margin of 35 of the strengthening bridge againstexternal load is acquired
0
00005
0001
00015
0002
00025
0003
00035
0004
00045
Prob
abili
ty d
ensit
y
0 500 1000 1500 2000 2500 3000Flexural moment (kNmiddotm)
Q(LS-18)Q(LS-22)R for LS-18Case1 (120588cfrp = 00001)
Figure 7 Probability distribution curves for external load andresistance
Figure 7 is the probability distribution curves for externalload and resistance resulted from the reliability analysisFor external loads the probability distribution of LS-22was additionally considered to investigate the how muchthe strengthening effect of CFRP strips can decrease theprobability of failure compared LS-22 design load 119876 meansthe external load and 119877 is for the resistance moment
8 Mathematical Problems in Engineering
Table 4 Sensitive analysis for damage factor standard deviation of damage factor and live load effect
Degree of sensitive for COV of Degree of sensitive for COV of live load factorDegree of sensitive for average value of
120588cf
rp
Df
Df
Figure 9 Sensitive analysis for COV and average value of 119863119891and
COV of live load factor
Strengthening effect is denoted as a case series FEM analysiswas performed to calculate the external moment for LS-18and LS-22 design railway load For probability distribution ofLS-22 which is the present design load of railway in Korea
probability characteristics for LS-18 were used in the sameway In order to acquire the reliability-based strengtheningratio for 120573
119879= 35 the range of probability parameters was
roughly considered then the final 5 cases for 120588cfrp from 00001to 000013 were analyzed Each probability distribution curveis illustrated in Figure 7 Figure 8 is the result of reliability-based strengthening ratio According to the result of thestrengthening effect by probability distribution the targetbridge strengthened by the CFRP strip strengthening ratioresulting from the reliability analysis could be sufficientlysafe against the LS-22 present design railway load As thestrengthening ratio of CFRP strip that could satisfy 120573
119879= 35
it was with 120588cfrp = 0000114
53 Sensitive Analysis for Three Important ParametersFigure 9 shows the result of sensitive analysis for three param-eters such as damage factor standard deviation of damagefactor and live load effect The CFRP strip strengtheningratio resulting from the reliability analysis is plotted withthree important parameters The purpose of this process isto identify how sensitively the strengthening ratio will beaffected when the three parameters are varied independentlyThe determination of the variation ranges of the parameterswas considered to simply but effectively apply the sensitivecharacteristics For live loads and damage factor there weresimilar degrees of sensitivity Variation of COV of damagefactor however was more sensitive than that of the otherparameters Itmight be concluded that COVof damage factorlargely affected to estimate the reliability-based strengtheningusing about the CFRP strip For more reliable estimation ofdamage factor many of structural diagnosis data should beanalyzed in future Table 4 summarizes the input parametersused in the sensitive analysis
6 Conclusions
This study suggested the reliability-based strengthening ratiofor 30-year-old railway bridge using CFRP strips Conclu-sions are as follows
(1) In previous strengthening schemes it has beenuncertain to determine how much the strengthen-ing effect should be required The methodology forthe reliability-based strengthening ratio can improve
Mathematical Problems in Engineering 9
these problems of the previous strengtheningmethodThe target reliability index for CFRP strip strengthen-ing is considered as 35 according to AASHTO spec-ification As using the reliability-based strengtheningratio in this studymore effective strengthening designto concrete structure having a specified strength-ening target as well as reflecting the structural andmaterial uncertainties is possible
(2) In the result of a sensitive analysis variation of COVfor damage factor mostly affected to the reliability-based strengthening ratio of CFRP strip Thereforedamage factor should be studied more properly onthe target bridge This may be possible by analyzingthe database for long-term safety inspection historyand its reasonable quantification Stabilization andnormalization processes of the damage factor are alsorequired
(3) One of the important factors for determining thesafety margin against the resistance is external loadeffect In order to improve the reliability-basedstrengthening ratio of CFRP strip in this study uncer-tainties for external load of a railway bridge should beanalytically and experimentally verified This can besolved by analyzing the acquired data from long-termmonitoring then the reliability of the strengtheningratio of CFRP strip will be promoted
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by Korea Institute of EnergyTechnology Evaluation and Planning (0000000015513) andResearch grant from Gyeongnam National University ofScience and Technology
References
[1] FHWA Bridge Programs NBI data 2009 httpwwwfhwadotgovbridgenbi
[2] ACI Committee 440 Guide for the Design and Constructionof Externally Bonded FRP Systems for Strengthening Con-crete Structures (ACI 4402R-08) American Concrete InstituteFarmington Hills Mich USA 2008
[3] J M de Sena Cruz and J A O De Barros ldquoBond between near-surface mounted carbon-fiber-reinforced polymer laminatestrips and concreterdquo Journal of Composites for Construction vol8 no 6 pp 519ndash527 2004
[4] T Hassan and S Rizkalla ldquoInvestigation of bond in concretestructures strengthened with near surface mounted carbonfiber reinforced polymer stripsrdquo Journal of Composites forConstruction vol 7 no 3 pp 248ndash257 2003
[5] S M Soliman E El-Salakawy and B Benmokrane ldquoFlexuralbehavior of concrete beams strengthened with near surfacemounted FRP barsrdquo in Proceedings of 4th International confer-ence on FRP composites in civil engineering (CICE rsquo08) 2008
[6] J P Firmo J R Correia and P Franca ldquoFire behaviour ofreinforced concrete beams strengthened with CFRP laminatesprotection systems with insulation of the anchorage zonesrdquoComposites Part B Engineering vol 43 no 3 pp 1545ndash15562012
[7] S M Soliman E El-Salakawy and B Benmokrane ldquoBondperformance of near-surface-mounted FRP barsrdquo Journal ofComposites for Construction vol 15 no 1 pp 103ndash111 2011
[8] THassan and S Rizkalla ldquoFlexural strengthening of prestressedbridge slabs with FRP systemsrdquo PCI Journal vol 47 no 1 pp76ndash93 2002
[9] J R Yost S P Gross and D W Dinehart ldquoNear surfacemounted CFRP reinforcement for structural retrofit of concreteflexural membersrdquo in Proceedings of the 4th InternationalConference on Advanced Composite Materials in Bridges andStructures Calgary Canada 2004
[10] Z He and F Qiu ldquoProbabilistic assessment on flexural capacityof GFRP-reinforced concrete beams designed by guideline ACI4401R-06rdquo Construction and Building Materials vol 25 no 4pp 1663ndash1670 2011
[11] Z He and L Jiang ldquoFlexural reliability assessment of FRP-strengthened reinforced concrete beams designed by ChineseCECS-146 Guidelinerdquo Pacific Science Review vol 9 no 1 pp123ndash133 2007
[12] International Organization for Standardization ldquoDetermina-tion of tensile properties-part 5 test conditions for unidirec-tional fibre reinforced plastic compositesrdquo ISO 527-5 Interna-tional Organization for Standardization Geneva Switzerland1997
[13] B H Oh C K Koh S W Baik H J Lee and S H HanldquoRealistic reliability analysis of reinforced concrete structuresrdquoJournal of Korea Society of Civil Engineering vol 13 no 2 pp121ndash133 1993 (Korean)
[14] Steel bars for concrete reinforcement KS D 3504 KoreanIndustrial Standards 2011 (Korean)
[15] KR Network Design Specification of Railway Railway BridgeKorea Rail Network Authority Seoul Republic of Korea 2004(Korean)
[16] S K Hwang J T Oh J S Lee et al Performance Enhancementof Railway System-Track amp Civil Development of the DesignSpecification for Improving Dynamic Characteristics of RailwayBridges Korea Railway Research Institute Seoul Republic ofKorea 2003 (Korean)
[17] H S Shang T H Yi and L S Yang ldquoExperimental studyon the compressive strength of big mobility concrete withnondestructive testing methodrdquo Advances in Materials Scienceand Engineering vol 2012 Article ID 345214 6 pages 2012
[18] TH YiHN Li andHM Sun ldquoMulti-stage structural damagediagnosis method based on ldquoenergy-damagerdquo theoryrdquo SmartStructures And Systems vol 12 no 3-4 pp 345ndash361 2013
