seismic performance of a corroded reinforce concrete...

Research ArticleSeismic Performance of a Corroded Reinforce Concrete FrameStructure Using Pushover Method

Meng Zhang 1 Ran Liu 1 Yaoliang Li12 and Guifeng Zhao 1

1School of Civil Engineering Zhengzhou University Zhengzhou 450001 China2Liuzhou Administration of Power Supply of Guangxi Grid Company China Southern Power Grid Liuzhou 545005 China

Correspondence should be addressed to Guifeng Zhao gfzhaozzueducn

Received 7 January 2018 Revised 17 March 2018 Accepted 1 April 2018 Published 2 May 2018

Academic Editor Song Han

Copyright copy 2018 Meng Zhang et al is 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

SAP2000 software was used to build the finite element model of a six-storey-three-span reinforced concrete (RC) frame structuree numerical simulation of the seismic performance of the RC frame structure incorporating different levels of rebar corrosionwas conducted using pushover analysis method e degradation characteristics of the seismic performance of the corrodedstructure under severe earthquake were also analyzed e results show that the seismic performance of the RC frame decreasedsignificantly due to corrosion of the longitudinal rebars And the interstory drift ratios increase dramatically with the increasing ofthe corrosion rate At the same time the formation and development of plastic hinges (beam hinges or column hinges) willaccelerate which leads to a more aggravated deformation of the structure under rare earthquake action resulting in a negativeeffect to the seismic bearing capacity of the structure

1 Introduction

e building seismic fortification requirements are graduallyimproving around the world and the buildings in strictaccordance with design and construction code also showedgood seismic performance during earthquakes But in recentyears the houses collapses highway cracks [1] and casu-alties caused by earthquakes are still high such as theWenchuan earthquake the India-Pakistan earthquake [2]and the Chilean earthquake [3] e postdisaster survey datashow that collapsed or severely damaged houses are mainlymultistorey masonry buildings or concrete frame structureswith relatively poor seismic performance [4]

Currently multistory masonry houses have been grad-ually restricted to be built and used in large and medium-sized cities while the reinforced concrete frame buildingsare still widely used in schools office buildings residentialbuildings street shops and other buildings due to theirflexible plan layout and strong adaptability With the in-crease of service years under the induction of externalcorrosion factors the material of reinforced concrete framestructure will deteriorate [5ndash8] resulting in the durabilitydamage (such as surface cracks [9] carbonization spalling

and steel corrosion [10]) Among which the corrosion ofsteel bar is regarded as the prime factor that affecting thedurability of concrete structures [11ndash13] Corrosion leads tothe degradation of geometric parameters and mechanicalproperties of the rebar and to some extent weaken the staticbearing capacity of a concrete structure and increase itsbrittleness Meanwhile the seismic performance will beinevitably impaired [14ndash17] erefore it is of importanttheoretical significance and engineering guiding value tostudy the degradation law of seismic performance of cor-roded reinforced concrete frame structures At the sametime it can also provide reference about the seismic per-formance evaluation and maintenance reinforcement for theold reinforced concrete frame structures in the seismic area

In this paper the finite element model of a six-storey-three-span corroded reinforced concrete (RC) framestructure was built using SAP2000 software [18 19] enumerical simulation of the seismic performance of thecorroded RC frame structure was conducted using pushoveranalysis method [20] because pushover analysis method isthe most widely used and convenient method for the seismicperformance analysis of the middle-low level RC framestructure Pushover method is based on the structural static

HindawiAdvances in Civil EngineeringVolume 2018 Article ID 7208031 12 pageshttpsdoiorg10115520187208031

elastic-plastic analysis theory by increasing the lateral loadon the inertial force center of each floor of the structure toobtain the relationship between internal forces and de-formation response in this process Finally using the seismicdemand spectrum and capacity spectrum (ATC-40 responsespectrum or Chinese code response spectrum) to estimatethe performance point index of the structure one can easilyevaluate the seismic performance of the structure [21] emain advantage of the pushover analysis method is that theelastic-plastic response of the structure can be consideredand the calculation results are stable is paper also ana-lyzed the degradation law of the seismic performance in-dicators of the corroded RC frame structure under severeearthquake e results were expected to provide a referencefor seismic safety analysis reliability assessment mainte-nance reinforcement and reconstruction of corroded RCframe structures

2 Mechanical Properties of CorrodedReinforced Concrete Materials

21 Degradation of the Mechanical Properties of ConcreteCover A large number of experiments and theoreticalanalyses have shown that the concrete cover of a RC framestructure will be cracked and peeled off due to the role of rustexpansion force after the steel corrosion In addition itweakens the bond strength between the rebar and concretehence reducing the service life of the structure [22 23]Considering that the core concrete binding force of anordinary reinforced cement concrete member is mainly fromthe protective layer the cracking and peeling of the concretecover will reduce its restraint on the core concrete andfurther weaken the load and deformation capacity of themember erefore the degradation of mechanical prop-erties of the protective concrete cover should not be ignoredduring structural analysis Due to the strong randomcharacteristics of the deterioration of the cover concrete it isdifficult to use analytic methods to determine the degree andlocation of deterioration In order to simplify the calculation(1) is used here to calculate the strength of the cover concrete[24 25]

fcminuscor fc

1 + c εt-corεc( 1113857

εtminuscor bcor minus b

b

bcor b + nωcor

ωcor 1113944i

uicor 2π υcor minus 1( 1113857X

ρs 2X

rminus

X

r1113874 1113875

2

(1)

where fcminuscor is the peak value of the compressive strength ofthe concrete cover after the steel bar corrosion c is thecorrelation coefficient between the rebar surface shape andits diameter and it is usually suggested to be 01 εtminuscor is thegeneralized cracking strain of concrete b is the originalwidth of the member bcor is the cross-sectional width of the

corrosion member n is the number of longitudinal rebarsωcor is the total width of the corrosion crack υcor is rustoxidation products and the volume ratio coefficient beforerust and it can be taken value 20 uicor is the width of the ithcorrosion crack X is the depth of steel bar corrosion ρs isthe corrosion loss rate of the rebar section and r is the radiusof the steel rebar before corrosion and it can be taken as theweighted average value when the reinforcement diametersare different

22 Degradation of the Corrosion Steel Bar MechanicalProperties Usually because the distribution of rust factors(such as cracks chloride ions and sulfate ions [26]) hassignificant random characteristics the corrosion status ofreinforcement in RC members often appears as pittingcorrosion Numerical analysis usually adopts the method ofequivalent uniform corrosion to deal with the degradation ofmechanical properties of pit corroded steel bars so as toimprove the accuracy of numerical simulation or theoreticalanalysis [27] It is assumed that the cross section of the rebaris in a uniform corrosion state but its mechanical propertiesare degradated according to the pit corrosion equation Inorder to consider the effect of pitting corrosion on themechanical properties of corroded rebar the nominal yieldstress and elastic modulus of the corroded rebar are cal-culated by (2) [28] and the ultimate stress and strain [29]can be calculated by (3)

fyc (1minus 00198δ)fy

Esc (1minus 00113δ)Es(2)

fuc (10minus 0019δ)fu

εuc (10minus 0021δ)εu(3)

where fy (fyc) is the nominal yield strength of the steel barbefore (after) corrosion Es (Esc) is the nominal modulus ofelasticity of the steel bar before (after) corrosion fu (fuc) isthe nominal ultimate strength of the steel bar before (after)corrosion εu (εuc) is the nominal ultimate strain of the steelbar before (after) corrosion and δ stands for the mass lossrate of the corroded steel e relationship between ρs and δcan be seen in (4) [28]

