EvaluationoftheAmericanApproachforDetecting PlanIrregularitydownloads.hindawi.com/journals/ace/2019/2861093.pdf · 2019. 7. 30. · buildings, as follows: (i) Torsional irregularity:

Research ArticleEvaluation of the American Approach for DetectingPlan Irregularity

V Alecci 1 M De Stefano1 S Galassi1 M Lapi2 and M Orlando2

1Department of Architecture University of Florence Piazza Brunelleschi 6 50121 Florence Italy2Department of Civil and Environmental Engineering University of Florence Via di Santa Marta 3 50139 Florence Italy

Correspondence should be addressed to V Alecci valerioalecciunifiit

Received 31 October 2018 Revised 12 January 2019 Accepted 6 February 2019 Published 3 March 2019

Academic Editor Melina Bosco

Copyright copy 2019 V Alecci et al +is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

+e European seismic code 8 (Eurocode 8) classifies buildings as planwise regular according to four criteria which are mostlyqualitative and a fifth one which is based on parameters such as stiffness eccentricity and torsional radius that can be onlyapproximately defined formultistory buildings+erefore such plan-regularity criteria are in need of improvement ASCE seismiccode according to a different criterion considers plan (or ldquotorsionalrdquo) irregularity in a building when the maximum story drift atone end of the structure exceeds more than 12 times the average of the story drifts at the two ends of the structure underequivalent static analysis Nevertheless both the ASCE approach and the threshold value of 12 need to be supported by adequatebackground studies based also on nonlinear seismic analysis In this paper a numerical analysis is carried out by studying theseismic response of an existing RC school building taken as the reference structure Linear static analysis is developed byprogressively shifting the centre of mass until the ratio between the maximum lateral displacement of the floor at the level isconsidered and the average of the horizontal displacements at extreme positions of the floor at the same level matches and evenexceeds the value of 12+en nonlinear dynamic analyses are carried out to check the corresponding level of response irregularityin terms of uneven plan distribution of deformation and displacement demands and performance parameters +e abovecomparison leads to check the suitability of the ASCE approach and in particular of the threshold value of 12 for identifyingbuildings plan irregularity

1 Introduction

In-plan irregularity is very common in existing buildingsand it is one of the most frequent sources of severe damageduring earthquakes [1] In 1985 during the earthquake ofMexico City 42 of damaged or collapsed structures werecorner buildings Furthermore many buildings failed intorsion due to the asymmetric layout of masonry infills [2]+e need to define adequate provisions accounting for thetorsional effect due to structural asymmetry was reconfirmedby this event [3]

During the 1970sndash1980s the equivalent static analysisrepresented themost commonmethod for computing seismicloads Such a method applied to asymmetric structuresunderestimates the actions on flexible side elements as it doesnot take into account the dynamic amplification of the

torsional response For this reason researchers suggested theintroduction of a design eccentricity in order to provide atorsional moment corresponding to each story of thebuilding In the last decades several studies on the designeccentricity were carried out [3ndash12] Later spatial models andmodal analysis became widely used by designers +us theelastic response determination of in-plan irregular buildingsturned easier

In recent years researchers focused on the inelasticresponse of in-plan irregular buildings +e response ofasymmetric buildings was investigated by varying severalparameters like centre of mass (CM) eccentricity [13]uneven distribution of concrete strength [14 15] torsionalstiffness and periods of vibration [16] Furthermore severalstudies were developed focusing on the application ofnonlinear static analysis to in-plan irregular buildings

HindawiAdvances in Civil EngineeringVolume 2019 Article ID 2861093 10 pageshttpsdoiorg10115520192861093

[17ndash22] +en an important contribution that deals withtorsion issue and plan regularity of building structures isprovided by Anagnostopoulos et al [23]

+is paper is focused on the evaluation of the ASCEtorsional provision (ASCE Standard 7-10) [24] +e re-sponse of a case study building is investigated in order toevaluate the torsional irregularity provided by the code andthe corresponding uneven distribution of inelastic demandwhich is detected using the nonlinear dynamic analysismethod