[19] H S Shang T H Yi and X X Guo ldquoStudy on strength andultrasonic of air-entrained concrete and plain concrete in coldenvironmentrdquo Advances in Materials Science and Engineeringvol 2014 Article ID 706986 7 pages 2014
[20] Korea High Speed Rail Construction Authority (KHRC)ldquoBridge designmanual (BRDM)rdquo Technical Report KoreaHighSpeed Rail Construction Authority (KHRC) Pusan Public ofKorea 1995 (Korean)
[21] International Union of Railway UIC Code 776-1R Loads to BeConsidered in Railway Bridge Design International Union ofRailway Paris France 4th edition 1994
10 Mathematical Problems in Engineering
[22] M Abdessemed S Kenai A Bali and A Kibboua ldquoDynamicanalysis of a bridge repaired by CFRP experimental andnumerical modellingrdquoConstruction and BuildingMaterials vol25 no 3 pp 1270ndash1276 2011
[23] G Zanardo H Hao Y Xia and A J Deeks ldquoStiffness assess-ment through modal analysis of an RC slab bridge before andafter strengtheningrdquo Journal of Bridge Engineering vol 11 no 5pp 590ndash601 2006
[24] Korea Infrastructure Safety and Technology corporation(KISTEC) A Database of Maintenance History KoreaInfrastructure Safety and Technology corporation (KISTEC)Gyeonggi-do Republic of Korea 2003 (Korean)
[25] MIDAS IT MIDAS Civil Program Manual MIDAS ITGyeonggi Republic of Korea 2009
[26] S W Tabsh and A S Nowak ldquoReliability of highway girderbridgesrdquo Journal of Structural Engineering ASCE vol 117 no 8pp 2372ndash2388 1991
[27] H N Cho K H Kwak and S J Lee ldquoReliability-based safetyand capacity evaluation of high-speed railway bridgesrdquo Journalof Computational Structural Engineering Institute in KoreaCOSEIK vol 10 no 3 pp 133ndash143 1997 (Korean)
[28] ACI Committee 440 Guide for the Design and Constructionof Externally Bonded FRP Systems for Strengthening ConcreteStructures American Concrete Institute Farmington HillsMich USA 2008
[29] L C Bank Composites for Construction-Structural Design withFRP Materials John Wiley amp Sons New York NY USA 2006
[30] R Rackwitz and B Flessler ldquoStructural reliability under com-bined random load sequencesrdquo Computers and Structures vol9 no 5 pp 489ndash494 1978
[31] H N Cho H H Choi S Y Lee and J W Sun ldquoMethodologyfor reliability-based assessment of capacity-rating of plate girderrailway bridges using ambient measurement datardquo Journal ofKorea Society of Steel Construction vol 15 no 2 pp 187ndash1962003 (Korean)
[32] B Ellingwood Reliability Bases of Load and Resistance Factorsfor Reinforced Concrete Design National Bureau of StandardsBuilding Science Series 110 Washington DC USA 1978
[33] US Department of CommreceNational Bureau of StandardsldquoDevelopment of a probability based load criteria for Amer-ican National Standard A58rdquo NBS Special Publication 577US Department of CommreceNational Bureau of StandardsGaithersburg Md USA 1980
[34] J A O Barros and A S Fortes ldquoFlexural strengthening ofconcrete beamswithCFRP laminates bonded into slitsrdquoCementand Concrete Composites vol 27 no 4 pp 471ndash480 2005
[35] S H Kim H K Cho H W Bae and H S Park ldquoReliabilityevaluation of structures-a case of reinforced concrete buildingsunder dead live and wind loadsrdquo Technical Report KoreaInstitute of Construction Technology 1989 (Korean)
[36] J G MacGregor ldquoLoad and resistance factors for concretedesignrdquo Journal of the American Concrete Institute vol 80 no4 pp 279ndash287 1983
[37] J M Kulicki D R Mertz and W G Wassef ldquoLRFD Designof highway bridgesrdquo NHI Course 13061 Federal HighwayAdministration Washington DC USA 1994
[38] AASHTO Bridge Design Practice American Association ofState Highway and Transportation Officials Washington DCUSA 2011
[39] A S Nowak and A M Rakoczy ldquoReliability-based calibrationof design code for concrete structures (ACI 318)rdquo in Proceeding
of the Anais do 54 Congress Brasileiro do Concreto CBC2012-54CBC pp 1ndash12 2012
Calculate the resistance moment and perform reliability analysis
Determine the strengthening ratio of CFRP strip
Reassuming the CFRP
strengthening ratio
No
Yes
120573 = 35
Figure 6 A procedure for determining the reliability-based strengthening ratio of CFRP strip with a target reliability index of 35
approaches it can be calculated by using the ratio of powerof natural frequency for a damaged structure to that fora nondamaged structure In actual state however it is notasserted that this ratio can directly represent the degreeof damage Estimating the damage factor is hard to bedetermined without the plentiful history data so that thedamage factor in this study is assumed by previous research[29] Therefore the average of damage factor is ranged from06 to 09 anduncertainty of damage factor is considered from01 to 03 of coefficient of variation With this statistical datathe probability and reliability analysis are carried out and aresult of sensitive analysis for the variation of damage factoris discussed
4 Characteristics of Random Variables
For reliability analyses the statistics of random variables aredefined in advance There are three variables considered inthis analysis external load for dead and live ones materialstrength of concrete steel rebar and CFRP strip and designof cross-section
In the reliability analysis for structural safety it is essentialthat the load effect must be considered by combining thevariability of loads dead and live loads A related study wasconducted and suggested the load and resistance factors forRC concrete design [32] Table 1 shows the statistics of theload effect for dead and live load for reliability analysis [33]Among these mean value is the external moment resulting
from FE analysis to the target bridge and load factor is basedon the KR specification
The statistics of resistance-related variables such as 1198911015840119888 ℎ
and 119889 listed in Table 2 are adopted from Ellingwood [32]Also included in Table 2 are the statistics of the strength ofCFRP strip (119891fu) for Barros and Fortes [34] and of the width(119887) of T-beam for Oh et al [13] In the case of the nominalvalue of ℎ and 119889 the real dimension of the cross section inthe target bridge is used For steel rebar statistics from manyof tensile tests are summarized in Table 3 [35] As comparedwith Grade series by ASTM A 165 SD30 SD35 and SD40rebar considered in the reliability analysis showed relativelybetter coefficient of variation The probability distributionwas considered as normal type In this study statistics ofSD40 in Korea were adopted in reliability analysis
5 Reliability-Based Strengthening Ratio ofCFRP Strip
51 Target Safety Index in Reliability Analysis This studyis to calculate the reliability-based strengthening ratio ofCFRP strip to the existing railway bridge which has struc-tural uncertainties Therefore it is important to define howmuch structural safety should be acquired This is simplydetermined by using the reliability index or the target safetyfactor 120573 in the load and resistance analysis Previous studyhas shown that 120573 values of 25sim30 and 30sim35 were used
Mathematical Problems in Engineering 7
Table 1 Result of FEM analysis for external railway load
Probability distribution MeanNominal Mean COVa Load factorDead load Normal 105 1800 kNsdotm 01 14Live load Lognormal 100 5808 kNsdotm 02ndash04 20aCOV coefficient of variation
Table 2 Statistics of random design variables (I)
Design variable Nominal value Mean value Standard deviation Probability distribution119891119888
1015840 (MPa) 4134 4616 194 Normal119891fu (MPa)a mdash 2790 857 Normal119887 (mm)b 1900 119887 + 094 60 Normalℎ (mm)c 1250 ℎ minus 305 635 Normal119889 (mm)c 1200 119889 minus 470 1270 NormalaISO 527-3 (1997)[12] bOh et al (1993) [13] ccross-sectional dimension of the target bridge
Table 3 Statistics of random design variables (II)
MeanNominal COV Average strength Number of data Standard deviation Probability distributionSD 30a 120 0064 3600 822 2304 NormalSD 35a 113 0038 3955 80 1503 NormalSD 40a 109 0048 4360 773 2093 NormalGrade 40b 113 0116 3170 mdash 3672 NormalGrade 60b 112 0098 4725 mdash 4631 NormalaKS D 3504bASTM A 615 Standard Specification for Deformed and Plain Carbon Steel Bars for Concrete Reinforcement-AASHTO No M 31 [14]
for tension failure and compression failure respectively [36]Kulicki et al [37] proposed the target or code-specifiedreliability indices obtained from reliability analysis of a groupof 175 existing actual bridges designed by either ASD or LFDmethod and then suggested the range of values using the newload and resistance factors From this research AASHTOaltered the reliability index to 35 when either a higher levelof safety or taking more risk was appropriate [38] Accordingto the recent research [39] the target beta for beam is 35for flexural strength of RC beams constructed with lightweight and normal weight concrete In this study the targetreliability index is determined with 35 and a reliability-basedstrengthening ratio satisfying the probability index 120573 = 35will be calculated
