Research Article Analytical Modeling of Masonry Infilled ...

Research ArticleAnalytical Modeling of Masonry Infilled RC Frames andVerification with Experimental Data

S Skafida L Koutas and S N Bousias

Department of Civil Engineering University of Patras Rio 26500 Patras Greece

Correspondence should be addressed to S Skafida stavroulaskgmailcom

Received 30 September 2013 Accepted 5 February 2014 Published 22 April 2014

Academic Editor Zhongwei Guan

Copyright copy 2014 S Skafida et alThis is an open access article distributed under theCreative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The assessment of the response of masonry infilled RC frame structures has been a major challenge over the last decades Whileseveral modeling approaches have been proposed none can cover all aspects observed in the tests The present paper introduces asimplified model built on the approach established by Crisafulli and Carr (2007) and addresses its calibration and implementationin a nonlinear analysis software for the evaluation of the in-plane lateral response of infilled RC frames The proposed model usesa set of elementssprings to account separately for the compressive and shear behavior of masonry The efficiency of the modelingapproach is validated with available experimental data yielding satisfactory matching The most intricate issue encountered whenattempting to represent a masonry panel is the plethora of the material parameters involved and the lack of complete and availabletest results Thus the numerical investigation is accompanied by a parametric study on the sensitivity of the model to the variousparameters to identify the critical modeling quantities and provide guidance on their selection

1 Introduction

The evaluation of the seismic performance of masonryinfilled RC frame structures is a widespread problem that hasnot yet been resolved despite the numerous efforts reportedin the literature during the last decades As a result andcontrary to the finding from the response of masonry infilledstructures under actual seismic action infill is often treated asnonstructural elements and is omitted by the analysismodelsNevertheless the uncertainty associated with the interactionof the infill with the bounding frame and the different failuremodes exhibited the variability of the material propertiesgeometrical configurations and constructionmethods revealthe complexity of the problem and justify the lack of unifiedreliable and widely accepted approaches for the design andassessment of structural systems that include infill panels

From the computational point of view the modelingtechniques used for the analysis of infilled frames can bedivided into two main categories (i) local or micromodelsand (ii) simplified macromodels The first category is basedon the nonlinear finite elementmethod and strives to providean accurate representation of the frame-infill interaction atthe local level Many of the researchers who adopted this

methodology for example Lotfi [2] Lourenco [3] Attardet al [4] and Mehrabi and Shing [5] used a combinationof continuum and interface line elements to simulate thefracture behavior of brick units and mortar joints In Chiouet al [6] infilled RC frames have been modeled by dis-cretizing the brick units and concrete members into blocksinterconnected with contact springs to account for the tensileand shear failure One of the most recent studies on thisfield conducted by Stavridis and Shing [7] combines theadvantages of the smeared and discrete crack approachesto capture the different failure modes expected to occureither in the RC bounding frame elements or in the masonrypanel Although appealing the complexity of the constitutivemodels incorporated in finite element analysis involvingintensive computational effort hinders their application inthe analysis of large structures

On the other hand macromodels utilize the ldquoequivalenttrussrdquo concept to provide a simple and efficient tool ableto represent the global response of the infill panel and itsinteraction with the surrounding RC frame The basic ideaof this family of models was first suggested by Polyakov [8]and lies in the observation that when subjected to lateralloads the infill wall tends to separate from the bounding

Hindawi Publishing CorporationJournal of StructuresVolume 2014 Article ID 216549 17 pageshttpdxdoiorg1011552014216549

2 Journal of Structures

Yoi

hz

Internal node

Dummy node

1 2

34 Compressiontension struts Shear spring

Active (compression)

Inactive (tension)

Figure 1 Schematic representation of the Crisafulli and Carr masonry panel element [1]

frame at a relatively low drift level forming a resistancemechanism similar to that of a diagonal strut connecting thetwo opposite compression corners where contact with theframe is still retained Various studies have been conducted inorder to define the appropriate modeling configuration theproperties and the constitutive law of the equivalent strutsSome of the earlier works in this area like the investigationsconducted by Holmes [9] Smith [10] and Mainstone [11]considered a single strut connecting the corner nodes alongeach diagonal and tried to evaluate the width of the strut thatcontrols the initial stiffness of the infilled frame Others whoworked in the same direction refined themodeling techniqueeither by introducing multiple strut configurations to allow amore reliable estimation of the interaction between the paneland the frame (eg [1 12ndash14]) or by developing appropriateconstitutive laws to describe the hysteretic behavior of thepanel when subjected to cyclic loading The hysteretic rulesdeveloped by Fardis and Panagiotakos [15] to model theglobal behavior of the infill and the constitutive modelproposed by Crisafulli [16] to describe the cyclic responseof axially loaded masonry are two of the more interestingapproaches in this regard

Summarizing the available solutions it seems that evenif macromodeling schemes are not capable of simulating in adetailed manner all the possible failure mechanisms encoun-tered in infilled frame structures the limited computationaleffort required for their implementation makes them the bestalternative especially when analyzing large structures Thechallenge is yet to develop a broadly applicable frameworkfor determining the effective properties and the hystereticbehavior of the appropriate simplified model for each casestudy

The aim of this paper is to provide an analytical toolfor assessing the in-plane behavior of masonry infilled RCframes focusing on the establishment of a set of specificguidelines for the evaluation of the various parametersrequired to define the monotonic and hysteretic response ofthe masonry infill The modeling scheme presented hereinconstitutes a modification of the ldquomasonry-panelrdquo approachoriginally developed by Crisafulli and Carr [1] The proposedmethodology has been validated with experimental resultsfrommasonry infilled RC frames subjected to in-plane cyclicquasi-static loading histories Five of the experimental studiesconsidered are presented in this paper to demonstrate the

implementation procedure and the efficiency of the modelAdditionally an extensive parametric study has been con-ducted to clarify the influence of the various parameters onthe overall structural response

2 Materials and Methods

21 ProposedModeling Scheme As previouslymentioned themodeling scheme presented in this study is based on theldquomasonry-panelrdquo model proposed by Crisafulli and Carr [1]that is a 4-node panel element connected to the frame at thebeam-column joints Internally the panel element consists oftwo parallel struts and a shear spring acting in each diagonal(Figure 1) to account for both the compressive and the shearbehavior of the masonry panel Encapsulation of the multiplesprings involved in the definition of the model into a 4-node element serves to establish an interrelation between thecompressed diagonal and the shear spring while reducing thelevel of complexity from the userrsquos point of view Still thisconvenience also results in a limited control and some sortof obscurity behind the several parts that comprise the paneland define its behavior

The configuration of the model as presented here main-tains the idea of combining diagonal strut and shear springelements with the difference that no interrelation betweenthe individual elements that comprise the panel has beenexternally imposed except the one arising from the distribu-tion of strength and stiffness among the various componentsduring a loading event As the original model by Crisafulliwas not available in the software framework used in thisstudy (OpenSees) the scope of this research was limitedto relaxing a number of parameters in the original modeland checking if the resulting approach can reliably predictthe experimental results Thus the infill is modeled hereemploying two ldquostrutsrdquo each one connecting the two oppositediagonal corners of the panel and a ldquoshear springrdquo as shownin Figure 2 The behavior of each element is controlled byits own constitutive lawmdashhere a different constitutive law isassigned to the shear spring with respect to that of the modelby Crisafulli

Themodel has been implemented inOpenSees [17] usingthe existing ldquotwo-node linkrdquo element (Figure 3) The elementconnects two diagonally opposite nodes and can generallycomprise from 1 to 6 degrees of freedom where only the

Journal of Structures 3

Strut undercompression Shear spring

Figure 2 Schematic representation of the proposed model (modi-fication of [1])

transverse and rotational DOFs are coupled as long as theelement has a nonzero lengthThe behavior in each directionis defined by a specific material model

In this particular modeling scheme the struts are mod-eled with ldquotwo-node linkrdquo objects connecting the oppositecorner nodes of the panel that are active solely in the directionof the diagonal As far as the shear spring is concerned itis modeled with a ldquotwo-node linkrdquo object that connects twoof the opposite corner nodes of the panel and acts in thehorizontal direction In the proposed formulation the shearspring represents only part of the response of the infill panelin shear and does not contribute to the axial force assumedby the columns

For the numerical simulation of the RC frame membera nonlinear fiber-based element formulation was selected Aldquoforce based beam columnrdquo element with several (usually 6to 8) integration points along its height was used to modeleach beamcolumn member The model takes into accountthe interaction between axial and bending forces but it isincapable of representing the shear behavior of the framemembers

22 Constitutive Material Models

221 Concrete and Reinforcing Steel Material Models Thematerial models employed in the inelastic fiber-based ele-ments for the numerical simulation of RC frame componentsare available in the OpenSees framework More specificallyldquoConcrete02rdquo and ldquoSteel02rdquo were employed to model theconcrete and the reinforcing bar fibers respectively Theproperties of the confined concrete core in beam and columnelements are determined by the constant-confinement modelof Mander et al [18] Bond-slip conditions at overlappingregions are not taken into consideration in the present study

222 Cyclic CompressionTension Strut Relation The axialforce-deformation relationship developed by Crisafulli [16]

Y

X

i

j

ub2 q2

ub1 q1

ub3 q3

Figure 3 Generic representation of the ldquotwo-node link elementrdquoOpenSees framework

to describe the behavior of masonry under axial cyclicloading was regarded as the most suitable alternative forthe diagonal struts The hysteresis rules describing the modelwere coded in OpenSees to yield a new material model Ananalytical description of the model can be found elsewhere[16] Nevertheless some of the hysteretic modeling aspectswill be presented in brief so that the reader becomes familiarwith some basic concepts discussed later

The constitutive law for the axial cyclic behavior ofthe strut is expressed in terms of stress-strain relationships(Figure 4) Six material parameters are required to define theenvelope curve in compression namely (i) initial modulusof elasticity 119864mo (ii) compressive strength 1198911015840

119898 (iii) tensile

strength 1198911015840119905 (iv) strain at maximum stress 1205761015840

119898 (v) ultimate

strain 120576ult and (vi) closing strain 120576cl which defines the strainat which the cracks partially close allowing compressionstresses to develop In addition to these mechanical materialparameters a set of nine empirical factors associated exclu-sively with the hysteretic response need to be defined Theempirical factors and a short explanation of their significanceare given here

119866un defines the unloading modulus in proportion tothe initial modulus 119864mo

119860 re predicts the strain at which the loop reaches theenvelope after unloading

119860ch predicts the strain at which the reloading curveexhibits an inflection point controlling the ldquofatnessrdquoof the loops

119861119886defines an auxiliary point used to determine the

plastic deformation after complete unloading

119861ch predicts the stress at which the reloading curveexhibits an inflection point


fm

f2

f1

Es

1205761 1205762 120576a

1

2

(a)

fm

Emo

1

2

Eun

Eplu

120576a

(120576un fun)

(b)

fm

5Ech

(120576ch fch)

4

120576pl 120576a

Eplr

(120576re fre)

(c)

fm

5

4

120576pl 120576b 120576a

(120576ch fch)

120576un minus funEun

(d)

fm

120576pl 120576pl

f998400t

ft

120576998400m

(e)

fm

120576a

(f)

Figure 4 Cyclic response of axially loaded masonry proposed by Crisafulli [16] (a) unloading and reloading rules (b) Rule 1 for theenvelope curve and Rule 2 for unloading (c) Rules 4 and 5 for reloading (d) definition of change point (e) rule for tensile behavior and(f) representation of the hysteretic model

119866plu defines the modulus of the hysteretic curve atzero stress after complete unloading in proportion tothe initial modulus 119864mo

119866plr defines the modulus of the reloading curve aftertotal unloading in proportion to the initial modulus119864mo

1198901controls the influence of the strain at which

unloading occurs 120576un in the degradation of stiffness

1198902increases the strain at which the envelope curve

is reached after unloading and is used to control thecumulative damage inside repeated cycles


Table 1 Suggested values proposed by Crisafulli [16] for theempirical parameters

Parameter Suggested values Limit values119866un 15ndash25 ge0119860 re 02ndash04 ge0119860 ch 03ndash06 01ndash07119861a 15ndash20 ge0119861ch 06-07 05ndash09119866plu 05ndash07 0ndash10119866plr 11ndash15 ge11198901

15ndash20 ge01198902

10ndash15 ge0

Feasible ranges for all nine empirical parameters were sug-gested by Crisafulli [16] and are presented in Table 1

The stress-strain relationship can be easily expressed interms of the force-deformation quantities developed in theequivalent strut according to the following formulas

119865 = 120590Α = 120590 (119908119905)

120575120572= 120576119871diag

(1)

where 119908 is the effective width of the diagonal strut 119905 is thepanel thickness and 119871diag is the length of the strut

An interesting characteristic of the model by Crisafulli isthat the area of the equivalent strut is assumed to decreasewith the increase in the lateral displacement (and conse-quently in the axial deformation of the strut) due to thereduction of the contact length between the panel and theframe and the development of extensive cracking in the panelTo account for this effect the area (or equally thewidth) of thediagonal strut is assumed to vary as a function of the axialdisplacement 120575

120572(Figure 5)

223 Cyclic Shear Spring Relationship The cyclic response ofthe shear spring used in the present model differs from theone adopted by Crisafulli et al [1 19] in that a simplificationwas introduced towards uncoupling the shear behavior fromthe axial compression in the struts while the materialmodel used to describe the behavior of the shear spring isthemodified Ibarra-Medina-Krawinkler deteriorationmodel(ldquoBilin Materialrdquo in OpenSees) Information on the modelformulation can be found in Lignos and Krawinkler [20 21]

The envelope of the modified IK model (Figure 6) isdefined by six parameters (i) the initial stiffness119870

119904 (ii) yield-

ing force 119865119910 (iii) strain hardening ratio b (iv) precapping

displacement capacity 120575119901 (v) ultimate displacement 120575ult and

(vi) residual strength as a ratio 120581 of the yielding forceThe hysteretic response of the model follows a bilinear

curve accounting for three modes of deterioration withrespect to the backbone curve (a) basic strength dete-rioration (b) postcapping strength deterioration and (c)unloadingreloading stiffness deterioration

The rate of cyclic deterioration relates to the hystereticenergy dissipated during a cyclic event according to theproposal by Fardis [22] The basic assumption is that every

Stru

t are

a

Initial area

Residual area

120575a1 120575a2 120575a

Axial displacement

A1

A2

Figure 5 Variation of the area of the strut as a function of the axialdisplacement

F

FcFy

120573KsprCapping point (peak)

Residual strength

Elastic branch

Postcapping branchHardening branch

120575y 120575c 120575u 120575

Fr = 120581FyKspr

(a)

F

120575

Basic strengthdeterioration

Postcapping strengthdeterioration

Stiffness deterioration

(b)

Figure 6 The Modified Ibarra-Krawinkler (IK) deteriorationmodel (a) monotonic curve and (b) basic modes of cyclic deteri-oration

component has an inherent energy dissipation capacity 119864119905

which can be expressed as a multiple of (119865119910sdot 120575119901) that is

119864119905= (120582120575

119901) 119865119910= 119871 sdot 119865

119910 (2)

where L is a reference cumulative displacement capacity and120575p and 119865

119910are as defined previously

Cyclic strength deterioration (either basic or postcap-ping) is modeled by translating the two strength boundstowards the origin at a rate equal to

119865119894= [

[

1 minus (119864119894

119864119905minus sum119894minus1

119895=1119864119895

)

119888

]

]

sdot 119865119894minus1

= (1 minus 120573119894) sdot 119865119894minus1

(3)

where 120573119894is an energy deterioration parameter 119864

119894is the

hysteretic energy dissipated in excursion 119894 sum119864119895is the total


energy dissipated in past excursions 119864119905is the reference

energy dissipation capacity and 119888 is an empirical parameterThe same concepts apply to modeling unloading stiffness

deteriorationIn the present application of themodel basic strength and

stiffness deterioration are considered for capturing the shearbehavior of the panel by evaluating the appropriate values of119871 and 119888 parameters for each deterioration mode To accountfor the basic strength deterioration 119871

119878-values between 03

and 04 and 119888-values from 05 to 08 yield satisfactoryresults The unloading stiffness deterioration parameter 119871

119870

is inactive when assigned a very high value (for unloadingwith the elastic stiffness) Should the unloading stiffnessdeterioration bemore pronounced values in the range of 02ndash04 are suggested Exponent 119888

119870is unit for elastic unloading

or between 025 and 10 for soft unloading response Theinfluence of the deterioration parameters on the response ofthe panel will be clarified in the parametric study presentedafterwards

23 Evaluation of the Infill Material Properties

231 Initial Stiffness For the evaluation of the initial stiffnessof the masonry panel the following formula suggested byBertoldi et al [23] has been adopted

119870panel =119866119898119860

119867panel=

119866119898

(119871panel119905panel)

119867panel (4)

where 119871panel is the clear length of the panel119867panel is the clearheight of the panel 119905panel is the panel thickness taken as equalto the thickness of the infill wall and119866

119898is the shearmodulus

of themasonry infill as determined from thewallette diagonalcompression test (ASTM E519-81)

The total initial stiffness (defined in the horizontal direc-tion) of the panel is shared between the shear spring and thediagonal struts according to the following expressions

119870sprℎ = 120574 sdot 119870panel = 120574119866119898

119871panel119905panel

119867panel

119870strutℎ = (1 minus 120574) sdot 119870panel = (1 minus 120574)119866119898


119867panel

(5)

where the parameter 120574 defines the portion of the initialstiffness of the panel assigned to the shear spring Its valueusually ranges between 05 and 07

Nevertheless the initial stiffness of the diagonal strutelement expressed in the horizontal direction is equal to

119870inistrutℎ =119864mo1199081119905panel

119871 strutcos2120579 (6)

where 1199081is the initial effective width of the strut 119905panel the

masonry panel thickness 119871 strut the length of the diagonalstrut and 120579 the angle defined between the diagonal of thepanel and the horizontal axis

The initial modulus of elasticity assigned to the strutelements is derived through equating (5) and (6)

119864mo = (1 minus 120574)119866119898

(119871 strut1199081

)(

119871panel

119867panel)

1

cos2120579 (7)