2 Torsional Provisions

+e previous generation of seismic codes was providingdesign eccentricities for equivalent static analysis as follows

ed α middot e0 + β middot b (1)

where ed is the design eccentricity e0 is the distance betweenthe centre of mass (CM) and the centre of rigidity (CR)measured orthogonally to the loading direction b is thebuilding dimension perpendicular to the loading direction αis a coefficient accounting for dynamic amplification of thetorsional response and β is a coefficient accounting foraleatoric position of the CM

In Table 1 coefficients α and β are provided according toEurocode 8 1993 (EC8-93) [25] National Building Code ofCanada 1995 (NBCC-95) [26] and ASCE Standard 7-10(ASCE 7-10) [24] where Ax is the amplification factorprovided by ASCE 7-10 (defined in the following) and e2 isthe additional eccentricity provided by EC8-93 equal to thesmaller of the following values

e2 min

01 middot (L + B) middot

10 middot e0

L

1113970

le 01 middot (L + B)

12 middot e0

middot ℓ2s minus e20 minus r

2+

ℓ2s minus e20 minus r2( 11138572

+ 4 middot e20 middot r21113969

1113876 1113877

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(2)

where ℓs is the radius of gyration of the floor mass in-plan(square root of the ratio of the polar moment of inertia of thefloor mass in-plan (a) with respect to the centre of mass ofthe floor to (b) the floor mass (b)) and r is the square root ofthe ratio of the torsional stiffness to the lateral stiffness in theloading direction (ldquotorsional radiusrdquo)

In current code provisions such as Eurocode 8 2004(EC8-04) [27] and National Building Code of Canada 2010(NBCC-10) [28] in the case of torsional irregularity only a3D dynamic analysis is allowed Even when adopting aspatial model and the CQC modal combination the acci-dental eccentricity is considered accounting for the randomposition of CM and the design eccentricity is computed bythe following equation

ed e0 + β middot b (3)

However criteria for assessing in-plan irregularity arestill very important indeed it affects the choice of themethod of analysis and the definition of the behaviourfactor

Qualitatively in-plan irregularity is due to asymmetricdistributions of mass and stiffness but quantitatively adefinition universally shared does not exist Eurocode 8 2004(EC8-04) provides a list of conditions to classify a building asregular in-plan

(i) With respect to the lateral stiffness and mass dis-tribution the building structure shall be approxi-mately symmetrical in plan with respect to twoorthogonal axes

(ii) +e plan configuration shall be compact ie eachfloor shall be delimited by a polygonal convex line Ifin-plan setbacks (ie reentrant corners or edgerecesses) exist regularity in plan may still be con-sidered as being satisfied provided that these set-backs do not affect the floor in-plan stiffness andthat for each setback the area between the outline ofthe floor and a convex polygonal line enveloping thefloor does not exceed 5 of the floor area

(iii) +e in-plan stiffness of the floors shall be sufficientlylarge in comparison with the lateral stiffness of thevertical structural elements so that the deformationof the floor shall have a small effect on the distri-bution of the forces among the vertical structuralelements In this respect the L C H I and X planshapes should be carefully examined notably asconcerns the stiffness of the lateral branches whichshould be comparable to that of the central part inorder to satisfy the rigid diaphragm condition +eapplication of this paragraph should be consideredfor the global behaviour of the building

(iv) +e slenderness λ LmaxLmin of the building in-plan shall not be higher than 4 where Lmax and Lminare respectively the larger in-plan and smallerdimension of the building measured in two or-thogonal directions

(v) At each level and for each direction of analysis thestructural eccentricity e0 and the torsional radius r

shall conform to the following conditions

eo le 030 middot r

rge ℓs(4)

+e first four criteria are almost qualitative while thefifth one if strictly applied is valid only for single-storybuildings For multistory buildings only approximate def-initions of the centre of stiffness and the torsional radius arepossible [27] Similarly ASCE Standard 7-10 [24] provides a

Table 1 Design eccentricity coefficients

Analyzed elements Flexible-side elements Stiff-sideelements

Code α β α βEC8-93 10 + e2e0 005 10 minus005NBCC-95 15 010 05 minus010ASCE 7-10 10 005 middot Ax 10 minus005 middot Ax

2 Advances in Civil Engineering

list of conditions to detect horizontal irregularity inbuildings as follows

(i) Torsional irregularity it is dened to exist if themaximum story drift computed including accidentaltorsion with Ax 10 at one end of the structuretransverse to an axis is more than 12 times theaverage of the story drifts at the two ends of thestructure Torsional irregularity (equation (5)) re-quirements apply only to structures in which thediaphragms are rigid or semirigid