ρs

0013 + 0987δ δ le 10

0061 + 0939δ 10lt δ le 20

0129 + 0871δ 20lt δ le 30

0199 + 0810δ 30lt δ le 40

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(4)

3 Pushover Analysis Results of theNoncorroded RC Frame Structure

31 Engineering Background and Calculation ParametersFor the purposes of comparison a model of noncorroded RCframe building was presented here e building model hassix stories with typical story height 36m and the overallplan area is 24times12m All beams are 300times 550mm ecolumns in 1ndash3 storeys are 500times 500mm while the columns

2 Advances in Civil Engineering

in 4ndash6 storeys are 400times 400mm rectangular Figure 1 showsthe typical structural layout It can be seen that the buildingmodel is a typical biaxially symmetric structure ereforeto simplify the following computation only the plane framein axis ③-③ (Figure 1(b)) is selected to perform pushoveranalysis

According to Chinese Standard GB50011-2010 Code forSeismic Design of Buildings [30] the building is located inclass II site with the design earthquake group of 2 and thedesign basic acceleration of ground motion 020 g e loadsacting on the building are in strict accordance with ChineseStandard GB50009-2012 Load Code for the Design ofBuilding Structures [31] and the representative values of thegravity load are shown in Table 1

e design strength of concrete was C30 grade and thelongitudinal reinforcement was Grade II rebar (HRB335) whileGrade I rebar (HPB300) was used for the stirrups Figure 2shows the geometric parameters and the reinforcement layoutof the beams and columns e detailed design material pa-rameters and reinforcement parameters of the beams andcolumns are shown in Tables 2 and 3 respectively

32 Pushover AnalysisMethod Pushover analysis is a static-nonlinear analysis method [20] During pushover analysisa structure is subjected to lateral load which continuouslyincreases through elastic and inelastic behaviours until theultimate condition is reached e key thing here is that theplastic hinge theory plays an important role in pushover

analysis Plastic hinges are often used to simulate thenonlinear behaviour of the structure the plastic develop-ment degree of the plastic hinges is used to reect the plasticdevelopment degree of the structure In the SAP2000 pro-gram yielding and postyielding behaviour can be modelledusing either default hinges or user-dened hinges Eachhinge represents concentrated postyield behaviour in one ormore degrees of freedom Default hinges include uncoupledmoment (M) torsion (T) axial force (P) shear (V) hingesand coupled P-M2-M3 (or P-M-M) hinge which yields basedon the interaction of axial force and bending moments at thehinge location For the P-M-M hinge an interaction (yield)surface should be specied in the three-dimensional P-M2-M3 space that represents the rst yielding location fordierent combinations of axial force P minor moment M2and major moment M3 In the SAP2000 program the built-in default hinge properties for steel members are providedbased on FEMA-356 criteria [32] and the built-in defaulthinge properties for concrete members are generally basedon ATC-40 criteria [33] For the user-dened plastic hingesXTRACT [34] software is generally utilized to determine themoment-rotation curves for beam and P-M-M interactioncurves for columns When analyzing an RC frame structureplastic hinge regions are usually assigned to the ends of themembers For the beam element the plastic hinge is usuallyyielded only by the bending moment (M) and the plastichinge is generally considered by the axial force and the two-way bending moment correlation (P-M-M) for the columnelement When the default hinge is adopted to simulate the

4500

3000

4500

6000 6000 600024000

24000

6000

6000

1

6000 6000 6000

12000

4500

3000

4500

12000

2 3 4 5

1 2 3 4 5

D

C

B

A

D

C

B

A

(a)

1

4500

A B C D

3000 450012000

3600

21600

3600

3600

3600

3600

3600

2 1

121

1 2 1

222

2 2 2

222

(b)

Figure 1 Layout of the RC frame building (a) Plane of the RC frame structure (b) Elevation of the RC frame structure in axis ③-③

Table 1 Representative values of the gravity load on the RC frame

Distributed span load (kNm) Concentrated load (kN)Beam in side span Beam in middle span Node in side span Node in middle span

Standard storeys 229 113 1114 1228Top storey 182 121 783 1519

Advances in Civil Engineering 3

nonlinear behavior of the structure only the inuence ofrebar corrosion on degradation law of the plastic hingeparameters can be considered However from the aboveanalysis it can be seen that the degradation of mechanicalproperties of the protective concrete cover should not beignored during the structural analysis e user-denedhinge can fully consider the eects of rebar corrosion andthe degradation of mechanical properties of the protectiveconcrete cover as well as the plastic hinge parametersdegradation law so we adopt a user-dened plastic hinges inthe nonlinear analysis of the structure

To determine the development of the plastic hinges onthe frame structure a force-displacement (moment-rotation)curve can be dened according to FEMA-356 criteria whichgives the yield value and the plastic deformation following

yield is is done in terms of a curve with values at vepoints A-B-C-D-E as shown in Figure 3

As is suggested by Figure 3 there are four line segments(ie AB BC CD and DE) in the skeleton curve repre-senting the elastic stage the strengthening stage theunloading stage and the failure stage respectively More-over FEMA-356 criteria also set three performance points(ie IO LS and CP) between the characteristic points B andC IO is the abbreviation for ldquoImmediate Occupancyrdquo whichmeans that the structure is in the serviceability limit state LSis the abbreviation for ldquoLife Safetyrdquo which means that thestructure is close to the safety limit state CP is the

250

250

250 250

183

8100

183

(a)

200

200 200

200

8100

163

163

(b)

300

550 8100

204

164

(c)

300

550 8100

184

203

(d)

Figure 2 Dimensions and reinforcement layout of the RC frame members (a) Reinforcement layout of columns in 1ndash3 storey (b)Reinforcement layout of columns in 4ndash6 storey (c) Reinforcement layout of beams① (Figure 1(b)) (d) Reinforcement layout of beams②(Figure 1(b))

Table 2 Material parameters of noncorroded members

Concrete (C30) fcu (MPa) fc (MPa) ft (MPa) Ec (MPa)30 24 24 245952

Longitudinalreinforcement(HRB335)

fy (MPa) fu (MPa) εu Es (MPa)

335 455 015 200000

Table 3 Detailed reinforcement parameters of beams and columns

Columnreinforcement

(mm2)Beam reinforcement (mm2)

Storey mdash Beamnumbering

Upperreinforcement

Bottomreinforcement

1ndash3 2036 ① 1256 8044ndash6 1608 ② 1017 942


abbreviation for ldquoCollapse Preventionrdquo which means thatthe structure is close to the collapse limit state

33 Pushover Analysis Results

331 Comparison of the P-M-M Curves between DefaultHinges and User-Dened Plastic Hinges In view of the bi-axial symmetry of the cross section of the noncorroded framecolumn Figure 4 presents only the correlation curve of theaxial force P and the major moment M3 in the x direction ofthe column section It can be seen that the P-M-M curvesobtained by user-dened plastic hinge are in good agreementwith those by the built-in default hinge in SAP2000 software

Table 4 provides the parameters of the P-M-M curves ofthe noncorroded column section It can be seen from Figure 4and Table 4 that the computed key-point parameters of theP-M-M curves using user-dened hinge are generally con-sistent with those acquired by the built-in default hinge inSAP2000 software e maximum discrepancy is within 5is indicated that the user-dened hinge has relatively higherprecision and can be used in the subsequent analysis

