AComparativeTestStudyontheSeismicDamage SustainedbyFrame ...downloads.hindawi.com/journals/ace/2019/3202959.pdf · on the overall seismic performance of the structure are currently

Research ArticleA Comparative Test Study on the Seismic DamageSustained by Frame-Core Tube Structures

Zuohua Li Liang Chen and Jun Teng

Shenzhen Graduate School Harbin Institute of Technology Shenzhen 518055 China

Correspondence should be addressed to Jun Teng tengjhiteducn

Received 24 October 2018 Revised 9 January 2019 Accepted 13 February 2019 Published 3 March 2019

Academic Editor Melina Bosco

Copyright copy 2019 Zuohua Li 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

-e overall damage sustained by a structure can be controlled in the current damage-based seismic design but the ra-tionality of the relationship among the damage states of the components in the structure and the influences of those stateson the overall seismic performance of the structure are currently ignored In response to this problem a comparativetest was performed in this paper to study the seismic damage performances of two frame-core tube structure modelsnamely an optimization model designed through the optimization of the component damage states to achieve the re-lationship among those damage states proposed in this paper and a normative model designed through the seismic designmethod based on Chinese codes By comparing the experimental data of these two models the relationship among thecomponent damage states was discussed comprehensively and the influences of those states on the overall seismicperformance of the frame-core tube structure were analyzed -e proposed relationship among the component damagestates in the optimization model can effectively limit the development of overall damage and improve the internal forceresponse of the structure

1 Introduction

Damage-based seismic design theory can intuitively controldamage behaviors experienced during an earthquake andhas consequently received substantial attention spanning amultitude of studies [1 2] In early research on damage-based seismic design methods [3 4] validating calculationsof the damage performance replaced those of elastic-plasticdeformation and the damage index did not play a primarycontrolling role in the seismic design process In consid-eration of this problem various direct damage-based seismicdesign theories have been proposed [5ndash7] Among them theoverall damage can be actively controlled within the seismicdesign process however these theories ignored both therationality of the relationship among the componentdamage states throughout the structure and the influences ofcomponent damage on the overall seismic performance ofthe structure Nevertheless in the process of damage-basedseismic design the overall damage to the structure must bedesigned and the relationship among component damage

states throughout the structure must be considered effec-tively -us the seismic damage performance of thestructure including the rationality of the componentdamage state relationships and the influences of the damagestates of the components on the overall seismic performanceof the structure should be thoroughly understood by thedesigner to direct the design process

In the current damage-based seismic design for simpletypes of structures such as frame structures and shear wallstructures the design process can be guided by determiningthe relationship among the component damage statesthrough two seismic concepts namely ldquostrong column-weak beamrdquo and ldquostrong wall limb-weak coupling beamrdquo[8ndash11] However in the damage-based seismic designprocedure for high-rise building structures such as frame-core tube structures the relationships among the com-ponent damage states are much more complex than thoseamong the components in simple types of structures due tothe diversity of component types For example there arerelationships among the damage states of the vertical and

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horizontal components on the same floor applied to pre-vent soft-story behaviors [12] in addition there are re-lationships among the damage states of the verticalcomponents on the ground floor and the horizontalcomponents on the upper floors employed to investigatethe global damage mechanism [13] furthermore there arerelationships among the damage states of the verticalcomponents for understanding the cooperative workingmechanism of the outer frame and core tube [14] Ac-cordingly it is difficult for designers to comprehensivelydetermine and satisfy reasonable variations of the above-mentioned relationships among these component damagestates in frame-core tube structures through only seismicconcepts Hence in damage-based seismic design theinfluences of the damage states of these components on theoverall seismic performance including the overall struc-tural damage and interstory internal force should beunderstood effectively by the designer to actively determinethe sensible relationships among the component damagestates To date it has been proposed that the componentdamage states will influence the overall structural damagethrough the damage weighted coefficient however thiscoefficient reflects merely the numerical relationship be-tween the component damage index and the overalldamage index and thus it cannot reflect the influencesof the component damage states on the overall damage ofthe structure Although many theoretical analyses andexperimental studies on the seismic damage performancehave been performed [15ndash17] the influences of compo-nent damage states on the overall seismic performanceof frame-core tube structures have not been discussedcomprehensively

-erefore in this paper the seismic damage perfor-mance of a frame-core tube structure under an earthquakewill be studied in detail to direct the damage-based seismicdesign To reflect the seismic damage performance of thestructure under earthquake activity as much as possible aseries of shaking table tests which represent one of the mosteffective tools employed by researchers and designers tounderstand the seismic performance of structures was usedto comparatively study the seismic damage performances oftwo scaled models of frame-core tube structures In thesetests the seismic damage performances of the two modelswere compared to determine the most reasonable re-lationship among component damage states therein Inaddition the influences of the component damage states onthe overall seismic performance were analyzed and theinterstory internal force was quantified to validate the ra-tionality and advantages of the relationship among thecomponent damage states proposed in this paper

2 Model Design and Construction

21ModelDesign Twomodels of frame-core tube structureswere designed to comprehensively compare their seismicdamage performances One was an optimization modelwhose component damage states were optimized throughfinite element analysis and the other was a normative modeldesigned with the seismic design method based on Chinese

codes [18ndash20] -ese two model structures were designed toallow them to reach serious damage states without experi-encing overall structural collapse under a rare earthquakewhich is in accordance with the target damage states ofcollapse-forbidden under rare earthquake specified in theCode for Seismic Design of Buildings (GB 50011-2010) thusthe maximum elastic-plastic interstory drift is limited to 1100 under the rare earthquake to control the target damagestates according to the Chinese code

In the design of the optimization model the componentdamage states were optimized to achieve a reasonabledamage target that satisfies the damage optimization prin-ciples proposed in this paper Considering that the com-ponent damage states can be effectively described based onthe concrete material damage states [21] the concretematerial damage index in this paper is defined by thedegradation of the concrete material unloading stiffness todetermine the component damage states according toChinese codes -e relationship between the materialdamage index and material unloading stiffness is given asfollows [20]

Ed (1minusd)E0 (1)

where E0 is the initial stiffness of concrete Ed is theunloading stiffness of concrete and d is the tension orcompression damage index of the concrete material that canbe calculated based on the procedure specified in the Chi-nese code For d 0 no damage occurs within the materialfor d 09 the material fails Considering that the failure ofthe concrete component is usually caused by the crushing ofthe concrete material in the component section the concretematerial pressure damage of the component section is usedto determine the component damage According to theprevious literature the damage index D that represents theaverage damage value of the components at the same floor isgiven as follows [22]

D 1113936

Ni1dn

N (2)

where dn is the maximum concrete material damage valueunder compression in the component section and N is thestatistical number of components at the same floor Todetermine the damage of a single component for comparingand optimizing the damage scale of each component in theoptimization model the value of N can be taken as 1 hencethe value of D is equal to the value of dn -erefore thedamage index dn is used to represent the damage of a singlecomponent -e component damage index values at dif-ferent damage levels are given in Table 1 in reference toprevious studies [4] -e damage optimization principlesand damage scale are summarized as follows

(1) -e horizontal components such as the couplingbeam and frame beam in the frame-core tubestructure may suffer greater damage consideringboth their ductility under a nonlinear damagestage and their postyield bearing capacity which isbeneficial for effectively exhibiting a cumulativeenergy dissipation capacity -erefore to permit the

2 Advances in Civil Engineering

component damage states to reach the corre-sponding serious damage levels reached under astrong earthquake the horizontal componentdamage index is designed to be between 06 and 09-e cross-sectional reinforcement of the horizontalcomponents can be reduced appropriately to in-crease the damage index during the damage opti-mization process

(2) -e damage states of the vertical components such asthe frame column and wall limb in the frame-coretube structure should be effectively limited to retain astable bearing capacity during an earthquake that isthe damage states of the vertical components (exceptfor the wall limb on the ground floor) should be ableto retain their basic integrity under strong earth-quake activity hence the damage index is controlledwithin 02 In contrast it is both difficult and un-necessary to retain a state of basic integrity for thewall limb on the ground floor since the wall limbbears most of the base shear and bending momentduring an earthquake hence the wall limb is per-mitted to remain in a state of slight damage and thedamage index is controlled within 04 -e cross-sectional reinforcement of the vertical componentmay be increased appropriately to decrease thedamage index during the damage optimizationprocess

(3) As they constitute the second design level of forti-fication under earthquake activity within a frame-core tube structure the frame columns within theouter frame should possess smaller damage statesthan the wall limbs in consideration of their col-laborative working mechanism

According to the damage optimization principles theoptimization design steps are as follows

(1) -e optimization model was designed preliminarilyaccording to Chinese codes [18ndash20] to determine thecomponent section and initial cross-sectionalreinforcement

(2) To ascertain the component damage states pushoveranalysis was performed on the structure To select thelateral load distribution pattern a modal inertialforce distribution pattern was adopted for thepushover analysis according to previous research[23] A maximum component damage value of 09was established as the target limiting state within thepushover analysis

(3) Optimize the component damage states For thehorizontal components reduce the cross-sectionalreinforcement if the damage index DL for the framebeams and the index DLL for the coupling beams are

less than 06 and end the optimization if the damageindices are greater than 06 For the vertical com-ponents (except for the wall limb on the groundfloor) increase the cross-sectional reinforcement ifthe damage index Dc for the frame columns and theindex Dw for the wall limbs on the upper floors aregreater than 02 and end the optimization if thedamage indices are less than 02 However for thewall limbs on the ground floor increase the cross-sectional reinforcement if the damage index isgreater than 04 and end the optimization if thedamage index is less than 04 -e damage re-lationship between the wall limbs and frame columnsshould be checked accordingly increase the cross-sectional reinforcement of the frame columns if Dc isgreater than Dw and end the check if Dc is less thanDw

(4) Repeat steps 2 and 3 after adjusting the componentsection reinforcements until the component damagestates in the structure satisfy the requirementsproposed in the abovementioned damage optimi-zation principles

(5) Verify whether the maximum elastic-plastic inter-story drift satisfies the limiting value specified in theChinese code [18] under the design earthquake If therequirement can be met end the optimizationotherwise increase the section reinforcements of thevertical components and recheck the interstory driftuntil it satisfies the limiting value

-e normative model was designed by following theChinese design code [18ndash20] to meet the required bearingcapacity and deformation In the design of the componentbearing capacity the seismic forces were evaluated by thevibration mode response spectrum method and the internalforces of the components were adjusted according to thetype of structure the structural height and the fortificationintensity -e reinforcement for each component wasdesigned by the ultimate limit states design method Toinvestigate elastic-plastic deformation the time historyanalysis method was used to verify the elastic-plasticinterstory drift angle under a rare earthquake to avoidoverall structural collapse

To compare the two models the component section ofthe optimization model was designed to be the same as thatof the normative model whose prototype componentsection structure is shown in Table 2 -e prototypestructures of the two models also have a same total heightof 100m a constant story height of 4m and plan di-mensions of 228m times 228m as shown in Figures 1 and 2-e two prototype buildings are assumed to be located in aregion with a seismic design intensity of 7 and a site class ofII -e floor loads of the structure are designed according

Table 1 Component damage index value at different damage levels

Damage level Basic integrity Slight damage Moderate damage Serious damage CollapseDamage index 0sim02 02sim04 04sim06 06sim09 ge09