δmax ge 12 middot δavg (5)

where δavg (δA + δB)2 is the average deectiondetermined by an elastic analysis (Figure 1) and1ltAx [δmax12 middot δavg]2 le 3 is the amplicationfactor of the accidental torsional moment

(ii) Extreme torsional irregularity it is dened to exist ifthe maximum story drift computed including ac-cidental torsion with Ax 10 at one end of thestructure transverse to an axis is more than 14 timesthe average of the story drifts at the two ends of thestructure Extreme torsional irregularity re-quirements (equation (6)) apply only to structures inwhich the diaphragms are rigid or semirigid


(iii) Reentrant corner irregularity it is dened to existwhere both plan projections of the structure beyonda reentrant corner are greater than 15 of the plandimension of the structure in the given direction

(iv) Diaphragm discontinuity irregularity it is denedto exist where there is a diaphragm with an abruptdiscontinuity or variation in stiness including onehaving a cut-out or open area greater than 50 ofthe gross enclosed diaphragm area or a change ineective diaphragm stiness of more than 50 fromone story to the next

(v) Out-of-plane oset irregularity it is dened to existwhere there is a discontinuity in a lateral force-resistance path such as an out-of-plane oset of atleast one of the vertical elements

(vi) Nonparallel system irregularity it is dened to existwhere vertical lateral force-resisting elements arenot parallel to the major orthogonal axes of theseismic force-resisting system

e ASCE Code (ASCE 7-10) [24] provides a simplerapproach for detecting torsional irregularity Such a methodinvolves directly the structural response of the building andit does not require the knowledge of specic characteristics(that are mandatory in Eurocode 8) such as the torsionalradius that can be only approximately dened for multistorybuildings e criterion provides the implementation of alinear static analysis taking into account the accidental ec-centricity (β 5) As shown previously when the

maximum story drift is more than 12 times the average driftthe torsional irregularity is detected e use of this elasticindex (ie the ratio between the maximum and the averageelastic drift) appears to be very simple and eective how-ever some further researches are needed Both the ASCEapproach and the threshold value of 12 must be supportedby adequate background studies

With this aim in this paper a numerical analysis iscarried out by studying the seismic response of an existingRC school building As provided by ASCE 7-10 staticelastic analyses are performed varying step by step the CMposition and checking the ratio between the maximum andthe average lateral displacements (δmaxδavg) Lastly non-linear dynamic analyses are carried out in order to evaluatethe corresponding level of response irregularity in terms ofuneven distribution of inelastic demand

3 Case Study

e school building under analysis is about 40 years of ageand it is situated on a at ground in theMunicipality of Prato(PO) Italy It consists of two independent blocks the schooland the gym

e school block has been chosen as the case study forthe seismic analyses because it is made of a RC framedstructure (conversely the gym block has a precast structure)

e school block (Figure 2) has an elongated rectangularplan approximately 49 by 13meters and it is a three-storybuilding above the ground level e oor-to-oor height is330meters At the ground oor along the shorter side of theplan there is a portico that covers the rst span of the framesand that provides access to the entrance hall After theentrance hall a central corridor leads to the classes andocentces along the two long sides of the plan is distributionpattern is repeated almost unchanged at the upper oors aswell e external cladding in precast panels and the in-terior walls which divide the classes are made of hollowbricks and follow the frame scheme and they also haveribbon windows outwards

e building structure (Figure 3) is entirely made of RCcolumns and beams which form only three plane moment-

δA

δB

Figure 1 Determination of the average deection δavg adaptedfrom [18]

Advances in Civil Engineering 3

resisting frames (MRF) running along the longitudinaldirection In the transversal direction there are not MRFexcepting for the frames at the ends of the structure +efloor slabs can be considered as the rigid diaphragms

+e structural symmetry of the plan fails in particular atthe ground floor where due to the presence of a larger roomdevoted to refectory in the central longitudinal frame thesecond column is missing +erefore the frame beam has aspan doubled and supports the column of the upper floor atmidspan and the rectangular beam cross section is 25 by90 cm while the others are flat beams with a cross section of80 by 22 cm Cross section 25 by 90 cm was also used for thecorresponding beams at the two upper floors +e storyfloors are made of casted-in-place one-way hollow blockslabs