Alternatively the appropriate values for the parameters 120574 and119864mo can be evaluated through a repetitive procedure so thatthe final value of119864mo approximates the value calculated by thefollowing expression proposed by Pauley and Priestley [24]

119864mo asymp 119864119898120579

= 1 times (cos4120579119864mh

+sin4120579119864mv

+ sin2120579cos2120579 (1

119866119898

minus2V119864mh

))

minus1

(8)

where V is Poissonrsquos ratio for the masonry panel and 119864mhand 119864mv are the elastic moduli for compression parallel andperpendicular to the bed joints calculated via compressivetests on masonry prisms As (8) requires the definition ofthree additional parameters it is only presented here as analternative way of obtaining 119864mo

232 Shear Spring Yielding Strength and Hardening RatioIn the early stages of the response of a laterally loadedinfilled frame the infill panel acts as a shear wall exhibitingsubstantially high lateral stiffness However as the infill paneldeforms and the contact with the surrounding frame islimited to the vicinity of the beam-column joints the lateralstiffness starts to degrade In the present model this highinitial stiffness is attributed to the elastic branch of the shearspring response Yielding of the shear spring is reached ata force level equal to a 119886

1-fraction of the infill cracking

force calculated according to the expression proposed byPanagiotakos and Fardis [15] Hence the yielding force in theshear spring is

119865spr119910 = 1198861119865cr = 119886

1120591cr119871panel119905panel (9)

Parameter 1205721depends on the mechanical characteristics

of the infilled frame values between 025 and 035 yieldreasonable results Yielding is followed by a hardening branchof the backbone curve with a strain hardening ratio equal to119887 = 005

233 Strut Strength The compressive strength of the diago-nal strut is estimated taking into account four possible failuremechanisms as it was suggested by Pauley and Priestley[24] The four basic failure modes encountered in infilledRC frames are (i) diagonal compression (ii) crushing in thecorners (iii) sliding shear along the horizontal joints and (iv)


diagonal tensionThe corresponding resistances are obtainedby

1198911198981

=116 tan 120579

1198701+ 1198702120582ℎ

119891mv

1198911198982

=112 sin 120579 cos 120579

1198701(120582ℎ)minus012

+ 1198702(120582ℎ)088

120591119900

1198911198983

=(12 sin 120579 + 045 cos 120579) 120591cr + 03120590V

119908119871diag

1198911198984

=06120591cr + 03120590V

119908119871diag

(10)

where 119891mv is the vertical compression strength measured onmasonry specimens 120591

119900is the shear bond strength measured

from the triplet test 120591cr is the shear strength measuredfrom the diagonal compression test and 120590

119907is the vertical

stress acting on the masonry panel due to working loadsParameters 119870

1and 119870

2depend on the relative panel-frame

elements stiffness as expressed by parameter 120582 and are takenaccording to Table 2

The final compressive strength of the strut components isdetermined as theminimumof the four resistances calculatedby (10) that is

1198911015840

119898= min (119891

1198981 1198911198982

1198911198983

1198911198984

) (11)

The tensile strength of masonry is generally negligible com-pared to the value of compressive strength and is eitherassumed as nil or given a very small value (eg1198911015840

119905= 005MPa

adopted here)

234 Initial and Reduced Area of the Strut A suitable valuefor the effective strut width has been sought by manyresearchers Holmes [9] was the first to suggest that theequivalent strut width is equal to 13 of the diagonal lengthwhile Pauley and Priestley [24] claimed that the value of 14of the diagonal length is more appropriate In the presentstudy the equations proposed by Decanini and Fantin [25]considering two different states of the infill wall are employed

1199081

119871diag=

0085 +0748

120582ℎ

if997888997888rarr 120582

ℎle 785

0130 +0393

120582ℎ

if997888997888rarr 120582

ℎgt 785

uncracked

1199082

119871diag=

0010 +0707

120582ℎ

if997888997888rarr 120582

ℎle 785

0040 +0470

120582ℎ

if997888997888rarr 120582

ℎgt 785

cracked

(12)

where 120582ℎis the relative panel-to-frame stiffness parameter

calculated as

120582ℎ= 119867

4radic

119864119898119905panel sin 2120579

4119864119888119868119888119867panel

(13)

Table 2 Parameters for the calculation of the compressive strengthof the strut [23]

120582ℎ lt 314 314 lt 120582ℎ lt 785 120582ℎ gt 785

1198701

13 0707 0471198702

minus0178 0010 004

where 119864119888and 119868119888are the elastic modulus and the moment of

inertia of the columns and 119867 is the height of the frameThe area reduction factor used in the definition of the

strut model is therefore determined as the ratio 119860 red =

11990821199081

235 Characteristic IDR-Levels of the Infill Response Inter-storey drift level (IDR) is taken as the unifying parameter toconnect the global deformation level to those of the diagonalstruts and the shear spring according to the followingassumptions

(i) There exists a characteristic interstorey drift levelIDR1 for which extensive cracks have been formed in

the panel indicating the start of a higher rate of dete-rioration Thus it is assumed that IDR

1corresponds

to the starting point of both the falling branch of theshear spring backbone curve and the reduction of thearea of the compressive strut

(ii) Interstorey drift level IDR2 is related to the point

where the area of the diagonal reaches its residualvalue 119860

2

(iii) Ultimate state conditions are considered at an inter-storey drift level named IDR

3 for which both the

shear spring and the compressive diagonal strut haveexhausted their resistance It should be emphasizedthat the value of IDR

3is usually higher than the

one observed during test events This issue can beattributed to the fact that either some other kind offailuremechanism related to the frame response (egshear failures in the beam-column connections) haspreceded the development of excessive damage on theinfill or the experiment has been interrupted beforethe actual collapse of the panel

The axial strain of the diagonal strut and the horizontaldisplacement of the shear spring can be related to the relevantdrift level using the following expressions

120575 = IDR sdot 119867

120576 = 1 minus radic1 + ((119871119867) minus IDR)

2

1 + (119871119867)2

(14)

where 119871 and 119867 are respectively the length and height ofthe frame and IDR = 120575119867 the interstorey drift ratio Thesecond expression relating the axial strain in the strut tothe IDR-level of the panel is derived geometrically assumingthat the vertical displacement at the beam-column joints isnegligible The shear spring and diagonal strut deformationquantities associated with the three IDR-levels defined aboveare summarized in Table 3


Table 3 Dependence of shear spring and diagonal strut deforma-tion quantities on the specified IDR-levels

IDR-level Shear spring Diagonal strutIDR1 mdash 120575

1198861or 1205761198861

IDR2 120575119888

1205751198862

or 1205761198862

IDR3 120575119906

120575119886ult or 120576119886ult

012

01

008

006

Axi

al fo

rceFast

rust

(kN

)

80

60

40

20

0

120575a(I

DR 1

)

120575a(I

DR 2

)

120575a(I

DR 3

)

Axial displacement 120575a (m)

Are

aA

(m2)

times10minus2

times10minus2

0 1 1505 2 25 3 35 4

0 1 1505 2 25 3 35 4

A1

A2

120576998400 m120575a(

)

Figure 7 Compressive envelope in the diagonal strut characteristicpoints of the force-deformation response and variation of theeffective area

236 Strain at Maximum Stress and Closing Strain on theStrut For completing the formulation of the model twoadditional deformation quantities remain to be defined (a)the axial strain at maximum stress and (b) the closing strainon the strut elements

The axial strain 1205761015840119898 when the maximum stress is reached

on the compressive strut is an experimentally defined param-eter Since infilled frame systems display a steep initial branchto the peak strength the value of the strain 120576

1015840

119898is relatively low

corresponding to a drift value within 001ndash005As it was previously mentioned the closing strain 120576cl

represents the strain level in tension after which the crackspartially close allowing the development of compressionstresses According to Crisafulli [16] its value ranges from 0to 0003

Figures 7 and 8 demonstrate the basic characteristics oftheir backbone curves described in the previous paragraphsrendering the response of both the compressed strut and theshear spring during a monotonic pushover analysis of aninfilled frame

3 Model Application Discussion of Results

31 Experimental Data The predictions of the proposedapproach are compared to a number of test results frommasonry infilled RC frames subjected to quasi-static or cyclicdisplacement histories Five of the investigated experimentsare presented here to demonstrate the efficiency of themodelThe first three are 23-scale models of one-storey single

Sprin

g fo

rceF

spr

(kN

) 120573Kspr

Kspr

120575ys

pr

120575(I

DR1)

120575(I

DR3)

0 001 002 003 004 005

Horizontal displacement 120575 (m)

25

20

15

10

5

0

Figure 8 Shear spring envelope curve and characteristic points ofthe force-deformation response

bay masonry infilled frames tested by Pires and Carvalho[26 27] The masonry units consisted of hollow clay brickswith dimensions 300mm times 200mm on the front side and150mm deep In addition the results from 23-scale model ofa one-storey single bay infilled frame tested at the Universityof Colorado [28 29] are used In this case a two-wythemasonry panelmade of solid clay brickswith dimensions 200times 57 times 95mm was employed Finally the last experimentalcampaign regards a 23-scale model of a three-storey singlebay infilled frame tested at the Structural Laboratory ofthe University of Patras [30] The infill panel consisted oftwo single-wythe masonry walls with an internal gap of60mm Perforated fired clay bricks with dimensions 185 times

85 times 55mm were used for the construction of the infill Acementitious mortar was used to fill the joints in all the abovecasesThe basic geometrical andmechanical properties of thespecimens are reproduced in Tables 4 and 5

32 Numerical Results Theresults obtained from the analysisof the above specimens are compared with the experimentalresults in terms of total base shear and interstorey drift exceptfor the test by Koutas et al [30] for which the results areexpressed in terms of base shear and total drift calculatedas the ratio of the top displacement to the total height of thestructure IDRtot = 120575top119867tot The parameters assigned to thestrut and spring elements were evaluated according to theprocedure described in Section 23 and all the assignmentsare summarized in Tables 6 7 and 8

The comparison of model predictions and experimentalresults is quantified via a dimensionless index 119891 calculatedas the fraction of the aforementioned difference in the forcevalues to the maximum experimentally achieved base shearthat is

Index 119891 =

10038161003816100381610038161003816119865anal119894

10038161003816100381610038161003816minus

1003816100381610038161003816119865exp119894

1003816100381610038161003816

|119865exp

|max

=

10038161003816100381610038161003816119865anal119894

10038161003816100381610038161003816minus

1003816100381610038161003816119865exp119894

1003816100381610038161003816

((10038161003816100381610038161003816119865exp(+)max

10038161003816100381610038161003816+

10038161003816100381610038161003816119865exp(minus)max

10038161003816100381610038161003816) 2)

(15)

where the maximum value of the experimental base shearis calculated as the mean of the positive and negative shear


Table 4 Geometry of the investigated specimens

Specimen 119905panel 119871 119867 (119887 times ℎ)column (119887 times ℎ)beam119860119904col 119860

119904beam 119860 sw(mm) (mm) (mm) (mm) times (mm) (mm) times (mm)

Pires M2 150 2250 1825 150 times 150 150 times 200 8Φ83Φ8 (top)

Φ4503Φ8 (bot)


Φ41003Φ8 (bot)


Φ4503Φ8 (bot)

Colorado T1 1905 3600 1930 280 times 280 240 times 280 8Φ112Φ19 (top)

Φ642672Φ19 (bot)

Koutas U1 110 2500 2000 170 times 230 170 times 330 6Φ122Φ12 (top)

Φ61302Φ12 (bot)

Table 5 Material properties in the experimental studies considered

Specimen 119891119888

119891119910

119891yw 119866119898

120591cr 120591119900

119891vm

(MPa) (MPa) (MPa) (MPa) (MPa) (MPa) (MPa)Pires M2 283 434 523 590 040 035 210Pires M3 332 434 523 590 040 035 210Pires M6 352 434 523 1000 051 040 230Colorado T1 301 458 458 2900 10lowast mdash 1793Koutas U1 280 500 220 1620lowastlowast 090lowastlowast mdash 507Note lowastthe value of the parameter 120591cr was not availablemdashthe value was selected on the basis of satisfactory agreement with the analytical resultsNote lowastlowast119866

119898and 120591cr have been evaluated on the basis of only 3 masonry prisms

Table 6 Definition of IDR-levels for the selected specimens

Specimen IDR1 () IDR2 () IDR3 ()Pires M2 0050 120 80Pires M3 0021 060 80Pires M6 0035 110 80Colorado T1 050 055 28Koutas U1 10 250 80

resistances A close observation of the history of index 119891

allows a step-by-step investigation of the ability of the modelto capture the actual response of the examined specimenFour additional quantities are calculated to provide a moregeneric evaluation of the adequacy of the numerical simula-tion

(i) themedian of the positive f -values offering an insightinto the level of overestimation of the base shear

(ii) the median of the negative f -values that reflects thelevel of underestimation of the base shear

(iii) the maximum and the minimum f -values that pro-vide a measure of the maximum error

The previously defined quantities are computed on theremaining part of the data after excluding some low-levelinitial cycles (before the peak force is reached) and some ofthe final cycles for which shear effects on the frame elementswere identified to dominate the response

Another way to assess the efficiency of the proposedmodel is to compare the strain energy dissipated during eachtest with the dissipated energy calculated analytically Thecumulative dissipated strain energy 119878 at step 119894 is computedaccording to the following formula

119878119894= 119878119894minus1

+1

2(119877119894+ 119877119894minus1

) (119880119894minus 119880119894minus1

) (16)

where 119878119894minus1

is the energy dissipated in previous steps 119877119894and

119877119894minus1

are the base shear at two adjacent steps and 119880119894and 119880

119894minus1

are the corresponding top displacements The average errorbetween the cumulative strain energy dissipated in themodeland the actual strain energy dissipated during the experimentis calculated as

error =

sum119899

119894=1

10038161003816100381610038161003816119878anal119894

minus 119878exp119894

10038161003816100381610038161003816

sum119899

119894=1

1003816100381610038161003816119878exp119894

1003816100381610038161003816

(17)

The cumulative strain energy dissipated in the model is com-pared to the cumulative strain energy dissipated during theexperiment in each of the examined specimens Moreoverthe error in the dissipated strain energy determined by (17) isused as a global measure of the accuracy of every numericalsimulation

In the following paragraphs the comparative resultsobtained after interpreting the experimental and analyticaldata referring to each case study are presented and dis-cussed Generally a smaller step-size was considered for theevaluation of the strain energy dissipation to allow a more


Table 7 Material properties assigned to the strutspring elements for the selected specimens

Specimen 1198911015840

1198981198911015840

119905 (wd)ini (wd)res 1205761015840

119898120576cl 120574 119886

1(MPa) (MPa)Pires M2 minus097 005 025 0175 minus000013 0002 06 03Pires M3 minus097 005 025 0163 minus000010 0002 06 03Pires M6 minus125 005 025 0163 minus000013 0002 06 03Colorado T1 minus255 005 027 0189 minus000013 0002 07 03Koutas U1 minus214lowast 005 028 0196 minus000050 0002 07 03lowastThe compressive strength at 2nd3rd floor is reduced to minus207MPaminus200MPa respectively due to the lower level of axial stress (see Section 233)

Table 8 Empirical parameters assigned to the strutspring elements for the selected specimens

Specimen Ach Are 119861119886

Bch Gun Gplu Gplr 1198901

1198902

119871119878

119871119870

119888119878

119888119870

Pires M2 03 15 10 09 07 10 11 30 10 03 1000 05 10Pires M3 03 15 10 09 05 10 11 30 10 03 1000 05 10Pires M6 03 15 10 09 07 10 11 30 10 03 020 09 10Colorado T1 03 08 10 09 05 10 11 30 10 04 020 06 025Koutas U1 03 08 10 09 07 10 11 30 10 03 025 05 10

Vb

80

40

0

minus40

minus80

minusminus minus minus 0

= 120575H

Figure 9 Pires M2 specimen

accurate estimation of the area enclosed in the ldquoBase shear-Displacementrdquo loops which explains the difference in theldquopseudotimerdquo measures in the relevant figures compared tothe ones depicting the variation of index f

Comparison of the analytically derived response forPires M2 specimen with the corresponding experimentallyobtained results (Figure 9) shows very good agreement Itis evident that both the shape of the hysteretic loops andthe resistance of the infilled frame system are capturedwith acceptable accuracy A more detailed interpretationof the results is achieved by observing the fluctuation ofindex f throughout the displacement history (Figure 10)After omitting the shaded parts of the response (initial andfinal cycles) the level of overestimation of the base shear iscalculated at 2 of the maximum experimental base shearvalue while the level of underestimation is approximatedat minus58 both indicating a very slight deviation from theexperimental results

006003

0minus003minus006

0 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800

Inde

xf

04

03

02

0

minus01

minus02

minus03

Pseudotime t

IDR=120575H

Median(+) = 0020 median(minus) = 0058 max = 010 min = minus021

Figure 10 Variation of index f for Pires M2 specimen

The range of119891-values (minus021 010) implies that the modelexhibits greater differences from the experiment at somepoints of the response These points are usually related tothe initial phase of an unloadingreloading cycle and theytend to diminish after a few steps Differences are also noticedwhen the specimen is driven through the origin and until thediagonal strut that was previously loaded in tension developssubstantial compressive stresses to contribute to the overallstrength and stiffness

As far as the cumulative strain energy dissipated by theinfilled frame is concerned it is generally underestimated inthe numerical model (Figure 11)The average error calculatedby (17) equals 149 which can be regarded as an acceptabledifference

Similar conclusions are drawn after evaluating the analyt-ical results of specimenM3 by Pires As depicted in Figure 12the test showed an essentially asymmetric response makingthe calibration of an analytical model and the investigation ofits efficiency a difficult task The level of underestimation in


0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Error = 139

Pseudotime t

Cumulative dissipated strain energy S

Figure 11 Cumulative strain energy comparison for Pires M2specimen

Vb

80

40

0

minus40

minus80

minusminus minus 0

= 120575Hminus006


this case is computed atminus62 and the level of overestimationat 34 of the maximum experimentally obtained base shearThe range of index 119891 is now evaluated at (minus023 017) asshown in Figure 13

The cumulative strain energy presented in Figure 14 forboth the experiment and the analysis is underestimated inthe numerical model The average error is 139 slightly dif-ferent from the corresponding error measured for specimenM2 by Pires