52 Result of Reliability Analysis To evaluate the reliability-based strengthening ratio of the target bridge the probabilitydistribution between the external load and structural resis-tance from the limit state function was analyzed A safetymargin was used and 120573
119879= 35 of target reliability index was
specified by AASHTO [38] Figure 6 is a process to calculatestrengthening ratio of CFRP strip by reliability analysis witha reliability index of 35 FEM analysis should be conductedto determine the external moment for dead and live loadsStructural resistance is affected as when strengthening ratioof CFRP strip is variedTherefore iteration process is neededuntil safety margin of 35 of the strengthening bridge againstexternal load is acquired
0
00005
0001
00015
0002
00025
0003
00035
0004
00045
Prob
abili
ty d
ensit
y
0 500 1000 1500 2000 2500 3000Flexural moment (kNmiddotm)
Q(LS-18)Q(LS-22)R for LS-18Case1 (120588cfrp = 00001)
Figure 7 Probability distribution curves for external load andresistance
Figure 7 is the probability distribution curves for externalload and resistance resulted from the reliability analysisFor external loads the probability distribution of LS-22was additionally considered to investigate the how muchthe strengthening effect of CFRP strips can decrease theprobability of failure compared LS-22 design load 119876 meansthe external load and 119877 is for the resistance moment
8 Mathematical Problems in Engineering
Table 4 Sensitive analysis for damage factor standard deviation of damage factor and live load effect
Degree of sensitive for COV of Degree of sensitive for COV of live load factorDegree of sensitive for average value of
120588cf
rp
Df
Df
Figure 9 Sensitive analysis for COV and average value of 119863119891and
COV of live load factor
Strengthening effect is denoted as a case series FEM analysiswas performed to calculate the external moment for LS-18and LS-22 design railway load For probability distribution ofLS-22 which is the present design load of railway in Korea
probability characteristics for LS-18 were used in the sameway In order to acquire the reliability-based strengtheningratio for 120573
119879= 35 the range of probability parameters was
roughly considered then the final 5 cases for 120588cfrp from 00001to 000013 were analyzed Each probability distribution curveis illustrated in Figure 7 Figure 8 is the result of reliability-based strengthening ratio According to the result of thestrengthening effect by probability distribution the targetbridge strengthened by the CFRP strip strengthening ratioresulting from the reliability analysis could be sufficientlysafe against the LS-22 present design railway load As thestrengthening ratio of CFRP strip that could satisfy 120573
119879= 35
it was with 120588cfrp = 0000114
53 Sensitive Analysis for Three Important ParametersFigure 9 shows the result of sensitive analysis for three param-eters such as damage factor standard deviation of damagefactor and live load effect The CFRP strip strengtheningratio resulting from the reliability analysis is plotted withthree important parameters The purpose of this process isto identify how sensitively the strengthening ratio will beaffected when the three parameters are varied independentlyThe determination of the variation ranges of the parameterswas considered to simply but effectively apply the sensitivecharacteristics For live loads and damage factor there weresimilar degrees of sensitivity Variation of COV of damagefactor however was more sensitive than that of the otherparameters Itmight be concluded that COVof damage factorlargely affected to estimate the reliability-based strengtheningusing about the CFRP strip For more reliable estimation ofdamage factor many of structural diagnosis data should beanalyzed in future Table 4 summarizes the input parametersused in the sensitive analysis
6 Conclusions
This study suggested the reliability-based strengthening ratiofor 30-year-old railway bridge using CFRP strips Conclu-sions are as follows
(1) In previous strengthening schemes it has beenuncertain to determine how much the strengthen-ing effect should be required The methodology forthe reliability-based strengthening ratio can improve
Mathematical Problems in Engineering 9
these problems of the previous strengtheningmethodThe target reliability index for CFRP strip strengthen-ing is considered as 35 according to AASHTO spec-ification As using the reliability-based strengtheningratio in this studymore effective strengthening designto concrete structure having a specified strength-ening target as well as reflecting the structural andmaterial uncertainties is possible
(2) In the result of a sensitive analysis variation of COVfor damage factor mostly affected to the reliability-based strengthening ratio of CFRP strip Thereforedamage factor should be studied more properly onthe target bridge This may be possible by analyzingthe database for long-term safety inspection historyand its reasonable quantification Stabilization andnormalization processes of the damage factor are alsorequired
(3) One of the important factors for determining thesafety margin against the resistance is external loadeffect In order to improve the reliability-basedstrengthening ratio of CFRP strip in this study uncer-tainties for external load of a railway bridge should beanalytically and experimentally verified This can besolved by analyzing the acquired data from long-termmonitoring then the reliability of the strengtheningratio of CFRP strip will be promoted
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by Korea Institute of EnergyTechnology Evaluation and Planning (0000000015513) andResearch grant from Gyeongnam National University ofScience and Technology
References
[1] FHWA Bridge Programs NBI data 2009 httpwwwfhwadotgovbridgenbi
[2] ACI Committee 440 Guide for the Design and Constructionof Externally Bonded FRP Systems for Strengthening Con-crete Structures (ACI 4402R-08) American Concrete InstituteFarmington Hills Mich USA 2008
[3] J M de Sena Cruz and J A O De Barros ldquoBond between near-surface mounted carbon-fiber-reinforced polymer laminatestrips and concreterdquo Journal of Composites for Construction vol8 no 6 pp 519ndash527 2004
[4] T Hassan and S Rizkalla ldquoInvestigation of bond in concretestructures strengthened with near surface mounted carbonfiber reinforced polymer stripsrdquo Journal of Composites forConstruction vol 7 no 3 pp 248ndash257 2003
[5] S M Soliman E El-Salakawy and B Benmokrane ldquoFlexuralbehavior of concrete beams strengthened with near surfacemounted FRP barsrdquo in Proceedings of 4th International confer-ence on FRP composites in civil engineering (CICE rsquo08) 2008
[6] J P Firmo J R Correia and P Franca ldquoFire behaviour ofreinforced concrete beams strengthened with CFRP laminatesprotection systems with insulation of the anchorage zonesrdquoComposites Part B Engineering vol 43 no 3 pp 1545ndash15562012
[7] S M Soliman E El-Salakawy and B Benmokrane ldquoBondperformance of near-surface-mounted FRP barsrdquo Journal ofComposites for Construction vol 15 no 1 pp 103ndash111 2011
[8] THassan and S Rizkalla ldquoFlexural strengthening of prestressedbridge slabs with FRP systemsrdquo PCI Journal vol 47 no 1 pp76ndash93 2002
[9] J R Yost S P Gross and D W Dinehart ldquoNear surfacemounted CFRP reinforcement for structural retrofit of concreteflexural membersrdquo in Proceedings of the 4th InternationalConference on Advanced Composite Materials in Bridges andStructures Calgary Canada 2004
[10] Z He and F Qiu ldquoProbabilistic assessment on flexural capacityof GFRP-reinforced concrete beams designed by guideline ACI4401R-06rdquo Construction and Building Materials vol 25 no 4pp 1663ndash1670 2011
[11] Z He and L Jiang ldquoFlexural reliability assessment of FRP-strengthened reinforced concrete beams designed by ChineseCECS-146 Guidelinerdquo Pacific Science Review vol 9 no 1 pp123ndash133 2007
[12] International Organization for Standardization ldquoDetermina-tion of tensile properties-part 5 test conditions for unidirec-tional fibre reinforced plastic compositesrdquo ISO 527-5 Interna-tional Organization for Standardization Geneva Switzerland1997
[13] B H Oh C K Koh S W Baik H J Lee and S H HanldquoRealistic reliability analysis of reinforced concrete structuresrdquoJournal of Korea Society of Civil Engineering vol 13 no 2 pp121ndash133 1993 (Korean)
[14] Steel bars for concrete reinforcement KS D 3504 KoreanIndustrial Standards 2011 (Korean)
[15] KR Network Design Specification of Railway Railway BridgeKorea Rail Network Authority Seoul Republic of Korea 2004(Korean)