Instead the rafters and the edge beams supporting theattic floor have a section of 12 by 40 cm and form a hip roof+e covering is made of insulated sandwich panels +e atticfloor is not serviceable

+e columns have three different cross sections 25 by30 cm 25 by 40 cm and 25 by 55 cm In the two longi-tudinal edge frames the longer section side is arrangedorthogonally to the frames while in the central frame thelonger side follows the frame direction In Table 2 thecharacteristics of the column sections at the ground floorare provided

+e concrete compressive strength was assumed to beequal to fc 25MPa and the steel yield stress was assumed tobe fy 430MPa

A finite element structural model has been created andnumerical analyses have been carried out using theSAP2000 software [29] In addition to the dead weight ofthe structural elements the following loads have beenconsidered the weights of the story and roof floors (G1)the permanent loads (G2) such as the partition walls thescreed and the tiles and the live loads (Q) In the fol-lowing the seismic combination (7) for the ultimate limitstates is provided according to the Italian Code (NTC2018) [30]

E + G1 + G2 + 06 middot Q (7)

where E is the seismic action along the considered direction+e seismic base shear Fh has been computed in accordancewith equation (8) provided by the NTC 2018

Fh Sd T1( 1113857 middotW

gmiddot λ (8)

where Sd(T1) is the design spectral acceleration calculatedaccording to the fundamental period T1 of the building (as inthis case the elastic response spectrum has been adoptedand Sd(T1) is equal to Se(T1)) T1 is the fundamental periodof the building W is the effective seismic weight g is thegravity acceleration and λ factor equal to 085 in the case of amultistory building (with the story number greater than orequal to 3)

+e elastic response spectrum Se(T) is used to calculatethe seismic input for SLV verifications assuming a buildinglife of 50 years and importance of class III (Cu 15) hasbeen obtained considering the building site (Figure 4)

In the structural model rigid diaphragms have beenconsidered at each building floor so as to easily define theposition centre of masses (CM)

Firstly the model has been seismically analyzed by theequivalent static method [31] by applying the horizontalaction at the CM of each story floor +e seismic forcecomputed according to the formulae of the Italian NTC 2018[30] has been assumed acting in the direction of the shorterbuilding side (y direction) where only the two edge framesexist in order to catch the greatest displacements

+en nonlinear dynamic analyses have been performedusing a natural earthquake accelerogram (Figure 5)

+e adopted accelerogram is the record 147ya of Friuli(aftershock) earthquake happened in 1976 September 15th+e recorded magnitude (Mw) is 6 and the peak groundacceleration (PGA) is equal to 232ms2

+is accelerogram was chosen because it is spectrumcompatible with the adopted elastic response spectrum Inthe following a comparison between the elastic responsespectrum from the Italian NTC 2018 and the 147ya spectrumis proposed (Figure 6)

To assess the seismic performance of a building througha nonlinear dynamic analysis the Italian NTC 2018 requiresat least three accelerograms +erefore the choice of usingonly one accelerogram could appear inadequate Actuallysuch request aims to reduce the uncertainties of the analysisand more in general it aims at increasing the structuralsafety Since the assessment of the structural safety of thebuilding is out of the purpose of this paper that deals

(a) (b) (c)

Figure 2 School building (a) frontal elevation where the portico and the entrance hall are present (b) and (c) longitudinal elevations


instead with the influence of the in-plan irregularity on thestructural inelastic response only one accelerogram hasbeen considered It is evident that also the seismic actionboth in terms of intensity and frequency content has aninfluence on the response of in-plan irregular buildingshowever the evaluation of this influence is out of the scopeof this work

+e nonlinear dynamic analyses were conducted usinglumped plasticity In particular at both extremities of all

beams and columns potential plastic hinges were placed+e latter were developed according to the ASCE 41-13 [32]

025 times 030m

670

m

132

0m

345m 345m 375m 345m 345m 345m 345m 345m 345m 345m 345m 375m 345m 345m

650

m

Raer012 times 040m

(a)