Advances in Civil Engineering 3

to the Load Code for the Design of Building Structures(LCDBS GB 50009-2012)-e component damage scales ofthe two models are obtained (as shown in Table 3) after the

two models are designed -e component cross-sectionalreinforcement ratio ρO of the optimization model and ρNof the normative model can be subsequently acquired andthe value of ρOρN is shown in Tables 4ndash7 In comparisonthe section reinforcements of the vertical components inthe optimization model were greater than those in thenormative model whereas the section reinforcements ofthe horizontal components in the optimization modelwere smaller than those in the normative model which isin accordance with the damage optimization principlesadopted herein

22 Model Material and Similitude Ratio -e modelstructure was designed and manufactured according to thestructure of the corresponding prototype Given the simi-larity requirements the selected materials must have a lowerYoungrsquos modulus and a higher volume weight than theprototype materials In addition the stress-strain relation-ship of the selected materials should be similar to that of theprototype materials In view of these considerationsmicroconcrete was used to simulate the concrete in themodel and galvanized steel wire was used to simulate thereinforcing bars To guarantee an appropriate model simi-larity factors such as the performance parameters of theshaking table construction conditions lifting capacity andlaboratory height should be considered Based on the ca-pacity and size of the shaking table and the ease with whichthe model can be fabricated a scaling factor of 115 waschosen for the model dimensions To determine the accel-eration scaling ratio the influence of laboratory environ-mental noise on the shaking table experiment the weight ofthe experimental model and the bearing capacity of theshaking table must all be taken into account therefore thescaling ratio of the acceleration was determined to be 3Furthermore according to the measured concrete stress-strain relationship the scaling factor for the elastic moduluswas determined to be 13 -e scaling factors for otherphysical quantities can be derived by the correspondingsimilarity principles and the typical scaling factors adoptedfor the model structure are shown in Table 8

-e basic design principles of the reinforcements in themodel are as follows (a) the bearing capacity of the normalsection was controlled in accordance with the equivalentbending capacity principle and (b) the bearing capacity ofthe oblique section was controlled in accordance with theequivalent shear capacity principle

23 Model Construction High precision and quality controlwere required for the construction of the two models due tothe size requirements for the fabrication of scale models

Table 2 Component section of prototype structure

Floor Frame column (mm) Outer frame beam (mm) Inner frame beam (mm) Coupling beam (mm) -ickness of wall (mm)1sim5 1100times1100 400times 700 400times 700 400times 700 4006sim10 1100times1100 400times 800 400times 800 400times 800 40011sim15 800times 800 400times 900 300times 900 300times 900 30016sim25 800times 800 400times 700 300times 700 300times 700 300

Frame column Outer frame beam

Wall limb

Coupling beam

Embedded column 2

9000

6900

6900

B

D

Inner frame

beam

A C

Embedded column 1

6900

9000

2280

0

690022800

2400

Figure 1 Structure layout

20000

40000

60000

80000

100000

0000

5F

20F

15F

25F

10F

Figure 2 Structure elevation


Accordingly foam plastic was selected for the concreteformwork Prior to constructing the model foam plasticboards were incised and shaped according to need After thegalvanized steel wires of a component were bundledmicroconcrete was poured with an accompanying vibration

until the microconcrete became compact -is process wasrepeated until all the models had been poured -e qualityand verticality of each component were checked continu-ously throughout the entire construction process -econstruction process is shown in Figure 3 the completed

Table 3 Component damage scale of the two models

ModelComponent type

Frame columnWall limb

Coupling beam Frame beamUpper floors Ground floor

Optimization model Dc lt 02 Dw lt 015 Dw lt 04 06ltDLL lt 09 06ltDL lt 082Normative model Dc lt 049 Dw lt 022 Dw lt 055 043ltDLL lt 09 042ltDL lt 082

Table 4 Value of ρOρN in frame column

Component Floor StirrupFlexural reinforcement

Corner column Side column

Frame column

1sim5F 1 15 156sim10F 1 126 12611sim15F 1 14 1416sim25F 1 1 1

Table 5 Value of ρOρN in wall limb

Component FloorDistribution reinforcement Flexural reinforcement

Horizontal Vertical Embedded column 1 Embedded column 2

Wall limb1sim2F 13 13 12 1153sim14F 1 1 115 11515sim25F 1 1 1 1

Table 6 Value of ρOρN in frame beam

Component Stirrup LocationFlexural reinforcement

1F 2sim5F 6sim10F 11sim15F 16sim21F 22sim25FFrame beam 1 Beam end 067 058 067 053 067 05

Table 7 Value of ρOρN in coupling beam

Component StirrupFlexural reinforcement

1F 2sim4F 5sim10F 11sim15F 16sim25FCoupling beam 1 057 067 067 05 057

Table 8 Typical scaling factors for converting model response to full-size prototype response

Category Variable Scaling factor NoteDimension Length 115 Controlling parameter of dimension

Material

Strain 10

Controlling parameter of materialElastic modulus 13

Stress 13Density 53Mass 4938times10minus4

Dynamic behavior

Damping 3313times10minus3

Controlling parameter of the testPeriod 0149Velocity 0447

Acceleration 3Acceleration of gravity 10


model structure is shown in Figure 3(d) and a panorama ofthe shaking table model is shown in Figure 3(e) Aftermaintenance was performed on the model the iron blocks ofthe model counterweights were evenly arranged on the slab-e total height of the model was 6917m of which thebasement height was 025m and the structural height was6667m-e total weight of the model was 13392 t of whichthe basement weight was 4967 t and the structural weightwas 8525 t

3 Test Program

31 Instruments and Transducer To monitor the globalresponses as well as the local states of the model struc-tures during the experiments three kinds of sensors wereused an acceleration transducer a displacement trans-ducer and an electrical resistance strain gauge-e layoutof sensors throughout the model should be arrangedeffectively according to the force characteristics of thestructure After performing finite element analysis onthe damage to the prototype structure a total of 122sensors were placed at different measuring points -e

acceleration and displacement sensors were arrangedevenly along the structural height the positions of themeasuring points on the floors are shown in Figure 1Seventeen acceleration transducers were installed atmeasuring point A located in the plan while sixteendisplacement transducers were established at measuringpoints B C and D To measure the strain and damage ofeach component in the structure under shaking condi-tions strain gauges were placed in unfavorable regionsthat is in regions where the components in the structureare likely to become severely damaged during an earth-quake -rough finite element analysis the regions weredetermined as follows (a) the damage region in the framebeam is concentrated mainly at the beam end (b) thedamage region in the coupling beam is concentratedmainly at the beam end and within the oblique section atthe midspan of the beam (c) the damage region in theframe column is concentrated mainly at the column endand the root of the frame column at the base and (d) thedamage region of the wall limb is concentrated mainly atthe end of the wall limb A total of eight-nine straingauges were installed

Optimization model

Basement

Normative model

(a)

(b)

(c) (e)

(d)

Figure 3Model construction (a) basement construction (b) layout of iron wire and foam template (c) pouring of microconcrete (d) finishconstruction of models and (e) shaking table model panorama


32 Input Seismic Waves -e seismic waves are selectedaccording to the Chinese code -e selection principles offrequency contents intensity and duration of the seismicwaves are as follows

(1) No fewer than two natural accelerograms and anartificial accelerogram are selected according to thesite category and the design seismic group -eaverage value of the response spectra of the threeseismic waves at the primary periodic point of themodel structure is no more than 20 of the designresponse spectrum

(2) -e peak acceleration of each seismic wave should bemagnified or reduced to reflect different levels ofearthquakes according to the design seismic accel-eration peaks specified in the Chinese code

(3) -e duration of each seismic wave should be morethan 5ndash10 times the structural primary period

According to the abovementioned principles threeearthquake waves namely the El Centro wave and theHollywood wave in addition to an artificial wave were se-lected in this paper as shown in Figure 4 -e responsespectrum values of the three seismic waves at the primaryperiodic point were obtained from which the input se-quences of the three earthquake waves were determined asan artificial wave an El Centro wave and a Hollywood wave

33 Test Program -e peak accelerations corresponding todifferent intensities which were chosen according to theChinese code (as shown in Table 9) were magnified to obtainthe peak accelerations of the seismic input waves for the testcases -e peak acceleration values for the test cases can bemagnified to 0105sim066 g according to the scaling factor ofthe acceleration To further investigate the damage perfor-mance under an incredibly rare earthquake an experimentwith an acceleration peak of 076 g was performed Since acomparison of the response spectrum values of the threeseismic waves reveals that the response spectrum reaches amaximum under the action of the Hollywood seismic wavethe Hollywood seismic wave was selected for the experimentwith an acceleration peak of 076 g A summary of the inputwaves for these shaking tests is provided in Table 10 Duringthe experiments a total of 23 working conditions were appliedin the normative model and the optimization model Beforethe input of each event white noise was input first to acquirethe model dynamic behavior at that moment simulations ofthe artificial record El Centro record and Hollywood recordwere then input to the model in succession

In addition the durations of the seismic waves shouldalso be reduced according to the scaling factor of the period-e relationship among the periodic similarity ratio thegeometric similarity ratio and the acceleration similarityratio can be given as follows

ST S05l Sminus05a 0667 times 1732 0149 (3)

where ST is the periodic similarity ratio Sa is the accelerationsimilarity ratio and Sl is the geometric similarity ratio -us

the time interval and the duration of the seismic waves werereduced to 0149 times those of the original seismic wavesaccording to the value of ST and the input direction was one-way horizontal

4 Results and Discussion

41 Experimental Phenomena After the tests comprisingfrequent earthquake intensities of 7 and 8 visible cracks didnot appear on the surfaces of the components-emeasurednatural vibration frequencies of the two models remainedconstant throughout the tests thereby explaining why nodamage occurred in either model during the experimentsAfter the test with a basic earthquake intensity of 7 therewere still no obvious visible cracks on the surfaces of thecomponents but the natural vibration frequencies of the twomodels decreased indicating that damage had begun tooccur in both models In the tests with a basic earthquakeintensity of 7 (015 g) and a rare earthquake intensity of 7 themodels exhibited slight levels of noise during the vibrationsand visible cracks appeared in the coupling beam and framebeam moreover the natural frequencies of the two modelsfurther decreased indicating that the damage in the twomodels became further aggravated To evaluate the damagesuffered by the components during the earthquake in greaterdetail a test with an acceleration peak of 076 g was con-ducted using the Hollywood seismic wave During thisexperiment the vibration amplitudes of the twomodels werelarger than those during the previous tests and someconcrete debris fell from the model exhibiting obvious noiseAfter the completion of the test visible cracks were clearlyobserved in both models with distributions concentrated onthe surfaces of the coupling beams and frame beams Bycontrast no obvious visible cracks were observed on thesurfaces of the shear walls and frame columns Typicalexamples of cracks in the component are shown in Figure 5

42 Dynamic Characteristics -e frequencies of the twomodels at different phases were obtained through a whitenoise scan the variations in the first two frequencies at theend of each instant phase are shown in Tables 11 and 12With an increase in the earthquake acceleration the first twofrequencies gradually decreased whereas the damping ratiogradually increased indicating that the two models had beendamaged under the earthquake and that the degree ofdamage increased with an increase in the earthquake ac-celeration In comparison the first two frequencies of thenormative model were reduced by 377 and 174 at theend of case 22 similarly the first two frequencies of theoptimization model were reduced by 327 and 167showing that the natural vibration frequency of the nor-mative model decreased faster than that of the optimizationmodel Under the action of an earthquake structuraldamage will lead to a decrease in the natural vibrationfrequency Many previous studies have shown that the levelof damage becomes more serious with faster decreases in thenatural frequency under the action of an earthquake [24 25]-erefore the normative model was damaged more severely


0 5 10 15 20

ndash003

ndash002

ndash001

000

001

002

003

004

Time (s)

Acc

eler

atio

n (g

)