[16] S K Hwang J T Oh J S Lee et al Performance Enhancementof Railway System-Track amp Civil Development of the DesignSpecification for Improving Dynamic Characteristics of RailwayBridges Korea Railway Research Institute Seoul Republic ofKorea 2003 (Korean)
[17] H S Shang T H Yi and L S Yang ldquoExperimental studyon the compressive strength of big mobility concrete withnondestructive testing methodrdquo Advances in Materials Scienceand Engineering vol 2012 Article ID 345214 6 pages 2012
[18] TH YiHN Li andHM Sun ldquoMulti-stage structural damagediagnosis method based on ldquoenergy-damagerdquo theoryrdquo SmartStructures And Systems vol 12 no 3-4 pp 345ndash361 2013
[19] H S Shang T H Yi and X X Guo ldquoStudy on strength andultrasonic of air-entrained concrete and plain concrete in coldenvironmentrdquo Advances in Materials Science and Engineeringvol 2014 Article ID 706986 7 pages 2014
[20] Korea High Speed Rail Construction Authority (KHRC)ldquoBridge designmanual (BRDM)rdquo Technical Report KoreaHighSpeed Rail Construction Authority (KHRC) Pusan Public ofKorea 1995 (Korean)
[21] International Union of Railway UIC Code 776-1R Loads to BeConsidered in Railway Bridge Design International Union ofRailway Paris France 4th edition 1994
10 Mathematical Problems in Engineering
[22] M Abdessemed S Kenai A Bali and A Kibboua ldquoDynamicanalysis of a bridge repaired by CFRP experimental andnumerical modellingrdquoConstruction and BuildingMaterials vol25 no 3 pp 1270ndash1276 2011
[23] G Zanardo H Hao Y Xia and A J Deeks ldquoStiffness assess-ment through modal analysis of an RC slab bridge before andafter strengtheningrdquo Journal of Bridge Engineering vol 11 no 5pp 590ndash601 2006
[24] Korea Infrastructure Safety and Technology corporation(KISTEC) A Database of Maintenance History KoreaInfrastructure Safety and Technology corporation (KISTEC)Gyeonggi-do Republic of Korea 2003 (Korean)
[25] MIDAS IT MIDAS Civil Program Manual MIDAS ITGyeonggi Republic of Korea 2009
[26] S W Tabsh and A S Nowak ldquoReliability of highway girderbridgesrdquo Journal of Structural Engineering ASCE vol 117 no 8pp 2372ndash2388 1991
[27] H N Cho K H Kwak and S J Lee ldquoReliability-based safetyand capacity evaluation of high-speed railway bridgesrdquo Journalof Computational Structural Engineering Institute in KoreaCOSEIK vol 10 no 3 pp 133ndash143 1997 (Korean)
[28] ACI Committee 440 Guide for the Design and Constructionof Externally Bonded FRP Systems for Strengthening ConcreteStructures American Concrete Institute Farmington HillsMich USA 2008
[29] L C Bank Composites for Construction-Structural Design withFRP Materials John Wiley amp Sons New York NY USA 2006
[30] R Rackwitz and B Flessler ldquoStructural reliability under com-bined random load sequencesrdquo Computers and Structures vol9 no 5 pp 489ndash494 1978
[31] H N Cho H H Choi S Y Lee and J W Sun ldquoMethodologyfor reliability-based assessment of capacity-rating of plate girderrailway bridges using ambient measurement datardquo Journal ofKorea Society of Steel Construction vol 15 no 2 pp 187ndash1962003 (Korean)
[32] B Ellingwood Reliability Bases of Load and Resistance Factorsfor Reinforced Concrete Design National Bureau of StandardsBuilding Science Series 110 Washington DC USA 1978
[33] US Department of CommreceNational Bureau of StandardsldquoDevelopment of a probability based load criteria for Amer-ican National Standard A58rdquo NBS Special Publication 577US Department of CommreceNational Bureau of StandardsGaithersburg Md USA 1980
[34] J A O Barros and A S Fortes ldquoFlexural strengthening ofconcrete beamswithCFRP laminates bonded into slitsrdquoCementand Concrete Composites vol 27 no 4 pp 471ndash480 2005
[35] S H Kim H K Cho H W Bae and H S Park ldquoReliabilityevaluation of structures-a case of reinforced concrete buildingsunder dead live and wind loadsrdquo Technical Report KoreaInstitute of Construction Technology 1989 (Korean)
[36] J G MacGregor ldquoLoad and resistance factors for concretedesignrdquo Journal of the American Concrete Institute vol 80 no4 pp 279ndash287 1983
[37] J M Kulicki D R Mertz and W G Wassef ldquoLRFD Designof highway bridgesrdquo NHI Course 13061 Federal HighwayAdministration Washington DC USA 1994
[38] AASHTO Bridge Design Practice American Association ofState Highway and Transportation Officials Washington DCUSA 2011
[39] A S Nowak and A M Rakoczy ldquoReliability-based calibrationof design code for concrete structures (ACI 318)rdquo in Proceeding
of the Anais do 54 Congress Brasileiro do Concreto CBC2012-54CBC pp 1ndash12 2012
Table 1 Result of FEM analysis for external railway load
Probability distribution MeanNominal Mean COVa Load factorDead load Normal 105 1800 kNsdotm 01 14Live load Lognormal 100 5808 kNsdotm 02ndash04 20aCOV coefficient of variation
Table 2 Statistics of random design variables (I)
Design variable Nominal value Mean value Standard deviation Probability distribution119891119888
1015840 (MPa) 4134 4616 194 Normal119891fu (MPa)a mdash 2790 857 Normal119887 (mm)b 1900 119887 + 094 60 Normalℎ (mm)c 1250 ℎ minus 305 635 Normal119889 (mm)c 1200 119889 minus 470 1270 NormalaISO 527-3 (1997)[12] bOh et al (1993) [13] ccross-sectional dimension of the target bridge
Table 3 Statistics of random design variables (II)
MeanNominal COV Average strength Number of data Standard deviation Probability distributionSD 30a 120 0064 3600 822 2304 NormalSD 35a 113 0038 3955 80 1503 NormalSD 40a 109 0048 4360 773 2093 NormalGrade 40b 113 0116 3170 mdash 3672 NormalGrade 60b 112 0098 4725 mdash 4631 NormalaKS D 3504bASTM A 615 Standard Specification for Deformed and Plain Carbon Steel Bars for Concrete Reinforcement-AASHTO No M 31 [14]
for tension failure and compression failure respectively [36]Kulicki et al [37] proposed the target or code-specifiedreliability indices obtained from reliability analysis of a groupof 175 existing actual bridges designed by either ASD or LFDmethod and then suggested the range of values using the newload and resistance factors From this research AASHTOaltered the reliability index to 35 when either a higher levelof safety or taking more risk was appropriate [38] Accordingto the recent research [39] the target beta for beam is 35for flexural strength of RC beams constructed with lightweight and normal weight concrete In this study the targetreliability index is determined with 35 and a reliability-basedstrengthening ratio satisfying the probability index 120573 = 35will be calculated
52 Result of Reliability Analysis To evaluate the reliability-based strengthening ratio of the target bridge the probabilitydistribution between the external load and structural resis-tance from the limit state function was analyzed A safetymargin was used and 120573
119879= 35 of target reliability index was
specified by AASHTO [38] Figure 6 is a process to calculatestrengthening ratio of CFRP strip by reliability analysis witha reliability index of 35 FEM analysis should be conductedto determine the external moment for dead and live loadsStructural resistance is affected as when strengthening ratioof CFRP strip is variedTherefore iteration process is neededuntil safety margin of 35 of the strengthening bridge againstexternal load is acquired
0
00005
0001
00015
0002
00025
0003
00035
0004
00045
Prob
abili
ty d
ensit
y
0 500 1000 1500 2000 2500 3000Flexural moment (kNmiddotm)
Q(LS-18)Q(LS-22)R for LS-18Case1 (120588cfrp = 00001)
Figure 7 Probability distribution curves for external load andresistance
Figure 7 is the probability distribution curves for externalload and resistance resulted from the reliability analysisFor external loads the probability distribution of LS-22was additionally considered to investigate the how muchthe strengthening effect of CFRP strips can decrease theprobability of failure compared LS-22 design load 119876 meansthe external load and 119877 is for the resistance moment
8 Mathematical Problems in Engineering
Table 4 Sensitive analysis for damage factor standard deviation of damage factor and live load effect
Degree of sensitive for COV of Degree of sensitive for COV of live load factorDegree of sensitive for average value of
120588cf
rp
Df
Df
Figure 9 Sensitive analysis for COV and average value of 119863119891and
COV of live load factor
Strengthening effect is denoted as a case series FEM analysiswas performed to calculate the external moment for LS-18and LS-22 design railway load For probability distribution ofLS-22 which is the present design load of railway in Korea
probability characteristics for LS-18 were used in the sameway In order to acquire the reliability-based strengtheningratio for 120573
119879= 35 the range of probability parameters was