Beam 080 times 022m

Frame X3

Frame X2

Frame X1

Fram

e Y2

Fram

e Y1

Beam 025 times 090m

025 times 040m040 times 025m

025 times 030m

035 times 025m

670

m

132

0 m

345m 345m 375m 345m 345m 345m 345m 345m 345m 345m 345m 375m 345m 345m

650

m

(b)

X

Y

670

m

132

0 m

345m 345m 375m 345m 345m 345m 345m

4890m

345m 345m 345m 345m 375m

025 times 030m

025 times 055m

040 times 025m

345m 345m

650

m

(c)

Figure 3 Reference plan of the building that shows the three longitudinal frames (x direction) and the two transversal frames (y direction)(a) roof plan (b) upper floors plan (c) ground floor plan

Table 2 Characteristics of the column sections at the ground floor

Size Longitudinal reinforcement Stirrups25times 30 4Oslash16 Oslash620025times 40 6Oslash16 Oslash620025times 55 8Oslash16 Oslash6200


and the inelastic demand (D) is expressed in terms of theplastic rotation at the chord (θpl) e capacity (C) is givenby the limit life safety (LS) as dened by ASCE 41-13 InFigure 7 the idealized full backbone curve denedaccording to ASCE 41-13 is shown

e rst part of the backbone curve (A-B) represents theelastic behaviour of the section and the activation of theplastic hinge occurs beyond the point B e peak of thestrength is reached in correspondence to the point C (notethat the point C does not represent the capacity) and then thestrength decreases rapidly until reaching the point D where asmall residual strength is still provided by the section efailure occurs at point E where the strength drops to zero

erefore points A to E describe the nonlinear behav-iour of the section while the acronyms IO LS and CPindicate respectively the acceptance criteria for immediateoccupancy (IO) life safety (LS) and collapse prevention(CP) For both life safety and collapse prevention the ac-ceptance criteria are dierentiated for primary components(P) and secondary components (S) For primary compo-nents LS 075 C and CPC but not greater than CP 075E while for secondary components LS 075 E and CPE

erefore the capacity of the section (C) is representedby the plastic component of the LS deformation calculated asC LSminusB

4 Results and Discussion

In this section results of numerical analyses are presentedand discussed e gross member exural rigidity wasconsidered and the concrete elasticity modulus was assumedto be equal to 30GPa

In Table 3 the periods of vibration the percentage ofparticipating mass ux along the longitudinal direction of thebuilding (x direction) the percentage of the participatingmass uy along the transversal direction of the building (ydirection) and the percentage of the mass participating tothe torsional mode rz are listed for each mode of vibrationconsidered

Referring to the spectral ordinate Sd(T1) associated tothe fundamental period of vibration along the y directionthe static forces at each oor level are calculated enequivalent static force analyses are performed in the y di-rection by varying the CM position along the x directione same procedure is repeated for the response spectrumanalysis and the ratios between the maximum and the av-erage lateral displacements (δmaxδavg) calculated with bothmethods at varying of the CM position are presented inFigure 8 e eect of variation of the periods of vibrationinduced by the variation of CM position is considerednegligible

Two considerations arise from previous results Whenthe CM is placed in the actual position the oor dis-placement includes rotational components (indeed δmaxδavgne 1) this means that CM and CR are not aligned (CR isdetected when δmaxδavg 1) e two methods the

000005010015020025030035040045050

Spec

tral

acce

lera

tion

(g)

05 1 15 2 25 3 35 40Period (s)

Figure 4 Elastic response spectrum

ndash025ndash020ndash015ndash010ndash005

000005010015020025

Gro

und

acce

lera

tion

(g)

2 4 6 8 10 12 14 16 180Time (s)

Figure 5 Record 147yamdashFriuli (aftershock) 1976 September 15th

000010020030040050060070080

0 05 1 15 2 25 3 35 4

Spec

tral

acce

lera

tion

(g)

Period (s)

Figure 6 Comparison between the elastic response spectrum(NTC 2018) and the spectrum obtained by the record 147ya ofFriuli