332 Comparison of the Pushover Analysis Results betweenDefault Hinges and User-Dened Hinges Considering thatthe load pattern may aect the pushover analysis results dra-matically it is important to consider at least two dierent lateralpushover cases to represent dierent sequences of response thatcould occur during dynamic loading [29] erefore thepushover analysis in this paper should be performed using bothof the following lateral load patterns the uniform patterncorresponding to uniform unidirectional lateral accelerationand the 1st modal patterne 1st modal pattern is a pattern offorces on the joints that is proportional to the product of thefundamental mode shape times its circular frequency squaredtimes the mass tributary to the joint In view of the remarkablematerial nonlinear of concrete the load pattern based ondisplacement control is chosen in this paper to avoid troubleconverging e pushover curves for the plane frame in axis③-③ under dierent load patterns are shown in Figure 5

From the simulation results in Figure 5 we can see thatalthough the pushover curves of the frame are quite dierentunder dierent lateral load patterns the pushover curves

obtained by using user-dened hinges almost exactly co-incide with those by using the default plastic hinges inSAP2000 under the same lateral load pattern

Table 5 gives the calculation results of the elastoplasticinterstory drift ratios of the noncorroded plane frame underrare earthquake action From Table 5 it could also be seenthat the story drift ratios obtained by using user-denedhinges are generally consistent with those obtained by usingthe default hinges in SAP2000 under the same lateral loadpattern e maximum discrepancy is less than 5 and themaximum story drift ratio is very close to 1120 which canmeet the code requirement [32]

4 Pushover Analysis Results of the CorrodedFrame Structure

41 Plastic Hinge Properties of Corroded Beams and ColumnsWhen considering rebar corrosion the geometric parame-ters and mechanical properties of the rebar will degeneratewhich will inevitably aect the plastic hinge properties of

I0 LSB

A

Forc

e

Displacement

CP

C

ED

Figure 3 Typical nonlinear skeleton curve in SAP2000 accordingto FEMA-356 Default hinge

User-defined hinge

ndash1000

0

1000

2000

3000

4000

5000

6000

8000

Axi

al fo

rce P

(kN

)

100 200 300 400 500Moment M (kNmiddotm)

0

7000

(a)

Default hingeUser-defined hinge

ndash1000

0

1000

2000

3000

4000

5000

Axi

al fo

rce P

(kN

)

100 200 3000Moment M (kNmiddotm)

(b)

Figure 4 Comparison of the P-M-M curves of the noncorrodedRC column section (a) RC column with cross section of 500times 500mm(b) RC column with cross section of 400times 400mm


corroded beam and columns To simplify the followingcomputation in this paper the P-M-M interaction curvesfor dierent corroded RC columns are calculated using user-dened hinge with the help of XTRACT software while themoment curvature (M3) for dierent corroded RC beamscan be obtained using user-dened hinge by literature [35]

To understand the inuence of dierent amounts of rebarcorrosion on the seismic performance of the RC framestructure four sets of operating conditions including non-corroded slight corrosion moderate corrosion and severecorrosion were selected According to the literature [35] thecorresponding uniform corrosion rates of the rebar crosssection under the four conditions above were 0 5 10and 18 respectively e corresponding concrete cover andreinforcement parameters under the four cases including thestrength of concrete cover the yield strength of the rebar theelastic modulus of the rebar etc are listed in Table 6

411 Degradation of the P-M-M Curves of Corroded ColumnUsing User-Dened Hinge According to the parameters inTable 6 the P-M-M curves of the RC column under dierentdegrees of corrosion can be obtained and the results areshown in Figure 6 It can be seen that with an increasedcorrosion rate the ultimate bearing capacity of compression

tension and bending of the frame column section decreasedafter the rebar corrosion However comparatively speakingthe ultimate bending moment of the section deterioratesobservably Table 7 shows the detailed results of the

Table 4 Parameters of the key points of the P-M-M curves of the RC frame column

Maximum compressionforce (kN)

Maximum tensionforce (kN)

Maximum bendingmoment (kNmiddotm)

(a) Column with cross section of 500times 500mmDefault hinge (i) 70051 6823 4923User-dened hinge (ii) 72310 6820 4837Relative error () ((ii)minus (i)(i))times 100 322 minus004 minus175(b) Column with cross section of 400times 400mmDefault hinge (i) 45774 5388 2586User-dened hinge (ii) 46970 5388 2579Relative error () ((ii)minus (i)(i))times 100 261 0 -027

0

100

200

300

400

500

600

Base

shea

r (kN

)

100 200 300 4000Top displacement (mm)

User-defined hingeDefault hinge

(a)

100 200 3000Top displacement (mm)

0

100

200

300

400

500

Base

shea

r (kN

)


(b)

Figure 5 Comparison of the pushover curves of the noncorroded RC frame under dierent load patterns (a) Under the uniform loadpattern (b) Under the 1st modal load pattern

Table 5 Story drift ratios of the noncorroded plane frame underrare earthquake action

Storey Defaulthinge (i)

User-denedhinge (ii)

Relative error ()((ii)minus (i)(i))times 100

(a) Under the uniform load pattern1 11623 11639 minus0972 11259 11261 minus0133 11488 11486 0154 12208 12217 minus0445 15746 15650 1726 112346 112195 123(b) Under the 1st modal load pattern1 12016 12016 0002 11259 11256 0253 11193 11196 minus0244 11372 11403 minus2195 13968 13802 4376 19009 18850 180


degradation of maximum bending moments under caseswith dierent corrosion rates

412 Degradation of the Bending Strength of Corroded FrameBeam In this paper the bending strength for noncorrodedbeam hinge (M3) can be computed using the built-in defaulthinge properties in SAP2000 For the plastic hinge propertiesof corroded beams the bending strength of the beam hinge(M3) can be obtained with the help of the calculation resultsof literature [35] e ultimate bending moment of corrodedbeams with four dierent amounts of corrosion are shown inTable 8

42 Pushover Analysis Results for Corroded RC FrameGenerally the corrosion of rebar in RC frame structures ismainly caused by carbonisation cracking and spalling of theconcrete cover erefore it can be reasonably assumed thatthe corrosion rates of columns and beams are the same [12]On the base of the parameters for plastic hinge properties ofcorroded beams and columns in Figure 6 and Tables 6ndash8 thestatic pushover analysis under rare earthquake action wascarried out incorporating inelastic material behaviour forconcrete and steel with dierent corrosion rates

Table 6 Mechanical property parameters of corroded RC material under dierent degrees of corrosion(a) Strength of concrete coverCorrosion rate () fc (MPa)00 24050 167100 127180 92(b) Mechanical properties of corroded rebarCorrosion rate () fy (MPa) fu (MPa) Es (MPa) εu00 3350 4550 200000 01550 2998 4091 188002 013100 2667 3660 176739 012180 2141 2975 158821 009

100 200 300 400 500Moments (kNmiddotm)ndash1000

0

1000

2000

3000

4000

5000

6000

7000

8000

Axi

al fo

rce P

(kN

)

0 corrosion rate5 corrosion rate


0

(a)

ndash1000

0

1000

2000

3000

4000

5000

Axi

al fo

rce P

(kN

)

100 200 300Moments (kNmiddotm)



0

(b)

Figure 6 Comparison of the P-M-M curves of the column under dierent degrees of corrosion (a) Column with cross section of500times 500mm (b) Column with cross section of 400times 400mm

Table 7 Degradation of the ultimate bending moment of corrodedcolumn section

Corrosion rate()

Mmax (kNmiddotm)Column

(500times 500mm)Column

(400times 400mm)00 4837 257950 4555 2402100 4176 2212180 3836 2131

Table 8 Bending strength of corroded beam hinge (M3) underdierent degrees of corrosion