Test M6 by Pires was also used which compared tothe previous two specimens of the same research featureslighter reinforcement in the columns and stronger infill Thecomparative results (Figures 15 and 16) provide evidence ofsatisfactory agreement between experimental data andmodelresults The values of the over- and underestimation indicesresult as 26 and minus44 respectively while index 119891 fallswithin (minus027 010) range of values

The cumulative strain energy dissipated in the numer-ical model is overestimated until a drift level of around

006003

0minus003minus006

0 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800 900

900

Inde

xf

03

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H

Median(+) = 0034 median(minus) = minus0062 max = 017 min = minus023


0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)Error = 132

Pseudotime t



IDR = 120575H (mdash)

Base

shea

rVb

(kN

)

150

100

50

0

minus50

minus100

minus150minus006 minus004 minus002 0 002 004 006

AnalysisExperiment



006003

0minus003minus006

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

Inde

xf

02

01

0

minus01

minus02

minus03

Pseudotime t

IDR=120575

H



0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 58


3 is reached and underestimated in the following cycles(Figure 17) The final average error is calculated at 52revealing that the total energy dissipated throughout theexperiment is reproduced well

The response of an even stronger masonry infill isexamined by the case of Colorado T1 specimen A satisfactoryfit is achieved in the numerical model as depicted in Figures18 and 19 The measure of the over- and underestimationindices is calculated at 30 andminus74 respectively while thevariation of index 119891 is within the (minus027 018) range

It is important to note that a shear-dominated failuremechanism appeared in the framemembers during the test atquite early stages of the loading history limiting the ability ofthe proposed model to accurately capture the response of thesystem More specifically the rapid decrease of the strengthof the structure noticed at +05 drift is a result of theformation of a wide shear crack in the top east column of thespecimen followed by another shear crack at the lower eastand top west columns during the next half cycle Such failuremechanism cannot be reproduced with the fiber elementsused in the present study Nonetheless the general behavior


Base

shea

rVb

(kN

)

AnalysisExperiment

800

600

400

200

0

minus200

minus400

minus600


Figure 18 Colorado T1 specimen

Inde

xf

02

01

0

minus01

minus02

minus03

minus04

Pseudotime t

IDR=120575

H0015

000750

minus00075minus0015

0 500 1000 1500 2000 2500

0 500 1000 1500 2000 2500


Figure 19 Variation of index f for Colorado T1 specimen

of the infilled frame system ismdashup to that pointmdashrepresentedadequately

The comparison of cumulative strain energies derivedby the experimental and analytical data is illustrated inFigure 20 It is observed that a similar pattern as in the case ofPires M6 specimen discussed previously is encountered alsoin the case of Colorado T1 specimen The average error isequal to 56 which proves a very satisfying match betweenthe experiment and the analysis as far as energy dissipationis concerned

Finally the response of the 3-storey infilled frame testedby Koutas et al is compared to the analytically obtainedresults The final half cycle of the response is excludedfrom the comparison as a shear failure mechanism thatoccurred to the west column is responsible for the divergencebetween the experimental and the numerical results fromthat point onwards As presented in Figures 21 and 22 theglobal behavior of the numerical model shows satisfactoryagreement with the experimental results The median over-and underestimation indices are calculated as 62 and


AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 56

70

60

50

40

30

20

10

00 1000 2000 3000 4000 5000

Figure 20 Cumulative strain energy comparison for Colorado T1specimen


Base

shea

rVb

(kN

)

AnalysisExperiment

300

200

100

0

minus100

minus200

minus300minus001 minus0005 0 0005 001

Figure 21 Koutas et al U1 specimen

minus65 respectively while the range of119891-index lies on (minus025015)

The strain energy dissipated in the numerical simulationseems to overestimate the actual energy dissipated during theexperiment (Figure 23)The average error is 127 which canbe considered acceptable

An interesting outcome of the present comparison is thatnot only is the global behavior of the infilled frame systemadequately reproduced but also the individual response ofeach floor is captured quite well The relations betweenthe shear force at the 1st 2nd and 3rd floors and thecorresponding (absolute) floor displacement are illustratedin Figure 24 The magnitude of the shear force in each floorand the concentration of damage in the level of the 1st floorare represented in sufficient accuracy Some deviation fromthe experimental results that is more evident in the shearforce-displacement response of the 1st floor is attributed tothe propagation of a shear crack at the top of the 1st floor

Inde

xf

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H

0010005

0minus0005minus001

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900


Figure 22 Variation of index f for Koutas et al U1 specimen

AnalysisExperiment

S(k

Nm

)

Pseudotime t


0 1000 2000 3000 4000 5000

Error = 125

40

35

30

25

20

15

10

5

0

Figure 23 Cumulative strain energy comparison for Koutas et alU1 specimen

west column and therefore should not be considered as adeficiency of the proposed model

33 Parametric Investigation A parametric study has beenconducted to investigate the sensitivity of the numericalresults to the various material parameters involved in modelThe study considered all the empirical parameters as wellas some of the mechanical properties and was implementedusing the numerical simulation of Pires M2 specimen Theparameters were individually varied keeping all the otherquantities fixed to the value used in the calibrated modelpresented in the previous section Some of the modelingparameters although examined during the parametric pro-cess are not included in the following discussion as theirinfluence was found to be negligible

In order to quantify the influence of a certain parameteron the structural response the index 119891 defined in (15) is cal-culated and compared for all the variations of the consideredparameter The results of this comparative procedure for themost influential of the investigated parameters (Figure 25) arepresented as a comparative plot for each parameter with the


300

200

100

0

minus100

minus200


1st

floor

shea

r for

ceV

1(k

N)

1st floor displacement D1 (mm)

(a)

minus60 minus40 minus20 0 20 40 60

300

200

100

0

minus100

minus200

minus300

2nd

floo

r she

ar fo

rceV2

(kN

)

2nd floor displacement D2 (mm)

(b)


AnalysisExperiment

150

100

50

0

minus50

minus100

minus150

3rd

floo

r she

ar fo

rceV3

(kN

)

3rd floor displacement D3 (mm)

(c)

Figure 24 Koutas et al U1 specimen Floor shear force versus floor displacement (absolute) comparative results (a) 1st floor (b) 2nd floorand (c) 3rd floor

variation of the value of the parameter under investigationpresented on the horizontal axis On the vertical axis fourvalues of index 119891 are reported that is the positive andnegative medians as well as the maximum and minimum119891-values A red dashed line is used to indicate the selectedparameter-value used in the model presented in Section 32

The parameters that were found to have an importantimpact on the response are (i) the strut area reduction factor119860 red = 119908

21199081 (ii) parameter 119886

1controlling the end of the

elastic branch on the shear spring (iii) parameter 120574 definingthe proportion of the initial panel stiffness assigned to theshear spring (iv) ultimate drift level IDR

3 (v) parameter

119866un which controls the unloading stiffness on the strut (vi)parameter119860 re controlling the reloading stiffness on the strut(vii) parameter 119871

119878that imposes strength deterioration on the

shear spring response and (iix) parameter 119888119878that controls the

rate of strength deterioration on the shear springAs expected the reduction of the effective width of

the diagonal strut seems to be one of the most influential

parameters Nevertheless the selection of the area reductionfactor 119860 red proposed in Section 234 is not arbitrary but ittakes into account the relative panel-to-frame stiffness Theprocedure has led to the use of 119860 red = 07 in the calibratedmodel that is verified by the parametric study conducted here

The estimated response is also very sensitive to theselection of parameter 119886

1 The extent of the elastic branch

of the shear spring behavior is decisive for the initial stageof the response Higher values of the parameter amplify theresistance of the infill at low-level drifts which is confirmedby the higher values of the index f that correspond to 119886

1= 06

or even better to 1198861= 08

Parameter 120574 seems to have a significant impact on theresponse of the system as well It can be observed that themaximum level of underestimation can vary from minus269for 120574 = 02 to minus208 for 120574 = 06 and to minus243 for 120574 =

08 The overestimation percentage is 114 99 and 140respectively However the selection of the appropriate 120574-parameter is highly dependent on the selection of the effective


04

04

03

03

02

02

01

01

0 0

minus01

minus02

minus03

03

02

01

0 0

minus01

minus02

minus03

minus04

04

03

02

01

minus01

minus02

minus03

minus04

Inde

xf

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

Parameter-value Y

05 06 07 08 09

04030201 05 06 07 08 09

1 04030201 05 06 07 08 09 1

Parameter-value a1

00890020

minus0124

minus0415

00900020

minus0097

minus0302

00920018

minus0062

minus0211

0120

0033

minus0204

0108

0022

minus0066

minus0220

0107

0021

minus0055

minus0245

0199

0031

minus0050

minus0323

0304

0044

minus0050

minus0295

Parameter-value IDR3

0114

0025

minus0078

minus0269

0103

0020

minus0068

minus0208

0140

0025

minus0046

minus0243

0092

0019

minus0066

minus0209

0099

0020

minus0058

minus0208

0130

0032

minus0059

minus0207minus0223

0099

0020

minus0058

Parameter-value Gun

04 06 08 1 12 14 16 18 2 22 24 04 06 08 1 12 14 16 18 2 22 24

0118

0023

minus0058

minus0177

0092

0019

minus0060

minus0234

0091

0020

minus0062

minus0260

0091

0020

minus0063

minus0276

0164

0038

minus0053

minus0188

0120

0029

minus0056

minus0202

0099

0020

minus0058

minus0208

0092

0018

minus0058

minus0211

Parameter-value Are

04030201 05 06 07 08 09 1 0403 05 06 07 08 09 111

Parameter-value CSParameter-value LS

0105

0021

minus0064

minus0194

0092

0021

minus0056

minus0217

0093

0024

minus0051

minus0229

0100

0026

minus0046

minus0237

0106

0020

minus0067

minus0207

0090

0020

minus0054

minus0232

0115

0021

minus0051

minus0266

0131

0025

minus0056

minus0286

005 006 007 008 009 01 02

minus0054

Parameter-value Ared

Figure 25 Parametric investigation of M2 specimen by Pires

width of the strut 1199081 and the yielding force on the shear

spring 119865119910 controlled by 119886

1-parameterThus the results from

the variation of 120574-parameter alone should be treated withcaution

The ultimate drift IDR3 is also of importance for the

determination of the response Applying higher values ofultimate drift capacity index f exhibits a shift in the positive

direction denoting overestimation conditions Nonethelessthe relevant results illustrated in Figure 25 are quite conserva-tive since they do not capture the final stages of the responsewhere the IDR

3-value applied is even more influential

Among the various empirical parameters used to definethe hysteretic response of the diagonal struts the globalresponse of the infilled frame system is more sensitive in 119866un


and 119860 re controlling the unloading and reloading stiffnessrespectively Actually it seems that the use of a lower valuefor 119866un (asymp10) and a higher value for 119860 re (asymp15) compared tothe values suggested by Crisafulli (Table 1) yields better fit tothe experimental data

Parameters 119871119878and 119888119878which control the deterioration of

strength of the shear spring element are also crucial Variationof 119871119878from 02 to 08 results in quite smooth modification of

f -indices while that of 119888119878from 04 to 10 is relatively more

drasticFinally based on the parametric investigation of M2

specimen by Pires and the numerical results obtained fromthe analysis of all the considered specimens generalizedconclusions are drawn regarding the selection of the materialparameters incorporated in the proposed model

(i) A number of parameters can be characterized asnoncritical and thus assigned a fixed value119860ch = 03119861119886

= 10 119861ch = 09 119866plu = 10 119866plr = 11 1198901= 30

1198902= 10 120576cl = 0002 and 119891

1015840

119905= 005MPa

(ii) The values of the parameters 1198911015840

119898and 119860 red = 119908

21199081

calculated according to the relevant formulas pre-sented in Section 23 yield satisfactory results

(iii) Appropriate values for parameter 1205761015840

119898 referring to the

strain at maximum strength on the strut fall within(minus00005 minus00001) range of values

(iv) For parameter 120574 defining the distribution of the panelstiffness among the strut and shear spring elementsvalues in the range of 06ndash07 are suggested

(v) Parameter 1198861is dependent on the selection of 120574-

parameter as they both control the yielding forceand displacement on the shear spring Values between025 and 035 result in satisfactory fit to the experi-mental data

(vi) Higher values than the ones suggested by Crisafulli(Table 1) are proposed for parameter 119860 re Valueswithin (08 15) are considered more suitable

(vii) The suggested values for parameter 119866un fall within(05 07) range lower than the corresponding rangeproposed by Crisafulli (Table 1)

(viii) Parameter 119871119878 controlling strength deterioration

should be taken between 03 and 04 while the rateof strength deterioration controlled by cS-parametervaries between 05 and10

(ix) Parameter 119871119870 controlling unloading stiffness dete-

rioration can be deactivated (assignment of a highvalue eg 119871

119870= 1000) to reduce the unknown

quantities incorporated in the model However giventhe characteristics of the masonry infill studied 119871

119870

values between 02 and 03 should be used whenunloading stiffness deterioration is expected to bemore pronounced Specimens T1 at Colorado U1 byKoutas et al and M6 by Pires in which a strongerinfill was employed constitute such cases Unitycan be adopted for the rate of unloading stiffnessdeterioration cK

(x) The variance of IDR1

(0021ndash10) and IDR2

(055ndash25) levels used in the present study isindicative of their high dependence on the charac-teristics of the masonry infill and the surroundingframe and impedes the suggestion of a feasible rangeof values for practical applications

(xi) IDR3-parameter controlling the ultimate state of the

infill response can be assigned a value between 5and 8

4 Conclusions

The paper presents an approach for assessing the nonlinearresponse of masonry infilled RC frames under in-planelateral loads The model based on the masonry panel byCrisafulli combines three elements to provide a relativelyaccurate representation of the global behavior of the infillpanel The constitutive models adopted for each elementinvolve a number of parameters either empirical or linkedto the mechanical properties of the infill A procedure for theevaluation of the various parameters is established followedby the validation of the proposed methods with availableexperimental data

The comparison between experimental data and numeri-cal results is conducted on the basis of two quantities (i) thedimensionless index f that is basically the difference in thebase shear (at the same displacement levels) divided by themaximum experimentally obtained base shear and (ii) theaverage error in the cumulative strain energy dissipated bythe numerical model and the actual specimen

It is concluded that the model can adequately reproducethe load-displacement response exhibited by infilled RCframes The medians of the positive and negative f -valuesindicating overestimation and underestimation conditionsrespectively vary from 20 to 74 proving a satisfying fitto the experimental data The error in the dissipated strainenergy is also acceptable ranging from 52 to 149

In addition a parametric study carried out to evaluatethe sensitivity of the numerical results to the selection ofthe modeling parameters (especially those with empiricalnature) shows that only few of the parameters show a signif-icant impact on the overall response providing evidence thata possible reduction of the unknown and noneasily identifiedparameters could be considered

Based on the results of both the parametric investigationand the analysis of the individual specimens consideredproposals regarding appropriate selection of the parametersemployed in the model are provided

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] F J Crisafulli and A J Carr ldquoProposed macro-model for theanalysis of infilled frame structuresrdquoBulletin of theNewZealand


Society for Earthquake Engineering vol 40 no 2 pp 69ndash772007

[2] H R Lotfi Finite element analysis of fracure of concrete andmasonry structures [PhD dissertation] University of ColoradoBoulder Colorado 1992

[3] P B Lourenco Computational strategies for masonry structures[PhD dissertation] Delft University of Technology Delft TheNetherlands 1996

[4] M M Attard A Nappi and F Tin-Loi ldquoModeling fracture inmasonryrdquo Journal of Structural Engineering vol 133 no 10 pp1385ndash1392 2007

[5] A B Mehrabi and P B Shing ldquoFinite element modeling ofmasonry-infilled RC framesrdquo Journal of Structural Engineeringvol 123 no 5 pp 604ndash613 1997

[6] Y-J Chiou J-C Tzeng andY-W Liou ldquoExperimental and ana-lytical study of masonry infilled framesrdquo Journal of StructuralEngineering vol 125 no 10 pp 1109ndash1117 1999

[7] A Stavridis and P B Shing ldquoFinite-element modeling ofnonlinear behavior of masonry-infilled RC framesrdquo Journal ofStructural Engineering vol 136 no 3 pp 285ndash296 2010

[8] S V Polyakov ldquoOn the interaction betweenmasonry filler wallsand enclosing frame when loaded in the plane of the wallrdquo inTranslation in Earthquake Engineering pp 36ndash42 EarthquakeEngineering Research Institute (EERI) San Francisco CalifUSA 1960

[9] M Holmes ldquoSteel frames with brickwork and concrete infill-ingrdquo ICE Proceedings vol 19 no 4 pp 473ndash478 1961

[10] B S Smith ldquoLateral stiffness of infilled framesrdquo Journal ofStructural Engineering vol 88 no 6 pp 182ndash199 1962

[11] R J Mainstone ldquoOn the stiffnesses and strengths of infilledframesrdquo ICE Proceedings vol 49 no 2 p 230 1971

[12] C A Syrmakezis and V Y Vratsanou ldquoInfluence of infill wallsto RC frames responserdquo in Proceedings of the 8th European Con-ference on Earthquake Engineering of the European Associationfor Earthquake Engineering (EAEE) pp 47ndash53 Instabul Turkey1986

[13] C Z Chrysostomou P Gergely and J F Abel ldquoA six-strutmodel for nonlinear dynamic analysis of steel infilled framesrdquoInternational Journal of Structural Stability and Dynamics vol2 no 3 pp 335ndash353 2002

[14] WW El-DakhakhniM Elgaaly andA AHamid ldquoThree-strutmodel for concrete masonry-infilled steel framesrdquo Journal ofStructural Engineering vol 129 no 2 pp 177ndash185 2003

[15] M N Fardis and T B Panagiotakos ldquoSeismic design andresponse of bare and masonry-infilled reinforced concretebuildings Part II infilled structuresrdquo Journal of EarthquakeEngineering vol 1 no 3 pp 475ndash503 1997

[16] F J Crisafulli Seismic behavior of reinforced concrete struc-tures with masonry infills [PhD dissertation] Department ofCivil Engineering University of Cantebury Cantebury NewZealand 1997