A

BC

D E

IOPS LS

P S CPP S

Deformation

Nor

mal

ized

forc

e

Figure 7 Idealized full backbone curve acceptance criteriaaccording to ASCE 41-13 [32]


equivalent static force and the response spectrum analysisgive almost the same results in term of displacements whenCM is close to CR However increasing the distance betweenCM and CR the agreement between the results gets worsebut this dierence is in accordance with several researches[11 12] and it is widely discussed in Torsional Provisions Inthe present case according to ASCE Code (ASCE 7-10) andconsidering the 5 of accidental eccentricity the buildingresulted in regular in-plan since the ratio between maximumand average displacement resulted lower than δmaxδavglt 12(Figure 8)

en nonlinear dynamic analyses are performed in orderto assess the uneven distribution of inelastic response atvarying CM position In particular four analyses are per-formed the rst considers CM coincident with CR thesecond considers CM in its actual position and the third andfourth consider CM in the positions that give δmaxδavg equalto 12 and 14 respectively in the equivalent static forceanalysis (Figure 8)

In Figure 9 the ratios between inelastic demand D andcapacity C (DC) calculated by means of nonlinear dynamicanalyses of all columns at the ground oor are shown inorder to evaluate the damage levels As previously said in they direction the only frames are placed on the left and rightside of the building All the other columns placed betweenthese two frames have to be considered as cantilever sincesuch columns are not connected by beams in the y direction

is fact explains why the columns placed on the left andright side of the building are much more aected by theinelastic demand than the others

Furthermore the columns placed in the centerlinehave the longer side of the cross section oriented along thex direction instead the columns placed on the rst andthird line have the longer side of the cross section orientedalong the y direction For this reason the inelastic demandof the centerline columns is lower than that of the col-umns placed on the rst and third lines due to the greatershear force brought by the latter Although the unevendistribution of stiness the demand to capacity ratios aresymmetrically distributed excepted for the abrupt vari-ation shown at the extremities such ratios are almostconstant

When the CM is placed in its actual position thescenario is dierent because the symmetrical distributionof the ratios DC is lost e inelastic demands on theexible side are greater than those shown on the sti sideMoving from the sti to the exible side the inelasticdemand increases progressively as shown in Figure 10

As previously shown (Figure 8) assuming an eccentricityof 6 for the CM the ratio δmaxδavg obtained by per-forming an equivalent linear static analysis becomes equal to12 In this conguration the inelastic demand appearsclearly irregular In approximately 40 of the building(Figure 11) the ratios DC are almost zero while in the otherpart the inelastic demand increases rapidly moving to theexible side

When CM is placed with 14 of eccentricity the ratioδmaxδavg calculated by an equivalent linear static analysis isequal to 14 (Figure 8) Adopting this conguration theinelastic response is strongly irregular As shown in Fig-ure 12 approximately 50 of the building provides noinelastic demand Conversely moving to the exible sidethe plastic demand increases rapidly providing high valuesof the ratio DC

In Figure 13 the demand to capacity ratios calculatedby means of nonlinear dynamic analyses of the threecolumns on sti and exible side (respectively left columnsof frame Y1 and right columns of frame Y2 in Figure 3(b))are plotted at varying δmaxδavg calculated by the equivalentlinear static analysis In this case it is worth noting that theinelastic demand is highly dependent on δmaxδavg and thatthe demand decreases on the sti side and increases on theexible side

10

11

12

13

14

15

δ max

δav

g

ndash2 0 2 4 6 8 10 12 14 16ndash4Eccentricity of CM ()

Figure 8 Ratios betweenmaximum δmax and average displacementδavg at varying CM position Comparison between linear dynamicanalysis (continuous line) and linear static analysis (dotted line)e position of CM is given in of the building longitudinaldimension (L 4885m) for e 0 CM is in the actual position

Table 3 Results of the modal analysis

Mode Period ux uy rz Σ(ux) Σ(uy) Σ(rz)1 1497 000 080 001 000 080 0012 1042 000 000 081 000 080 0823 0689 087 000 000 087 080 0824 0347 000 015 000 087 095 0825 0296 000 000 013 087 095 0956 0242 010 000 000 097 095 0957 0168 000 004 000 097 100 0968 0158 002 000 002 099 100 0989 0151 001 000 002 100 100 100

000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)

Spatial column position

Figure 9 Demand to capacity ratios DC uneven distribution ofinelastic response CM coincident with CR