Corrosion rate()

Beam ① Beam ②+M

(kNmiddotm)minusM

(kNmiddotm)+M

(kNmiddotm)minusM

(kNmiddotm)00 1299 1988 1513 162850 1181 1807 1375 1480100 1034 1582 1204 1295180 740 1133 862 928+M represents the bending strength of the bottom longitudinal re-inforcement minusM represents the bending strength of the upper longitudinalreinforcement


421 Plastic Hinges Formation andDevelopment Figures 7 and8 show the distribution of plastic hinges for the corrodedplane frame in axis ③-③ when the performance point(shown in Figure 3) is reached As can be seen from thegures with an increasing rebar corrosion rate the number ofplastic hinges in beams and columns increased graduallyMeanwhile the hinges developed rapidly from the bottom tothe higher storey with an increasing development level Underslight corrosion condition (corrosion rate is less than 5) thenumber and distribution of the plastic hinges for the corrodedframe are approximately the same as that for the noncorrodedframe (corrosion rate is equal to 0) For moderately orseriously corroded frame the number of plastic hinges in-creased signicantly relative to the noncorroded structureand the beam hinges have a large development rate thancolumn hinges By comparison under the uniform lateral

load pattern the development degree of the plastic hinges forthe same corroded frame is higher than that under the 1stmodal load pattern

As shown in Figures 7 and 8 there are 6 segments(ie B-IO IO-LS LS-CP CP-C C-D and D-E) in the legendband Each legend band is represented by a dierent colourwhich can help the reader to judge the damage state of thestructure or member For example it can be seen from theframe gure that there are pink points blue points andgreen points in the frame beams and columns which aredistributed in the B-IO segment IO-LS segment and LS-CPsegment of the legend band respectively ereforeaccording to the explanation shown in Figure 3 we candetermine the stress states of these points as the service-ability stage the safety stage and the prevention of thecollapse stage respectively

E

D

C

CP

LS

IO

Bx

z

(a)

E

D

C

CP

LS

IO

Bx

z

(b)

E

D

C

CP

LS

IO

Bx

z

(c)

E

D

C

CP

LS

IO

Bx

z

(d)

Figure 7 Distribution of plastic hinges under the uniform load pattern (a) 0 corrosion rate (b) 5 corrosion rate (c) 10 corrosion rate(d) 18 corrosion rate


422 Degradation of the Seismic Performance of the Cor-roded Structure under Rare Earthquake Action Figure 9provides the pushover curves for the corroded frameunder dierent degrees of corrosion It is easy to see thatthe trend of the pushover curves and the degradation lawsare basically the same despite the slight dierence of thecurves under dierent lateral load patterns Table 9 liststhe values of seismic bearing capacity of the frame underdierent corrosion rates From the results in Figure 9 andTable 9 it can be concluded that the seismic bearingcapacity of the corroded frame decreased signicantly dueto corrosion of its rebars In addition with increasingrebar corrosion rate the degradation of the bearing ca-pacity gradually increased

423 Deformation Performance of the Corroded Structureunder Rare Earthquake Action In order to better un-derstand the lateral deformation capacity of the corrodedstructure this paper also provides the story drift ratios asshown in Table 10 Similarly we can see that the interstorydrift ratios increase dramatically with the increasing of thecorrosion rate of the structure However the increasingextent varies by oor position for instance there is a phe-nomenon of negative increase in the fth and sixth oorwhich is mainly caused by the redistribution of internalforces under dierent lateral load patterns

Adding the interstory drift of each storey one can get thestorey displacements of the structure which also representthe global behaviour of the corroded frame with stiness and

E

D

C

CP

LS

IO

Bx

z

(a)

E

D

C

CP

LS

IO

Bx

z

(b)

E

D

C

CP

LS

IO

Bx

z

(c)

E

D

C

CP

LS

IO

Bx

z

(d)

Figure 8 Distribution of plastic hinges under the 1st modal load pattern (a) 0 corrosion rate (b) 5 corrosion rate (c) 10 corrosionrate (d) 18 corrosion rate


ductility Figure 10 reveals the storey displacements of thecorroded structure under dierent lateral load patternse results indicate that the storey displacement increaseswith the increasing of corrosion rate In addition thedeformation diagram of the frame is consistent with its 1stmodal shape

0

100

200

300

400

500

600Ba

se sh

ear (

kN)




(a)

0

100

200

300

400

500

Base

shea

r (kN

)

50 100 150 200 250 300 3500Top displacement (mm)



(b)

Figure 9 Comparison of the pushover curves of the corroded RCframe under dierent load patterns (a) Under the uniform loadpattern (b) Under the 1st modal load pattern

Table 9 Seismic bearing capacity of the corroded frame under rareearthquake action

Corrosionrate ()

Maximum base shear (kN)Under the uniform

load patternUnder the 1st modal

load pattern00 6285 518550 5819 4796100 5081 4177180 3592 2903

Table 10 Interstory drift ratios of the corroded frame structure

Corrosionrate () 00 50 100 180

(a) Under the uniform load pattern

Storey

1 11639 11563 11427 112792 11261 11209 11114 18653 11486 11401 11252 17994 12217 12083 11852 18785 15650 15747 15988 113836 112195 112987 114493 16897

(b) Under the 1st modal load pattern

Storey

1 12016 11866 11610 112792 11266 11196 11081 18653 11196 11136 11027 17994 11403 11326 11192 18785 13802 13922 13774 113836 18880 19346 110309 16897

20 40 60 80 100 120 140 1600Storey displacement (mm)

0

1

2

3

4

5

6

Stor

ey



(a)

20 40 60 80 100 120 140 160 180 2000Storey displacement (mm)

0

1

2

3

4

5

6

Stor

ey



(b)

Figure 10 Comparison of the story displacements under dierentdegrees of corrosion (a) Under the uniform load pattern (b) Underthe 1st modal load pattern


5 Conclusions

In this paper the finite element model of a six-storey-three-span corroded reinforced concrete (RC) frame structure wasestablished using SAP2000 software e numerical simu-lation of the seismic performance of the corroded RC framestructure with four different amounts of corrosion wasconducted using pushover analysis method e mainconclusions are as follows

(1) For the noncorroded RC frame the P-M-M curvesof column section obtained by using user-definedhinges with the help of XTRACT software aregenerally consistent with those acquired by thebuilt-in default hinges in SAP2000 For the cor-roded RC frame column section the calculatedP-M-M curves based on user-defined hinges pres-ent out the same change trends as the noncorrodedone erefore XTRACTsoftware can be utilized todetermine the properties of user-defined P-M-Mplastic hinges

(2) With the increasing corrosion rate of rebars theplastic hinges in beams and columns of the RC framedeveloped rapidly from the bottom to the higherstorey with an increasing development level whichleads to a more aggravated deformation of thestructure under severe earthquake

(3) e seismic bearing capacity of the corroded framedecreased significantly due to corrosion of its rebarsIn addition with increasing rebar corrosion rate thedegradation of the bearing capacity gradually increased

(4) e interstory drift ratios increase dramatically withthe increase of the corrosion rate of the structureHowever the increase varies with by the location ofstoreys and it has a strong correlation with thelateral load pattern

Conflicts of Interest

e authors declare that there are no conflicts of interestsregarding the publication of this paper

Acknowledgments

is research has been funded by the Outstanding YoungTalent Research Fund of Zhengzhou University (Grant no1521322004) and Guangdong Provincial Key Laboratory ofDurability for Civil Engineering Shenzhen University (Grantno GDDCE 12-06) and Foundation for University YoungKey Teacher by Henan Province (Grant no 2015GGJS-151)