roughly considered then the final 5 cases for 120588cfrp from 00001to 000013 were analyzed Each probability distribution curveis illustrated in Figure 7 Figure 8 is the result of reliability-based strengthening ratio According to the result of thestrengthening effect by probability distribution the targetbridge strengthened by the CFRP strip strengthening ratioresulting from the reliability analysis could be sufficientlysafe against the LS-22 present design railway load As thestrengthening ratio of CFRP strip that could satisfy 120573
119879= 35
it was with 120588cfrp = 0000114
53 Sensitive Analysis for Three Important ParametersFigure 9 shows the result of sensitive analysis for three param-eters such as damage factor standard deviation of damagefactor and live load effect The CFRP strip strengtheningratio resulting from the reliability analysis is plotted withthree important parameters The purpose of this process isto identify how sensitively the strengthening ratio will beaffected when the three parameters are varied independentlyThe determination of the variation ranges of the parameterswas considered to simply but effectively apply the sensitivecharacteristics For live loads and damage factor there weresimilar degrees of sensitivity Variation of COV of damagefactor however was more sensitive than that of the otherparameters Itmight be concluded that COVof damage factorlargely affected to estimate the reliability-based strengtheningusing about the CFRP strip For more reliable estimation ofdamage factor many of structural diagnosis data should beanalyzed in future Table 4 summarizes the input parametersused in the sensitive analysis
6 Conclusions
This study suggested the reliability-based strengthening ratiofor 30-year-old railway bridge using CFRP strips Conclu-sions are as follows
(1) In previous strengthening schemes it has beenuncertain to determine how much the strengthen-ing effect should be required The methodology forthe reliability-based strengthening ratio can improve
Mathematical Problems in Engineering 9
these problems of the previous strengtheningmethodThe target reliability index for CFRP strip strengthen-ing is considered as 35 according to AASHTO spec-ification As using the reliability-based strengtheningratio in this studymore effective strengthening designto concrete structure having a specified strength-ening target as well as reflecting the structural andmaterial uncertainties is possible
(2) In the result of a sensitive analysis variation of COVfor damage factor mostly affected to the reliability-based strengthening ratio of CFRP strip Thereforedamage factor should be studied more properly onthe target bridge This may be possible by analyzingthe database for long-term safety inspection historyand its reasonable quantification Stabilization andnormalization processes of the damage factor are alsorequired
(3) One of the important factors for determining thesafety margin against the resistance is external loadeffect In order to improve the reliability-basedstrengthening ratio of CFRP strip in this study uncer-tainties for external load of a railway bridge should beanalytically and experimentally verified This can besolved by analyzing the acquired data from long-termmonitoring then the reliability of the strengtheningratio of CFRP strip will be promoted
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by Korea Institute of EnergyTechnology Evaluation and Planning (0000000015513) andResearch grant from Gyeongnam National University ofScience and Technology
References
[1] FHWA Bridge Programs NBI data 2009 httpwwwfhwadotgovbridgenbi
[2] ACI Committee 440 Guide for the Design and Constructionof Externally Bonded FRP Systems for Strengthening Con-crete Structures (ACI 4402R-08) American Concrete InstituteFarmington Hills Mich USA 2008
[3] J M de Sena Cruz and J A O De Barros ldquoBond between near-surface mounted carbon-fiber-reinforced polymer laminatestrips and concreterdquo Journal of Composites for Construction vol8 no 6 pp 519ndash527 2004
[4] T Hassan and S Rizkalla ldquoInvestigation of bond in concretestructures strengthened with near surface mounted carbonfiber reinforced polymer stripsrdquo Journal of Composites forConstruction vol 7 no 3 pp 248ndash257 2003
[5] S M Soliman E El-Salakawy and B Benmokrane ldquoFlexuralbehavior of concrete beams strengthened with near surfacemounted FRP barsrdquo in Proceedings of 4th International confer-ence on FRP composites in civil engineering (CICE rsquo08) 2008
[6] J P Firmo J R Correia and P Franca ldquoFire behaviour ofreinforced concrete beams strengthened with CFRP laminatesprotection systems with insulation of the anchorage zonesrdquoComposites Part B Engineering vol 43 no 3 pp 1545ndash15562012
[7] S M Soliman E El-Salakawy and B Benmokrane ldquoBondperformance of near-surface-mounted FRP barsrdquo Journal ofComposites for Construction vol 15 no 1 pp 103ndash111 2011
[8] THassan and S Rizkalla ldquoFlexural strengthening of prestressedbridge slabs with FRP systemsrdquo PCI Journal vol 47 no 1 pp76ndash93 2002
[9] J R Yost S P Gross and D W Dinehart ldquoNear surfacemounted CFRP reinforcement for structural retrofit of concreteflexural membersrdquo in Proceedings of the 4th InternationalConference on Advanced Composite Materials in Bridges andStructures Calgary Canada 2004
[10] Z He and F Qiu ldquoProbabilistic assessment on flexural capacityof GFRP-reinforced concrete beams designed by guideline ACI4401R-06rdquo Construction and Building Materials vol 25 no 4pp 1663ndash1670 2011
[11] Z He and L Jiang ldquoFlexural reliability assessment of FRP-strengthened reinforced concrete beams designed by ChineseCECS-146 Guidelinerdquo Pacific Science Review vol 9 no 1 pp123ndash133 2007
[12] International Organization for Standardization ldquoDetermina-tion of tensile properties-part 5 test conditions for unidirec-tional fibre reinforced plastic compositesrdquo ISO 527-5 Interna-tional Organization for Standardization Geneva Switzerland1997
[13] B H Oh C K Koh S W Baik H J Lee and S H HanldquoRealistic reliability analysis of reinforced concrete structuresrdquoJournal of Korea Society of Civil Engineering vol 13 no 2 pp121ndash133 1993 (Korean)
[14] Steel bars for concrete reinforcement KS D 3504 KoreanIndustrial Standards 2011 (Korean)
[15] KR Network Design Specification of Railway Railway BridgeKorea Rail Network Authority Seoul Republic of Korea 2004(Korean)
[16] S K Hwang J T Oh J S Lee et al Performance Enhancementof Railway System-Track amp Civil Development of the DesignSpecification for Improving Dynamic Characteristics of RailwayBridges Korea Railway Research Institute Seoul Republic ofKorea 2003 (Korean)
[17] H S Shang T H Yi and L S Yang ldquoExperimental studyon the compressive strength of big mobility concrete withnondestructive testing methodrdquo Advances in Materials Scienceand Engineering vol 2012 Article ID 345214 6 pages 2012
[18] TH YiHN Li andHM Sun ldquoMulti-stage structural damagediagnosis method based on ldquoenergy-damagerdquo theoryrdquo SmartStructures And Systems vol 12 no 3-4 pp 345ndash361 2013
[19] H S Shang T H Yi and X X Guo ldquoStudy on strength andultrasonic of air-entrained concrete and plain concrete in coldenvironmentrdquo Advances in Materials Science and Engineeringvol 2014 Article ID 706986 7 pages 2014
[20] Korea High Speed Rail Construction Authority (KHRC)ldquoBridge designmanual (BRDM)rdquo Technical Report KoreaHighSpeed Rail Construction Authority (KHRC) Pusan Public ofKorea 1995 (Korean)
[21] International Union of Railway UIC Code 776-1R Loads to BeConsidered in Railway Bridge Design International Union ofRailway Paris France 4th edition 1994
10 Mathematical Problems in Engineering
[22] M Abdessemed S Kenai A Bali and A Kibboua ldquoDynamicanalysis of a bridge repaired by CFRP experimental andnumerical modellingrdquoConstruction and BuildingMaterials vol25 no 3 pp 1270ndash1276 2011
[23] G Zanardo H Hao Y Xia and A J Deeks ldquoStiffness assess-ment through modal analysis of an RC slab bridge before andafter strengtheningrdquo Journal of Bridge Engineering vol 11 no 5pp 590ndash601 2006
[24] Korea Infrastructure Safety and Technology corporation(KISTEC) A Database of Maintenance History KoreaInfrastructure Safety and Technology corporation (KISTEC)Gyeonggi-do Republic of Korea 2003 (Korean)
[25] MIDAS IT MIDAS Civil Program Manual MIDAS ITGyeonggi Republic of Korea 2009
[26] S W Tabsh and A S Nowak ldquoReliability of highway girderbridgesrdquo Journal of Structural Engineering ASCE vol 117 no 8pp 2372ndash2388 1991
[27] H N Cho K H Kwak and S J Lee ldquoReliability-based safetyand capacity evaluation of high-speed railway bridgesrdquo Journalof Computational Structural Engineering Institute in KoreaCOSEIK vol 10 no 3 pp 133ndash143 1997 (Korean)