00 05 10 15 20 25 30 35 40 45001

002

003

004

005

006

007

008

009

Period (s)

Design response spectrum of Chinese codeResponse spectrum of artificial wave

Acc

eler

atio

n (g

)

(a)

0 10 20 30 40 50 60ndash004ndash003ndash002ndash001

000001002003004

Time (s)

Acc

eler

atio

n (g

)

Design response spectrum of Chinese codeResponse spectrum of El Centro wave

00 05 10 15 20 25 30 35 40 45000001002003004005006007008009010

Period (s)

Acc

eler

atio

n (g

)

(b)

0 15 30 45 60 75ndash004ndash003ndash002ndash001

000001002003004

Time (s)

Acc

eler

atio

n (g

)

Design response spectrum of Chinese codeResponse spectrum of Hollywood wave

00 05 10 15 20 25 30 35 40 45000001002003004005006007008009010011012

Period (s)

Acc

eler

atio

n (g

)

(c)

Figure 4 Time-history curve and response spectrum of the input ground motion (a) Artificial wave (b) El Centro and (c) Hollywood

Table 9 Peak accelerations of different level of intensity (cms2)

Fortification intensity Intensity 7 Intensity 7 (015 g) Intensity 8Frequent 35 55 70Basic 100 150 200Rare 220 310 400


than the optimization model under the action of a strongearthquake according to the relationship between thedamage and the natural frequency In addition the dampingratio in the optimization model became larger than that inthe normative model under the action of a strong earth-quake which means that the optimization model has astronger energy dissipation potential

43 Damage Analysis for Components -e damage sufferedby an actual structure is generally described by the charac-teristics of cracks on the surfaces of the components of thatstructure However such cracks can be described only bylimited qualitative descriptions that is they cannot be ef-fectively described quantitatively In response to this problemsome influencing factors should be chosen to analyze thecomponent damage states -e component-based Park-Angdamage model [26] and the material-based damage model[27] show that the deformation and strain of a componenthave a direct correlation with the damage suffered by thecomponent Excessive deformation of a component will leadto excessive strain which inevitably leads to the cracking ofconcrete or the crushing of a component in other words thelarger the deformation or strain of a component the moresevere the component damage In view of this relationshipthe strain of a component can be chosen to quantitativelycompare the seismic damage performances of the two modelsin the tests Because the damage done to a structure cumu-latively increases under an earthquake and does not disappearwith variations in the seismic wave it is more meaningful tocompare the cumulative damage suffered under the threeseismic waves under the same earthquake intensity -ere-fore the envelope of the maximum strain value under each

seismic wave was selected for an analysis of the damagesuffered by the components

431 Horizontal Component -e strains of the horizontalcomponents such as the coupling beam and frame beamwere extracted for a comparison of their damage states asshown in Figures 6 and 7 A comparison shows that thestrain distributions of the horizontal components in both ofthe models were similar under the same earthquake activityand the maximum strain appeared on the middle floors ofboth models In the case of a frequent earthquake with anintensity of 7 the distributions of the strain values in bothmodels were approximately identical along the structuralheight as shown in Figures 6(a) and 7(a) However with anincrease in the earthquake acceleration the strain values inthe two models became different As shown in Figures 6(b)and 7(b) the strains of the coupling beams and the framebeams in the optimization model were obviously larger thanthose in the normative model under the basic earthquakewith an intensity of 7 and the difference in the strain be-tween the two models became increasingly obvious underthe rare earthquake with an intensity of 7 as shown inFigures 6(c) and 7(c) To analyze the strain evolutionthroughout the entire experiment the strains of the hori-zontal components on the 8th and 11th floors wereextracted as shown in Figure 8 In comparison the strain inthe optimization model increased more rapidly than that inthe normative model throughout the entire test except forthe cases involving frequent earthquakes with intensities of 7and 8 -rough detailed observations acquired after the testwas complete the bearing capacities of the horizontalcomponents remained stable -ese findings indicate that

Table 10 Test procedure

Test cases Case designation Intensity Input excitation Peak value of input acceleration (g)1 W1 White noise 01052 F7R

Frequent 7RH1TG035 0105

3 F7E El Centro 01054 F7H Hollywood 01055 W2 White noise 01056 F8R


7 F8E El Centro 0218 F8H Hollywood 0219 W3 White noise 010510 B7R

Basic 7RH1TG035 03

11 B7E El Centro 0312 B7H Hollywood 0313 W4 White noise 010514 B75R

Basic 7 (015 g)RH1TG035 045

15 B75E El Centro 04516 B75H Hollywood 04517 W5 White noise 010518 R7R

Rare 7RH1TG035 066

19 R7E El Centro 06620 R7H Hollywood 06621 W6 White noise 010522 H076 076 g Hollywood 07623 W7 White noise 0105


the horizontal components in the optimization model suf-fered greater damage and that the damage suffered by thosecomponents increased more rapidly during the strongearthquake than did those in the normative model which isin accordance with the aim of damage optimization

432 Vertical Component No observations revealed obvi-ous visible cracks on the surfaces of the vertical components-e strains of the vertical components of the two modelswere compared and analyzed to further investigate thedamage suffered by the vertical components Figures 9 and

Table 11 Damping and frequency of normative model

PGA (g) 0105 021 03 045 066 076Primary frequency 313 313 295 273 234 195Second mode frequency 1016 977 977 938 878 839Damping ratio () 57 57 581 642 735 754

Table 12 Damping and frequency of optimization model


(a) (b)

(c) (d)

Figure 5 Crack of typical components (a) coupling beam (b) frame beam (c) slab of beam end and (d) intersection of column and beam


10 show that the strain distributions in both models weresimilar under the same earthquake activity and the strainvalues on the ground floor were much larger than those onthe upper floors However the strain values in the twomodels developed different characteristics with an increasein the earthquake acceleration In the case of frequentearthquakes with an intensity of 7 the strain values of thevertical components in both models were approximatelyidentical along the structural height However in the cases ofboth basic and rare earthquakes with an intensity of 7 thestrain values in the normative model became larger thanthose in the optimization model on the same floors-rougha further comparison of the damage suffered by the framecolumns in the two models comparatively large strains were

found on the middle floors of the normative model (but notthe ground floor) under the action of a strong earthquake asshown in Figure 10(c) whereas the strains in the optimi-zation model were reasonably limited -is result indicatesthat abrupt changes in the damage state may have occurredin the frame columns on the middle floors of the normativemodel To analyze the strain evolution throughout the entireexperiment the strains of the vertical component on the 1stand 11th floors were extracted as shown in Figure 11 -estrains in the normative model were obviously larger thanthose in the optimization model during the entire test exceptfor the cases involving frequent earthquakes -is findingmeans that the development of damage in the verticalcomponents in the optimization model can be limited under

0

3

6

9

12

15

18

21

24

0 100 200 300 400Strain amplitude (10ndash6)

Normative modelOptimization model

Stor

y

(a)

Strain amplitude (10ndash6)


0

3

6

9

12

15

18

21

24

0 300 600 900 1200

Stor

y

(b)



0

3

6

9

12

15

18

21

24

0 800 1600 2400

Stor

y

(c)

Figure 6 Maximum strain value of coupling beam at different story (a) Frequent intensity 7 (b) basic intensity 7 and (c) rare intensity 7



0

3

6

9

12

15

18

21

24

0 70 140 210 280 350

Stor

y

(a)



Stor

y

0

3

6

9

12

15

18

21

24

0 250 500 750 1000

(b)



Stor

y

0

3

6

9

12

15

18

21

24

0 500 1000 1500 2000

(c)

Figure 7 Maximum strain value of frame beam at different story (a) Frequent intensity 7 (b) basic intensity 7 and (c) rare intensity 7


Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500

Acceleration peak (g)

(a)

Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(b)

Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 08Acceleration peak (g)

0

500

1000

1500

2000

(c)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(d)

Figure 8 Damage evolution of horizontal component (a) Coupling beam at 8 story (b) coupling beam at 11 story (c) frame beam at 8 storyand (d) frame beam at 11 story

0

3

6

9

12

15

18

21

24

0 60 120 180 240

Stor

y



(a)

Stor

y

0

3

6

9

12

15

18

21

24

0 100 200 300 400 500Strain amplitude (10ndash6)


(b)

Stor

y

0

3

6

9

12

15

18

21

24



(c)

Figure 9 Maximum strain value of wall limb at different story (a) Frequent intensity 7 (b) basic intensity 7 and (c) rare intensity 7


Stor

y

0

4

8

12

16

20

24



(a)

Stor

y

0

4

8

12

16

20

24



(b)

Stor

y

0

4

8

12

16

20

24



(c)

Figure 10 Maximum strain value of frame column at different story (a) Frequent intensity 7 (b) basic intensity 7 and (c) rare intensity 7

00 02 04 06 080

200

400

600

800

1000

1200

1400


Stra

in am

plitu

de (1

0ndash6)


(a)

00 02 04 06 080

200

400

600

800

1000

1200


Stra

in am

plitu

de (1

0ndash6)


(b)

00 02 04 06 080

50

100

150

200

250

300


Stra

in am

plitu

de (1

0ndash6)


(c)

00 02 04 06 080

100

200

300

400

500

600


Stra

in am

plitu

de (1

0ndash6)


(d)

Figure 11 Damage evolution of vertical component (a) Wall limb at 1 story (b) frame column at 1 story (c) wall limb at 11 story and (d)frame column at 11 story


strong earthquakes and that the bearing capacity of thosevertical components may remain more stable during astrong earthquake

433 Relationship between Damages in Horizontal Com-ponent and Vertical Component According to the com-parative analysis of the component damage states in theprevious section the increase in the damage sustained by thehorizontal components and the decrease in the damage sus-tained by the vertical components in the optimization modelchange the relationship among the damage states in both kindsof components As shown in Figure 12 the values of εLεc andεLLεw can reflect the relationship among the damage states inthe horizontal and vertical components where εL εLL εc andεw represent the maximum strain values for the frame beamcoupling beam frame column and wall limb respectively oneach floor -e values of εLεc and εLLεw in the two modelstructures are both greater than 1 indicating that the damagesuffered by the horizontal components is greater than that bythe vertical components which suggests that the two seismicdamage mechanisms namely ldquostrong wall limb-weak cou-pling beamrdquo and ldquostrong frame column-weak frame beamrdquoare both realized on each floor However the values of εLεcand εLLεw in the optimization model are apparently greaterthan those in the normative model on each floor indicatingthat regions with greater damage were concentrated on thehorizontal components and that the damage to the verticalcomponent was relatively reduced in the optimization modelin comparison with the normative model

In the seismic design for a frame-core tube structure theabovementioned relationship among the damage states inthe vertical and horizontal components on the same floor isable to prevent only the development of soft-story behaviorsthat is this relationship does not ensure the development ofa global damage mechanism [28ndash31] -is kind of damagemechanism can be described by the relationship among thedamage states in the vertical components on the groundfloor and the horizontal components on the upper floors inthis case the damage suffered by the vertical componentsshould be reasonably limited to ensure that its damage issmaller than that suffered by the horizontal components onthe upper floors As shown in Figures 13 and 14 under a rareearthquake the damage sustained by the horizontal com-ponents on the upper floors in the normative model is closeto that sustained by the vertical components on the groundfloor However this kind of relationship among componentdamage states cannot ensure that the energy dissipationcapacity and ductility of the horizontal components aremaximized [13] In contrast the damage sustained by thehorizontal components on each floor in the optimizationmodel were apparently greater than those sustained by thevertical components on the ground floor consequently aglobal damage mechanism developed easily under earth-quake activity In other words the ldquostrong wall limb-weakcoupling beamrdquo and ldquostrong frame column-weak framebeamrdquo damage mechanisms in the optimization model canbe applied more effectively to the entire structure than to theindividual floors of the structure