References

[1] Z Peng and L Qingfu ldquoEffect of polypropylene fibre onmechanical and shrinkage properties of cement-stabilisedmacadamrdquo International Journal of Pavement Engineeringvol 10 no 6 pp 435ndash445 2009

[2] S J Kim and A S Elnashai ldquoCharacterization of shakingintensity distribution and seismic assessment of RC buildings

for the Kashmir (Pakistan) earthquake of October 2005rdquoEngineering Structures vol 31 no 12 pp 2998ndash3015 2009

[3] R Junemann J C de la Llera M A Hube L A Cifuentesand E Kausel ldquoA statistical analysis of reinforced concretewall buildings damaged during the 2010 Chile earthquakerdquoEngineering Structures vol 82 pp 168ndash185 2015

[4] B Zhao F Taucer and T Rossetto ldquoField investigation on theperformance of building structures during the 12 May 2008Wenchuan earthquake in Chinardquo Engineering Structuresvol 31 no 8 pp 1707ndash1723 2009

[5] Y G Du L A Clark and A H C Chan ldquoResidual capacity ofcorroded reinforcing barsrdquo Magazine of Concrete Researchvol 57 no 3 pp 135ndash147 2005

[6] F J Molina C Alonso and C Andrade ldquoCover cracking asa function of rebar corrosion part IImdashnumerical modelrdquoMaterials and Structures vol 26 no 9 pp 532ndash548 1993

[7] X G Wang W P Zhang X L Gu and H C Dai ldquoDe-termination of residual cross sectional areas of corroded barsin reinforced concrete structures using easy-to-measurevariablesrdquo Construction and Building Materials vol 38pp 846ndash853 2013

[8] A N Kallias and M L Rafiq ldquoFinite element investigation ofthe structural response of RC beamsrdquo Engineering Structuresvol 32 no 9 pp 2984ndash2994 2010

[9] P Zhang and Q F Li ldquoExperimental study on shrinkageproperties of cement-stabilized macadam reinforced withpolypropylene fiberrdquo Journal of Reinforced Plastics andComposites vol 29 no 12 pp 1851ndash1860 2010

[10] G Zhao M Zhang Y Li and D Li ldquoe hysteresis per-formance and restoring force model for corroded reinforcedconcrete frame columnsrdquo Journal of Engineering vol 2016Article ID 7615385 19 pages 2016

[11] O Troconis de Rincon and D Colaboration ldquoDurability ofconcrete structures DURACON an iberoamerican projectPreliminary resultsrdquo Building Environment vol 41 no 7pp 952ndash962 2006

[12] H Yalciner S Sensoy and O Eren ldquoTime-dependent seismicperformance assessment of a single-degree-of-freedom framesubject to corrosionrdquo Engineering Failure Analysis vol 19pp 109ndash122 2012

[13] S Pour-Ali C Dehghanian and A Kosari ldquoCorrosionprotection of the reinforcing steels in chloride-laden concreteenvironment through exoxypolyaniline-camphorsulfonaterdquoCorrosion Science vol 90 pp 239ndash247 2015

[14] D E Choe P Gardoni D Rosowsky and T HaukaasldquoProbabilistic capacity models and seismic fragility estimatesfor RC columns subject to corrosionrdquo Reliability Engineeringand System Safety vol 93 no 3 pp 383ndash393 2008

[15] L Berto R Vitaliani A Saetta and P Simioni ldquoSeismic as-sessment of existing RC structures affected by degradationphenomenardquo Structural Safety vol 31 no 4 pp 284ndash297 2009

[16] L Berto A Saetta and P Simioni ldquoStructural risk assessmentof corroding RC structures under seismic excitationrdquo Con-struction and Building Materials vol 30 pp 803ndash813 2012

[17] E A P Liberati C G Nogueira E D Leonel andA Chateauneuf ldquoNonlinear formulation based on FEMMazars damage criterion and Fickrsquos law applied to failureassessment of reinforced concrete structures subjected tochloride ingress and reinforcements corrosionrdquo EngineeringFailure Analysis vol 46 pp 247ndash268 2014

[18] Computers and Structures Inc (CSI) SAP2000 =ree Di-mensional Static and Dynamic Finite Element Analysis andDesign of Structures V1602 Computers and Structures IncBerkeley CA USA 2013


[19] A Koccedilak B Zengin and F Kadioglu ldquoPerformance assessmentof irregular RC buildings with shear walls after earthquakerdquoEngineering Failure Analysis vol 55 pp 157ndash168 2015

[20] SAP2000 Integrated Finite Element Analysis and Design ofStructure Analysis Reference Computers and Structures IncBerkeley CA USA 2000

[21] ATC-40 Seismic Evaluation and Retrofit of Concrete BuildingsApplied Technology Council Redwood City CA USA 1996

[22] I Khan R Francois and A Castel ldquoPrediction of re-inforcement corrosion using corrosion induced cracks widthin corroded reinforced concrete beamsrdquoCement and ConcreteResearch vol 56 pp 84ndash96 2014

[23] J Rodriguez L M Ortega and J Casal ldquoLoad carrying ca-pacity of concrete structures with corroded reinforcementrdquoConstruction and Building Materials vol 11 no 4 pp 239ndash248 1997

[24] G H Xing and D T Niu ldquoAnalytical model of flexuralbehavior of corroded reinforced concrete beamsrdquo Journal ofCentral South University (Science and Technology) vol 45no 1 pp 193ndash201 2014

[25] D Coronelli and P Gambarova ldquoStructural assessment ofcorroded reinforced concrete beams modeling guidelinesrdquoJournal of Structural Engineering vol 130 no 8 pp 1214ndash1224 2004

[26] S Han and P Johanne ldquoMechanistic study on the effect ofsulfate ions on polycarboxylate superplasticisers in cementrdquoAdvances in Cement Research vol 25 no 4 pp 200ndash2072013

[27] W L Jin and J Xia ldquoInfluence of pitting corrosion o-n thebending capacity of reinforced concrete beamsrdquo BuildingStructures vol 39 no 4 pp 100ndash111 2009

[28] X H Wang and X L Liu ldquoModeling the flexural carryingcapacity of corroded RC beamrdquo Journal of Shanghai JiaotongUniversity vol 13 no 2 pp 129ndash135 2008

[29] Q Wu and Y S Yuan ldquoExperimental study on the de-terioration of mechanical properties of corroded steel barsrdquoChina Civil Engineering Journal vol 41 no 12 pp 42ndash472008

[30] GB50011 Code for Seismic Design of Buildings NationalStandard of P R China China Architecture amp Beijing PressBeijing China 2010

[31] GB50009 Load Code for the Design of Building StructuresNational standard of P R China China Architecture ampBeijing Press Beijing China 2012

[32] FEMA-356 Prestandard and Commentary for the SeismicRehabilitation of Buildings American Society of Civil Engi-neers Reston Virginia USA 2000

[33] C D Comartin R W Niewiarowski S A Freeman andF M Turner ldquoSeismic evaluation and retrofit of concretebuildings a practical overview of the ATC 40 documentrdquoEarthquake Spectra vol 16 no 1 pp 241ndash261 2000

[34] XTRACT Cross Section Analysis Program for Structural Engi-neers IMBSEN amp Associates Inc Sacramento CA USA 2007

[35] Y L Li Analysis for Seismic Performance of Corroded RCFrame Structures Zhengzhou University Zhengzhou China2016