[28] ACI Committee 440 Guide for the Design and Constructionof Externally Bonded FRP Systems for Strengthening ConcreteStructures American Concrete Institute Farmington HillsMich USA 2008
[29] L C Bank Composites for Construction-Structural Design withFRP Materials John Wiley amp Sons New York NY USA 2006
[30] R Rackwitz and B Flessler ldquoStructural reliability under com-bined random load sequencesrdquo Computers and Structures vol9 no 5 pp 489ndash494 1978
[31] H N Cho H H Choi S Y Lee and J W Sun ldquoMethodologyfor reliability-based assessment of capacity-rating of plate girderrailway bridges using ambient measurement datardquo Journal ofKorea Society of Steel Construction vol 15 no 2 pp 187ndash1962003 (Korean)
[32] B Ellingwood Reliability Bases of Load and Resistance Factorsfor Reinforced Concrete Design National Bureau of StandardsBuilding Science Series 110 Washington DC USA 1978
[33] US Department of CommreceNational Bureau of StandardsldquoDevelopment of a probability based load criteria for Amer-ican National Standard A58rdquo NBS Special Publication 577US Department of CommreceNational Bureau of StandardsGaithersburg Md USA 1980
[34] J A O Barros and A S Fortes ldquoFlexural strengthening ofconcrete beamswithCFRP laminates bonded into slitsrdquoCementand Concrete Composites vol 27 no 4 pp 471ndash480 2005
[35] S H Kim H K Cho H W Bae and H S Park ldquoReliabilityevaluation of structures-a case of reinforced concrete buildingsunder dead live and wind loadsrdquo Technical Report KoreaInstitute of Construction Technology 1989 (Korean)
[36] J G MacGregor ldquoLoad and resistance factors for concretedesignrdquo Journal of the American Concrete Institute vol 80 no4 pp 279ndash287 1983
[37] J M Kulicki D R Mertz and W G Wassef ldquoLRFD Designof highway bridgesrdquo NHI Course 13061 Federal HighwayAdministration Washington DC USA 1994
[38] AASHTO Bridge Design Practice American Association ofState Highway and Transportation Officials Washington DCUSA 2011
[39] A S Nowak and A M Rakoczy ldquoReliability-based calibrationof design code for concrete structures (ACI 318)rdquo in Proceeding
of the Anais do 54 Congress Brasileiro do Concreto CBC2012-54CBC pp 1ndash12 2012
Degree of sensitive for COV of Degree of sensitive for COV of live load factorDegree of sensitive for average value of
120588cf
rp
Df
Df
Figure 9 Sensitive analysis for COV and average value of 119863119891and
COV of live load factor
Strengthening effect is denoted as a case series FEM analysiswas performed to calculate the external moment for LS-18and LS-22 design railway load For probability distribution ofLS-22 which is the present design load of railway in Korea
probability characteristics for LS-18 were used in the sameway In order to acquire the reliability-based strengtheningratio for 120573
119879= 35 the range of probability parameters was
roughly considered then the final 5 cases for 120588cfrp from 00001to 000013 were analyzed Each probability distribution curveis illustrated in Figure 7 Figure 8 is the result of reliability-based strengthening ratio According to the result of thestrengthening effect by probability distribution the targetbridge strengthened by the CFRP strip strengthening ratioresulting from the reliability analysis could be sufficientlysafe against the LS-22 present design railway load As thestrengthening ratio of CFRP strip that could satisfy 120573
119879= 35
it was with 120588cfrp = 0000114
53 Sensitive Analysis for Three Important ParametersFigure 9 shows the result of sensitive analysis for three param-eters such as damage factor standard deviation of damagefactor and live load effect The CFRP strip strengtheningratio resulting from the reliability analysis is plotted withthree important parameters The purpose of this process isto identify how sensitively the strengthening ratio will beaffected when the three parameters are varied independentlyThe determination of the variation ranges of the parameterswas considered to simply but effectively apply the sensitivecharacteristics For live loads and damage factor there weresimilar degrees of sensitivity Variation of COV of damagefactor however was more sensitive than that of the otherparameters Itmight be concluded that COVof damage factorlargely affected to estimate the reliability-based strengtheningusing about the CFRP strip For more reliable estimation ofdamage factor many of structural diagnosis data should beanalyzed in future Table 4 summarizes the input parametersused in the sensitive analysis
6 Conclusions
This study suggested the reliability-based strengthening ratiofor 30-year-old railway bridge using CFRP strips Conclu-sions are as follows
(1) In previous strengthening schemes it has beenuncertain to determine how much the strengthen-ing effect should be required The methodology forthe reliability-based strengthening ratio can improve
Mathematical Problems in Engineering 9
these problems of the previous strengtheningmethodThe target reliability index for CFRP strip strengthen-ing is considered as 35 according to AASHTO spec-ification As using the reliability-based strengtheningratio in this studymore effective strengthening designto concrete structure having a specified strength-ening target as well as reflecting the structural andmaterial uncertainties is possible
(2) In the result of a sensitive analysis variation of COVfor damage factor mostly affected to the reliability-based strengthening ratio of CFRP strip Thereforedamage factor should be studied more properly onthe target bridge This may be possible by analyzingthe database for long-term safety inspection historyand its reasonable quantification Stabilization andnormalization processes of the damage factor are alsorequired
(3) One of the important factors for determining thesafety margin against the resistance is external loadeffect In order to improve the reliability-basedstrengthening ratio of CFRP strip in this study uncer-tainties for external load of a railway bridge should beanalytically and experimentally verified This can besolved by analyzing the acquired data from long-termmonitoring then the reliability of the strengtheningratio of CFRP strip will be promoted
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by Korea Institute of EnergyTechnology Evaluation and Planning (0000000015513) andResearch grant from Gyeongnam National University ofScience and Technology
References
[1] FHWA Bridge Programs NBI data 2009 httpwwwfhwadotgovbridgenbi
[2] ACI Committee 440 Guide for the Design and Constructionof Externally Bonded FRP Systems for Strengthening Con-crete Structures (ACI 4402R-08) American Concrete InstituteFarmington Hills Mich USA 2008
[3] J M de Sena Cruz and J A O De Barros ldquoBond between near-surface mounted carbon-fiber-reinforced polymer laminatestrips and concreterdquo Journal of Composites for Construction vol8 no 6 pp 519ndash527 2004
[4] T Hassan and S Rizkalla ldquoInvestigation of bond in concretestructures strengthened with near surface mounted carbonfiber reinforced polymer stripsrdquo Journal of Composites forConstruction vol 7 no 3 pp 248ndash257 2003
[5] S M Soliman E El-Salakawy and B Benmokrane ldquoFlexuralbehavior of concrete beams strengthened with near surfacemounted FRP barsrdquo in Proceedings of 4th International confer-ence on FRP composites in civil engineering (CICE rsquo08) 2008
[6] J P Firmo J R Correia and P Franca ldquoFire behaviour ofreinforced concrete beams strengthened with CFRP laminatesprotection systems with insulation of the anchorage zonesrdquoComposites Part B Engineering vol 43 no 3 pp 1545ndash15562012
[7] S M Soliman E El-Salakawy and B Benmokrane ldquoBondperformance of near-surface-mounted FRP barsrdquo Journal ofComposites for Construction vol 15 no 1 pp 103ndash111 2011
[8] THassan and S Rizkalla ldquoFlexural strengthening of prestressedbridge slabs with FRP systemsrdquo PCI Journal vol 47 no 1 pp76ndash93 2002
[9] J R Yost S P Gross and D W Dinehart ldquoNear surfacemounted CFRP reinforcement for structural retrofit of concreteflexural membersrdquo in Proceedings of the 4th InternationalConference on Advanced Composite Materials in Bridges andStructures Calgary Canada 2004
[10] Z He and F Qiu ldquoProbabilistic assessment on flexural capacityof GFRP-reinforced concrete beams designed by guideline ACI4401R-06rdquo Construction and Building Materials vol 25 no 4pp 1663ndash1670 2011
[11] Z He and L Jiang ldquoFlexural reliability assessment of FRP-strengthened reinforced concrete beams designed by ChineseCECS-146 Guidelinerdquo Pacific Science Review vol 9 no 1 pp123ndash133 2007