434 Relationship between Damages in the Wall Limb andFrame Column Due to the differences in the damage sus-tained by the vertical components in the two models underthe action of a strong earthquake the relationship among thedamage states of these components may influence the col-laborative working mechanism between the outer frame andcore tube -e value of εcεw can reflect the relationshipamong the damage states of the frame column and wall limbwhere εc and εw represent the maximum strain values for theframe column and wall limb respectively on each floorAccording to the distributions of damage within the framecolumns and shear walls the damage on the ground floor isgenerally the largest and thus the damage sustained at theground floor plays a substantial role in controlling theabovementioned collaborative workingmechanism-e εcεwvalues on the ground floors of the two models were extracted

0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18

Stor

y

εLLεw


(a)

Stor

y

0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18εLεc


(b)

Figure 12 Strain ratio between vertical component and horizontalcomponent (a) Strain ratio of coupling beam and wall limb(b) strain ratio of frame beam and frame column

Stor

y

0

3

6

9

12

15

18

21

24


Wall limbCoupling beam

(a)

Stor

y0

3

6

9

12

15

18

21

24



(b)

Figure 13 Comparison of strains in coupling beam and wall limbunder rare earthquake (a) Normative model (b) optimizationmodel


as shown in Figure 15 -e values of εcεw in the two modelsare both less than 1 indicating that the damage sustained bythe frame column is less severe than that sustained by the walllimb hence the collaborative working mechanism is realizedin both models -rough further comparison the values ofεcεw in the normative model clearly increased more thanthose in the optimization model with an increase in theacceleration peak -is finding indicates that the frame col-umn on the ground floor in the normative model wasdamaged more severely with an increase in the earthquakelevel and thus the reliability of the bearing capacity of theouter frame serving as the second line of fortification cannotbe ensured In contrast the damage sustained by the framecolumn on the ground floor was limited more effectively inthe optimization model with which an antiseismic designfortification line can be better implemented and the collab-orative working mechanism can be better realized

44 Overall Damage Analysis -e increase in the damagesustained by the horizontal components and the decrease inthe damage sustained by the vertical componentsthroughout the structure inevitably influence the overallstructural damage In this paper to comprehensively con-sider the adverse effects of structural stiffness degradationand second-order gravity effects on high-rise buildings anevaluation index based on the degradation of the equivalentrigidity-to-weight ratio is used to represent the overalldamage [32] and is expressed as follows

F 1minusλ2iλ20

(4)

where F is the structure failure index λ0 is the initial ratio ofequivalent rigid-to-weight and λi is the instantaneous ratioof equivalent rigidity-to-weight after suffering structuraldamage -e formula for λi is [32]

λi Keqi

GH2(5)

whereKeqi is the equivalent lateral stiffness at anymoment ofstiffness degradation G is the weight of the structure and H

is the total height of the structure -e two model structureshave the same value of G and H -erefore λi is determinedby Keqi Due to the different damage performance of the twomodel structure the variations in equivalent lateral stiffnessare inevitably affected during the tests According to theliterature [32] the equivalent stiffness Keqi is a parameterwhich is used to represent the overall stiffness of structureunder the action of an earthquake -us in this paper thestiffness of equivalent single-degree-of-freedom system(SDOF) can be used to represent Keqi To calculate Keqi themodel structure was transformed into the SDOF systemusing the shape vector based on the first modal shape of thestructure -e equation for the equivalent SDOF system isgiven as follows [33]

M eurox + C _x + Kx minusM euroxg (6)

where M C and K denote the properties of the equivalentSDOF system -erefore Keqi can be expressed by K asfollows

Keqi K Mlowast (2πf)2 (7)

where fi is the primary natural frequency of the structureafter the ith earthquake

Equations (5) and (7) are presented in equation (4) toobtain the variation in the overall damage index at differentearthquake levels as shown in Table 13

-e relationship between the damage grade and therange of the index is shown in Table 14 [32] Figure 16 showsthe curves of the overall damage sustained by both models atdifferent earthquake levels -e overall damage indices ofboth models are 0 under frequent earthquakes with in-tensities of 7 and 8 in accordance with experimental phe-nomena With an increase in the acceleration the overalldamage suffered within the optimization model under basicearthquake activities was larger than that within the nor-mative model because the horizontal components became

Stor

y

0

3

6

9

12

15

18

21

24


Frame columnFrame beam

(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)

Figure 14 Comparison of strains in frame beam and frame columnunder rare earthquake (a) Normative model (b) optimizationmodel

00 02 04 06 0800

02

04

06

08

10


ε cε

w


Figure 15 Strain ratio of column and wall limb


damaged in the optimization model faster than those in thenormative model due to the damage optimization which ledto faster degradation in the early stage of the overall stiffnessdeterioration of the structure With a further increase in theacceleration the overall damage suffered within the opti-mization model became smaller than that within the nor-mative model under the action of a strong earthquakeshowing that the overall stiffness deterioration of the op-timization model was effectively controlled during thestrong earthquake because the damage sustained by thevertical components especially the frame column in theouter frame was effectively limited under such conditions

45 Shear Force and Overturning Moment Due to the in-crease in the damage sustained by the horizontal compo-nents and the decrease in the damage sustained by thevertical components the structures consequently exhibiteddifferent internal force responses -e maximum storyshears of the two models are shown in Figures 17 and 18Under the activities of frequent earthquakes with an in-tensity of 7 the story shears in both models gradually in-creased from the upper floor to the lower floor therebyshowing an obvious triangular distribution along thestructural height -e distributions were similar under thethree different seismic waves because the two models stillbehaved elastically under frequent earthquakes With anincrease in the acceleration peak the distribution of the storyshear in the normative model changed obviously under theactivities of strong earthquakes whereas that in the opti-mization model varied little as shown in Figures 17(b) and18(b) -ese results indicate that the internal force responseof the optimization model under the activities of strong

earthquakes was more stable than that of the normativemodel making it easier to actively control the seismic ca-pability of the structure in the seismic design By furthercomparing the story shear with the overturning moment oneach floor the story shear and the overturning moment ofthe optimization model under the action of a rare earth-quake were both smaller than those in the normative model

Table 13 Overall damage index value at different earthquake levels

PGA (g) 0105 021 03 045 066 076Normative model 0 0 011 024 044 061Optimization model 0 0 01 029 041 054

Table 14 Damage index range at different damage levels

Damage level Basic integrity Slight damage Moderate damage Serious damage CollapseF le01 01sim02 02sim05 05sim075 ge075

00 02 04 06 08

00

02

04

06

08 CollapseSerious damage

Moderate damageSlight damage

Basic integrity

Dam

age i

ndex


Figure 16 Overall damage0

5

10

15

20

25

00 05 10 15 20 25Shear (103) (kN)

Stor

y

Artificial waveEl Centro waveHollywood wave

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)

Figure 17 Story maximum shear of optimization model (a)Frequent intensity 7 (b) rare intensity 7


as shown in Figures 19 and 20 -e relationship among thecomponent damage states in the optimization model couldfurther reduce the seismic demand of the internal forcethereby making the structure more resistant to earthquakes

5 Conclusions

In this paper the component damage states in two modelswere experimentally and analytically investigated -e fol-lowing conclusions can be drawn from the shaking tabletests performed herein

(1) In comparison with the variations in the frequenciesand damping ratios of the two models the optimi-zation model was damaged less severely and had astronger energy dissipation potential than the nor-mative model under the action of a strong earthquake

(2) -e horizontal components whose damage wasoptimized in the optimization model can undergogreater damage thus the ductility in the nonlineardamage stage and the postyield bearing capacitycan be exploited during an earthquake -e con-straint on the damage sustained by the verticalcomponents in the optimization model can permitthe bearing capacity to remain more stable during astrong earthquake

(3) -e optimization of the relationship amongthe damage states of the horizontal and verticalcomponents in the optimization model causes theregions exhibiting greater damage to become con-centrated on the horizontal components Moreovera global damagemechanism can be developed duringa strong earthquake and thus the energy dissipation

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25 30

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)

Figure 18 Story maximum shear of normative model (a) Frequent intensity 7 (b) rare intensity 7

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 3 6 9 12 15 18 21 24

(b)

Figure 19 Comparison of story maximum shear (a) Frequent intensity 7 (b) rare intensity 7


capacity and ductility of the horizontal componentscan be more effectively maximized In addition theoptimization of the damage sustained by the verticalcomponents can ensure the reliability of the bearingcapacity of the outer frame acting as a second for-tification line further optimizing the relationshipamong the damage states of the frame columns andwall limbs and better implementing the collaborativeworking mechanism between the two lateral forcesystems in the frame-core tube structure

(4) -e results of an overall damage evaluation provethat an increase in the damage sustained by thehorizontal components and a decrease in the damagesustained by the vertical components in the opti-mization model can effectively limit the overallstiffness deterioration and the development ofoverall damage during strong earthquakes in com-parison with the normative model

(5) -e internal force response can be further optimizeddue to the increase in the damage sustained by thehorizontal components and the decrease in thedamage sustained by the vertical components in theoptimization model -e distribution of the storyshear along the height of the structure can be im-proved during a strong earthquake and the demandon the bearing capacity of the structure can befurther reduced making the structure more resistantto earthquakes

Data Availability

All data supporting the findings of this study are availableupon request from the corresponding author

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is research is supported by the National Key Researchand Development Program of China under grant no2016YFC0701102 the Major Program of National Nat-ural Science Foundation of China under grant no51538003 China Major Development Project for Scien-tific Research Instrument under grant no 51827811Shenzhen Technology Innovation Program undergrant no JCYJ20170811160003571 and the ResearchProject of Knowledge Innovation Plan in Shenzhen(JCYJ20160531193340540)

References

[1] G Ma H Hao and Y Zhou ldquoAssessment of structuredamage to blasting induced ground motionsrdquo EngineeringStructures vol 22 no 10 pp 1378ndash1389 2000

[2] M Sanchez-Silva and L Garcia ldquoEarthquake damage as-sessment based on fuzzy logic and neural networksrdquo Earth-quake Spectra vol 17 no 1 pp 89ndash112 2001

[3] P Khashaee ldquoDamage-based seismic design of structuresrdquoEarthquake Spectra vol 21 no 2 2005

[4] J Ou H Zheng B Wu et al ldquoSeismic damage performance-based design of reinforced concrete structuresrdquo EarthquakeEngineering amp Engineering Vibration vol 2 no 3 pp 173ndash184 1999

[5] D Jian ldquoResearch on seismic capacity design method of RCframe based on direct damagerdquo World Earthquake Engi-neering vol 23 no 4 pp 199ndash204 2007

[6] J Xia W Yang W Zhang et al ldquoDirect damage-basedseismic design method for RC frame structuresrdquo BuildingStructure vol 42 pp 210ndash214 2012

[7] G S Kamaris G D Hatzigeorgiou and D E Beskos ldquoDirectdamage controlled seismic design of plane steel degradingframesrdquo Bulletin of Earthquake Engineering vol 13 no 2pp 587ndash612 2015

[8] Z Tian X Zhang and T Zhao ldquoSeismic damage of multilayerreinforced concrete frame structures in Wenchuan earth-quakerdquo Building Structure vol 39 no 11 pp 67ndash71 2009

Stor

y


0

5

10

15

20

25

0 2 4 6 8 10 12Overturning moment (103) (kNmiddotm)

(a)

Stor

y


Overturning moment (103) (kNmiddotm)