International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

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Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

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Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

elastic-plastic analysis theory by increasing the lateral loadon the inertial force center of each floor of the structure toobtain the relationship between internal forces and de-formation response in this process Finally using the seismicdemand spectrum and capacity spectrum (ATC-40 responsespectrum or Chinese code response spectrum) to estimatethe performance point index of the structure one can easilyevaluate the seismic performance of the structure [21] emain advantage of the pushover analysis method is that theelastic-plastic response of the structure can be consideredand the calculation results are stable is paper also ana-lyzed the degradation law of the seismic performance in-dicators of the corroded RC frame structure under severeearthquake e results were expected to provide a referencefor seismic safety analysis reliability assessment mainte-nance reinforcement and reconstruction of corroded RCframe structures

2 Mechanical Properties of CorrodedReinforced Concrete Materials

21 Degradation of the Mechanical Properties of ConcreteCover A large number of experiments and theoreticalanalyses have shown that the concrete cover of a RC framestructure will be cracked and peeled off due to the role of rustexpansion force after the steel corrosion In addition itweakens the bond strength between the rebar and concretehence reducing the service life of the structure [22 23]Considering that the core concrete binding force of anordinary reinforced cement concrete member is mainly fromthe protective layer the cracking and peeling of the concretecover will reduce its restraint on the core concrete andfurther weaken the load and deformation capacity of themember erefore the degradation of mechanical prop-erties of the protective concrete cover should not be ignoredduring structural analysis Due to the strong randomcharacteristics of the deterioration of the cover concrete it isdifficult to use analytic methods to determine the degree andlocation of deterioration In order to simplify the calculation(1) is used here to calculate the strength of the cover concrete[24 25]

fcminuscor fc

1 + c εt-corεc( 1113857

εtminuscor bcor minus b

b

bcor b + nωcor

ωcor 1113944i

uicor 2π υcor minus 1( 1113857X

ρs 2X

rminus

X

r1113874 1113875

2

(1)

where fcminuscor is the peak value of the compressive strength ofthe concrete cover after the steel bar corrosion c is thecorrelation coefficient between the rebar surface shape andits diameter and it is usually suggested to be 01 εtminuscor is thegeneralized cracking strain of concrete b is the originalwidth of the member bcor is the cross-sectional width of the

corrosion member n is the number of longitudinal rebarsωcor is the total width of the corrosion crack υcor is rustoxidation products and the volume ratio coefficient beforerust and it can be taken value 20 uicor is the width of the ithcorrosion crack X is the depth of steel bar corrosion ρs isthe corrosion loss rate of the rebar section and r is the radiusof the steel rebar before corrosion and it can be taken as theweighted average value when the reinforcement diametersare different

22 Degradation of the Corrosion Steel Bar MechanicalProperties Usually because the distribution of rust factors(such as cracks chloride ions and sulfate ions [26]) hassignificant random characteristics the corrosion status ofreinforcement in RC members often appears as pittingcorrosion Numerical analysis usually adopts the method ofequivalent uniform corrosion to deal with the degradation ofmechanical properties of pit corroded steel bars so as toimprove the accuracy of numerical simulation or theoreticalanalysis [27] It is assumed that the cross section of the rebaris in a uniform corrosion state but its mechanical propertiesare degradated according to the pit corrosion equation Inorder to consider the effect of pitting corrosion on themechanical properties of corroded rebar the nominal yieldstress and elastic modulus of the corroded rebar are cal-culated by (2) [28] and the ultimate stress and strain [29]can be calculated by (3)

fyc (1minus 00198δ)fy

Esc (1minus 00113δ)Es(2)

fuc (10minus 0019δ)fu

εuc (10minus 0021δ)εu(3)

where fy (fyc) is the nominal yield strength of the steel barbefore (after) corrosion Es (Esc) is the nominal modulus ofelasticity of the steel bar before (after) corrosion fu (fuc) isthe nominal ultimate strength of the steel bar before (after)corrosion εu (εuc) is the nominal ultimate strain of the steelbar before (after) corrosion and δ stands for the mass lossrate of the corroded steel e relationship between ρs and δcan be seen in (4) [28]

ρs

0013 + 0987δ δ le 10

0061 + 0939δ 10lt δ le 20

0129 + 0871δ 20lt δ le 30

0199 + 0810δ 30lt δ le 40

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(4)

3 Pushover Analysis Results of theNoncorroded RC Frame Structure

31 Engineering Background and Calculation ParametersFor the purposes of comparison a model of noncorroded RCframe building was presented here e building model hassix stories with typical story height 36m and the overallplan area is 24times12m All beams are 300times 550mm ecolumns in 1ndash3 storeys are 500times 500mm while the columns







4500

3000

4500

6000 6000 600024000

24000

6000

6000

1

6000 6000 6000

12000

4500

3000

4500

12000

2 3 4 5

1 2 3 4 5

D

C

B

A

D

C

B

A

(a)

1

4500

A B C D

3000 450012000

3600

21600

3600

3600

3600

3600

3600

2 1

121

1 2 1

222

2 2 2

222

(b)










250

250

250 250

183

8100

183

(a)

200

200 200

200

8100

163

163

(b)

300

550 8100

204

164

(c)

300

550 8100

184

203

(d)






335 455 015 200000


Columnreinforcement



Upperreinforcement

Bottomreinforcement

1ndash3 2036 ① 1256 8044ndash6 1608 ② 1017 942












I0 LSB

A

Forc

e

Displacement

CP

C

ED


User-defined hinge

ndash1000

0

1000

2000

3000

4000

5000

6000

8000

Axi

al fo

rce P

(kN

)


0

7000

(a)


ndash1000

0

1000

2000

3000

4000

5000

Axi

al fo

rce P

(kN

)


(b)












0

100

200

300

400

500

600

Base

shea

r (kN

)



(a)


0

100

200

300

400

500

Base

shea

r (kN

)


(b)













0

1000

2000

3000

4000

5000

6000

7000

8000

Axi

al fo

rce P

(kN

)



0

(a)

ndash1000

0

1000

2000

3000

4000

5000

Axi

al fo

rce P

(kN

)




0

(b)



Corrosion rate()



(400times 400mm)00 4837 257950 4555 2402100 4176 2212180 3836 2131


Corrosion rate()

Beam ① Beam ②+M

(kNmiddotm)minusM

(kNmiddotm)+M

(kNmiddotm)minusM






E

D

C

CP

LS

IO

Bx

z

(a)

E

D

C

CP

LS

IO

Bx

z

(b)

E

D

C

CP

LS

IO

Bx

z

(c)

E

D

C

CP

LS

IO

Bx

z

(d)






E

D

C

CP

LS

IO

Bx

z

(a)

E

D

C

CP

LS

IO

Bx

z

(b)

E

D

C

CP

LS

IO

Bx

z

(c)

E

D

C

CP

LS

IO

Bx

z

(d)




0

100

200

300

400

500

600Ba

se sh

ear (

kN)




(a)

0

100

200

300

400

500

Base

shea

r (kN

)




(b)



Corrosionrate ()



load pattern00 6285 518550 5819 4796100 5081 4177180 3592 2903




Storey

1 11639 11563 11427 112792 11261 11209 11114 18653 11486 11401 11252 17994 12217 12083 11852 18785 15650 15747 15988 113836 112195 112987 114493 16897


Storey

1 12016 11866 11610 112792 11266 11196 11081 18653 11196 11136 11027 17994 11403 11326 11192 18785 13802 13922 13774 113836 18880 19346 110309 16897