[17] S Mazzoni F McKenna M H Scott and G L Fenves OpenSystem for Earthquake Engineering Simulation (OpenSees) UserCommand-Language Manual Pacific Earthquake EngineeringResearch Center University of California Berkeley Calif USA2006 httpopenseesberkeleyeduOpenSeesmanuals

[18] J B Mander M J N Priestley and R Park ldquoTheoreticalstress-strain model for confined concreterdquo Journal of StructuralEngineering vol 114 no 8 pp 1804ndash1826 1988

[19] E Smyrou C Blandon S Antoniou R Pinho and F CrisafullildquoImplementation and verification of a masonry panel model for

nonlinear dynamic analysis of infilled RC framesrdquo Bulletin ofEarthquake Engineering vol 9 no 5 pp 1519ndash1534 2011

[20] D G Lignos and H Krawinkler ldquoDeterioration modeling ofsteel components in support of collapse prediction of steelmoment frames under earthquake loadingrdquo Journal of Struc-tural Engineering vol 137 no 11 pp 1291ndash1302 2011

[21] D G Lignos and H Krawinkler ldquoSidesway collapse of deterio-rating structural systems under seismic excitationsrdquo Tech RepTB177 The John A Blume Earthquake Engineering ResearchCenter Stanford University Stanford Calif USA 2012

[22] M N Fardis ldquoExperimental and numerical investigations onthe seismic response of RC frames and recommendations forCode Provisionsrdquo Tech Rep 6 ECOEST PREEC8 1997

[23] S H Bertoldi L D Decanini andC Gavarini ldquoTelai tamponatisoggetti ad azione sismica un modelo semplificato confrontosperimentale e numericordquo in Atti del 6 Convegno NazionaleANIDIS Perugia Italy 1993 (Italian)

[24] T Pauley and M J N Priestley Seismic Design of ReinforcedConcrete and Masonry Buildings Wiley New York NY USA1992

[25] L D Decanini and G E Fantin ldquoModelos simplificados de lamamponesteria incluida en porticos Caracteristicas de rigidezy resistencia lateral en astado limiterdquo in Jornadas Argentinas deIngenieria Estructural III vol 2 pp 817ndash8605 Asociacion deIngenieros Estructurales Buenos Aires Argentina (Spanish)

[26] F M G Pires and E C Carvalho ldquoThe behaviour of infilledreinforced concrete frames under horizontal cyclic loadingrdquoin Proceedings of the 10th World Conference on EarthquakeEngineering vol 6 pp 3419ndash33422 Balkema Rotterdam 1992

[27] F M G Pires Influencia das paredes de alvenaria no comporta-mento de estruturas reticuladas de betao armado sujeitas a accoeshorizontais [PhD dissertation] National Laboratory in CivilEngineering Lisbon Portugal 1990 (Portugese)

[28] M Kyriakides Numerical analysis of unreinforced masonryinfills in non-ductile reinforced concrete frames using EngineeredCementitious Composites [PhD dissertation] Stanford Univer-sity Stanford Calif USA 2011

[29] I Koutromanos Numerical analysis of masonrymdashinfilled RCframes subjected to seismic loads and experimental evaluation ofretrofit techniques [PhD dissertation] University of CaliforniaSan Diego Calif USA 2011

[30] L Koutas S N Bousias and T C Triantafillou ldquoIn-planebehavior of a three-strorey masonry infilled RC framerdquo inProceedings of the 4th International fib Congress Mumbai IndiaFebruary 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Yoi

hz

Internal node

Dummy node

1 2

34 Compressiontension struts Shear spring

Active (compression)

Inactive (tension)

Figure 1 Schematic representation of the Crisafulli and Carr masonry panel element [1]

frame at a relatively low drift level forming a resistancemechanism similar to that of a diagonal strut connecting thetwo opposite compression corners where contact with theframe is still retained Various studies have been conducted inorder to define the appropriate modeling configuration theproperties and the constitutive law of the equivalent strutsSome of the earlier works in this area like the investigationsconducted by Holmes [9] Smith [10] and Mainstone [11]considered a single strut connecting the corner nodes alongeach diagonal and tried to evaluate the width of the strut thatcontrols the initial stiffness of the infilled frame Others whoworked in the same direction refined themodeling techniqueeither by introducing multiple strut configurations to allow amore reliable estimation of the interaction between the paneland the frame (eg [1 12ndash14]) or by developing appropriateconstitutive laws to describe the hysteretic behavior of thepanel when subjected to cyclic loading The hysteretic rulesdeveloped by Fardis and Panagiotakos [15] to model theglobal behavior of the infill and the constitutive modelproposed by Crisafulli [16] to describe the cyclic responseof axially loaded masonry are two of the more interestingapproaches in this regard

Summarizing the available solutions it seems that evenif macromodeling schemes are not capable of simulating in adetailed manner all the possible failure mechanisms encoun-tered in infilled frame structures the limited computationaleffort required for their implementation makes them the bestalternative especially when analyzing large structures Thechallenge is yet to develop a broadly applicable frameworkfor determining the effective properties and the hystereticbehavior of the appropriate simplified model for each casestudy

The aim of this paper is to provide an analytical toolfor assessing the in-plane behavior of masonry infilled RCframes focusing on the establishment of a set of specificguidelines for the evaluation of the various parametersrequired to define the monotonic and hysteretic response ofthe masonry infill The modeling scheme presented hereinconstitutes a modification of the ldquomasonry-panelrdquo approachoriginally developed by Crisafulli and Carr [1] The proposedmethodology has been validated with experimental resultsfrommasonry infilled RC frames subjected to in-plane cyclicquasi-static loading histories Five of the experimental studiesconsidered are presented in this paper to demonstrate the

implementation procedure and the efficiency of the modelAdditionally an extensive parametric study has been con-ducted to clarify the influence of the various parameters onthe overall structural response

2 Materials and Methods

21 ProposedModeling Scheme As previouslymentioned themodeling scheme presented in this study is based on theldquomasonry-panelrdquo model proposed by Crisafulli and Carr [1]that is a 4-node panel element connected to the frame at thebeam-column joints Internally the panel element consists oftwo parallel struts and a shear spring acting in each diagonal(Figure 1) to account for both the compressive and the shearbehavior of the masonry panel Encapsulation of the multiplesprings involved in the definition of the model into a 4-node element serves to establish an interrelation between thecompressed diagonal and the shear spring while reducing thelevel of complexity from the userrsquos point of view Still thisconvenience also results in a limited control and some sortof obscurity behind the several parts that comprise the paneland define its behavior

The configuration of the model as presented here main-tains the idea of combining diagonal strut and shear springelements with the difference that no interrelation betweenthe individual elements that comprise the panel has beenexternally imposed except the one arising from the distribu-tion of strength and stiffness among the various componentsduring a loading event As the original model by Crisafulliwas not available in the software framework used in thisstudy (OpenSees) the scope of this research was limitedto relaxing a number of parameters in the original modeland checking if the resulting approach can reliably predictthe experimental results Thus the infill is modeled hereemploying two ldquostrutsrdquo each one connecting the two oppositediagonal corners of the panel and a ldquoshear springrdquo as shownin Figure 2 The behavior of each element is controlled byits own constitutive lawmdashhere a different constitutive law isassigned to the shear spring with respect to that of the modelby Crisafulli

Themodel has been implemented inOpenSees [17] usingthe existing ldquotwo-node linkrdquo element (Figure 3) The elementconnects two diagonally opposite nodes and can generallycomprise from 1 to 6 degrees of freedom where only the










Y

X

i

j

ub2 q2

ub1 q1

ub3 q3






119898 (v) ultimate









fm

f2

f1

Es

1205761 1205762 120576a

1

2

(a)

fm

Emo

1

2

Eun

Eplu

120576a

(120576un fun)

(b)

fm

5Ech

(120576ch fch)

4

120576pl 120576a

Eplr

(120576re fre)

(c)

fm

5

4

120576pl 120576b 120576a

(120576ch fch)


(d)

fm

120576pl 120576pl

f998400t

ft

120576998400m

(e)

fm

120576a

(f)











15ndash20 ge01198902

10ndash15 ge0



119865 = 120590Α = 120590 (119908119905)

120575120572= 120576119871diag

(1)



120572(Figure 5)



119904 (ii) yield-






Stru

t are

a

Initial area

Residual area

120575a1 120575a2 120575a

Axial displacement

A1

A2


F

FcFy


Residual strength

Elastic branch


120575y 120575c 120575u 120575

Fr = 120581FyKspr

(a)

F

120575




(b)




119864119905= (120582120575

119901) 119865119910= 119871 sdot 119865

119910 (2)




119865119894= [

[

1 minus (119864119894

119864119905minus sum119894minus1

119895=1119864119895

)

119888

]

]

sdot 119865119894minus1

= (1 minus 120573119894) sdot 119865119894minus1

(3)


119894is the









119870






119870panel =119866119898119860

119867panel=

119866119898


119867panel (4)





119870sprℎ = 120574 sdot 119870panel = 120574119866119898


119867panel



119867panel

(5)




119871 strutcos2120579 (6)




119864mo = (1 minus 120574)119866119898

(119871 strut1199081

)(

119871panel

119867panel)

1

cos2120579 (7)


119864mo asymp 119864119898120579

= 1 times (cos4120579119864mh

+sin4120579119864mv

+ sin2120579cos2120579 (1

119866119898

minus2V119864mh

))

minus1

(8)





119865spr119910 = 1198861119865cr = 119886

1120591cr119871panel119905panel (9)






1198911198981

=116 tan 120579

1198701+ 1198702120582ℎ

119891mv

1198911198982

=112 sin 120579 cos 120579

1198701(120582ℎ)minus012

+ 1198702(120582ℎ)088

120591119900

1198911198983

=(12 sin 120579 + 045 cos 120579) 120591cr + 03120590V

119908119871diag

1198911198984

=06120591cr + 03120590V

119908119871diag

(10)






1and 119870




1198911015840

119898= min (119891

1198981 1198911198982

1198911198983

1198911198984

) (11)


119905= 005MPa

adopted here)


1199081

119871diag=

0085 +0748

120582ℎ

if997888997888rarr 120582

ℎle 785

0130 +0393

120582ℎ

if997888997888rarr 120582

ℎgt 785

uncracked

1199082

119871diag=

0010 +0707

120582ℎ

if997888997888rarr 120582

ℎle 785

0040 +0470

120582ℎ

if997888997888rarr 120582

ℎgt 785

cracked

(12)


calculated as

120582ℎ= 119867

4radic

119864119898119905panel sin 2120579

4119864119888119868119888119867panel

(13)


120582ℎ lt 314 314 lt 120582ℎ lt 785 120582ℎ gt 785

1198701

13 0707 0471198702

minus0178 0010 004




11990821199081




1corresponds




2







120575 = IDR sdot 119867


2

1 + (119871119867)2

(14)





1198861or 1205761198861

IDR2 120575119888

1205751198862

or 1205761198862

IDR3 120575119906

120575119886ult or 120576119886ult

012

01

008

006

Axi

al fo

rceFast

rust

(kN

)

80

60

40

20

0

120575a(I

DR 1

)

120575a(I

DR 2

)

120575a(I

DR 3

)


Are

aA

(m2)

times10minus2

times10minus2

0 1 1505 2 25 3 35 4

0 1 1505 2 25 3 35 4

A1

A2

120576998400 m120575a(

)





1015840







Sprin

g fo

rceF

spr

(kN

) 120573Kspr

Kspr

120575ys

pr

120575(I

DR1)

120575(I

DR3)

0 001 002 003 004 005


25

20

15

10

5

0






Index 119891 =

10038161003816100381610038161003816119865anal119894

10038161003816100381610038161003816minus

1003816100381610038161003816119865exp119894

1003816100381610038161003816

|119865exp

|max

=

10038161003816100381610038161003816119865anal119894

10038161003816100381610038161003816minus

1003816100381610038161003816119865exp119894

1003816100381610038161003816

((10038161003816100381610038161003816119865exp(+)max

10038161003816100381610038161003816+

10038161003816100381610038161003816119865exp(minus)max

10038161003816100381610038161003816) 2)

(15)







Φ4503Φ8 (bot)


Φ41003Φ8 (bot)


Φ4503Φ8 (bot)


Φ642672Φ19 (bot)


Φ61302Φ12 (bot)


Specimen 119891119888

119891119910

119891yw 119866119898

120591cr 120591119900

119891vm












119878119894= 119878119894minus1

+1

2(119877119894+ 119877119894minus1

) (119880119894minus 119880119894minus1

) (16)



119877119894minus1


119894minus1


error =

sum119899

119894=1

10038161003816100381610038161003816119878anal119894

minus 119878exp119894

10038161003816100381610038161003816

sum119899

119894=1

1003816100381610038161003816119878exp119894

1003816100381610038161003816

(17)





Specimen 1198911015840

1198981198911015840

119905 (wd)ini (wd)res 1205761015840

119898120576cl 120574 119886





1198902

119871119878

119871119870

119888119878

119888119870


Vb

80

40

0

minus40

minus80


= 120575H




006003

0minus003minus006

0 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800

Inde

xf

04

03

02

0

minus01

minus02

minus03

Pseudotime t

IDR=120575H







0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Error = 139

Pseudotime t



Vb

80

40

0

minus40

minus80

minusminus minus 0

= 120575Hminus006






006003

0minus003minus006

0 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800 900

900

Inde

xf

03

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H



0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)Error = 132

Pseudotime t




Base

shea

rVb

(kN

)

150

100

50

0

minus50

minus100


AnalysisExperiment



006003

0minus003minus006

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

Inde

xf

02

01

0

minus01

minus02

minus03

Pseudotime t

IDR=120575

H



0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 58






Base

shea

rVb

(kN

)

AnalysisExperiment

800

600

400

200

0

minus200

minus400

minus600



Inde

xf

02

01

0

minus01

minus02

minus03

minus04

Pseudotime t

IDR=120575

H0015

000750

minus00075minus0015

0 500 1000 1500 2000 2500

0 500 1000 1500 2000 2500







AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 56

70

60

50

40

30

20

10

00 1000 2000 3000 4000 5000



Base

shea

rVb

(kN

)

AnalysisExperiment

300

200

100

0

minus100

minus200






Inde

xf

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H

0010005

0minus0005minus001

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900



AnalysisExperiment

S(k

Nm

)

Pseudotime t


0 1000 2000 3000 4000 5000

Error = 125

40

35

30

25

20

15

10

5

0






300

200

100

0

minus100

minus200


1st

floor

shea

r for

ceV

1(k

N)


(a)


300

200

100

0

minus100

minus200

minus300

2nd

floo

r she

ar fo

rceV2

(kN

)


(b)


AnalysisExperiment

150

100

50

0

minus50

minus100

minus150

3rd

floo

r she

ar fo

rceV3

(kN

)


(c)




21199081 (ii) parameter 119886



3 (v) parameter










1= 06





04

04

03

03

02

02

01

01

0 0

minus01

minus02

minus03

03

02

01

0 0

minus01

minus02

minus03

minus04

04

03

02

01

minus01

minus02

minus03

minus04

Inde

xf

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

Parameter-value Y

05 06 07 08 09

04030201 05 06 07 08 09

1 04030201 05 06 07 08 09 1

Parameter-value a1

00890020

minus0124

minus0415

00900020

minus0097

minus0302

00920018

minus0062

minus0211

0120

0033

minus0204

0108

0022

minus0066

minus0220

0107

0021

minus0055

minus0245

0199

0031

minus0050

minus0323

0304

0044

minus0050

minus0295


0114

0025

minus0078

minus0269

0103

0020

minus0068

minus0208

0140

0025

minus0046

minus0243

0092

0019

minus0066

minus0209

0099

0020

minus0058

minus0208

0130

0032

minus0059

minus0207minus0223

0099

0020

minus0058

Parameter-value Gun

04 06 08 1 12 14 16 18 2 22 24 04 06 08 1 12 14 16 18 2 22 24

0118

0023

minus0058

minus0177

0092

0019

minus0060

minus0234

0091

0020

minus0062

minus0260

0091

0020

minus0063

minus0276

0164

0038

minus0053

minus0188

0120

0029

minus0056

minus0202

0099

0020

minus0058

minus0208

0092

0018

minus0058

minus0211

Parameter-value Are

04030201 05 06 07 08 09 1 0403 05 06 07 08 09 111


0105

0021

minus0064

minus0194

0092

0021

minus0056

minus0217

0093

0024

minus0051

minus0229

0100

0026

minus0046

minus0237

0106

0020

minus0067

minus0207

0090

0020

minus0054

minus0232

0115

0021

minus0051

minus0266

0131

0025

minus0056

minus0286

005 006 007 008 009 01 02

minus0054




















= 10 119861ch = 09 119866plu = 10 119866plr = 11 1198901= 30

1198902= 10 120576cl = 0002 and 119891

1015840

119905= 005MPa


119898and 119860 red = 119908

21199081
















119870







4 Conclusions








References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















Y

X

i

j

ub2 q2

ub1 q1

ub3 q3






119898 (v) ultimate









fm

f2

f1

Es

1205761 1205762 120576a

1

2

(a)

fm

Emo

1

2

Eun

Eplu

120576a

(120576un fun)

(b)

fm

5Ech

(120576ch fch)

4

120576pl 120576a

Eplr

(120576re fre)

(c)

fm

5

4

120576pl 120576b 120576a

(120576ch fch)


(d)

fm

120576pl 120576pl

f998400t

ft

120576998400m

(e)

fm

120576a

(f)











15ndash20 ge01198902

10ndash15 ge0



119865 = 120590Α = 120590 (119908119905)

120575120572= 120576119871diag

(1)



120572(Figure 5)



119904 (ii) yield-






Stru

t are

a

Initial area

Residual area

120575a1 120575a2 120575a

Axial displacement

A1

A2


F

FcFy


Residual strength

Elastic branch


120575y 120575c 120575u 120575

Fr = 120581FyKspr

(a)

F

120575




(b)




119864119905= (120582120575

119901) 119865119910= 119871 sdot 119865

119910 (2)




119865119894= [

[

1 minus (119864119894

119864119905minus sum119894minus1

119895=1119864119895

)

119888

]

]

sdot 119865119894minus1

= (1 minus 120573119894) sdot 119865119894minus1

(3)


119894is the









119870






119870panel =119866119898119860

119867panel=

119866119898


119867panel (4)