0

5

10

15

20

25

0 20 40 60 80 100 120

(b)

Figure 20 Comparison of maximum overturning moment (a) Frequent intensity 7 (b) rare intensity 7


[9] Z W Miao Z Y Qiu and Y Ming ldquoStudy on energydissipation mechanism and collapse-resistant performanceof RC frame-shear-wall structure under strong earth-quakerdquo Applied Mechanics and Materials vol 204ndash208pp 2550ndash2554 2012

[10] H D Yun P Wanshin L Joohwa et al ldquoBehavior charac-teristics of coupled shear wall on effects of coupling beamdetailsrdquo Journal of the Architectural Institute of KoreaStructure amp Construction vol 20 no 6 pp 19ndash26 2004

[11] Q U Zhe and Y E Lieping ldquoSeismic design methodologybased on damage mechanism control for reinforced concretestructuresrdquo Journal of Building Structures vol 32 no 10pp 21ndash29 2011

[12] G M Verderame F De Luca P Ricci and G ManfredildquoPreliminary analysis of a soft-storey mechanism after the2009 LrsquoAquila earthquakerdquo Earthquake Engineering ampStructural Dynamics vol 40 no 8 pp 925ndash944 2011

[13] R Montuori and R Muscati ldquoA general design procedure forfailure mechanism control of reinforced concrete framesrdquoEngineering Structures vol 118 pp 137ndash155 2016

[14] Z Miao ldquoDistribution mode of hysteretic energy and damagemechanism of RC frame-shear-wall structure under strongearthquakesrdquo Journal of Southeast University vol 42 no 5pp 933ndash939 2012

[15] J Zhang Y Wu C Yang et al ldquoStudy on seismic perfor-mance of super high-rise frame-core tube structures underlong-period ground motionsrdquo Building Structure vol 44no 19 pp 40ndash45 2014

[16] X Lu M Li H Guan X Lu and L Ye ldquoA comparative casestudy on seismic design of tall RC frame-core-tube structuresin China and USArdquo Structural Design of Tall and SpecialBuildings vol 24 no 9 pp 687ndash702 2015

[17] X Lu B Zhou B Zhao et al ldquoShaking table test and nu-merical analysis of a high-rise building with steel reinforceconcrete column and reinforce concrete core tuberdquo StructuralDesign of Tall amp Special Buildings vol 24 no 18 pp 1019ndash1037 2016

[18] Ministry of Housing and UrbanndashRural Development of thePeoplersquos Republic of China Technical Specification for Con-crete Structures of Tall Buildings JGJ3-2010 Architecture ampBuilding Press Beijing China 2010 English version

[19] Ministry of Housing and UrbanndashRural Development of thePeoplersquos Republic of China Code for Seismic Design ofBuildings GB 50011-2010 Architecture amp Building PressBeijing China 2010 English version

[20] Ministry of Housing and UrbanndashRural Development of thePeoplersquos Republic of China Code for Design of ConcreteStructure GB 50011-2010 Architecture amp Building PressBeijing China 2010 English version

[21] M Bosco and L Tirca ldquoNumerical simulation of steelI-shaped beams using a fiber-based damage accumulationmodelrdquo Journal of Constructional Steel Research vol 133pp 241ndash255 2017

[22] C He Q Cao J Teng et al ldquoResearch on the damage dis-tribution patterns of frame-core tube structure based onmaterial damage of componentsrdquo Building Structure vol 41pp 1003ndash1006 2011

[23] M Poursha and M A Amini ldquoA single-run multi-modepushover analysis to account for the effect of higher modes inestimating the seismic demands of tall buildingsrdquo Bulletin ofEarthquake Engineering vol 13 no 8 pp 2347ndash2365 2015

[24] A S Cakmak and S Rodriquezgomez ldquoEvaluation of seismicdamage indices for reinforced concrete structuresrdquo AppliedArtificial Intelligence vol 19 no 9-10 pp 861ndash879 1990

[25] J-F Wang C-C Lin and S-M Yen ldquoA story damage indexof seismically-excited buildings based on modal frequencyand mode shaperdquo Engineering Structures vol 29 no 9pp 2143ndash2157 2007

[26] Y J Park and A H S Ang ldquoMechanistic seismic damagemodel for reinforced concreterdquo Journal of Structural Engi-neering vol 111 no 4 pp 722ndash739 1985

[27] M R Salari S Saeb K J Willam S J Patchet andR C Carrasco ldquoA coupled elastoplastic damage model forgeomaterialsrdquo Computer Methods in Applied Mechanics andEngineering vol 193 no 27ndash29 pp 2625ndash2643 2004

[28] A Heidari and S Gharehbaghi ldquoSeismic performance im-provement of special truss moment frames using damage andenergy conceptsrdquo Earthquake Engineering amp Structural Dy-namics vol 44 no 7 pp 1055ndash1073 2015

[29] E A Godınez-Domınguez and A Tena-Colunga ldquoNonlinearbehavior of code-designed reinforced concrete concentricbraced frames under lateral loadingrdquo Engineering Structuresvol 32 no 4 pp 944ndash963 2010

[30] J Bai and J Ou ldquoRealization of the global yield mechanism ofRC frame structures by redesigning the columns using col-umn tree methodrdquo Science China Technological Sciencesvol 58 no 10 pp 1627ndash1637 2015

[31] B I Stojadinovic S C Goel and S Leelataviwat ldquoEnergy-based seismic design of structures using yield mechanism andtarget driftrdquo Journal of Structural Engineering vol 128 no 8pp 1046ndash1054 2002

[32] L Hai-Xia J Teng L I Zuo-Hua et al ldquoFailure discrimi-nation for high-rise diagrid tube structures based on overallstabilityrdquo Journal of Vibration amp Shock vol 32 no 24pp 96ndash103 2013

[33] H Krawinkler and G D P K Seneviratna ldquoPros and cons of apushover analysis of seismic performance evaluationrdquo En-gineering Structures vol 20 no 4ndash6 pp 452ndash464 1998


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horizontal components on the same floor applied to pre-vent soft-story behaviors [12] in addition there are re-lationships among the damage states of the verticalcomponents on the ground floor and the horizontalcomponents on the upper floors employed to investigatethe global damage mechanism [13] furthermore there arerelationships among the damage states of the verticalcomponents for understanding the cooperative workingmechanism of the outer frame and core tube [14] Ac-cordingly it is difficult for designers to comprehensivelydetermine and satisfy reasonable variations of the above-mentioned relationships among these component damagestates in frame-core tube structures through only seismicconcepts Hence in damage-based seismic design theinfluences of the damage states of these components on theoverall seismic performance including the overall struc-tural damage and interstory internal force should beunderstood effectively by the designer to actively determinethe sensible relationships among the component damagestates To date it has been proposed that the componentdamage states will influence the overall structural damagethrough the damage weighted coefficient however thiscoefficient reflects merely the numerical relationship be-tween the component damage index and the overalldamage index and thus it cannot reflect the influencesof the component damage states on the overall damage ofthe structure Although many theoretical analyses andexperimental studies on the seismic damage performancehave been performed [15ndash17] the influences of compo-nent damage states on the overall seismic performanceof frame-core tube structures have not been discussedcomprehensively

-erefore in this paper the seismic damage perfor-mance of a frame-core tube structure under an earthquakewill be studied in detail to direct the damage-based seismicdesign To reflect the seismic damage performance of thestructure under earthquake activity as much as possible aseries of shaking table tests which represent one of the mosteffective tools employed by researchers and designers tounderstand the seismic performance of structures was usedto comparatively study the seismic damage performances oftwo scaled models of frame-core tube structures In thesetests the seismic damage performances of the two modelswere compared to determine the most reasonable re-lationship among component damage states therein Inaddition the influences of the component damage states onthe overall seismic performance were analyzed and theinterstory internal force was quantified to validate the ra-tionality and advantages of the relationship among thecomponent damage states proposed in this paper

2 Model Design and Construction

21ModelDesign Twomodels of frame-core tube structureswere designed to comprehensively compare their seismicdamage performances One was an optimization modelwhose component damage states were optimized throughfinite element analysis and the other was a normative modeldesigned with the seismic design method based on Chinese

codes [18ndash20] -ese two model structures were designed toallow them to reach serious damage states without experi-encing overall structural collapse under a rare earthquakewhich is in accordance with the target damage states ofcollapse-forbidden under rare earthquake specified in theCode for Seismic Design of Buildings (GB 50011-2010) thusthe maximum elastic-plastic interstory drift is limited to 1100 under the rare earthquake to control the target damagestates according to the Chinese code

In the design of the optimization model the componentdamage states were optimized to achieve a reasonabledamage target that satisfies the damage optimization prin-ciples proposed in this paper Considering that the com-ponent damage states can be effectively described based onthe concrete material damage states [21] the concretematerial damage index in this paper is defined by thedegradation of the concrete material unloading stiffness todetermine the component damage states according toChinese codes -e relationship between the materialdamage index and material unloading stiffness is given asfollows [20]

Ed (1minusd)E0 (1)

where E0 is the initial stiffness of concrete Ed is theunloading stiffness of concrete and d is the tension orcompression damage index of the concrete material that canbe calculated based on the procedure specified in the Chi-nese code For d 0 no damage occurs within the materialfor d 09 the material fails Considering that the failure ofthe concrete component is usually caused by the crushing ofthe concrete material in the component section the concretematerial pressure damage of the component section is usedto determine the component damage According to theprevious literature the damage index D that represents theaverage damage value of the components at the same floor isgiven as follows [22]

D 1113936

Ni1dn

N (2)

where dn is the maximum concrete material damage valueunder compression in the component section and N is thestatistical number of components at the same floor Todetermine the damage of a single component for comparingand optimizing the damage scale of each component in theoptimization model the value of N can be taken as 1 hencethe value of D is equal to the value of dn -erefore thedamage index dn is used to represent the damage of a singlecomponent -e component damage index values at dif-ferent damage levels are given in Table 1 in reference toprevious studies [4] -e damage optimization principlesand damage scale are summarized as follows

(1) -e horizontal components such as the couplingbeam and frame beam in the frame-core tubestructure may suffer greater damage consideringboth their ductility under a nonlinear damagestage and their postyield bearing capacity which isbeneficial for effectively exhibiting a cumulativeenergy dissipation capacity -erefore to permit the

























Wall limb

Coupling beam

Embedded column 2

9000

6900

6900

B

D

Inner frame

beam

A C

Embedded column 1

6900

9000

2280

0

690022800

2400


20000

40000

60000

80000

100000

0000

5F

20F

15F

25F

10F






ModelComponent type







Frame column














Material

Strain 10



Dynamic behavior






3 Test Program



Optimization model

Basement

Normative model

(a)

(b)

(c) (e)

(d)

















0 5 10 15 20

ndash003

ndash002

ndash001

000

001

002

003

004

Time (s)

Acc

eler

atio

n (g

)

00 05 10 15 20 25 30 35 40 45001

002

003

004

005

006

007

008

009

Period (s)


Acc

eler

atio

n (g

)

(a)


000001002003004

Time (s)

Acc

eler

atio

n (g

)


00 05 10 15 20 25 30 35 40 45000001002003004005006007008009010

Period (s)

Acc

eler

atio

n (g

)

(b)


000001002003004

Time (s)

Acc

eler

atio

n (g

)


00 05 10 15 20 25 30 35 40 45000001002003004005006007008009010011012

Period (s)

Acc

eler

atio

n (g

)

(c)















Basic 7RH1TG035 03


Basic 7 (015 g)RH1TG035 045


Rare 7RH1TG035 066









(a) (b)

(c) (d)





0

3

6

9

12

15

18

21

24



Stor

y

(a)