In Figure 14 the demand to capacity ratios arenormalized by DC calculated in conguration CMequivCRwhere δmaxδavg is equal to 1 In correspondence of δmaxδavg 12 the normalized DC on the sti side is aboutequal to zero and on the exible side it is close to 2

To investigate the scattering of the damage levels overthe building plan the maximum (DC)max and average(DC)avg demand to capacity ratios of all columns atground oor were computed in the four studied cases(Figures 9ndash12)

In Figure 15 the inelastic indices (DC)max(DC)avgwere normalized by the corresponding (DC)max(DC)avgcomputed in the conguration in which CMequivCR (ie δmaxδavg 1)

Figure 15 clearly shows that the value δmaxδavg 12may be considered as a threshold value beyond which planscattering of the damage level DC does not increase sig-nicantly Of course this result may be aected by theparticular condition of the analyzed building and there-fore it needs to be validated by means of further in-vestigations on dierent building types

5 Conclusions

is paper is focused on the evaluation of the ASCE codeapproach for detecting building plan irregularity eresponse of an existing RC school building taken asreference case study is investigated to evaluate how welltorsional irregularity detected by the code corresponds touneven distribution of inelastic demand found by non-linear dynamic analyses In particular for the studiedcase the threshold value of 12 for identifying buildingsplan irregularity seems to be appropriate when planscattering of damage levels is considered In this speciccase the value of 12 seems already to characterize anextreme torsional irregularity condition and thereforethe value 14 provided by the ASCE code may be too largeHowever it is worth noting that this trend could alsoarise from the specicity of the building under in-vestigation and therefore a larger number of existingbuildings with dierent structural arrangements and plan

000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)


Figure 10 Demand to capacity ratios DC uneven distribution ofinelastic response CM placed in the actual position

000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)


Figure 11 Demand to capacity ratios DC uneven distribution ofinelastic response CM placed with 6 of eccentricity in order toobtain δmaxδavg 12 in the equivalent linear static analysis

000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)



00010102020303040405

1 105 11 115 12 125 13 135 14Dem

and-

to-c

apac

ity ra

tios (

DC

)

dmaxdavg

Stiff side

Flexible side

Figure 13 Demand to capacity ratios DC calculated by means ofnonlinear dynamic analyses at varying δmaxδavg provided byequivalent linear static analysis Comparison between the inelasticresponse of the column placed on the sti side and that provided bythe column on the exible side

Stiff side

Flexible side

00

05

10

15

20

25

30

1 105 11 115 12 125 13 135 14Nor

mal

ized

dem

and-

to-c

apac

ityra

tios (

DC

)

dmaxdavg

Figure 14 Normalized demand to capacity ratios DC calculatedby means of nonlinear dynamic analyses at varying δmaxδavgprovided by equivalent linear static analysis Comparison betweenthe inelastic response of the column placed on the sti side and thatprovided by the column on the exible side


congurations are currently under analysis to providesupport to this thesis

Data Availability

e authors state that data in the manuscript are freelyavailable

Conflicts of Interest

e authors declare that there are no conicts of interestregarding the publication of this paper

Acknowledgments

e nancial support of ReLUIS through the ProgettoEsecutivo Convenzione DPCReLUIS 2017mdashPR2 Strutturein cemento armatomdashis gratefully acknowledged

References

[1] M De Stefano and B Pintucchi ldquoA review of research onseismic behaviour of irregular building structures since 2002rdquoBulletin of Earthquake Engineering vol 6 no 2 pp 285ndash3082007

[2] E Rosenlueth and R Meli ldquoe 1985 earthquake causes andeects in Mexico cityrdquo Concrete International vol 8 no 5pp 23ndash34 1986

[3] W K Tso ldquoStatic eccentricity concept for torsional momentestimationsrdquo Journal of Structural Engineering vol 116 no 5pp 1199ndash1212 1990

[4] A M Chandler and G L Hutchinson ldquoEvaluation of codetorsional provisions by a time history approachrdquo EarthquakeEngineering amp Structural Dynamics vol 15 no 4 pp 491ndash5161987

[5] A K Chopra and R K Goel ldquoEvaluation of torsional pro-visions in seismic codesrdquo Journal of Structural Engineeringvol 117 no 12 pp 3762ndash3782 1991