119870sprℎ = 120574 sdot 119870panel = 120574119866119898


119867panel



119867panel

(5)




119871 strutcos2120579 (6)




119864mo = (1 minus 120574)119866119898

(119871 strut1199081

)(

119871panel

119867panel)

1

cos2120579 (7)


119864mo asymp 119864119898120579

= 1 times (cos4120579119864mh

+sin4120579119864mv

+ sin2120579cos2120579 (1

119866119898

minus2V119864mh

))

minus1

(8)





119865spr119910 = 1198861119865cr = 119886

1120591cr119871panel119905panel (9)






1198911198981

=116 tan 120579

1198701+ 1198702120582ℎ

119891mv

1198911198982

=112 sin 120579 cos 120579

1198701(120582ℎ)minus012

+ 1198702(120582ℎ)088

120591119900

1198911198983

=(12 sin 120579 + 045 cos 120579) 120591cr + 03120590V

119908119871diag

1198911198984

=06120591cr + 03120590V

119908119871diag

(10)






1and 119870




1198911015840

119898= min (119891

1198981 1198911198982

1198911198983

1198911198984

) (11)


119905= 005MPa

adopted here)


1199081

119871diag=

0085 +0748

120582ℎ

if997888997888rarr 120582

ℎle 785

0130 +0393

120582ℎ

if997888997888rarr 120582

ℎgt 785

uncracked

1199082

119871diag=

0010 +0707

120582ℎ

if997888997888rarr 120582

ℎle 785

0040 +0470

120582ℎ

if997888997888rarr 120582

ℎgt 785

cracked

(12)


calculated as

120582ℎ= 119867

4radic

119864119898119905panel sin 2120579

4119864119888119868119888119867panel

(13)


120582ℎ lt 314 314 lt 120582ℎ lt 785 120582ℎ gt 785

1198701

13 0707 0471198702

minus0178 0010 004




11990821199081




1corresponds




2







120575 = IDR sdot 119867


2

1 + (119871119867)2

(14)





1198861or 1205761198861

IDR2 120575119888

1205751198862

or 1205761198862

IDR3 120575119906

120575119886ult or 120576119886ult

012

01

008

006

Axi

al fo

rceFast

rust

(kN

)

80

60

40

20

0

120575a(I

DR 1

)

120575a(I

DR 2

)

120575a(I

DR 3

)


Are

aA

(m2)

times10minus2

times10minus2

0 1 1505 2 25 3 35 4

0 1 1505 2 25 3 35 4

A1

A2

120576998400 m120575a(

)





1015840







Sprin

g fo

rceF

spr

(kN

) 120573Kspr

Kspr

120575ys

pr

120575(I

DR1)

120575(I

DR3)

0 001 002 003 004 005


25

20

15

10

5

0






Index 119891 =

10038161003816100381610038161003816119865anal119894

10038161003816100381610038161003816minus

1003816100381610038161003816119865exp119894

1003816100381610038161003816

|119865exp

|max

=

10038161003816100381610038161003816119865anal119894

10038161003816100381610038161003816minus

1003816100381610038161003816119865exp119894

1003816100381610038161003816

((10038161003816100381610038161003816119865exp(+)max

10038161003816100381610038161003816+

10038161003816100381610038161003816119865exp(minus)max

10038161003816100381610038161003816) 2)

(15)







Φ4503Φ8 (bot)


Φ41003Φ8 (bot)


Φ4503Φ8 (bot)


Φ642672Φ19 (bot)


Φ61302Φ12 (bot)


Specimen 119891119888

119891119910

119891yw 119866119898

120591cr 120591119900

119891vm












119878119894= 119878119894minus1

+1

2(119877119894+ 119877119894minus1

) (119880119894minus 119880119894minus1

) (16)



119877119894minus1


119894minus1


error =

sum119899

119894=1

10038161003816100381610038161003816119878anal119894

minus 119878exp119894

10038161003816100381610038161003816

sum119899

119894=1

1003816100381610038161003816119878exp119894

1003816100381610038161003816

(17)





Specimen 1198911015840

1198981198911015840

119905 (wd)ini (wd)res 1205761015840

119898120576cl 120574 119886





1198902

119871119878

119871119870

119888119878

119888119870


Vb

80

40

0

minus40

minus80


= 120575H




006003

0minus003minus006

0 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800

Inde

xf

04

03

02

0

minus01

minus02

minus03

Pseudotime t

IDR=120575H







0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Error = 139

Pseudotime t



Vb

80

40

0

minus40

minus80

minusminus minus 0

= 120575Hminus006






006003

0minus003minus006

0 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800 900

900

Inde

xf

03

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H



0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)Error = 132

Pseudotime t




Base

shea

rVb

(kN

)

150

100

50

0

minus50

minus100


AnalysisExperiment



006003

0minus003minus006

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

Inde

xf

02

01

0

minus01

minus02

minus03

Pseudotime t

IDR=120575

H



0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 58






Base

shea

rVb

(kN

)

AnalysisExperiment

800

600

400

200

0

minus200

minus400

minus600



Inde

xf

02

01

0

minus01

minus02

minus03

minus04

Pseudotime t

IDR=120575

H0015

000750

minus00075minus0015

0 500 1000 1500 2000 2500

0 500 1000 1500 2000 2500







AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 56

70

60

50

40

30

20

10

00 1000 2000 3000 4000 5000



Base

shea

rVb

(kN

)

AnalysisExperiment

300

200

100

0

minus100

minus200






Inde

xf

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H

0010005

0minus0005minus001

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900



AnalysisExperiment

S(k

Nm

)

Pseudotime t


0 1000 2000 3000 4000 5000

Error = 125

40

35

30

25

20

15

10

5

0






300

200

100

0

minus100

minus200


1st

floor

shea

r for

ceV

1(k

N)


(a)


300

200

100

0

minus100

minus200

minus300

2nd

floo

r she

ar fo

rceV2

(kN

)


(b)


AnalysisExperiment

150

100

50

0

minus50

minus100

minus150

3rd

floo

r she

ar fo

rceV3

(kN

)


(c)




21199081 (ii) parameter 119886



3 (v) parameter










1= 06





04

04

03

03

02

02

01

01

0 0

minus01

minus02

minus03

03

02

01

0 0

minus01

minus02

minus03

minus04

04

03

02

01

minus01

minus02

minus03

minus04

Inde

xf

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

Parameter-value Y

05 06 07 08 09

04030201 05 06 07 08 09

1 04030201 05 06 07 08 09 1

Parameter-value a1

00890020

minus0124

minus0415

00900020

minus0097

minus0302

00920018

minus0062

minus0211

0120

0033

minus0204

0108

0022

minus0066

minus0220

0107

0021

minus0055

minus0245

0199

0031

minus0050

minus0323

0304

0044

minus0050

minus0295


0114

0025

minus0078

minus0269

0103

0020

minus0068

minus0208

0140

0025

minus0046

minus0243

0092

0019

minus0066

minus0209

0099

0020

minus0058

minus0208

0130

0032

minus0059

minus0207minus0223

0099

0020

minus0058

Parameter-value Gun

04 06 08 1 12 14 16 18 2 22 24 04 06 08 1 12 14 16 18 2 22 24

0118

0023

minus0058

minus0177

0092

0019

minus0060

minus0234

0091

0020

minus0062

minus0260

0091

0020

minus0063

minus0276

0164

0038

minus0053

minus0188

0120

0029

minus0056

minus0202

0099

0020

minus0058

minus0208

0092

0018

minus0058

minus0211

Parameter-value Are

04030201 05 06 07 08 09 1 0403 05 06 07 08 09 111


0105

0021

minus0064

minus0194

0092

0021

minus0056

minus0217

0093

0024

minus0051

minus0229

0100

0026

minus0046

minus0237

0106

0020

minus0067

minus0207

0090

0020

minus0054

minus0232

0115

0021

minus0051

minus0266

0131

0025

minus0056

minus0286

005 006 007 008 009 01 02

minus0054




















= 10 119861ch = 09 119866plu = 10 119866plr = 11 1198901= 30

1198902= 10 120576cl = 0002 and 119891

1015840

119905= 005MPa


119898and 119860 red = 119908

21199081
















119870







4 Conclusions








References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










fm

f2

f1

Es

1205761 1205762 120576a

1

2

(a)

fm

Emo

1

2

Eun

Eplu

120576a

(120576un fun)

(b)

fm

5Ech

(120576ch fch)

4

120576pl 120576a

Eplr

(120576re fre)

(c)

fm

5

4

120576pl 120576b 120576a

(120576ch fch)


(d)

fm

120576pl 120576pl

f998400t

ft

120576998400m

(e)

fm

120576a

(f)











15ndash20 ge01198902

10ndash15 ge0



119865 = 120590Α = 120590 (119908119905)

120575120572= 120576119871diag

(1)



120572(Figure 5)



119904 (ii) yield-






Stru

t are

a

Initial area

Residual area

120575a1 120575a2 120575a

Axial displacement

A1

A2


F

FcFy


Residual strength

Elastic branch


120575y 120575c 120575u 120575

Fr = 120581FyKspr

(a)

F

120575




(b)




119864119905= (120582120575

119901) 119865119910= 119871 sdot 119865

119910 (2)




119865119894= [

[

1 minus (119864119894

119864119905minus sum119894minus1

119895=1119864119895

)

119888

]

]

sdot 119865119894minus1

= (1 minus 120573119894) sdot 119865119894minus1

(3)


119894is the









119870






119870panel =119866119898119860

119867panel=

119866119898


119867panel (4)





119870sprℎ = 120574 sdot 119870panel = 120574119866119898


119867panel



119867panel

(5)




119871 strutcos2120579 (6)




119864mo = (1 minus 120574)119866119898

(119871 strut1199081

)(

119871panel

119867panel)

1

cos2120579 (7)


119864mo asymp 119864119898120579

= 1 times (cos4120579119864mh

+sin4120579119864mv

+ sin2120579cos2120579 (1

119866119898

minus2V119864mh

))

minus1

(8)





119865spr119910 = 1198861119865cr = 119886

1120591cr119871panel119905panel (9)






1198911198981

=116 tan 120579

1198701+ 1198702120582ℎ

119891mv

1198911198982

=112 sin 120579 cos 120579

1198701(120582ℎ)minus012

+ 1198702(120582ℎ)088

120591119900

1198911198983

=(12 sin 120579 + 045 cos 120579) 120591cr + 03120590V

119908119871diag

1198911198984

=06120591cr + 03120590V

119908119871diag

(10)






1and 119870




1198911015840

119898= min (119891

1198981 1198911198982

1198911198983

1198911198984

) (11)


119905= 005MPa

adopted here)


1199081

119871diag=

0085 +0748

120582ℎ

if997888997888rarr 120582

ℎle 785

0130 +0393

120582ℎ

if997888997888rarr 120582

ℎgt 785

uncracked

1199082

119871diag=

0010 +0707

120582ℎ

if997888997888rarr 120582

ℎle 785

0040 +0470

120582ℎ

if997888997888rarr 120582

ℎgt 785

cracked

(12)


calculated as

120582ℎ= 119867

4radic

119864119898119905panel sin 2120579

4119864119888119868119888119867panel

(13)


120582ℎ lt 314 314 lt 120582ℎ lt 785 120582ℎ gt 785

1198701

13 0707 0471198702

minus0178 0010 004




11990821199081




1corresponds




2







120575 = IDR sdot 119867


2

1 + (119871119867)2

(14)





1198861or 1205761198861

IDR2 120575119888

1205751198862

or 1205761198862

IDR3 120575119906

120575119886ult or 120576119886ult

012

01

008

006

Axi

al fo

rceFast

rust

(kN

)

80

60

40

20

0

120575a(I

DR 1

)

120575a(I

DR 2

)

120575a(I

DR 3

)


Are

aA

(m2)

times10minus2

times10minus2

0 1 1505 2 25 3 35 4

0 1 1505 2 25 3 35 4

A1

A2

120576998400 m120575a(

)





1015840







Sprin

g fo

rceF

spr

(kN

) 120573Kspr

Kspr

120575ys

pr

120575(I

DR1)

120575(I

DR3)

0 001 002 003 004 005


25

20

15

10

5

0






Index 119891 =

10038161003816100381610038161003816119865anal119894

10038161003816100381610038161003816minus

1003816100381610038161003816119865exp119894

1003816100381610038161003816

|119865exp

|max

=

10038161003816100381610038161003816119865anal119894

10038161003816100381610038161003816minus

1003816100381610038161003816119865exp119894

1003816100381610038161003816

((10038161003816100381610038161003816119865exp(+)max

10038161003816100381610038161003816+

10038161003816100381610038161003816119865exp(minus)max

10038161003816100381610038161003816) 2)

(15)







Φ4503Φ8 (bot)


Φ41003Φ8 (bot)


Φ4503Φ8 (bot)


Φ642672Φ19 (bot)


Φ61302Φ12 (bot)


Specimen 119891119888

119891119910

119891yw 119866119898

120591cr 120591119900

119891vm












119878119894= 119878119894minus1

+1

2(119877119894+ 119877119894minus1

) (119880119894minus 119880119894minus1

) (16)



119877119894minus1


119894minus1


error =

sum119899

119894=1

10038161003816100381610038161003816119878anal119894

minus 119878exp119894

10038161003816100381610038161003816

sum119899

119894=1

1003816100381610038161003816119878exp119894

1003816100381610038161003816

(17)





Specimen 1198911015840

1198981198911015840

119905 (wd)ini (wd)res 1205761015840

119898120576cl 120574 119886





1198902

119871119878

119871119870

119888119878

119888119870


Vb

80

40

0

minus40

minus80


= 120575H




006003

0minus003minus006

0 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800

Inde

xf

04

03

02

0

minus01

minus02

minus03

Pseudotime t

IDR=120575H







0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Error = 139

Pseudotime t



Vb

80

40

0

minus40

minus80

minusminus minus 0

= 120575Hminus006






006003

0minus003minus006

0 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800 900

900

Inde

xf

03

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H



0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)Error = 132

Pseudotime t




Base

shea

rVb

(kN

)

150

100

50

0

minus50

minus100


AnalysisExperiment



006003

0minus003minus006

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

Inde

xf

02

01

0

minus01

minus02

minus03

Pseudotime t

IDR=120575

H



0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 58






Base

shea

rVb

(kN

)

AnalysisExperiment

800

600

400

200

0

minus200

minus400

minus600



Inde

xf

02

01

0

minus01

minus02

minus03

minus04

Pseudotime t

IDR=120575

H0015

000750

minus00075minus0015

0 500 1000 1500 2000 2500

0 500 1000 1500 2000 2500







AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 56

70

60

50

40

30

20

10

00 1000 2000 3000 4000 5000



Base

shea

rVb

(kN

)

AnalysisExperiment

300

200

100

0

minus100

minus200






Inde

xf

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H

0010005

0minus0005minus001

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900



AnalysisExperiment

S(k

Nm

)

Pseudotime t


0 1000 2000 3000 4000 5000

Error = 125

40

35

30

25

20

15

10

5

0






300

200

100

0

minus100

minus200


1st

floor

shea

r for

ceV

1(k

N)


(a)


300

200

100

0

minus100

minus200

minus300

2nd

floo

r she

ar fo

rceV2

(kN

)


(b)


AnalysisExperiment

150

100

50

0

minus50

minus100

minus150

3rd

floo

r she

ar fo

rceV3

(kN

)


(c)




21199081 (ii) parameter 119886



3 (v) parameter










1= 06





04

04

03

03

02

02

01

01

0 0

minus01

minus02

minus03

03

02

01

0 0

minus01

minus02

minus03

minus04

04

03

02

01

minus01

minus02

minus03

minus04

Inde

xf

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

Parameter-value Y

05 06 07 08 09

04030201 05 06 07 08 09

1 04030201 05 06 07 08 09 1

Parameter-value a1

00890020

minus0124

minus0415

00900020

minus0097

minus0302

00920018

minus0062

minus0211

0120

0033

minus0204

0108

0022

minus0066

minus0220

0107

0021

minus0055

minus0245

0199

0031

minus0050

minus0323

0304

0044

minus0050

minus0295


0114

0025

minus0078

minus0269

0103

0020

minus0068

minus0208

0140

0025

minus0046

minus0243

0092

0019

minus0066

minus0209

0099

0020

minus0058

minus0208

0130

0032

minus0059

minus0207minus0223

0099

0020

minus0058

Parameter-value Gun

04 06 08 1 12 14 16 18 2 22 24 04 06 08 1 12 14 16 18 2 22 24

0118

0023

minus0058

minus0177

0092

0019

minus0060

minus0234

0091

0020

minus0062

minus0260

0091

0020

minus0063

minus0276

0164

0038

minus0053

minus0188

0120

0029

minus0056

minus0202

0099

0020

minus0058

minus0208

0092

0018

minus0058

minus0211

Parameter-value Are

04030201 05 06 07 08 09 1 0403 05 06 07 08 09 111


0105

0021

minus0064

minus0194

0092

0021

minus0056

minus0217

0093

0024

minus0051

minus0229

0100

0026

minus0046

minus0237

0106

0020

minus0067

minus0207

0090

0020

minus0054

minus0232

0115

0021

minus0051

minus0266

0131

0025

minus0056

minus0286

005 006 007 008 009 01 02

minus0054




















= 10 119861ch = 09 119866plu = 10 119866plr = 11 1198901= 30

1198902= 10 120576cl = 0002 and 119891

1015840

119905= 005MPa


119898and 119860 red = 119908

21199081
















119870







4 Conclusions








References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












15ndash20 ge01198902

10ndash15 ge0



119865 = 120590Α = 120590 (119908119905)

120575120572= 120576119871diag

(1)



120572(Figure 5)



119904 (ii) yield-






Stru

t are

a

Initial area

Residual area

120575a1 120575a2 120575a

Axial displacement

A1

A2


F

FcFy


Residual strength

Elastic branch


120575y 120575c 120575u 120575

Fr = 120581FyKspr

(a)

F

120575




(b)




119864119905= (120582120575

119901) 119865119910= 119871 sdot 119865

119910 (2)




119865119894= [

[

1 minus (119864119894

119864119905minus sum119894minus1

119895=1119864119895

)

119888

]