0

1

2

3

4

5

6

Stor

ey



(a)


0

1

2

3

4

5

6

Stor

ey



(b)



5 Conclusions








Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







4500

3000

4500

6000 6000 600024000

24000

6000

6000

1

6000 6000 6000

12000

4500

3000

4500

12000

2 3 4 5

1 2 3 4 5

D

C

B

A

D

C

B

A

(a)

1

4500

A B C D

3000 450012000

3600

21600

3600

3600

3600

3600

3600

2 1

121

1 2 1

222

2 2 2

222

(b)










250

250

250 250

183

8100

183

(a)

200

200 200

200

8100

163

163

(b)

300

550 8100

204

164

(c)

300

550 8100

184

203

(d)






335 455 015 200000


Columnreinforcement



Upperreinforcement

Bottomreinforcement

1ndash3 2036 ① 1256 8044ndash6 1608 ② 1017 942












I0 LSB

A

Forc

e

Displacement

CP

C

ED


User-defined hinge

ndash1000

0

1000

2000

3000

4000

5000

6000

8000

Axi

al fo

rce P

(kN

)


0

7000

(a)


ndash1000

0

1000

2000

3000

4000

5000

Axi

al fo

rce P

(kN

)


(b)












0

100

200

300

400

500

600

Base

shea

r (kN

)



(a)


0

100

200

300

400

500

Base

shea

r (kN

)


(b)













0

1000

2000

3000

4000

5000

6000

7000

8000

Axi

al fo

rce P

(kN

)



0

(a)

ndash1000

0

1000

2000

3000

4000

5000

Axi

al fo

rce P

(kN

)




0

(b)



Corrosion rate()



(400times 400mm)00 4837 257950 4555 2402100 4176 2212180 3836 2131


Corrosion rate()

Beam ① Beam ②+M

(kNmiddotm)minusM

(kNmiddotm)+M

(kNmiddotm)minusM






E

D

C

CP

LS

IO

Bx

z

(a)

E

D

C

CP

LS

IO

Bx

z

(b)

E

D

C

CP

LS

IO

Bx

z

(c)

E

D

C

CP

LS

IO

Bx

z

(d)






E

D

C

CP

LS

IO

Bx

z

(a)

E

D

C

CP

LS

IO

Bx

z

(b)

E

D

C

CP

LS

IO

Bx

z

(c)

E

D

C

CP

LS

IO

Bx

z

(d)




0

100

200

300

400

500

600Ba

se sh

ear (

kN)




(a)

0

100

200

300

400

500

Base

shea

r (kN

)




(b)



Corrosionrate ()



load pattern00 6285 518550 5819 4796100 5081 4177180 3592 2903




Storey

1 11639 11563 11427 112792 11261 11209 11114 18653 11486 11401 11252 17994 12217 12083 11852 18785 15650 15747 15988 113836 112195 112987 114493 16897


Storey

1 12016 11866 11610 112792 11266 11196 11081 18653 11196 11136 11027 17994 11403 11326 11192 18785 13802 13922 13774 113836 18880 19346 110309 16897


0

1

2

3

4

5

6

Stor

ey



(a)


0

1

2

3

4

5

6

Stor

ey



(b)



5 Conclusions








Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






250

250

250 250

183

8100

183

(a)

200

200 200

200

8100

163

163

(b)

300

550 8100

204

164

(c)

300

550 8100

184

203

(d)






335 455 015 200000


Columnreinforcement



Upperreinforcement

Bottomreinforcement

1ndash3 2036 ① 1256 8044ndash6 1608 ② 1017 942












I0 LSB

A

Forc

e

Displacement

CP

C

ED


User-defined hinge

ndash1000

0

1000

2000

3000

4000

5000

6000

8000

Axi

al fo

rce P

(kN

)


0

7000

(a)


ndash1000

0

1000

2000

3000

4000

5000

Axi

al fo

rce P

(kN

)


(b)












0

100

200

300

400

500

600

Base

shea

r (kN

)



(a)


0

100

200

300

400

500

Base

shea

r (kN

)


(b)













0

1000

2000

3000

4000

5000

6000

7000

8000

Axi

al fo

rce P

(kN

)



0

(a)

ndash1000

0

1000

2000

3000

4000

5000

Axi

al fo

rce P

(kN

)




0

(b)



Corrosion rate()



(400times 400mm)00 4837 257950 4555 2402100 4176 2212180 3836 2131


Corrosion rate()

Beam ① Beam ②+M

(kNmiddotm)minusM

(kNmiddotm)+M

(kNmiddotm)minusM






E

D

C

CP

LS

IO

Bx

z

(a)

E

D

C

CP

LS

IO

Bx

z

(b)

E

D

C

CP

LS

IO

Bx

z

(c)

E

D

C

CP

LS

IO

Bx

z

(d)






E

D

C

CP

LS

IO

Bx

z

(a)

E

D

C

CP

LS

IO

Bx

z

(b)

E

D

C

CP

LS

IO

Bx

z

(c)

E

D

C

CP

LS

IO

Bx

z

(d)




0

100

200

300

400

500

600Ba

se sh

ear (

kN)




(a)

0

100

200

300

400

500

Base

shea

r (kN

)




(b)



Corrosionrate ()



load pattern00 6285 518550 5819 4796100 5081 4177180 3592 2903




Storey

1 11639 11563 11427 112792 11261 11209 11114 18653 11486 11401 11252 17994 12217 12083 11852 18785 15650 15747 15988 113836 112195 112987 114493 16897


Storey

1 12016 11866 11610 112792 11266 11196 11081 18653 11196 11136 11027 17994 11403 11326 11192 18785 13802 13922 13774 113836 18880 19346 110309 16897


0

1

2

3

4

5

6

Stor

ey



(a)


0

1

2

3

4

5

6

Stor

ey



(b)



5 Conclusions








Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












I0 LSB

A

Forc

e

Displacement

CP

C

ED


User-defined hinge

ndash1000

0

1000

2000

3000

4000

5000

6000

8000

Axi

al fo

rce P

(kN

)


0

7000

(a)


ndash1000

0

1000

2000

3000

4000

5000

Axi

al fo

rce P

(kN

)


(b)












0

100

200

300

400

500

600

Base

shea

r (kN

)



(a)


0

100

200

300

400

500

Base

shea

r (kN

)


(b)













0

1000

2000

3000

4000

5000

6000

7000

8000

Axi

al fo

rce P

(kN

)



0

(a)

ndash1000

0

1000

2000

3000

4000

5000

Axi

al fo

rce P

(kN

)




0

(b)



Corrosion rate()



(400times 400mm)00 4837 257950 4555 2402100 4176 2212180 3836 2131


Corrosion rate()

Beam ① Beam ②+M

(kNmiddotm)minusM

(kNmiddotm)+M

(kNmiddotm)minusM






E

D

C

CP

LS

IO

Bx

z

(a)

E

D

C

CP

LS

IO

Bx

z

(b)

E

D

C

CP

LS

IO

Bx

z

(c)

E

D

C

CP

LS

IO

Bx

z

(d)






E

D

C

CP

LS

IO

Bx

z

(a)

E

D

C

CP

LS

IO

Bx

z

(b)

E

D

C

CP

LS

IO

Bx

z

(c)

E

D

C

CP

LS

IO

Bx

z

(d)




0

100

200

300

400

500

600Ba

se sh

ear (

kN)




(a)

0

100

200

300

400

500

Base

shea

r (kN

)




(b)