[12] International Organization for Standardization ldquoDetermina-tion of tensile properties-part 5 test conditions for unidirec-tional fibre reinforced plastic compositesrdquo ISO 527-5 Interna-tional Organization for Standardization Geneva Switzerland1997
[13] B H Oh C K Koh S W Baik H J Lee and S H HanldquoRealistic reliability analysis of reinforced concrete structuresrdquoJournal of Korea Society of Civil Engineering vol 13 no 2 pp121ndash133 1993 (Korean)
[14] Steel bars for concrete reinforcement KS D 3504 KoreanIndustrial Standards 2011 (Korean)
[15] KR Network Design Specification of Railway Railway BridgeKorea Rail Network Authority Seoul Republic of Korea 2004(Korean)
[16] S K Hwang J T Oh J S Lee et al Performance Enhancementof Railway System-Track amp Civil Development of the DesignSpecification for Improving Dynamic Characteristics of RailwayBridges Korea Railway Research Institute Seoul Republic ofKorea 2003 (Korean)
[17] H S Shang T H Yi and L S Yang ldquoExperimental studyon the compressive strength of big mobility concrete withnondestructive testing methodrdquo Advances in Materials Scienceand Engineering vol 2012 Article ID 345214 6 pages 2012
[18] TH YiHN Li andHM Sun ldquoMulti-stage structural damagediagnosis method based on ldquoenergy-damagerdquo theoryrdquo SmartStructures And Systems vol 12 no 3-4 pp 345ndash361 2013
[19] H S Shang T H Yi and X X Guo ldquoStudy on strength andultrasonic of air-entrained concrete and plain concrete in coldenvironmentrdquo Advances in Materials Science and Engineeringvol 2014 Article ID 706986 7 pages 2014
[20] Korea High Speed Rail Construction Authority (KHRC)ldquoBridge designmanual (BRDM)rdquo Technical Report KoreaHighSpeed Rail Construction Authority (KHRC) Pusan Public ofKorea 1995 (Korean)
[21] International Union of Railway UIC Code 776-1R Loads to BeConsidered in Railway Bridge Design International Union ofRailway Paris France 4th edition 1994
10 Mathematical Problems in Engineering
[22] M Abdessemed S Kenai A Bali and A Kibboua ldquoDynamicanalysis of a bridge repaired by CFRP experimental andnumerical modellingrdquoConstruction and BuildingMaterials vol25 no 3 pp 1270ndash1276 2011
[23] G Zanardo H Hao Y Xia and A J Deeks ldquoStiffness assess-ment through modal analysis of an RC slab bridge before andafter strengtheningrdquo Journal of Bridge Engineering vol 11 no 5pp 590ndash601 2006
[24] Korea Infrastructure Safety and Technology corporation(KISTEC) A Database of Maintenance History KoreaInfrastructure Safety and Technology corporation (KISTEC)Gyeonggi-do Republic of Korea 2003 (Korean)
[25] MIDAS IT MIDAS Civil Program Manual MIDAS ITGyeonggi Republic of Korea 2009
[26] S W Tabsh and A S Nowak ldquoReliability of highway girderbridgesrdquo Journal of Structural Engineering ASCE vol 117 no 8pp 2372ndash2388 1991
[27] H N Cho K H Kwak and S J Lee ldquoReliability-based safetyand capacity evaluation of high-speed railway bridgesrdquo Journalof Computational Structural Engineering Institute in KoreaCOSEIK vol 10 no 3 pp 133ndash143 1997 (Korean)
[28] ACI Committee 440 Guide for the Design and Constructionof Externally Bonded FRP Systems for Strengthening ConcreteStructures American Concrete Institute Farmington HillsMich USA 2008
[29] L C Bank Composites for Construction-Structural Design withFRP Materials John Wiley amp Sons New York NY USA 2006
[30] R Rackwitz and B Flessler ldquoStructural reliability under com-bined random load sequencesrdquo Computers and Structures vol9 no 5 pp 489ndash494 1978
[31] H N Cho H H Choi S Y Lee and J W Sun ldquoMethodologyfor reliability-based assessment of capacity-rating of plate girderrailway bridges using ambient measurement datardquo Journal ofKorea Society of Steel Construction vol 15 no 2 pp 187ndash1962003 (Korean)
[32] B Ellingwood Reliability Bases of Load and Resistance Factorsfor Reinforced Concrete Design National Bureau of StandardsBuilding Science Series 110 Washington DC USA 1978
[33] US Department of CommreceNational Bureau of StandardsldquoDevelopment of a probability based load criteria for Amer-ican National Standard A58rdquo NBS Special Publication 577US Department of CommreceNational Bureau of StandardsGaithersburg Md USA 1980
[34] J A O Barros and A S Fortes ldquoFlexural strengthening ofconcrete beamswithCFRP laminates bonded into slitsrdquoCementand Concrete Composites vol 27 no 4 pp 471ndash480 2005
[35] S H Kim H K Cho H W Bae and H S Park ldquoReliabilityevaluation of structures-a case of reinforced concrete buildingsunder dead live and wind loadsrdquo Technical Report KoreaInstitute of Construction Technology 1989 (Korean)
[36] J G MacGregor ldquoLoad and resistance factors for concretedesignrdquo Journal of the American Concrete Institute vol 80 no4 pp 279ndash287 1983
[37] J M Kulicki D R Mertz and W G Wassef ldquoLRFD Designof highway bridgesrdquo NHI Course 13061 Federal HighwayAdministration Washington DC USA 1994
[38] AASHTO Bridge Design Practice American Association ofState Highway and Transportation Officials Washington DCUSA 2011
[39] A S Nowak and A M Rakoczy ldquoReliability-based calibrationof design code for concrete structures (ACI 318)rdquo in Proceeding
of the Anais do 54 Congress Brasileiro do Concreto CBC2012-54CBC pp 1ndash12 2012
these problems of the previous strengtheningmethodThe target reliability index for CFRP strip strengthen-ing is considered as 35 according to AASHTO spec-ification As using the reliability-based strengtheningratio in this studymore effective strengthening designto concrete structure having a specified strength-ening target as well as reflecting the structural andmaterial uncertainties is possible
(2) In the result of a sensitive analysis variation of COVfor damage factor mostly affected to the reliability-based strengthening ratio of CFRP strip Thereforedamage factor should be studied more properly onthe target bridge This may be possible by analyzingthe database for long-term safety inspection historyand its reasonable quantification Stabilization andnormalization processes of the damage factor are alsorequired
(3) One of the important factors for determining thesafety margin against the resistance is external loadeffect In order to improve the reliability-basedstrengthening ratio of CFRP strip in this study uncer-tainties for external load of a railway bridge should beanalytically and experimentally verified This can besolved by analyzing the acquired data from long-termmonitoring then the reliability of the strengtheningratio of CFRP strip will be promoted
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgments
This work was supported by Korea Institute of EnergyTechnology Evaluation and Planning (0000000015513) andResearch grant from Gyeongnam National University ofScience and Technology
References
[1] FHWA Bridge Programs NBI data 2009 httpwwwfhwadotgovbridgenbi
[2] ACI Committee 440 Guide for the Design and Constructionof Externally Bonded FRP Systems for Strengthening Con-crete Structures (ACI 4402R-08) American Concrete InstituteFarmington Hills Mich USA 2008
[3] J M de Sena Cruz and J A O De Barros ldquoBond between near-surface mounted carbon-fiber-reinforced polymer laminatestrips and concreterdquo Journal of Composites for Construction vol8 no 6 pp 519ndash527 2004
[4] T Hassan and S Rizkalla ldquoInvestigation of bond in concretestructures strengthened with near surface mounted carbonfiber reinforced polymer stripsrdquo Journal of Composites forConstruction vol 7 no 3 pp 248ndash257 2003
[5] S M Soliman E El-Salakawy and B Benmokrane ldquoFlexuralbehavior of concrete beams strengthened with near surfacemounted FRP barsrdquo in Proceedings of 4th International confer-ence on FRP composites in civil engineering (CICE rsquo08) 2008
[6] J P Firmo J R Correia and P Franca ldquoFire behaviour ofreinforced concrete beams strengthened with CFRP laminatesprotection systems with insulation of the anchorage zonesrdquoComposites Part B Engineering vol 43 no 3 pp 1545ndash15562012
[7] S M Soliman E El-Salakawy and B Benmokrane ldquoBondperformance of near-surface-mounted FRP barsrdquo Journal ofComposites for Construction vol 15 no 1 pp 103ndash111 2011
[8] THassan and S Rizkalla ldquoFlexural strengthening of prestressedbridge slabs with FRP systemsrdquo PCI Journal vol 47 no 1 pp76ndash93 2002
[9] J R Yost S P Gross and D W Dinehart ldquoNear surfacemounted CFRP reinforcement for structural retrofit of concreteflexural membersrdquo in Proceedings of the 4th InternationalConference on Advanced Composite Materials in Bridges andStructures Calgary Canada 2004
[10] Z He and F Qiu ldquoProbabilistic assessment on flexural capacityof GFRP-reinforced concrete beams designed by guideline ACI4401R-06rdquo Construction and Building Materials vol 25 no 4pp 1663ndash1670 2011