0

3

6

9

12

15

18

21

24

0 300 600 900 1200

Stor

y

(b)



0

3

6

9

12

15

18

21

24

0 800 1600 2400

Stor

y

(c)




0

3

6

9

12

15

18

21

24

0 70 140 210 280 350

Stor

y

(a)



Stor

y

0

3

6

9

12

15

18

21

24

0 250 500 750 1000

(b)



Stor

y

0

3

6

9

12

15

18

21

24

0 500 1000 1500 2000

(c)



Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(a)

Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(b)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(c)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(d)


0

3

6

9

12

15

18

21

24

0 60 120 180 240

Stor

y



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)

Stor

y

0

3

6

9

12

15

18

21

24



(c)



Stor

y

0

4

8

12

16

20

24



(a)

Stor

y

0

4

8

12

16

20

24



(b)

Stor

y

0

4

8

12

16

20

24



(c)


00 02 04 06 080

200

400

600

800

1000

1200

1400


Stra

in am

plitu

de (1

0ndash6)


(a)

00 02 04 06 080

200

400

600

800

1000

1200


Stra

in am

plitu

de (1

0ndash6)


(b)

00 02 04 06 080

50

100

150

200

250

300


Stra

in am

plitu

de (1

0ndash6)


(c)

00 02 04 06 080

100

200

300

400

500

600


Stra

in am

plitu

de (1

0ndash6)


(d)







0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18

Stor

y

εLLεw


(a)

Stor

y

0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18εLεc


(b)


Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y0

3

6

9

12

15

18

21

24



(b)





F 1minusλ2iλ20

(4)


λi Keqi

GH2(5)









Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)


00 02 04 06 0800

02

04

06

08

10


ε cε

w











00 02 04 06 08

00

02

04

06



Basic integrity

Dam

age i

ndex



5

10

15

20

25

00 05 10 15 20 25Shear (103) (kN)

Stor

y


(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)




5 Conclusions





Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25 30

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)


Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 3 6 9 12 15 18 21 24

(b)






Data Availability




Acknowledgments


References









Stor

y


0

5

10

15

20

25


(a)

Stor

y



0

5

10

15

20

25

0 20 40 60 80 100 120

(b)































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia

























Wall limb

Coupling beam

Embedded column 2

9000

6900

6900

B

D

Inner frame

beam

A C

Embedded column 1

6900

9000

2280

0

690022800

2400


20000

40000

60000

80000

100000

0000

5F

20F

15F

25F

10F






ModelComponent type







Frame column














Material

Strain 10



Dynamic behavior






3 Test Program



Optimization model

Basement

Normative model

(a)

(b)

(c) (e)

(d)

















0 5 10 15 20

ndash003

ndash002

ndash001

000

001

002

003

004

Time (s)

Acc

eler

atio

n (g

)

00 05 10 15 20 25 30 35 40 45001

002

003

004

005

006

007

008

009

Period (s)


Acc

eler

atio

n (g

)

(a)


000001002003004

Time (s)

Acc

eler

atio

n (g

)


00 05 10 15 20 25 30 35 40 45000001002003004005006007008009010

Period (s)

Acc

eler

atio

n (g

)

(b)


000001002003004

Time (s)

Acc

eler

atio

n (g

)


00 05 10 15 20 25 30 35 40 45000001002003004005006007008009010011012

Period (s)

Acc

eler

atio

n (g

)

(c)















Basic 7RH1TG035 03


Basic 7 (015 g)RH1TG035 045


Rare 7RH1TG035 066









(a) (b)

(c) (d)





0

3

6

9

12

15

18

21

24



Stor

y

(a)



0

3

6

9

12

15

18

21

24

0 300 600 900 1200

Stor

y

(b)



0

3

6

9

12

15

18

21

24

0 800 1600 2400

Stor

y

(c)




0

3

6

9

12

15

18

21

24

0 70 140 210 280 350

Stor

y

(a)



Stor

y

0

3

6

9

12

15

18

21

24

0 250 500 750 1000

(b)



Stor

y

0

3

6

9

12

15

18

21

24

0 500 1000 1500 2000

(c)



Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(a)

Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(b)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(c)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(d)


0

3

6

9

12

15

18

21

24

0 60 120 180 240

Stor

y



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)

Stor

y

0

3

6

9

12

15

18

21

24



(c)



Stor

y

0

4

8

12

16

20

24



(a)

Stor

y

0

4

8

12

16

20

24



(b)

Stor

y

0

4

8

12

16

20

24



(c)


00 02 04 06 080

200

400

600

800

1000

1200

1400


Stra

in am

plitu

de (1

0ndash6)


(a)

00 02 04 06 080

200

400

600

800

1000

1200


Stra

in am

plitu

de (1

0ndash6)


(b)

00 02 04 06 080

50

100

150

200

250

300


Stra

in am

plitu

de (1

0ndash6)


(c)

00 02 04 06 080

100

200

300

400

500

600


Stra

in am

plitu

de (1

0ndash6)


(d)







0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18

Stor

y

εLLεw


(a)

Stor

y

0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18εLεc


(b)


Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y0

3

6

9

12

15

18

21

24



(b)





F 1minusλ2iλ20

(4)


λi Keqi

GH2(5)









Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)


00 02 04 06 0800

02

04

06

08

10


ε cε

w











00 02 04 06 08

00

02

04

06



Basic integrity

Dam

age i

ndex



5

10

15

20

25

00 05 10 15 20 25Shear (103) (kN)

Stor

y


(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)




5 Conclusions





Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25 30

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)


Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 3 6 9 12 15 18 21 24

(b)






Data Availability




Acknowledgments


References









Stor

y


0

5

10

15

20

25


(a)

Stor

y



0

5

10

15

20

25

0 20 40 60 80 100 120

(b)































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia










Wall limb

Coupling beam

Embedded column 2

9000

6900

6900

B

D

Inner frame

beam

A C

Embedded column 1

6900

9000

2280

0

690022800

2400


20000

40000

60000

80000

100000

0000

5F

20F

15F

25F

10F






ModelComponent type







Frame column














Material

Strain 10



Dynamic behavior






3 Test Program



Optimization model

Basement

Normative model

(a)

(b)

(c) (e)

(d)

















0 5 10 15 20

ndash003

ndash002

ndash001

000

001

002

003

004

Time (s)

Acc

eler

atio

n (g

)

00 05 10 15 20 25 30 35 40 45001

002

003

004

005

006

007

008

009

Period (s)


Acc

eler

atio

n (g

)

(a)


000001002003004

Time (s)

Acc

eler

atio

n (g

)


00 05 10 15 20 25 30 35 40 45000001002003004005006007008009010

Period (s)

Acc

eler

atio

n (g

)

(b)


000001002003004

Time (s)

Acc

eler

atio

n (g

)


00 05 10 15 20 25 30 35 40 45000001002003004005006007008009010011012

Period (s)

Acc

eler

atio

n (g

)

(c)















Basic 7RH1TG035 03


Basic 7 (015 g)RH1TG035 045


Rare 7RH1TG035 066









(a) (b)

(c) (d)





0

3

6

9

12

15

18

21

24



Stor

y

(a)



0

3

6

9

12

15

18

21

24

0 300 600 900 1200

Stor

y

(b)



0

3

6

9

12

15

18

21

24

0 800 1600 2400

Stor

y

(c)




0

3

6

9

12

15

18

21

24

0 70 140 210 280 350

Stor

y

(a)



Stor

y

0

3

6

9

12

15

18

21

24

0 250 500 750 1000

(b)



Stor

y

0

3

6

9

12

15

18

21

24

0 500 1000 1500 2000

(c)



Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(a)

Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(b)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(c)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(d)


0

3

6

9

12

15

18

21

24

0 60 120 180 240

Stor

y



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)

Stor

y

0

3

6

9

12

15

18

21

24



(c)



Stor

y

0

4

8

12

16

20

24



(a)

Stor

y

0

4

8

12

16

20

24



(b)

Stor

y

0

4

8

12

16

20

24



(c)


00 02 04 06 080

200

400

600

800

1000

1200

1400


Stra

in am

plitu

de (1

0ndash6)


(a)

00 02 04 06 080

200

400

600

800

1000

1200


Stra

in am

plitu

de (1

0ndash6)


(b)

00 02 04 06 080

50

100

150

200

250

300


Stra

in am

plitu

de (1

0ndash6)


(c)

00 02 04 06 080

100

200

300

400

500

600


Stra

in am

plitu

de (1

0ndash6)


(d)







0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18

Stor

y

εLLεw


(a)

Stor

y

0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18εLεc


(b)


Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y0

3

6

9

12

15

18

21

24



(b)





F 1minusλ2iλ20

(4)


λi Keqi

GH2(5)









Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)


00 02 04 06 0800

02

04

06

08

10


ε cε

w











00 02 04 06 08

00

02

04

06



Basic integrity

Dam

age i

ndex



5

10

15

20

25

00 05 10 15 20 25Shear (103) (kN)

Stor

y


(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)




5 Conclusions





Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25 30

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)


Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 3 6 9 12 15 18 21 24

(b)






Data Availability




Acknowledgments


References









Stor

y


0

5

10

15

20

25


(a)

Stor

y



0

5

10

15

20

25

0 20 40 60 80 100 120

(b)































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





ModelComponent type







Frame column














Material

Strain 10



Dynamic behavior






3 Test Program



Optimization model

Basement

Normative model

(a)

(b)

(c) (e)

(d)

















0 5 10 15 20

ndash003

ndash002

ndash001

000

001

002

003

004

Time (s)

Acc

eler

atio

n (g

)

00 05 10 15 20 25 30 35 40 45001

002

003

004

005

006

007

008

009

Period (s)


Acc

eler

atio

n (g

)

(a)


000001002003004

Time (s)

Acc

eler

atio

n (g

)


00 05 10 15 20 25 30 35 40 45000001002003004005006007008009010

Period (s)

Acc

eler

atio

n (g

)

(b)


000001002003004

Time (s)

Acc

eler

atio

n (g

)


00 05 10 15 20 25 30 35 40 45000001002003004005006007008009010011012

Period (s)

Acc

eler

atio

n (g

)

(c)















Basic 7RH1TG035 03


Basic 7 (015 g)RH1TG035 045


Rare 7RH1TG035 066









(a) (b)

(c) (d)





0

3

6

9

12

15

18

21

24



Stor

y

(a)



0

3

6

9

12

15

18

21

24

0 300 600 900 1200

Stor

y

(b)



0

3

6

9

12

15

18

21

24

0 800 1600 2400

Stor

y

(c)




0

3

6

9

12

15

18

21

24

0 70 140 210 280 350

Stor

y

(a)



Stor

y

0

3

6

9

12

15

18

21

24

0 250 500 750 1000

(b)



Stor

y

0

3

6

9

12

15

18

21

24

0 500 1000 1500 2000

(c)



Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(a)

Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(b)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(c)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(d)


0

3

6

9

12

15

18

21

24

0 60 120 180 240

Stor

y



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)

Stor

y

0

3

6

9

12

15

18

21

24



(c)



Stor

y

0

4

8

12

16

20

24



(a)

Stor

y

0

4

8

12

16

20

24



(b)

Stor

y

0

4

8

12

16

20

24



(c)


00 02 04 06 080

200

400

600

800

1000

1200

1400


Stra

in am

plitu

de (1

0ndash6)


(a)

00 02 04 06 080

200

400

600

800

1000

1200


Stra

in am

plitu

de (1

0ndash6)


(b)

00 02 04 06 080

50

100

150

200

250

300


Stra

in am

plitu

de (1

0ndash6)


(c)