Corrosionrate ()



load pattern00 6285 518550 5819 4796100 5081 4177180 3592 2903




Storey

1 11639 11563 11427 112792 11261 11209 11114 18653 11486 11401 11252 17994 12217 12083 11852 18785 15650 15747 15988 113836 112195 112987 114493 16897


Storey

1 12016 11866 11610 112792 11266 11196 11081 18653 11196 11136 11027 17994 11403 11326 11192 18785 13802 13922 13774 113836 18880 19346 110309 16897


0

1

2

3

4

5

6

Stor

ey



(a)


0

1

2

3

4

5

6

Stor

ey



(b)



5 Conclusions








Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia











0

100

200

300

400

500

600

Base

shea

r (kN

)



(a)


0

100

200

300

400

500

Base

shea

r (kN

)


(b)













0

1000

2000

3000

4000

5000

6000

7000

8000

Axi

al fo

rce P

(kN

)



0

(a)

ndash1000

0

1000

2000

3000

4000

5000

Axi

al fo

rce P

(kN

)




0

(b)



Corrosion rate()



(400times 400mm)00 4837 257950 4555 2402100 4176 2212180 3836 2131


Corrosion rate()

Beam ① Beam ②+M

(kNmiddotm)minusM

(kNmiddotm)+M

(kNmiddotm)minusM






E

D

C

CP

LS

IO

Bx

z

(a)

E

D

C

CP

LS

IO

Bx

z

(b)

E

D

C

CP

LS

IO

Bx

z

(c)

E

D

C

CP

LS

IO

Bx

z

(d)






E

D

C

CP

LS

IO

Bx

z

(a)

E

D

C

CP

LS

IO

Bx

z

(b)

E

D

C

CP

LS

IO

Bx

z

(c)

E

D

C

CP

LS

IO

Bx

z

(d)




0

100

200

300

400

500

600Ba

se sh

ear (

kN)




(a)

0

100

200

300

400

500

Base

shea

r (kN

)




(b)



Corrosionrate ()



load pattern00 6285 518550 5819 4796100 5081 4177180 3592 2903




Storey

1 11639 11563 11427 112792 11261 11209 11114 18653 11486 11401 11252 17994 12217 12083 11852 18785 15650 15747 15988 113836 112195 112987 114493 16897


Storey

1 12016 11866 11610 112792 11266 11196 11081 18653 11196 11136 11027 17994 11403 11326 11192 18785 13802 13922 13774 113836 18880 19346 110309 16897


0

1

2

3

4

5

6

Stor

ey



(a)


0

1

2

3

4

5

6

Stor

ey



(b)



5 Conclusions








Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







0

1000

2000

3000

4000

5000

6000

7000

8000

Axi

al fo

rce P

(kN

)



0

(a)

ndash1000

0

1000

2000

3000

4000

5000

Axi

al fo

rce P

(kN

)




0

(b)



Corrosion rate()



(400times 400mm)00 4837 257950 4555 2402100 4176 2212180 3836 2131


Corrosion rate()

Beam ① Beam ②+M

(kNmiddotm)minusM

(kNmiddotm)+M

(kNmiddotm)minusM






E

D

C

CP

LS

IO

Bx

z

(a)

E

D

C

CP

LS

IO

Bx

z

(b)

E

D

C

CP

LS

IO

Bx

z

(c)

E

D

C

CP

LS

IO

Bx

z

(d)






E

D

C

CP

LS

IO

Bx

z

(a)

E

D

C

CP

LS

IO

Bx

z

(b)

E

D

C

CP

LS

IO

Bx

z

(c)

E

D

C

CP

LS

IO

Bx

z

(d)




0

100

200

300

400

500

600Ba

se sh

ear (

kN)




(a)

0

100

200

300

400

500

Base

shea

r (kN

)




(b)



Corrosionrate ()



load pattern00 6285 518550 5819 4796100 5081 4177180 3592 2903




Storey

1 11639 11563 11427 112792 11261 11209 11114 18653 11486 11401 11252 17994 12217 12083 11852 18785 15650 15747 15988 113836 112195 112987 114493 16897


Storey

1 12016 11866 11610 112792 11266 11196 11081 18653 11196 11136 11027 17994 11403 11326 11192 18785 13802 13922 13774 113836 18880 19346 110309 16897


0

1

2

3

4

5

6

Stor

ey



(a)


0

1

2

3

4

5

6

Stor

ey



(b)



5 Conclusions








Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





E

D

C

CP

LS

IO

Bx

z

(a)

E

D

C

CP

LS

IO

Bx

z

(b)

E

D

C

CP

LS

IO

Bx

z

(c)

E

D

C

CP

LS

IO

Bx

z

(d)






E

D

C

CP

LS

IO

Bx

z

(a)

E

D

C

CP

LS

IO

Bx

z

(b)

E

D

C

CP

LS

IO

Bx

z

(c)

E

D

C

CP

LS

IO

Bx

z

(d)




0

100

200

300

400

500

600Ba

se sh

ear (

kN)




(a)

0

100

200

300

400

500

Base

shea

r (kN

)




(b)



Corrosionrate ()



load pattern00 6285 518550 5819 4796100 5081 4177180 3592 2903




Storey

1 11639 11563 11427 112792 11261 11209 11114 18653 11486 11401 11252 17994 12217 12083 11852 18785 15650 15747 15988 113836 112195 112987 114493 16897


Storey

1 12016 11866 11610 112792 11266 11196 11081 18653 11196 11136 11027 17994 11403 11326 11192 18785 13802 13922 13774 113836 18880 19346 110309 16897


0

1

2

3

4

5

6

Stor

ey



(a)


0

1

2

3

4

5

6

Stor

ey



(b)



5 Conclusions








Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





E

D

C

CP

LS

IO

Bx

z

(a)

E

D

C

CP

LS

IO

Bx

z

(b)

E

D

C

CP

LS

IO

Bx

z

(c)

E

D

C

CP

LS

IO

Bx

z

(d)




0

100

200

300

400

500

600Ba

se sh

ear (

kN)




(a)

0

100

200

300

400

500

Base

shea

r (kN

)




(b)



Corrosionrate ()



load pattern00 6285 518550 5819 4796100 5081 4177180 3592 2903




Storey

1 11639 11563 11427 112792 11261 11209 11114 18653 11486 11401 11252 17994 12217 12083 11852 18785 15650 15747 15988 113836 112195 112987 114493 16897


Storey

1 12016 11866 11610 112792 11266 11196 11081 18653 11196 11136 11027 17994 11403 11326 11192 18785 13802 13922 13774 113836 18880 19346 110309 16897


0

1

2

3

4

5

6

Stor

ey



(a)


0

1

2

3

4

5

6

Stor

ey



(b)



5 Conclusions








Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0

100

200

300

400

500

600Ba

se sh

ear (

kN)




(a)

0

100

200

300

400

500

Base

shea

r (kN

)




(b)



Corrosionrate ()



load pattern00 6285 518550 5819 4796100 5081 4177180 3592 2903




Storey

1 11639 11563 11427 112792 11261 11209 11114 18653 11486 11401 11252 17994 12217 12083 11852 18785 15650 15747 15988 113836 112195 112987 114493 16897


Storey

1 12016 11866 11610 112792 11266 11196 11081 18653 11196 11136 11027 17994 11403 11326 11192 18785 13802 13922 13774 113836 18880 19346 110309 16897


0

1

2

3

4

5

6

Stor

ey



(a)


0

1

2

3

4

5

6

Stor

ey



(b)



5 Conclusions








Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


5 Conclusions








Acknowledgments


References









































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






















RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


seismic performance of a corroded reinforce concrete...

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