]

sdot 119865119894minus1

= (1 minus 120573119894) sdot 119865119894minus1

(3)


119894is the









119870






119870panel =119866119898119860

119867panel=

119866119898


119867panel (4)





119870sprℎ = 120574 sdot 119870panel = 120574119866119898


119867panel



119867panel

(5)




119871 strutcos2120579 (6)




119864mo = (1 minus 120574)119866119898

(119871 strut1199081

)(

119871panel

119867panel)

1

cos2120579 (7)


119864mo asymp 119864119898120579

= 1 times (cos4120579119864mh

+sin4120579119864mv

+ sin2120579cos2120579 (1

119866119898

minus2V119864mh

))

minus1

(8)





119865spr119910 = 1198861119865cr = 119886

1120591cr119871panel119905panel (9)






1198911198981

=116 tan 120579

1198701+ 1198702120582ℎ

119891mv

1198911198982

=112 sin 120579 cos 120579

1198701(120582ℎ)minus012

+ 1198702(120582ℎ)088

120591119900

1198911198983

=(12 sin 120579 + 045 cos 120579) 120591cr + 03120590V

119908119871diag

1198911198984

=06120591cr + 03120590V

119908119871diag

(10)






1and 119870




1198911015840

119898= min (119891

1198981 1198911198982

1198911198983

1198911198984

) (11)


119905= 005MPa

adopted here)


1199081

119871diag=

0085 +0748

120582ℎ

if997888997888rarr 120582

ℎle 785

0130 +0393

120582ℎ

if997888997888rarr 120582

ℎgt 785

uncracked

1199082

119871diag=

0010 +0707

120582ℎ

if997888997888rarr 120582

ℎle 785

0040 +0470

120582ℎ

if997888997888rarr 120582

ℎgt 785

cracked

(12)


calculated as

120582ℎ= 119867

4radic

119864119898119905panel sin 2120579

4119864119888119868119888119867panel

(13)


120582ℎ lt 314 314 lt 120582ℎ lt 785 120582ℎ gt 785

1198701

13 0707 0471198702

minus0178 0010 004




11990821199081




1corresponds




2







120575 = IDR sdot 119867


2

1 + (119871119867)2

(14)





1198861or 1205761198861

IDR2 120575119888

1205751198862

or 1205761198862

IDR3 120575119906

120575119886ult or 120576119886ult

012

01

008

006

Axi

al fo

rceFast

rust

(kN

)

80

60

40

20

0

120575a(I

DR 1

)

120575a(I

DR 2

)

120575a(I

DR 3

)


Are

aA

(m2)

times10minus2

times10minus2

0 1 1505 2 25 3 35 4

0 1 1505 2 25 3 35 4

A1

A2

120576998400 m120575a(

)





1015840







Sprin

g fo

rceF

spr

(kN

) 120573Kspr

Kspr

120575ys

pr

120575(I

DR1)

120575(I

DR3)

0 001 002 003 004 005


25

20

15

10

5

0






Index 119891 =

10038161003816100381610038161003816119865anal119894

10038161003816100381610038161003816minus

1003816100381610038161003816119865exp119894

1003816100381610038161003816

|119865exp

|max

=

10038161003816100381610038161003816119865anal119894

10038161003816100381610038161003816minus

1003816100381610038161003816119865exp119894

1003816100381610038161003816

((10038161003816100381610038161003816119865exp(+)max

10038161003816100381610038161003816+

10038161003816100381610038161003816119865exp(minus)max

10038161003816100381610038161003816) 2)

(15)







Φ4503Φ8 (bot)


Φ41003Φ8 (bot)


Φ4503Φ8 (bot)


Φ642672Φ19 (bot)


Φ61302Φ12 (bot)


Specimen 119891119888

119891119910

119891yw 119866119898

120591cr 120591119900

119891vm












119878119894= 119878119894minus1

+1

2(119877119894+ 119877119894minus1

) (119880119894minus 119880119894minus1

) (16)



119877119894minus1


119894minus1


error =

sum119899

119894=1

10038161003816100381610038161003816119878anal119894

minus 119878exp119894

10038161003816100381610038161003816

sum119899

119894=1

1003816100381610038161003816119878exp119894

1003816100381610038161003816

(17)





Specimen 1198911015840

1198981198911015840

119905 (wd)ini (wd)res 1205761015840

119898120576cl 120574 119886





1198902

119871119878

119871119870

119888119878

119888119870


Vb

80

40

0

minus40

minus80


= 120575H




006003

0minus003minus006

0 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800

Inde

xf

04

03

02

0

minus01

minus02

minus03

Pseudotime t

IDR=120575H







0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Error = 139

Pseudotime t



Vb

80

40

0

minus40

minus80

minusminus minus 0

= 120575Hminus006






006003

0minus003minus006

0 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800 900

900

Inde

xf

03

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H



0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)Error = 132

Pseudotime t




Base

shea

rVb

(kN

)

150

100

50

0

minus50

minus100


AnalysisExperiment



006003

0minus003minus006

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

Inde

xf

02

01

0

minus01

minus02

minus03

Pseudotime t

IDR=120575

H



0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 58






Base

shea

rVb

(kN

)

AnalysisExperiment

800

600

400

200

0

minus200

minus400

minus600



Inde

xf

02

01

0

minus01

minus02

minus03

minus04

Pseudotime t

IDR=120575

H0015

000750

minus00075minus0015

0 500 1000 1500 2000 2500

0 500 1000 1500 2000 2500







AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 56

70

60

50

40

30

20

10

00 1000 2000 3000 4000 5000



Base

shea

rVb

(kN

)

AnalysisExperiment

300

200

100

0

minus100

minus200






Inde

xf

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H

0010005

0minus0005minus001

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900



AnalysisExperiment

S(k

Nm

)

Pseudotime t


0 1000 2000 3000 4000 5000

Error = 125

40

35

30

25

20

15

10

5

0






300

200

100

0

minus100

minus200


1st

floor

shea

r for

ceV

1(k

N)


(a)


300

200

100

0

minus100

minus200

minus300

2nd

floo

r she

ar fo

rceV2

(kN

)


(b)


AnalysisExperiment

150

100

50

0

minus50

minus100

minus150

3rd

floo

r she

ar fo

rceV3

(kN

)


(c)




21199081 (ii) parameter 119886



3 (v) parameter










1= 06





04

04

03

03

02

02

01

01

0 0

minus01

minus02

minus03

03

02

01

0 0

minus01

minus02

minus03

minus04

04

03

02

01

minus01

minus02

minus03

minus04

Inde

xf

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

Parameter-value Y

05 06 07 08 09

04030201 05 06 07 08 09

1 04030201 05 06 07 08 09 1

Parameter-value a1

00890020

minus0124

minus0415

00900020

minus0097

minus0302

00920018

minus0062

minus0211

0120

0033

minus0204

0108

0022

minus0066

minus0220

0107

0021

minus0055

minus0245

0199

0031

minus0050

minus0323

0304

0044

minus0050

minus0295


0114

0025

minus0078

minus0269

0103

0020

minus0068

minus0208

0140

0025

minus0046

minus0243

0092

0019

minus0066

minus0209

0099

0020

minus0058

minus0208

0130

0032

minus0059

minus0207minus0223

0099

0020

minus0058

Parameter-value Gun

04 06 08 1 12 14 16 18 2 22 24 04 06 08 1 12 14 16 18 2 22 24

0118

0023

minus0058

minus0177

0092

0019

minus0060

minus0234

0091

0020

minus0062

minus0260

0091

0020

minus0063

minus0276

0164

0038

minus0053

minus0188

0120

0029

minus0056

minus0202

0099

0020

minus0058

minus0208

0092

0018

minus0058

minus0211

Parameter-value Are

04030201 05 06 07 08 09 1 0403 05 06 07 08 09 111


0105

0021

minus0064

minus0194

0092

0021

minus0056

minus0217

0093

0024

minus0051

minus0229

0100

0026

minus0046

minus0237

0106

0020

minus0067

minus0207

0090

0020

minus0054

minus0232

0115

0021

minus0051

minus0266

0131

0025

minus0056

minus0286

005 006 007 008 009 01 02

minus0054




















= 10 119861ch = 09 119866plu = 10 119866plr = 11 1198901= 30

1198902= 10 120576cl = 0002 and 119891

1015840

119905= 005MPa


119898and 119860 red = 119908

21199081
















119870







4 Conclusions








References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















119870






119870panel =119866119898119860

119867panel=

119866119898


119867panel (4)





119870sprℎ = 120574 sdot 119870panel = 120574119866119898


119867panel



119867panel

(5)




119871 strutcos2120579 (6)




119864mo = (1 minus 120574)119866119898

(119871 strut1199081

)(

119871panel

119867panel)

1

cos2120579 (7)


119864mo asymp 119864119898120579

= 1 times (cos4120579119864mh

+sin4120579119864mv

+ sin2120579cos2120579 (1

119866119898

minus2V119864mh

))

minus1

(8)





119865spr119910 = 1198861119865cr = 119886

1120591cr119871panel119905panel (9)






1198911198981

=116 tan 120579

1198701+ 1198702120582ℎ

119891mv

1198911198982

=112 sin 120579 cos 120579

1198701(120582ℎ)minus012

+ 1198702(120582ℎ)088

120591119900

1198911198983

=(12 sin 120579 + 045 cos 120579) 120591cr + 03120590V

119908119871diag

1198911198984

=06120591cr + 03120590V

119908119871diag

(10)






1and 119870




1198911015840

119898= min (119891

1198981 1198911198982

1198911198983

1198911198984

) (11)


119905= 005MPa

adopted here)


1199081

119871diag=

0085 +0748

120582ℎ

if997888997888rarr 120582

ℎle 785

0130 +0393

120582ℎ

if997888997888rarr 120582

ℎgt 785

uncracked

1199082

119871diag=

0010 +0707

120582ℎ

if997888997888rarr 120582

ℎle 785

0040 +0470

120582ℎ

if997888997888rarr 120582

ℎgt 785

cracked

(12)


calculated as

120582ℎ= 119867

4radic

119864119898119905panel sin 2120579

4119864119888119868119888119867panel

(13)


120582ℎ lt 314 314 lt 120582ℎ lt 785 120582ℎ gt 785

1198701

13 0707 0471198702

minus0178 0010 004




11990821199081




1corresponds




2







120575 = IDR sdot 119867


2

1 + (119871119867)2

(14)





1198861or 1205761198861

IDR2 120575119888

1205751198862

or 1205761198862

IDR3 120575119906

120575119886ult or 120576119886ult

012

01

008

006

Axi

al fo

rceFast

rust

(kN

)

80

60

40

20

0

120575a(I

DR 1

)

120575a(I

DR 2

)

120575a(I

DR 3

)


Are

aA

(m2)

times10minus2

times10minus2

0 1 1505 2 25 3 35 4

0 1 1505 2 25 3 35 4

A1

A2

120576998400 m120575a(

)





1015840







Sprin

g fo

rceF

spr

(kN

) 120573Kspr

Kspr

120575ys

pr

120575(I

DR1)

120575(I

DR3)

0 001 002 003 004 005


25

20

15

10

5

0






Index 119891 =

10038161003816100381610038161003816119865anal119894

10038161003816100381610038161003816minus

1003816100381610038161003816119865exp119894

1003816100381610038161003816

|119865exp

|max

=

10038161003816100381610038161003816119865anal119894

10038161003816100381610038161003816minus

1003816100381610038161003816119865exp119894

1003816100381610038161003816

((10038161003816100381610038161003816119865exp(+)max

10038161003816100381610038161003816+

10038161003816100381610038161003816119865exp(minus)max

10038161003816100381610038161003816) 2)

(15)







Φ4503Φ8 (bot)


Φ41003Φ8 (bot)


Φ4503Φ8 (bot)


Φ642672Φ19 (bot)


Φ61302Φ12 (bot)


Specimen 119891119888

119891119910

119891yw 119866119898

120591cr 120591119900

119891vm












119878119894= 119878119894minus1

+1

2(119877119894+ 119877119894minus1

) (119880119894minus 119880119894minus1

) (16)



119877119894minus1


119894minus1


error =

sum119899

119894=1

10038161003816100381610038161003816119878anal119894

minus 119878exp119894

10038161003816100381610038161003816

sum119899

119894=1

1003816100381610038161003816119878exp119894

1003816100381610038161003816

(17)





Specimen 1198911015840

1198981198911015840

119905 (wd)ini (wd)res 1205761015840

119898120576cl 120574 119886





1198902

119871119878

119871119870

119888119878

119888119870


Vb

80

40

0

minus40

minus80


= 120575H




006003

0minus003minus006

0 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800

Inde

xf

04

03

02

0

minus01

minus02

minus03

Pseudotime t

IDR=120575H







0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Error = 139

Pseudotime t



Vb

80

40

0

minus40

minus80

minusminus minus 0

= 120575Hminus006






006003

0minus003minus006

0 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800 900

900

Inde

xf

03

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H



0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)Error = 132

Pseudotime t




Base

shea

rVb

(kN

)

150

100

50

0

minus50

minus100


AnalysisExperiment



006003

0minus003minus006

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

Inde

xf

02

01

0

minus01

minus02

minus03

Pseudotime t

IDR=120575

H



0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 58






Base

shea

rVb

(kN

)

AnalysisExperiment

800

600

400

200

0

minus200

minus400

minus600



Inde

xf

02

01

0

minus01

minus02

minus03

minus04

Pseudotime t

IDR=120575

H0015

000750

minus00075minus0015

0 500 1000 1500 2000 2500

0 500 1000 1500 2000 2500







AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 56

70

60

50

40

30

20

10

00 1000 2000 3000 4000 5000



Base

shea

rVb

(kN

)

AnalysisExperiment

300

200

100

0

minus100

minus200






Inde

xf

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H

0010005

0minus0005minus001

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900



AnalysisExperiment

S(k

Nm

)

Pseudotime t


0 1000 2000 3000 4000 5000

Error = 125

40

35

30

25

20

15

10

5

0






300

200

100

0

minus100

minus200


1st

floor

shea

r for

ceV

1(k

N)


(a)


300

200

100

0

minus100

minus200

minus300

2nd

floo

r she

ar fo

rceV2

(kN

)


(b)


AnalysisExperiment

150

100

50

0

minus50

minus100

minus150

3rd

floo

r she

ar fo

rceV3

(kN

)


(c)




21199081 (ii) parameter 119886



3 (v) parameter










1= 06





04

04

03

03

02

02

01

01

0 0

minus01

minus02

minus03

03

02

01

0 0

minus01

minus02

minus03

minus04

04

03

02

01

minus01

minus02

minus03

minus04

Inde

xf

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

Parameter-value Y

05 06 07 08 09

04030201 05 06 07 08 09

1 04030201 05 06 07 08 09 1

Parameter-value a1

00890020

minus0124

minus0415

00900020

minus0097

minus0302

00920018

minus0062

minus0211

0120

0033

minus0204

0108

0022

minus0066

minus0220

0107

0021

minus0055

minus0245

0199

0031

minus0050

minus0323

0304

0044

minus0050

minus0295


0114

0025

minus0078

minus0269

0103

0020

minus0068

minus0208

0140

0025

minus0046

minus0243

0092

0019

minus0066

minus0209

0099

0020

minus0058

minus0208

0130

0032

minus0059

minus0207minus0223

0099

0020

minus0058

Parameter-value Gun

04 06 08 1 12 14 16 18 2 22 24 04 06 08 1 12 14 16 18 2 22 24

0118

0023

minus0058

minus0177

0092

0019

minus0060

minus0234

0091

0020

minus0062

minus0260

0091

0020

minus0063

minus0276

0164

0038

minus0053

minus0188

0120

0029

minus0056

minus0202

0099

0020

minus0058

minus0208

0092

0018

minus0058

minus0211

Parameter-value Are

04030201 05 06 07 08 09 1 0403 05 06 07 08 09 111


0105

0021

minus0064

minus0194

0092

0021

minus0056

minus0217

0093

0024

minus0051

minus0229

0100

0026

minus0046

minus0237

0106

0020

minus0067

minus0207

0090

0020

minus0054

minus0232

0115

0021

minus0051

minus0266

0131

0025

minus0056

minus0286

005 006 007 008 009 01 02

minus0054




















= 10 119861ch = 09 119866plu = 10 119866plr = 11 1198901= 30

1198902= 10 120576cl = 0002 and 119891

1015840

119905= 005MPa


119898and 119860 red = 119908

21199081
















119870







4 Conclusions








References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











1198911198981

=116 tan 120579

1198701+ 1198702120582ℎ

119891mv

1198911198982

=112 sin 120579 cos 120579

1198701(120582ℎ)minus012

+ 1198702(120582ℎ)088

120591119900

1198911198983

=(12 sin 120579 + 045 cos 120579) 120591cr + 03120590V

119908119871diag

1198911198984

=06120591cr + 03120590V

119908119871diag

(10)






1and 119870




1198911015840

119898= min (119891

1198981 1198911198982

1198911198983

1198911198984

) (11)


119905= 005MPa

adopted here)


1199081

119871diag=

0085 +0748

120582ℎ

if997888997888rarr 120582

ℎle 785

0130 +0393

120582ℎ

if997888997888rarr 120582

ℎgt 785

uncracked

1199082

119871diag=

0010 +0707

120582ℎ

if997888997888rarr 120582

ℎle 785

0040 +0470

120582ℎ

if997888997888rarr 120582

ℎgt 785

cracked

(12)


calculated as

120582ℎ= 119867

4radic

119864119898119905panel sin 2120579

4119864119888119868119888119867panel

(13)


120582ℎ lt 314 314 lt 120582ℎ lt 785 120582ℎ gt 785

1198701

13 0707 0471198702

minus0178 0010 004




11990821199081




1corresponds




2







120575 = IDR sdot 119867


2

1 + (119871119867)2

(14)





1198861or 1205761198861

IDR2 120575119888

1205751198862

or 1205761198862

IDR3 120575119906

120575119886ult or 120576119886ult

012

01

008

006

Axi

al fo

rceFast

rust

(kN

)

80

60

40

20

0

120575a(I

DR 1

)

120575a(I

DR 2

)

120575a(I

DR 3

)


Are

aA

(m2)

times10minus2

times10minus2

0 1 1505 2 25 3 35 4

0 1 1505 2 25 3 35 4

A1

A2

120576998400 m120575a(

)