00 02 04 06 080

100

200

300

400

500

600


Stra

in am

plitu

de (1

0ndash6)


(d)







0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18

Stor

y

εLLεw


(a)

Stor

y

0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18εLεc


(b)


Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y0

3

6

9

12

15

18

21

24



(b)





F 1minusλ2iλ20

(4)


λi Keqi

GH2(5)









Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)


00 02 04 06 0800

02

04

06

08

10


ε cε

w











00 02 04 06 08

00

02

04

06



Basic integrity

Dam

age i

ndex



5

10

15

20

25

00 05 10 15 20 25Shear (103) (kN)

Stor

y


(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)




5 Conclusions





Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25 30

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)


Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 3 6 9 12 15 18 21 24

(b)






Data Availability




Acknowledgments


References









Stor

y


0

5

10

15

20

25


(a)

Stor

y



0

5

10

15

20

25

0 20 40 60 80 100 120

(b)































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



3 Test Program



Optimization model

Basement

Normative model

(a)

(b)

(c) (e)

(d)

















0 5 10 15 20

ndash003

ndash002

ndash001

000

001

002

003

004

Time (s)

Acc

eler

atio

n (g

)

00 05 10 15 20 25 30 35 40 45001

002

003

004

005

006

007

008

009

Period (s)


Acc

eler

atio

n (g

)

(a)


000001002003004

Time (s)

Acc

eler

atio

n (g

)


00 05 10 15 20 25 30 35 40 45000001002003004005006007008009010

Period (s)

Acc

eler

atio

n (g

)

(b)


000001002003004

Time (s)

Acc

eler

atio

n (g

)


00 05 10 15 20 25 30 35 40 45000001002003004005006007008009010011012

Period (s)

Acc

eler

atio

n (g

)

(c)















Basic 7RH1TG035 03


Basic 7 (015 g)RH1TG035 045


Rare 7RH1TG035 066









(a) (b)

(c) (d)





0

3

6

9

12

15

18

21

24



Stor

y

(a)



0

3

6

9

12

15

18

21

24

0 300 600 900 1200

Stor

y

(b)



0

3

6

9

12

15

18

21

24

0 800 1600 2400

Stor

y

(c)




0

3

6

9

12

15

18

21

24

0 70 140 210 280 350

Stor

y

(a)



Stor

y

0

3

6

9

12

15

18

21

24

0 250 500 750 1000

(b)



Stor

y

0

3

6

9

12

15

18

21

24

0 500 1000 1500 2000

(c)



Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(a)

Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(b)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(c)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(d)


0

3

6

9

12

15

18

21

24

0 60 120 180 240

Stor

y



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)

Stor

y

0

3

6

9

12

15

18

21

24



(c)



Stor

y

0

4

8

12

16

20

24



(a)

Stor

y

0

4

8

12

16

20

24



(b)

Stor

y

0

4

8

12

16

20

24



(c)


00 02 04 06 080

200

400

600

800

1000

1200

1400


Stra

in am

plitu

de (1

0ndash6)


(a)

00 02 04 06 080

200

400

600

800

1000

1200


Stra

in am

plitu

de (1

0ndash6)


(b)

00 02 04 06 080

50

100

150

200

250

300


Stra

in am

plitu

de (1

0ndash6)


(c)

00 02 04 06 080

100

200

300

400

500

600


Stra

in am

plitu

de (1

0ndash6)


(d)







0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18

Stor

y

εLLεw


(a)

Stor

y

0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18εLεc


(b)


Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y0

3

6

9

12

15

18

21

24



(b)





F 1minusλ2iλ20

(4)


λi Keqi

GH2(5)









Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)


00 02 04 06 0800

02

04

06

08

10


ε cε

w











00 02 04 06 08

00

02

04

06



Basic integrity

Dam

age i

ndex



5

10

15

20

25

00 05 10 15 20 25Shear (103) (kN)

Stor

y


(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)




5 Conclusions





Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25 30

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)


Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 3 6 9 12 15 18 21 24

(b)






Data Availability




Acknowledgments


References









Stor

y


0

5

10

15

20

25


(a)

Stor

y



0

5

10

15

20

25

0 20 40 60 80 100 120

(b)































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia
















0 5 10 15 20

ndash003

ndash002

ndash001

000

001

002

003

004

Time (s)

Acc

eler

atio

n (g

)

00 05 10 15 20 25 30 35 40 45001

002

003

004

005

006

007

008

009

Period (s)


Acc

eler

atio

n (g

)

(a)


000001002003004

Time (s)

Acc

eler

atio

n (g

)


00 05 10 15 20 25 30 35 40 45000001002003004005006007008009010

Period (s)

Acc

eler

atio

n (g

)

(b)


000001002003004

Time (s)

Acc

eler

atio

n (g

)


00 05 10 15 20 25 30 35 40 45000001002003004005006007008009010011012

Period (s)

Acc

eler

atio

n (g

)

(c)















Basic 7RH1TG035 03


Basic 7 (015 g)RH1TG035 045


Rare 7RH1TG035 066









(a) (b)

(c) (d)





0

3

6

9

12

15

18

21

24



Stor

y

(a)



0

3

6

9

12

15

18

21

24

0 300 600 900 1200

Stor

y

(b)



0

3

6

9

12

15

18

21

24

0 800 1600 2400

Stor

y

(c)




0

3

6

9

12

15

18

21

24

0 70 140 210 280 350

Stor

y

(a)



Stor

y

0

3

6

9

12

15

18

21

24

0 250 500 750 1000

(b)



Stor

y

0

3

6

9

12

15

18

21

24

0 500 1000 1500 2000

(c)



Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(a)

Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(b)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(c)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(d)


0

3

6

9

12

15

18

21

24

0 60 120 180 240

Stor

y



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)

Stor

y

0

3

6

9

12

15

18

21

24



(c)



Stor

y

0

4

8

12

16

20

24



(a)

Stor

y

0

4

8

12

16

20

24



(b)

Stor

y

0

4

8

12

16

20

24



(c)


00 02 04 06 080

200

400

600

800

1000

1200

1400


Stra

in am

plitu

de (1

0ndash6)


(a)

00 02 04 06 080

200

400

600

800

1000

1200


Stra

in am

plitu

de (1

0ndash6)


(b)

00 02 04 06 080

50

100

150

200

250

300


Stra

in am

plitu

de (1

0ndash6)


(c)

00 02 04 06 080

100

200

300

400

500

600


Stra

in am

plitu

de (1

0ndash6)


(d)







0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18

Stor

y

εLLεw


(a)

Stor

y

0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18εLεc


(b)


Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y0

3

6

9

12

15

18

21

24



(b)





F 1minusλ2iλ20

(4)


λi Keqi

GH2(5)









Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)


00 02 04 06 0800

02

04

06

08

10


ε cε

w











00 02 04 06 08

00

02

04

06



Basic integrity

Dam

age i

ndex



5

10

15

20

25

00 05 10 15 20 25Shear (103) (kN)

Stor

y


(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)




5 Conclusions





Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25 30

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)


Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 3 6 9 12 15 18 21 24

(b)






Data Availability




Acknowledgments


References









Stor

y


0

5

10

15

20

25


(a)

Stor

y



0

5

10

15

20

25

0 20 40 60 80 100 120

(b)































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


0 5 10 15 20

ndash003

ndash002

ndash001

000

001

002

003

004

Time (s)

Acc

eler

atio

n (g

)

00 05 10 15 20 25 30 35 40 45001

002

003

004

005

006

007

008

009

Period (s)


Acc

eler

atio

n (g

)

(a)


000001002003004

Time (s)

Acc

eler

atio

n (g

)


00 05 10 15 20 25 30 35 40 45000001002003004005006007008009010

Period (s)

Acc

eler

atio

n (g

)

(b)


000001002003004

Time (s)

Acc

eler

atio

n (g

)


00 05 10 15 20 25 30 35 40 45000001002003004005006007008009010011012

Period (s)

Acc

eler

atio

n (g

)

(c)















Basic 7RH1TG035 03


Basic 7 (015 g)RH1TG035 045


Rare 7RH1TG035 066









(a) (b)

(c) (d)





0

3

6

9

12

15

18

21

24



Stor

y

(a)



0

3

6

9

12

15

18

21

24

0 300 600 900 1200

Stor

y

(b)



0

3

6

9

12

15

18

21

24

0 800 1600 2400

Stor

y

(c)




0

3

6

9

12

15

18

21

24

0 70 140 210 280 350

Stor

y

(a)



Stor

y

0

3

6

9

12

15

18

21

24

0 250 500 750 1000

(b)



Stor

y

0

3

6

9

12

15

18

21

24

0 500 1000 1500 2000

(c)



Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(a)

Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(b)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(c)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(d)


0

3

6

9

12

15

18

21

24

0 60 120 180 240

Stor

y



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)

Stor

y

0

3

6

9

12

15

18

21

24



(c)



Stor

y

0

4

8

12

16

20

24



(a)

Stor

y

0

4

8

12

16

20

24



(b)

Stor

y

0

4

8

12

16

20

24



(c)


00 02 04 06 080

200

400

600

800

1000

1200

1400


Stra

in am

plitu

de (1

0ndash6)


(a)

00 02 04 06 080

200

400

600

800

1000

1200


Stra

in am

plitu

de (1

0ndash6)


(b)

00 02 04 06 080

50

100

150

200

250

300


Stra

in am

plitu

de (1

0ndash6)


(c)

00 02 04 06 080

100

200

300

400

500

600


Stra

in am

plitu

de (1

0ndash6)


(d)







0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18

Stor

y

εLLεw


(a)

Stor

y

0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18εLεc


(b)


Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y0

3

6

9

12

15

18

21

24



(b)





F 1minusλ2iλ20

(4)


λi Keqi

GH2(5)









Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)


00 02 04 06 0800

02

04

06

08

10


ε cε

w











00 02 04 06 08

00

02

04

06



Basic integrity

Dam

age i

ndex



5

10

15

20

25

00 05 10 15 20 25Shear (103) (kN)

Stor

y


(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)




5 Conclusions





Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25 30

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)


Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 3 6 9 12 15 18 21 24

(b)






Data Availability




Acknowledgments


References









Stor

y


0

5

10

15

20

25


(a)

Stor

y



0

5

10

15

20

25

0 20 40 60 80 100 120

(b)































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












Basic 7RH1TG035 03


Basic 7 (015 g)RH1TG035 045


Rare 7RH1TG035 066









(a) (b)

(c) (d)





0

3

6

9

12

15

18

21

24



Stor

y

(a)



0

3

6

9

12

15

18

21

24

0 300 600 900 1200

Stor

y

(b)



0

3

6

9

12

15

18

21

24

0 800 1600 2400

Stor

y

(c)




0

3

6

9

12

15

18

21

24

0 70 140 210 280 350

Stor

y

(a)



Stor

y

0

3

6

9

12

15

18

21

24

0 250 500 750 1000

(b)



Stor

y

0

3

6

9

12

15

18

21

24

0 500 1000 1500 2000

(c)



Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(a)

Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(b)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(c)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(d)


0

3

6

9

12

15

18

21

24

0 60 120 180 240

Stor

y



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)

Stor

y

0

3

6

9

12

15

18

21

24



(c)



Stor

y

0

4

8

12

16

20

24



(a)

Stor

y

0

4

8

12

16

20

24



(b)

Stor

y

0

4

8

12

16

20

24



(c)


00 02 04 06 080

200

400

600

800

1000

1200

1400


Stra

in am

plitu

de (1

0ndash6)


(a)

00 02 04 06 080

200

400

600

800

1000

1200


Stra

in am

plitu

de (1

0ndash6)


(b)

00 02 04 06 080

50

100

150

200

250

300


Stra

in am

plitu

de (1

0ndash6)