[11] Z He and L Jiang ldquoFlexural reliability assessment of FRP-strengthened reinforced concrete beams designed by ChineseCECS-146 Guidelinerdquo Pacific Science Review vol 9 no 1 pp123ndash133 2007
[12] International Organization for Standardization ldquoDetermina-tion of tensile properties-part 5 test conditions for unidirec-tional fibre reinforced plastic compositesrdquo ISO 527-5 Interna-tional Organization for Standardization Geneva Switzerland1997
[13] B H Oh C K Koh S W Baik H J Lee and S H HanldquoRealistic reliability analysis of reinforced concrete structuresrdquoJournal of Korea Society of Civil Engineering vol 13 no 2 pp121ndash133 1993 (Korean)
[14] Steel bars for concrete reinforcement KS D 3504 KoreanIndustrial Standards 2011 (Korean)
[15] KR Network Design Specification of Railway Railway BridgeKorea Rail Network Authority Seoul Republic of Korea 2004(Korean)
[16] S K Hwang J T Oh J S Lee et al Performance Enhancementof Railway System-Track amp Civil Development of the DesignSpecification for Improving Dynamic Characteristics of RailwayBridges Korea Railway Research Institute Seoul Republic ofKorea 2003 (Korean)
[17] H S Shang T H Yi and L S Yang ldquoExperimental studyon the compressive strength of big mobility concrete withnondestructive testing methodrdquo Advances in Materials Scienceand Engineering vol 2012 Article ID 345214 6 pages 2012
[18] TH YiHN Li andHM Sun ldquoMulti-stage structural damagediagnosis method based on ldquoenergy-damagerdquo theoryrdquo SmartStructures And Systems vol 12 no 3-4 pp 345ndash361 2013
[19] H S Shang T H Yi and X X Guo ldquoStudy on strength andultrasonic of air-entrained concrete and plain concrete in coldenvironmentrdquo Advances in Materials Science and Engineeringvol 2014 Article ID 706986 7 pages 2014
[20] Korea High Speed Rail Construction Authority (KHRC)ldquoBridge designmanual (BRDM)rdquo Technical Report KoreaHighSpeed Rail Construction Authority (KHRC) Pusan Public ofKorea 1995 (Korean)
[21] International Union of Railway UIC Code 776-1R Loads to BeConsidered in Railway Bridge Design International Union ofRailway Paris France 4th edition 1994
10 Mathematical Problems in Engineering
[22] M Abdessemed S Kenai A Bali and A Kibboua ldquoDynamicanalysis of a bridge repaired by CFRP experimental andnumerical modellingrdquoConstruction and BuildingMaterials vol25 no 3 pp 1270ndash1276 2011
[23] G Zanardo H Hao Y Xia and A J Deeks ldquoStiffness assess-ment through modal analysis of an RC slab bridge before andafter strengtheningrdquo Journal of Bridge Engineering vol 11 no 5pp 590ndash601 2006
[24] Korea Infrastructure Safety and Technology corporation(KISTEC) A Database of Maintenance History KoreaInfrastructure Safety and Technology corporation (KISTEC)Gyeonggi-do Republic of Korea 2003 (Korean)
[25] MIDAS IT MIDAS Civil Program Manual MIDAS ITGyeonggi Republic of Korea 2009
[26] S W Tabsh and A S Nowak ldquoReliability of highway girderbridgesrdquo Journal of Structural Engineering ASCE vol 117 no 8pp 2372ndash2388 1991
[27] H N Cho K H Kwak and S J Lee ldquoReliability-based safetyand capacity evaluation of high-speed railway bridgesrdquo Journalof Computational Structural Engineering Institute in KoreaCOSEIK vol 10 no 3 pp 133ndash143 1997 (Korean)
[28] ACI Committee 440 Guide for the Design and Constructionof Externally Bonded FRP Systems for Strengthening ConcreteStructures American Concrete Institute Farmington HillsMich USA 2008
[29] L C Bank Composites for Construction-Structural Design withFRP Materials John Wiley amp Sons New York NY USA 2006
[30] R Rackwitz and B Flessler ldquoStructural reliability under com-bined random load sequencesrdquo Computers and Structures vol9 no 5 pp 489ndash494 1978
[31] H N Cho H H Choi S Y Lee and J W Sun ldquoMethodologyfor reliability-based assessment of capacity-rating of plate girderrailway bridges using ambient measurement datardquo Journal ofKorea Society of Steel Construction vol 15 no 2 pp 187ndash1962003 (Korean)
[32] B Ellingwood Reliability Bases of Load and Resistance Factorsfor Reinforced Concrete Design National Bureau of StandardsBuilding Science Series 110 Washington DC USA 1978
[33] US Department of CommreceNational Bureau of StandardsldquoDevelopment of a probability based load criteria for Amer-ican National Standard A58rdquo NBS Special Publication 577US Department of CommreceNational Bureau of StandardsGaithersburg Md USA 1980
[34] J A O Barros and A S Fortes ldquoFlexural strengthening ofconcrete beamswithCFRP laminates bonded into slitsrdquoCementand Concrete Composites vol 27 no 4 pp 471ndash480 2005
[35] S H Kim H K Cho H W Bae and H S Park ldquoReliabilityevaluation of structures-a case of reinforced concrete buildingsunder dead live and wind loadsrdquo Technical Report KoreaInstitute of Construction Technology 1989 (Korean)
[36] J G MacGregor ldquoLoad and resistance factors for concretedesignrdquo Journal of the American Concrete Institute vol 80 no4 pp 279ndash287 1983
[37] J M Kulicki D R Mertz and W G Wassef ldquoLRFD Designof highway bridgesrdquo NHI Course 13061 Federal HighwayAdministration Washington DC USA 1994
[38] AASHTO Bridge Design Practice American Association ofState Highway and Transportation Officials Washington DCUSA 2011
[39] A S Nowak and A M Rakoczy ldquoReliability-based calibrationof design code for concrete structures (ACI 318)rdquo in Proceeding
of the Anais do 54 Congress Brasileiro do Concreto CBC2012-54CBC pp 1ndash12 2012
[22] M Abdessemed S Kenai A Bali and A Kibboua ldquoDynamicanalysis of a bridge repaired by CFRP experimental andnumerical modellingrdquoConstruction and BuildingMaterials vol25 no 3 pp 1270ndash1276 2011
[23] G Zanardo H Hao Y Xia and A J Deeks ldquoStiffness assess-ment through modal analysis of an RC slab bridge before andafter strengtheningrdquo Journal of Bridge Engineering vol 11 no 5pp 590ndash601 2006
[24] Korea Infrastructure Safety and Technology corporation(KISTEC) A Database of Maintenance History KoreaInfrastructure Safety and Technology corporation (KISTEC)Gyeonggi-do Republic of Korea 2003 (Korean)
[25] MIDAS IT MIDAS Civil Program Manual MIDAS ITGyeonggi Republic of Korea 2009
[26] S W Tabsh and A S Nowak ldquoReliability of highway girderbridgesrdquo Journal of Structural Engineering ASCE vol 117 no 8pp 2372ndash2388 1991
[27] H N Cho K H Kwak and S J Lee ldquoReliability-based safetyand capacity evaluation of high-speed railway bridgesrdquo Journalof Computational Structural Engineering Institute in KoreaCOSEIK vol 10 no 3 pp 133ndash143 1997 (Korean)
[28] ACI Committee 440 Guide for the Design and Constructionof Externally Bonded FRP Systems for Strengthening ConcreteStructures American Concrete Institute Farmington HillsMich USA 2008
[29] L C Bank Composites for Construction-Structural Design withFRP Materials John Wiley amp Sons New York NY USA 2006
[30] R Rackwitz and B Flessler ldquoStructural reliability under com-bined random load sequencesrdquo Computers and Structures vol9 no 5 pp 489ndash494 1978
[31] H N Cho H H Choi S Y Lee and J W Sun ldquoMethodologyfor reliability-based assessment of capacity-rating of plate girderrailway bridges using ambient measurement datardquo Journal ofKorea Society of Steel Construction vol 15 no 2 pp 187ndash1962003 (Korean)
[32] B Ellingwood Reliability Bases of Load and Resistance Factorsfor Reinforced Concrete Design National Bureau of StandardsBuilding Science Series 110 Washington DC USA 1978
[33] US Department of CommreceNational Bureau of StandardsldquoDevelopment of a probability based load criteria for Amer-ican National Standard A58rdquo NBS Special Publication 577US Department of CommreceNational Bureau of StandardsGaithersburg Md USA 1980
[34] J A O Barros and A S Fortes ldquoFlexural strengthening ofconcrete beamswithCFRP laminates bonded into slitsrdquoCementand Concrete Composites vol 27 no 4 pp 471ndash480 2005
[35] S H Kim H K Cho H W Bae and H S Park ldquoReliabilityevaluation of structures-a case of reinforced concrete buildingsunder dead live and wind loadsrdquo Technical Report KoreaInstitute of Construction Technology 1989 (Korean)
[36] J G MacGregor ldquoLoad and resistance factors for concretedesignrdquo Journal of the American Concrete Institute vol 80 no4 pp 279ndash287 1983
[37] J M Kulicki D R Mertz and W G Wassef ldquoLRFD Designof highway bridgesrdquo NHI Course 13061 Federal HighwayAdministration Washington DC USA 1994
[38] AASHTO Bridge Design Practice American Association ofState Highway and Transportation Officials Washington DCUSA 2011
[39] A S Nowak and A M Rakoczy ldquoReliability-based calibrationof design code for concrete structures (ACI 318)rdquo in Proceeding
of the Anais do 54 Congress Brasileiro do Concreto CBC2012-54CBC pp 1ndash12 2012