1015840







Sprin

g fo

rceF

spr

(kN

) 120573Kspr

Kspr

120575ys

pr

120575(I

DR1)

120575(I

DR3)

0 001 002 003 004 005


25

20

15

10

5

0






Index 119891 =

10038161003816100381610038161003816119865anal119894

10038161003816100381610038161003816minus

1003816100381610038161003816119865exp119894

1003816100381610038161003816

|119865exp

|max

=

10038161003816100381610038161003816119865anal119894

10038161003816100381610038161003816minus

1003816100381610038161003816119865exp119894

1003816100381610038161003816

((10038161003816100381610038161003816119865exp(+)max

10038161003816100381610038161003816+

10038161003816100381610038161003816119865exp(minus)max

10038161003816100381610038161003816) 2)

(15)







Φ4503Φ8 (bot)


Φ41003Φ8 (bot)


Φ4503Φ8 (bot)


Φ642672Φ19 (bot)


Φ61302Φ12 (bot)


Specimen 119891119888

119891119910

119891yw 119866119898

120591cr 120591119900

119891vm












119878119894= 119878119894minus1

+1

2(119877119894+ 119877119894minus1

) (119880119894minus 119880119894minus1

) (16)



119877119894minus1


119894minus1


error =

sum119899

119894=1

10038161003816100381610038161003816119878anal119894

minus 119878exp119894

10038161003816100381610038161003816

sum119899

119894=1

1003816100381610038161003816119878exp119894

1003816100381610038161003816

(17)





Specimen 1198911015840

1198981198911015840

119905 (wd)ini (wd)res 1205761015840

119898120576cl 120574 119886





1198902

119871119878

119871119870

119888119878

119888119870


Vb

80

40

0

minus40

minus80


= 120575H




006003

0minus003minus006

0 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800

Inde

xf

04

03

02

0

minus01

minus02

minus03

Pseudotime t

IDR=120575H







0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Error = 139

Pseudotime t



Vb

80

40

0

minus40

minus80

minusminus minus 0

= 120575Hminus006






006003

0minus003minus006

0 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800 900

900

Inde

xf

03

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H



0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)Error = 132

Pseudotime t




Base

shea

rVb

(kN

)

150

100

50

0

minus50

minus100


AnalysisExperiment



006003

0minus003minus006

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

Inde

xf

02

01

0

minus01

minus02

minus03

Pseudotime t

IDR=120575

H



0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 58






Base

shea

rVb

(kN

)

AnalysisExperiment

800

600

400

200

0

minus200

minus400

minus600



Inde

xf

02

01

0

minus01

minus02

minus03

minus04

Pseudotime t

IDR=120575

H0015

000750

minus00075minus0015

0 500 1000 1500 2000 2500

0 500 1000 1500 2000 2500







AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 56

70

60

50

40

30

20

10

00 1000 2000 3000 4000 5000



Base

shea

rVb

(kN

)

AnalysisExperiment

300

200

100

0

minus100

minus200






Inde

xf

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H

0010005

0minus0005minus001

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900



AnalysisExperiment

S(k

Nm

)

Pseudotime t


0 1000 2000 3000 4000 5000

Error = 125

40

35

30

25

20

15

10

5

0






300

200

100

0

minus100

minus200


1st

floor

shea

r for

ceV

1(k

N)


(a)


300

200

100

0

minus100

minus200

minus300

2nd

floo

r she

ar fo

rceV2

(kN

)


(b)


AnalysisExperiment

150

100

50

0

minus50

minus100

minus150

3rd

floo

r she

ar fo

rceV3

(kN

)


(c)




21199081 (ii) parameter 119886



3 (v) parameter










1= 06





04

04

03

03

02

02

01

01

0 0

minus01

minus02

minus03

03

02

01

0 0

minus01

minus02

minus03

minus04

04

03

02

01

minus01

minus02

minus03

minus04

Inde

xf

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

Parameter-value Y

05 06 07 08 09

04030201 05 06 07 08 09

1 04030201 05 06 07 08 09 1

Parameter-value a1

00890020

minus0124

minus0415

00900020

minus0097

minus0302

00920018

minus0062

minus0211

0120

0033

minus0204

0108

0022

minus0066

minus0220

0107

0021

minus0055

minus0245

0199

0031

minus0050

minus0323

0304

0044

minus0050

minus0295


0114

0025

minus0078

minus0269

0103

0020

minus0068

minus0208

0140

0025

minus0046

minus0243

0092

0019

minus0066

minus0209

0099

0020

minus0058

minus0208

0130

0032

minus0059

minus0207minus0223

0099

0020

minus0058

Parameter-value Gun

04 06 08 1 12 14 16 18 2 22 24 04 06 08 1 12 14 16 18 2 22 24

0118

0023

minus0058

minus0177

0092

0019

minus0060

minus0234

0091

0020

minus0062

minus0260

0091

0020

minus0063

minus0276

0164

0038

minus0053

minus0188

0120

0029

minus0056

minus0202

0099

0020

minus0058

minus0208

0092

0018

minus0058

minus0211

Parameter-value Are

04030201 05 06 07 08 09 1 0403 05 06 07 08 09 111


0105

0021

minus0064

minus0194

0092

0021

minus0056

minus0217

0093

0024

minus0051

minus0229

0100

0026

minus0046

minus0237

0106

0020

minus0067

minus0207

0090

0020

minus0054

minus0232

0115

0021

minus0051

minus0266

0131

0025

minus0056

minus0286

005 006 007 008 009 01 02

minus0054




















= 10 119861ch = 09 119866plu = 10 119866plr = 11 1198901= 30

1198902= 10 120576cl = 0002 and 119891

1015840

119905= 005MPa


119898and 119860 red = 119908

21199081
















119870







4 Conclusions








References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












1198861or 1205761198861

IDR2 120575119888

1205751198862

or 1205761198862

IDR3 120575119906

120575119886ult or 120576119886ult

012

01

008

006

Axi

al fo

rceFast

rust

(kN

)

80

60

40

20

0

120575a(I

DR 1

)

120575a(I

DR 2

)

120575a(I

DR 3

)


Are

aA

(m2)

times10minus2

times10minus2

0 1 1505 2 25 3 35 4

0 1 1505 2 25 3 35 4

A1

A2

120576998400 m120575a(

)





1015840







Sprin

g fo

rceF

spr

(kN

) 120573Kspr

Kspr

120575ys

pr

120575(I

DR1)

120575(I

DR3)

0 001 002 003 004 005


25

20

15

10

5

0






Index 119891 =

10038161003816100381610038161003816119865anal119894

10038161003816100381610038161003816minus

1003816100381610038161003816119865exp119894

1003816100381610038161003816

|119865exp

|max

=

10038161003816100381610038161003816119865anal119894

10038161003816100381610038161003816minus

1003816100381610038161003816119865exp119894

1003816100381610038161003816

((10038161003816100381610038161003816119865exp(+)max

10038161003816100381610038161003816+

10038161003816100381610038161003816119865exp(minus)max

10038161003816100381610038161003816) 2)

(15)







Φ4503Φ8 (bot)


Φ41003Φ8 (bot)


Φ4503Φ8 (bot)


Φ642672Φ19 (bot)


Φ61302Φ12 (bot)


Specimen 119891119888

119891119910

119891yw 119866119898

120591cr 120591119900

119891vm












119878119894= 119878119894minus1

+1

2(119877119894+ 119877119894minus1

) (119880119894minus 119880119894minus1

) (16)



119877119894minus1


119894minus1


error =

sum119899

119894=1

10038161003816100381610038161003816119878anal119894

minus 119878exp119894

10038161003816100381610038161003816

sum119899

119894=1

1003816100381610038161003816119878exp119894

1003816100381610038161003816

(17)





Specimen 1198911015840

1198981198911015840

119905 (wd)ini (wd)res 1205761015840

119898120576cl 120574 119886





1198902

119871119878

119871119870

119888119878

119888119870


Vb

80

40

0

minus40

minus80


= 120575H




006003

0minus003minus006

0 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800

Inde

xf

04

03

02

0

minus01

minus02

minus03

Pseudotime t

IDR=120575H







0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Error = 139

Pseudotime t



Vb

80

40

0

minus40

minus80

minusminus minus 0

= 120575Hminus006






006003

0minus003minus006

0 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800 900

900

Inde

xf

03

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H



0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)Error = 132

Pseudotime t




Base

shea

rVb

(kN

)

150

100

50

0

minus50

minus100


AnalysisExperiment



006003

0minus003minus006

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

Inde

xf

02

01

0

minus01

minus02

minus03

Pseudotime t

IDR=120575

H



0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 58






Base

shea

rVb

(kN

)

AnalysisExperiment

800

600

400

200

0

minus200

minus400

minus600



Inde

xf

02

01

0

minus01

minus02

minus03

minus04

Pseudotime t

IDR=120575

H0015

000750

minus00075minus0015

0 500 1000 1500 2000 2500

0 500 1000 1500 2000 2500







AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 56

70

60

50

40

30

20

10

00 1000 2000 3000 4000 5000



Base

shea

rVb

(kN

)

AnalysisExperiment

300

200

100

0

minus100

minus200






Inde

xf

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H

0010005

0minus0005minus001

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900



AnalysisExperiment

S(k

Nm

)

Pseudotime t


0 1000 2000 3000 4000 5000

Error = 125

40

35

30

25

20

15

10

5

0






300

200

100

0

minus100

minus200


1st

floor

shea

r for

ceV

1(k

N)


(a)


300

200

100

0

minus100

minus200

minus300

2nd

floo

r she

ar fo

rceV2

(kN

)


(b)


AnalysisExperiment

150

100

50

0

minus50

minus100

minus150

3rd

floo

r she

ar fo

rceV3

(kN

)


(c)




21199081 (ii) parameter 119886



3 (v) parameter










1= 06





04

04

03

03

02

02

01

01

0 0

minus01

minus02

minus03

03

02

01

0 0

minus01

minus02

minus03

minus04

04

03

02

01

minus01

minus02

minus03

minus04

Inde

xf

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

Parameter-value Y

05 06 07 08 09

04030201 05 06 07 08 09

1 04030201 05 06 07 08 09 1

Parameter-value a1

00890020

minus0124

minus0415

00900020

minus0097

minus0302

00920018

minus0062

minus0211

0120

0033

minus0204

0108

0022

minus0066

minus0220

0107

0021

minus0055

minus0245

0199

0031

minus0050

minus0323

0304

0044

minus0050

minus0295


0114

0025

minus0078

minus0269

0103

0020

minus0068

minus0208

0140

0025

minus0046

minus0243

0092

0019

minus0066

minus0209

0099

0020

minus0058

minus0208

0130

0032

minus0059

minus0207minus0223

0099

0020

minus0058

Parameter-value Gun

04 06 08 1 12 14 16 18 2 22 24 04 06 08 1 12 14 16 18 2 22 24

0118

0023

minus0058

minus0177

0092

0019

minus0060

minus0234

0091

0020

minus0062

minus0260

0091

0020

minus0063

minus0276

0164

0038

minus0053

minus0188

0120

0029

minus0056

minus0202

0099

0020

minus0058

minus0208

0092

0018

minus0058

minus0211

Parameter-value Are

04030201 05 06 07 08 09 1 0403 05 06 07 08 09 111


0105

0021

minus0064

minus0194

0092

0021

minus0056

minus0217

0093

0024

minus0051

minus0229

0100

0026

minus0046

minus0237

0106

0020

minus0067

minus0207

0090

0020

minus0054

minus0232

0115

0021

minus0051

minus0266

0131

0025

minus0056

minus0286

005 006 007 008 009 01 02

minus0054




















= 10 119861ch = 09 119866plu = 10 119866plr = 11 1198901= 30

1198902= 10 120576cl = 0002 and 119891

1015840

119905= 005MPa


119898and 119860 red = 119908

21199081
















119870







4 Conclusions








References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














Φ4503Φ8 (bot)


Φ41003Φ8 (bot)


Φ4503Φ8 (bot)


Φ642672Φ19 (bot)


Φ61302Φ12 (bot)


Specimen 119891119888

119891119910

119891yw 119866119898

120591cr 120591119900

119891vm












119878119894= 119878119894minus1

+1

2(119877119894+ 119877119894minus1

) (119880119894minus 119880119894minus1

) (16)



119877119894minus1


119894minus1


error =

sum119899

119894=1

10038161003816100381610038161003816119878anal119894

minus 119878exp119894

10038161003816100381610038161003816

sum119899

119894=1

1003816100381610038161003816119878exp119894

1003816100381610038161003816

(17)





Specimen 1198911015840

1198981198911015840

119905 (wd)ini (wd)res 1205761015840

119898120576cl 120574 119886





1198902

119871119878

119871119870

119888119878

119888119870


Vb

80

40

0

minus40

minus80


= 120575H




006003

0minus003minus006

0 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800

Inde

xf

04

03

02

0

minus01

minus02

minus03

Pseudotime t

IDR=120575H







0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Error = 139

Pseudotime t



Vb

80

40

0

minus40

minus80

minusminus minus 0

= 120575Hminus006






006003

0minus003minus006

0 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800 900

900

Inde

xf

03

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H



0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)Error = 132

Pseudotime t




Base

shea

rVb

(kN

)

150

100

50

0

minus50

minus100


AnalysisExperiment



006003

0minus003minus006

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

Inde

xf

02

01

0

minus01

minus02

minus03

Pseudotime t

IDR=120575

H



0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 58






Base

shea

rVb

(kN

)

AnalysisExperiment

800

600

400

200

0

minus200

minus400

minus600



Inde

xf

02

01

0

minus01

minus02

minus03

minus04

Pseudotime t

IDR=120575

H0015

000750

minus00075minus0015

0 500 1000 1500 2000 2500

0 500 1000 1500 2000 2500







AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 56

70

60

50

40

30

20

10

00 1000 2000 3000 4000 5000



Base

shea

rVb

(kN

)

AnalysisExperiment

300

200

100

0

minus100

minus200






Inde

xf

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H

0010005

0minus0005minus001

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900



AnalysisExperiment

S(k

Nm

)

Pseudotime t


0 1000 2000 3000 4000 5000

Error = 125

40

35

30

25

20

15

10

5

0






300

200

100

0

minus100

minus200


1st

floor

shea

r for

ceV

1(k

N)


(a)


300

200

100

0

minus100

minus200

minus300

2nd

floo

r she

ar fo

rceV2

(kN

)


(b)


AnalysisExperiment

150

100

50

0

minus50

minus100

minus150

3rd

floo

r she

ar fo

rceV3

(kN

)


(c)




21199081 (ii) parameter 119886



3 (v) parameter










1= 06





04

04

03

03

02

02

01

01

0 0

minus01

minus02

minus03

03

02

01

0 0

minus01

minus02

minus03

minus04

04

03

02

01

minus01

minus02

minus03

minus04

Inde

xf

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

Parameter-value Y

05 06 07 08 09

04030201 05 06 07 08 09

1 04030201 05 06 07 08 09 1

Parameter-value a1

00890020

minus0124

minus0415

00900020

minus0097

minus0302

00920018

minus0062

minus0211

0120

0033

minus0204

0108

0022

minus0066

minus0220

0107

0021

minus0055

minus0245

0199

0031

minus0050

minus0323

0304

0044

minus0050

minus0295


0114

0025

minus0078

minus0269

0103

0020

minus0068

minus0208

0140

0025

minus0046

minus0243

0092

0019

minus0066

minus0209

0099

0020

minus0058

minus0208

0130

0032

minus0059

minus0207minus0223

0099

0020

minus0058

Parameter-value Gun

04 06 08 1 12 14 16 18 2 22 24 04 06 08 1 12 14 16 18 2 22 24

0118

0023

minus0058

minus0177

0092

0019

minus0060

minus0234

0091

0020

minus0062

minus0260

0091

0020

minus0063

minus0276

0164

0038

minus0053

minus0188

0120

0029

minus0056

minus0202

0099

0020

minus0058

minus0208

0092

0018

minus0058

minus0211

Parameter-value Are

04030201 05 06 07 08 09 1 0403 05 06 07 08 09 111


0105

0021

minus0064

minus0194

0092

0021

minus0056

minus0217

0093

0024

minus0051

minus0229

0100

0026

minus0046

minus0237

0106

0020

minus0067

minus0207

0090

0020

minus0054

minus0232

0115

0021

minus0051

minus0266

0131

0025

minus0056

minus0286

005 006 007 008 009 01 02

minus0054




















= 10 119861ch = 09 119866plu = 10 119866plr = 11 1198901= 30

1198902= 10 120576cl = 0002 and 119891

1015840

119905= 005MPa


119898and 119860 red = 119908

21199081
















119870







4 Conclusions








References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Specimen 1198911015840

1198981198911015840

119905 (wd)ini (wd)res 1205761015840

119898120576cl 120574 119886





1198902

119871119878

119871119870

119888119878

119888119870


Vb

80

40

0

minus40

minus80


= 120575H




006003

0minus003minus006

0 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800

Inde

xf

04

03

02

0

minus01

minus02

minus03

Pseudotime t

IDR=120575H







0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Error = 139

Pseudotime t



Vb

80

40

0

minus40

minus80

minusminus minus 0

= 120575Hminus006






006003

0minus003minus006

0 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800 900

900

Inde

xf

03

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H



0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)Error = 132

Pseudotime t




Base

shea

rVb

(kN

)

150

100

50

0

minus50

minus100


AnalysisExperiment



006003

0minus003minus006

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

Inde

xf

02

01

0

minus01

minus02

minus03

Pseudotime t

IDR=120575

H



0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 58






Base

shea

rVb

(kN

)

AnalysisExperiment

800

600

400

200

0

minus200

minus400

minus600



Inde

xf

02

01

0

minus01

minus02

minus03

minus04

Pseudotime t

IDR=120575

H0015

000750

minus00075minus0015

0 500 1000 1500 2000 2500

0 500 1000 1500 2000 2500







AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 56

70

60

50

40

30

20

10

00 1000 2000 3000 4000 5000



Base

shea

rVb

(kN

)

AnalysisExperiment

300

200

100

0

minus100

minus200






Inde

xf

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H

0010005

0minus0005minus001

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900



AnalysisExperiment

S(k

Nm

)