(c)

00 02 04 06 080

100

200

300

400

500

600


Stra

in am

plitu

de (1

0ndash6)


(d)







0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18

Stor

y

εLLεw


(a)

Stor

y

0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18εLεc


(b)


Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y0

3

6

9

12

15

18

21

24



(b)





F 1minusλ2iλ20

(4)


λi Keqi

GH2(5)









Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)


00 02 04 06 0800

02

04

06

08

10


ε cε

w











00 02 04 06 08

00

02

04

06



Basic integrity

Dam

age i

ndex



5

10

15

20

25

00 05 10 15 20 25Shear (103) (kN)

Stor

y


(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)




5 Conclusions





Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25 30

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)


Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 3 6 9 12 15 18 21 24

(b)






Data Availability




Acknowledgments


References









Stor

y


0

5

10

15

20

25


(a)

Stor

y



0

5

10

15

20

25

0 20 40 60 80 100 120

(b)































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








(a) (b)

(c) (d)





0

3

6

9

12

15

18

21

24



Stor

y

(a)



0

3

6

9

12

15

18

21

24

0 300 600 900 1200

Stor

y

(b)



0

3

6

9

12

15

18

21

24

0 800 1600 2400

Stor

y

(c)




0

3

6

9

12

15

18

21

24

0 70 140 210 280 350

Stor

y

(a)



Stor

y

0

3

6

9

12

15

18

21

24

0 250 500 750 1000

(b)



Stor

y

0

3

6

9

12

15

18

21

24

0 500 1000 1500 2000

(c)



Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(a)

Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(b)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(c)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(d)


0

3

6

9

12

15

18

21

24

0 60 120 180 240

Stor

y



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)

Stor

y

0

3

6

9

12

15

18

21

24



(c)



Stor

y

0

4

8

12

16

20

24



(a)

Stor

y

0

4

8

12

16

20

24



(b)

Stor

y

0

4

8

12

16

20

24



(c)


00 02 04 06 080

200

400

600

800

1000

1200

1400


Stra

in am

plitu

de (1

0ndash6)


(a)

00 02 04 06 080

200

400

600

800

1000

1200


Stra

in am

plitu

de (1

0ndash6)


(b)

00 02 04 06 080

50

100

150

200

250

300


Stra

in am

plitu

de (1

0ndash6)


(c)

00 02 04 06 080

100

200

300

400

500

600


Stra

in am

plitu

de (1

0ndash6)


(d)







0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18

Stor

y

εLLεw


(a)

Stor

y

0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18εLεc


(b)


Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y0

3

6

9

12

15

18

21

24



(b)





F 1minusλ2iλ20

(4)


λi Keqi

GH2(5)









Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)


00 02 04 06 0800

02

04

06

08

10


ε cε

w











00 02 04 06 08

00

02

04

06



Basic integrity

Dam

age i

ndex



5

10

15

20

25

00 05 10 15 20 25Shear (103) (kN)

Stor

y


(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)




5 Conclusions





Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25 30

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)


Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 3 6 9 12 15 18 21 24

(b)






Data Availability




Acknowledgments


References









Stor

y


0

5

10

15

20

25


(a)

Stor

y



0

5

10

15

20

25

0 20 40 60 80 100 120

(b)































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




0

3

6

9

12

15

18

21

24



Stor

y

(a)



0

3

6

9

12

15

18

21

24

0 300 600 900 1200

Stor

y

(b)



0

3

6

9

12

15

18

21

24

0 800 1600 2400

Stor

y

(c)




0

3

6

9

12

15

18

21

24

0 70 140 210 280 350

Stor

y

(a)



Stor

y

0

3

6

9

12

15

18

21

24

0 250 500 750 1000

(b)



Stor

y

0

3

6

9

12

15

18

21

24

0 500 1000 1500 2000

(c)



Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(a)

Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(b)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(c)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(d)


0

3

6

9

12

15

18

21

24

0 60 120 180 240

Stor

y



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)

Stor

y

0

3

6

9

12

15

18

21

24



(c)



Stor

y

0

4

8

12

16

20

24



(a)

Stor

y

0

4

8

12

16

20

24



(b)

Stor

y

0

4

8

12

16

20

24



(c)


00 02 04 06 080

200

400

600

800

1000

1200

1400


Stra

in am

plitu

de (1

0ndash6)


(a)

00 02 04 06 080

200

400

600

800

1000

1200


Stra

in am

plitu

de (1

0ndash6)


(b)

00 02 04 06 080

50

100

150

200

250

300


Stra

in am

plitu

de (1

0ndash6)


(c)

00 02 04 06 080

100

200

300

400

500

600


Stra

in am

plitu

de (1

0ndash6)


(d)







0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18

Stor

y

εLLεw


(a)

Stor

y

0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18εLεc


(b)


Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y0

3

6

9

12

15

18

21

24



(b)





F 1minusλ2iλ20

(4)


λi Keqi

GH2(5)









Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)


00 02 04 06 0800

02

04

06

08

10


ε cε

w











00 02 04 06 08

00

02

04

06



Basic integrity

Dam

age i

ndex



5

10

15

20

25

00 05 10 15 20 25Shear (103) (kN)

Stor

y


(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)




5 Conclusions





Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25 30

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)


Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 3 6 9 12 15 18 21 24

(b)






Data Availability




Acknowledgments


References









Stor

y


0

5

10

15

20

25


(a)

Stor

y



0

5

10

15

20

25

0 20 40 60 80 100 120

(b)































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(a)

Stra

in am

plitu

de (1

0ndash6)


00 02 04 06 080

500

1000

1500

2000

2500


(b)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(c)

Stra

in am

plitu

de (1

0ndash6)



0

500

1000

1500

2000

(d)


0

3

6

9

12

15

18

21

24

0 60 120 180 240

Stor

y



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)

Stor

y

0

3

6

9

12

15

18

21

24



(c)



Stor

y

0

4

8

12

16

20

24



(a)

Stor

y

0

4

8

12

16

20

24



(b)

Stor

y

0

4

8

12

16

20

24



(c)


00 02 04 06 080

200

400

600

800

1000

1200

1400


Stra

in am

plitu

de (1

0ndash6)


(a)

00 02 04 06 080

200

400

600

800

1000

1200


Stra

in am

plitu

de (1

0ndash6)


(b)

00 02 04 06 080

50

100

150

200

250

300


Stra

in am

plitu

de (1

0ndash6)


(c)

00 02 04 06 080

100

200

300

400

500

600


Stra

in am

plitu

de (1

0ndash6)


(d)







0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18

Stor

y

εLLεw


(a)

Stor

y

0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18εLεc


(b)


Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y0

3

6

9

12

15

18

21

24



(b)





F 1minusλ2iλ20

(4)


λi Keqi

GH2(5)









Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)


00 02 04 06 0800

02

04

06

08

10


ε cε

w











00 02 04 06 08

00

02

04

06



Basic integrity

Dam

age i

ndex



5

10

15

20

25

00 05 10 15 20 25Shear (103) (kN)

Stor

y


(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)




5 Conclusions





Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25 30

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)


Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 3 6 9 12 15 18 21 24

(b)






Data Availability




Acknowledgments


References









Stor

y


0

5

10

15

20

25


(a)

Stor

y



0

5

10

15

20

25

0 20 40 60 80 100 120

(b)































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Stor

y

0

4

8

12

16

20

24



(a)

Stor

y

0

4

8

12

16

20

24



(b)

Stor

y

0

4

8

12

16

20

24



(c)


00 02 04 06 080

200

400

600

800

1000

1200

1400


Stra

in am

plitu

de (1

0ndash6)


(a)

00 02 04 06 080

200

400

600

800

1000

1200


Stra

in am

plitu

de (1

0ndash6)


(b)

00 02 04 06 080

50

100

150

200

250

300


Stra

in am

plitu

de (1

0ndash6)


(c)

00 02 04 06 080

100

200

300

400

500

600


Stra

in am

plitu

de (1

0ndash6)


(d)







0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18

Stor

y

εLLεw


(a)

Stor

y

0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18εLεc


(b)


Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y0

3

6

9

12

15

18

21

24



(b)





F 1minusλ2iλ20

(4)


λi Keqi

GH2(5)









Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)


00 02 04 06 0800

02

04

06

08

10


ε cε

w











00 02 04 06 08

00

02

04

06



Basic integrity

Dam

age i

ndex



5

10

15

20

25

00 05 10 15 20 25Shear (103) (kN)

Stor

y


(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)




5 Conclusions





Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25 30

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)


Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 3 6 9 12 15 18 21 24

(b)






Data Availability




Acknowledgments


References









Stor

y


0

5

10

15

20

25


(a)

Stor

y



0

5

10

15

20

25

0 20 40 60 80 100 120

(b)































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18

Stor

y

εLLεw


(a)

Stor

y

0

3

6

9

12

15

18

21

24

0 3 6 9 12 15 18εLεc


(b)


Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y0

3

6

9

12

15

18

21

24



(b)





F 1minusλ2iλ20

(4)


λi Keqi

GH2(5)









Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)


00 02 04 06 0800

02

04

06

08

10


ε cε

w











00 02 04 06 08

00

02

04

06



Basic integrity

Dam

age i

ndex



5

10

15

20

25

00 05 10 15 20 25Shear (103) (kN)

Stor

y


(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)




5 Conclusions





Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25 30

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)


Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 3 6 9 12 15 18 21 24

(b)






Data Availability




Acknowledgments


References









Stor

y


0

5

10

15

20

25


(a)

Stor

y



0

5

10

15

20

25

0 20 40 60 80 100 120

(b)































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




F 1minusλ2iλ20

(4)


λi Keqi

GH2(5)









Stor

y

0

3

6

9

12

15

18

21

24



(a)

Stor

y

0

3

6

9

12

15

18

21

24



(b)


00 02 04 06 0800

02

04

06

08

10


ε cε

w











00 02 04 06 08

00

02

04

06



Basic integrity

Dam

age i

ndex



5

10

15

20

25

00 05 10 15 20 25Shear (103) (kN)

Stor

y


(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)




5 Conclusions





Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25 30

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)


Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 3 6 9 12 15 18 21 24

(b)






Data Availability




Acknowledgments


References









Stor

y


0

5

10

15

20

25


(a)

Stor

y



0

5

10

15

20

25

0 20 40 60 80 100 120

(b)































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









00 02 04 06 08

00

02

04

06



Basic integrity

Dam

age i

ndex



5

10

15

20

25

00 05 10 15 20 25Shear (103) (kN)

Stor

y


(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)




5 Conclusions





Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25 30

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)


Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 3 6 9 12 15 18 21 24

(b)






Data Availability




Acknowledgments


References









Stor

y


0

5

10

15

20

25


(a)

Stor

y



0

5

10

15

20

25

0 20 40 60 80 100 120

(b)































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





Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25 30

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 5 10 15 20 25

(b)


Shear (103) (kN)

Stor

y


0

5

10

15

20

25

00 05 10 15 20 25

(a)

Shear (103) (kN)

Stor

y


0

5

10

15

20

25

0 3 6 9 12 15 18 21 24

(b)






Data Availability




Acknowledgments


References









Stor

y


0

5

10

15

20

25


(a)

Stor

y



0

5

10

15

20

25

0 20 40 60 80 100 120

(b)































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





Data Availability




Acknowledgments


References









Stor

y


0

5

10

15

20

25


(a)

Stor

y



0

5

10

15

20

25

0 20 40 60 80 100 120

(b)































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




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

AComparativeTestStudyontheSeismicDamage SustainedbyFrame ...downloads.hindawi.com/journals/ace/2019/3202959.pdf · on the overall seismic performance of the structure are currently