Pseudotime t


0 1000 2000 3000 4000 5000

Error = 125

40

35

30

25

20

15

10

5

0






300

200

100

0

minus100

minus200


1st

floor

shea

r for

ceV

1(k

N)


(a)


300

200

100

0

minus100

minus200

minus300

2nd

floo

r she

ar fo

rceV2

(kN

)


(b)


AnalysisExperiment

150

100

50

0

minus50

minus100

minus150

3rd

floo

r she

ar fo

rceV3

(kN

)


(c)




21199081 (ii) parameter 119886



3 (v) parameter










1= 06





04

04

03

03

02

02

01

01

0 0

minus01

minus02

minus03

03

02

01

0 0

minus01

minus02

minus03

minus04

04

03

02

01

minus01

minus02

minus03

minus04

Inde

xf

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

Parameter-value Y

05 06 07 08 09

04030201 05 06 07 08 09

1 04030201 05 06 07 08 09 1

Parameter-value a1

00890020

minus0124

minus0415

00900020

minus0097

minus0302

00920018

minus0062

minus0211

0120

0033

minus0204

0108

0022

minus0066

minus0220

0107

0021

minus0055

minus0245

0199

0031

minus0050

minus0323

0304

0044

minus0050

minus0295


0114

0025

minus0078

minus0269

0103

0020

minus0068

minus0208

0140

0025

minus0046

minus0243

0092

0019

minus0066

minus0209

0099

0020

minus0058

minus0208

0130

0032

minus0059

minus0207minus0223

0099

0020

minus0058

Parameter-value Gun

04 06 08 1 12 14 16 18 2 22 24 04 06 08 1 12 14 16 18 2 22 24

0118

0023

minus0058

minus0177

0092

0019

minus0060

minus0234

0091

0020

minus0062

minus0260

0091

0020

minus0063

minus0276

0164

0038

minus0053

minus0188

0120

0029

minus0056

minus0202

0099

0020

minus0058

minus0208

0092

0018

minus0058

minus0211

Parameter-value Are

04030201 05 06 07 08 09 1 0403 05 06 07 08 09 111


0105

0021

minus0064

minus0194

0092

0021

minus0056

minus0217

0093

0024

minus0051

minus0229

0100

0026

minus0046

minus0237

0106

0020

minus0067

minus0207

0090

0020

minus0054

minus0232

0115

0021

minus0051

minus0266

0131

0025

minus0056

minus0286

005 006 007 008 009 01 02

minus0054




















= 10 119861ch = 09 119866plu = 10 119866plr = 11 1198901= 30

1198902= 10 120576cl = 0002 and 119891

1015840

119905= 005MPa


119898and 119860 red = 119908

21199081
















119870







4 Conclusions








References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Error = 139

Pseudotime t



Vb

80

40

0

minus40

minus80

minusminus minus 0

= 120575Hminus006






006003

0minus003minus006

0 100 200 300 400 500 600 700 800

0 100 200 300 400 500 600 700 800 900

900

Inde

xf

03

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H



0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)Error = 132

Pseudotime t




Base

shea

rVb

(kN

)

150

100

50

0

minus50

minus100


AnalysisExperiment



006003

0minus003minus006

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

Inde

xf

02

01

0

minus01

minus02

minus03

Pseudotime t

IDR=120575

H



0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 58






Base

shea

rVb

(kN

)

AnalysisExperiment

800

600

400

200

0

minus200

minus400

minus600



Inde

xf

02

01

0

minus01

minus02

minus03

minus04

Pseudotime t

IDR=120575

H0015

000750

minus00075minus0015

0 500 1000 1500 2000 2500

0 500 1000 1500 2000 2500







AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 56

70

60

50

40

30

20

10

00 1000 2000 3000 4000 5000



Base

shea

rVb

(kN

)

AnalysisExperiment

300

200

100

0

minus100

minus200






Inde

xf

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H

0010005

0minus0005minus001

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900



AnalysisExperiment

S(k

Nm

)

Pseudotime t


0 1000 2000 3000 4000 5000

Error = 125

40

35

30

25

20

15

10

5

0






300

200

100

0

minus100

minus200


1st

floor

shea

r for

ceV

1(k

N)


(a)


300

200

100

0

minus100

minus200

minus300

2nd

floo

r she

ar fo

rceV2

(kN

)


(b)


AnalysisExperiment

150

100

50

0

minus50

minus100

minus150

3rd

floo

r she

ar fo

rceV3

(kN

)


(c)




21199081 (ii) parameter 119886



3 (v) parameter










1= 06





04

04

03

03

02

02

01

01

0 0

minus01

minus02

minus03

03

02

01

0 0

minus01

minus02

minus03

minus04

04

03

02

01

minus01

minus02

minus03

minus04

Inde

xf

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

Parameter-value Y

05 06 07 08 09

04030201 05 06 07 08 09

1 04030201 05 06 07 08 09 1

Parameter-value a1

00890020

minus0124

minus0415

00900020

minus0097

minus0302

00920018

minus0062

minus0211

0120

0033

minus0204

0108

0022

minus0066

minus0220

0107

0021

minus0055

minus0245

0199

0031

minus0050

minus0323

0304

0044

minus0050

minus0295


0114

0025

minus0078

minus0269

0103

0020

minus0068

minus0208

0140

0025

minus0046

minus0243

0092

0019

minus0066

minus0209

0099

0020

minus0058

minus0208

0130

0032

minus0059

minus0207minus0223

0099

0020

minus0058

Parameter-value Gun

04 06 08 1 12 14 16 18 2 22 24 04 06 08 1 12 14 16 18 2 22 24

0118

0023

minus0058

minus0177

0092

0019

minus0060

minus0234

0091

0020

minus0062

minus0260

0091

0020

minus0063

minus0276

0164

0038

minus0053

minus0188

0120

0029

minus0056

minus0202

0099

0020

minus0058

minus0208

0092

0018

minus0058

minus0211

Parameter-value Are

04030201 05 06 07 08 09 1 0403 05 06 07 08 09 111


0105

0021

minus0064

minus0194

0092

0021

minus0056

minus0217

0093

0024

minus0051

minus0229

0100

0026

minus0046

minus0237

0106

0020

minus0067

minus0207

0090

0020

minus0054

minus0232

0115

0021

minus0051

minus0266

0131

0025

minus0056

minus0286

005 006 007 008 009 01 02

minus0054




















= 10 119861ch = 09 119866plu = 10 119866plr = 11 1198901= 30

1198902= 10 120576cl = 0002 and 119891

1015840

119905= 005MPa


119898and 119860 red = 119908

21199081
















119870







4 Conclusions








References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










006003

0minus003minus006

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900

Inde

xf

02

01

0

minus01

minus02

minus03

Pseudotime t

IDR=120575

H



0 500 1000 1500 2000 2500 30000

5

10

15

20

25

30

35

40

AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 58






Base

shea

rVb

(kN

)

AnalysisExperiment

800

600

400

200

0

minus200

minus400

minus600



Inde

xf

02

01

0

minus01

minus02

minus03

minus04

Pseudotime t

IDR=120575

H0015

000750

minus00075minus0015

0 500 1000 1500 2000 2500

0 500 1000 1500 2000 2500







AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 56

70

60

50

40

30

20

10

00 1000 2000 3000 4000 5000



Base

shea

rVb

(kN

)

AnalysisExperiment

300

200

100

0

minus100

minus200






Inde

xf

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H

0010005

0minus0005minus001

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900



AnalysisExperiment

S(k

Nm

)

Pseudotime t


0 1000 2000 3000 4000 5000

Error = 125

40

35

30

25

20

15

10

5

0






300

200

100

0

minus100

minus200


1st

floor

shea

r for

ceV

1(k

N)


(a)


300

200

100

0

minus100

minus200

minus300

2nd

floo

r she

ar fo

rceV2

(kN

)


(b)


AnalysisExperiment

150

100

50

0

minus50

minus100

minus150

3rd

floo

r she

ar fo

rceV3

(kN

)


(c)




21199081 (ii) parameter 119886



3 (v) parameter










1= 06





04

04

03

03

02

02

01

01

0 0

minus01

minus02

minus03

03

02

01

0 0

minus01

minus02

minus03

minus04

04

03

02

01

minus01

minus02

minus03

minus04

Inde

xf

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

Parameter-value Y

05 06 07 08 09

04030201 05 06 07 08 09

1 04030201 05 06 07 08 09 1

Parameter-value a1

00890020

minus0124

minus0415

00900020

minus0097

minus0302

00920018

minus0062

minus0211

0120

0033

minus0204

0108

0022

minus0066

minus0220

0107

0021

minus0055

minus0245

0199

0031

minus0050

minus0323

0304

0044

minus0050

minus0295


0114

0025

minus0078

minus0269

0103

0020

minus0068

minus0208

0140

0025

minus0046

minus0243

0092

0019

minus0066

minus0209

0099

0020

minus0058

minus0208

0130

0032

minus0059

minus0207minus0223

0099

0020

minus0058

Parameter-value Gun

04 06 08 1 12 14 16 18 2 22 24 04 06 08 1 12 14 16 18 2 22 24

0118

0023

minus0058

minus0177

0092

0019

minus0060

minus0234

0091

0020

minus0062

minus0260

0091

0020

minus0063

minus0276

0164

0038

minus0053

minus0188

0120

0029

minus0056

minus0202

0099

0020

minus0058

minus0208

0092

0018

minus0058

minus0211

Parameter-value Are

04030201 05 06 07 08 09 1 0403 05 06 07 08 09 111


0105

0021

minus0064

minus0194

0092

0021

minus0056

minus0217

0093

0024

minus0051

minus0229

0100

0026

minus0046

minus0237

0106

0020

minus0067

minus0207

0090

0020

minus0054

minus0232

0115

0021

minus0051

minus0266

0131

0025

minus0056

minus0286

005 006 007 008 009 01 02

minus0054




















= 10 119861ch = 09 119866plu = 10 119866plr = 11 1198901= 30

1198902= 10 120576cl = 0002 and 119891

1015840

119905= 005MPa


119898and 119860 red = 119908

21199081
















119870







4 Conclusions








References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










AnalysisExperiment

S(k

Nm

)

Pseudotime t


Error = 56

70

60

50

40

30

20

10

00 1000 2000 3000 4000 5000



Base

shea

rVb

(kN

)

AnalysisExperiment

300

200

100

0

minus100

minus200






Inde

xf

02

01

0

minus01

minus02

Pseudotime t

IDR=120575

H

0010005

0minus0005minus001

0 100 200 300 400 500 600 700 800 900

0 100 200 300 400 500 600 700 800 900



AnalysisExperiment

S(k

Nm

)

Pseudotime t


0 1000 2000 3000 4000 5000

Error = 125

40

35

30

25

20

15

10

5

0






300

200

100

0

minus100

minus200


1st

floor

shea

r for

ceV

1(k

N)


(a)


300

200

100

0

minus100

minus200

minus300

2nd

floo

r she

ar fo

rceV2

(kN

)


(b)


AnalysisExperiment

150

100

50

0

minus50

minus100

minus150

3rd

floo

r she

ar fo

rceV3

(kN

)


(c)




21199081 (ii) parameter 119886



3 (v) parameter










1= 06





04

04

03

03

02

02

01

01

0 0

minus01

minus02

minus03

03

02

01

0 0

minus01

minus02

minus03

minus04

04

03

02

01

minus01

minus02

minus03

minus04

Inde

xf

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

Parameter-value Y

05 06 07 08 09

04030201 05 06 07 08 09

1 04030201 05 06 07 08 09 1

Parameter-value a1

00890020

minus0124

minus0415

00900020

minus0097

minus0302

00920018

minus0062

minus0211

0120

0033

minus0204

0108

0022

minus0066

minus0220

0107

0021

minus0055

minus0245

0199

0031

minus0050

minus0323

0304

0044

minus0050

minus0295


0114

0025

minus0078

minus0269

0103

0020

minus0068

minus0208

0140

0025

minus0046

minus0243

0092

0019

minus0066

minus0209

0099

0020

minus0058

minus0208

0130

0032

minus0059

minus0207minus0223

0099

0020

minus0058

Parameter-value Gun

04 06 08 1 12 14 16 18 2 22 24 04 06 08 1 12 14 16 18 2 22 24

0118

0023

minus0058

minus0177

0092

0019

minus0060

minus0234

0091

0020

minus0062

minus0260

0091

0020

minus0063

minus0276

0164

0038

minus0053

minus0188

0120

0029

minus0056

minus0202

0099

0020

minus0058

minus0208

0092

0018

minus0058

minus0211

Parameter-value Are

04030201 05 06 07 08 09 1 0403 05 06 07 08 09 111


0105

0021

minus0064

minus0194

0092

0021

minus0056

minus0217

0093

0024

minus0051

minus0229

0100

0026

minus0046

minus0237

0106

0020

minus0067

minus0207

0090

0020

minus0054

minus0232

0115

0021

minus0051

minus0266

0131

0025

minus0056

minus0286

005 006 007 008 009 01 02

minus0054




















= 10 119861ch = 09 119866plu = 10 119866plr = 11 1198901= 30

1198902= 10 120576cl = 0002 and 119891

1015840

119905= 005MPa


119898and 119860 red = 119908

21199081
















119870







4 Conclusions








References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










300

200

100

0

minus100

minus200


1st

floor

shea

r for

ceV

1(k

N)


(a)


300

200

100

0

minus100

minus200

minus300

2nd

floo

r she

ar fo

rceV2

(kN

)


(b)


AnalysisExperiment

150

100

50

0

minus50

minus100

minus150

3rd

floo

r she

ar fo

rceV3

(kN

)


(c)




21199081 (ii) parameter 119886



3 (v) parameter










1= 06





04

04

03

03

02

02

01

01

0 0

minus01

minus02

minus03

03

02

01

0 0

minus01

minus02

minus03

minus04

04

03

02

01

minus01

minus02

minus03

minus04

Inde

xf

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

Parameter-value Y

05 06 07 08 09

04030201 05 06 07 08 09

1 04030201 05 06 07 08 09 1

Parameter-value a1

00890020

minus0124

minus0415

00900020

minus0097

minus0302

00920018

minus0062

minus0211

0120

0033

minus0204

0108

0022

minus0066

minus0220

0107

0021

minus0055

minus0245

0199

0031

minus0050

minus0323

0304

0044

minus0050

minus0295


0114

0025

minus0078

minus0269

0103

0020

minus0068

minus0208

0140

0025

minus0046

minus0243

0092

0019

minus0066

minus0209

0099

0020

minus0058

minus0208

0130

0032

minus0059

minus0207minus0223

0099

0020

minus0058

Parameter-value Gun

04 06 08 1 12 14 16 18 2 22 24 04 06 08 1 12 14 16 18 2 22 24

0118

0023

minus0058

minus0177

0092

0019

minus0060

minus0234

0091

0020

minus0062

minus0260

0091

0020

minus0063

minus0276

0164

0038

minus0053

minus0188

0120

0029

minus0056

minus0202

0099

0020

minus0058

minus0208

0092

0018

minus0058

minus0211

Parameter-value Are

04030201 05 06 07 08 09 1 0403 05 06 07 08 09 111


0105

0021

minus0064

minus0194

0092

0021

minus0056

minus0217

0093

0024

minus0051

minus0229

0100

0026

minus0046

minus0237

0106

0020

minus0067

minus0207

0090

0020

minus0054

minus0232

0115

0021

minus0051

minus0266

0131

0025

minus0056

minus0286

005 006 007 008 009 01 02

minus0054




















= 10 119861ch = 09 119866plu = 10 119866plr = 11 1198901= 30

1198902= 10 120576cl = 0002 and 119891

1015840

119905= 005MPa


119898and 119860 red = 119908

21199081
















119870







4 Conclusions








References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










04

04

03

03

02

02

01

01

0 0

minus01

minus02

minus03

03

02

01

0 0

minus01

minus02

minus03

minus04

04

03

02

01

minus01

minus02

minus03

minus04

Inde

xf

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

0

03

02

01

minus01

minus02

minus03

0

03

02

01

minus01

minus02

minus03

Inde

xf

Parameter-value Y

05 06 07 08 09

04030201 05 06 07 08 09

1 04030201 05 06 07 08 09 1

Parameter-value a1

00890020

minus0124

minus0415

00900020

minus0097

minus0302

00920018

minus0062

minus0211

0120

0033

minus0204

0108

0022

minus0066

minus0220

0107

0021

minus0055

minus0245

0199

0031

minus0050

minus0323

0304

0044

minus0050

minus0295


0114

0025

minus0078

minus0269

0103

0020

minus0068

minus0208

0140

0025

minus0046

minus0243

0092

0019

minus0066

minus0209

0099

0020

minus0058

minus0208

0130

0032

minus0059

minus0207minus0223

0099

0020

minus0058

Parameter-value Gun

04 06 08 1 12 14 16 18 2 22 24 04 06 08 1 12 14 16 18 2 22 24

0118

0023

minus0058

minus0177

0092

0019

minus0060

minus0234

0091

0020

minus0062

minus0260

0091

0020

minus0063

minus0276

0164

0038

minus0053

minus0188

0120

0029

minus0056

minus0202

0099

0020

minus0058

minus0208

0092

0018

minus0058

minus0211

Parameter-value Are

04030201 05 06 07 08 09 1 0403 05 06 07 08 09 111


0105

0021

minus0064

minus0194

0092

0021

minus0056

minus0217

0093

0024

minus0051

minus0229

0100

0026

minus0046

minus0237

0106

0020

minus0067

minus0207

0090

0020

minus0054

minus0232

0115

0021

minus0051

minus0266

0131

0025

minus0056

minus0286

005 006 007 008 009 01 02

minus0054




















= 10 119861ch = 09 119866plu = 10 119866plr = 11 1198901= 30

1198902= 10 120576cl = 0002 and 119891

1015840

119905= 005MPa


119898and 119860 red = 119908

21199081
















119870







4 Conclusions








References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















= 10 119861ch = 09 119866plu = 10 119866plr = 11 1198901= 30

1198902= 10 120576cl = 0002 and 119891

1015840

119905= 005MPa


119898and 119860 red = 119908

21199081
















119870







4 Conclusions








References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article Analytical Modeling of Masonry Infilled ...

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