[6] M De Stefano G Faella and R Ramasco ldquoInelastic responseand design criteria of plan-wise asymmetric systemsrdquoEarthquake Engineering amp Structural Dynamics vol 22 no 3pp 245ndash259 1993

[7] C M Wong and W K Tso ldquoEvaluation of seismic torsionalprovisions in uniform building coderdquo Journal of StructuralEngineering vol 121 no 10 pp 1436ndash1442 1995

[8] A M Chandler J C Correnza and G L HutchinsonldquoInuence of accidental eccentricity on inelastic seismictorsional eects in buildingsrdquo Engineering Structures vol 17no 3 pp 167ndash178 1995

[9] M De Stefano and A Rutenberg ldquoA comparison of thepresent SEAOCUBC torsional provisions with the old onesrdquoEngineering Structures vol 19 no 8 pp 655ndash664 1997

10

11

12

13

14

15

1 105 11 115 12 125 13 135 14

Nor

mal

ized

ratio

s (D

C) m

ax(

DC

) avg

dmaxdavg

1

2

34

2

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


3

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


4

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


1

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


Figure 15 Normalized demand to capacity ratios (DC)max(DC)avg calculated by means of nonlinear dynamic analyses at varying δmaxδavg provided by the equivalent linear static analysis


[10] A M Chandler and X N Duan ldquoPerformance of asymmetriccode-designed buildings for serviceability and ultimate limitstatesrdquo Earthquake Engineering amp Structural Dynamicsvol 26 no 7 pp 717ndash735 1997

[11] A P Harasimowicz and R K Goel ldquoSeismic code analysis ofmulti-storey asymmetric buildingsrdquo Earthquake Engineeringamp Structural Dynamics vol 27 no 2 pp 173ndash185 1998

[12] K Anastassiadis A Athanatopoulou and T MakariosldquoEquivalent static eccentricities in the simplified methods ofseismic analysis of buildingsrdquo Earthquake Spectra vol 14no 1 pp 1ndash34 1998

[13] I Perus and P Fajfar ldquoOn the inelastic torsional response ofsingle-storey structures under bi-axial excitationrdquo EarthquakeEngineering amp Structural Dynamics vol 34 no 8 pp 931ndash9412005

[14] M De Stefano M Tanganelli and S Viti ldquoEffect of thevariability in plan of concrete mechanical properties on theseismic response of existing RC framed structuresrdquo Bulletin ofEarthquake Engineering vol 11 no 4 pp 1049ndash1060 2012

[15] A Athanatopoulou G Manoukas and A +roumoulopoulosldquoParametric study of inelastic seismic response of reinforcedconcrete frame buildingsrdquo in Chapter 15 Geotechnical Geo-logical and Earthquake Engineering vol 40 of Seismic Be-haviour and Design of Irregular and Complex Civil StructuresII Z Zembaty M De Stefano Eds pp 171ndash180 SpringerBerlin Germany 2015 ISBN 978-3-319-14245-6

[16] R K Goel and A K Chopra Inelastic Seismic Response ofOne-Story Asymmetric-Plan Systems John Wiley amp SonsRichmond CA USA 1990

[17] A DrsquoAmbrisi M De Stefano and M Tanganelli ldquoUse ofpushover analysis for predicting seismic response of irregularbuildings a case studyrdquo Journal of Earthquake Engineeringvol 13 no 8 pp 1089ndash1100 2009

[18] G Magliulo G Maddaloni and E Cosenza ldquoExtension of N2method to plan irregular buildings considering accidentaleccentricityrdquo Soil Dynamics and Earthquake Engineeringvol 43 pp 69ndash84 2012

[19] M Bosco A Ghersi E M Marino and P P Rossi ldquoCom-parison of nonlinear static methods for the assessment ofasymmetric buildingsrdquo Bulletin of Earthquake Engineeringvol 11 no 6 pp 2287ndash2308 2013

[20] G Manoukas A Athanatopoulou and I Avramidis ldquoMul-timode pushover analysis for asymmetric buildings underbiaxial seismic excitation based on a new concept of theequivalent single degree of freedom systemrdquo Soil Dynamicsand Earthquake Engineering vol 38 pp 88ndash96 2012

[21] P Fajfar D Marusic and I Perus ldquoTorsional effects in thepushover-based seismic analysis of buildingsrdquo Journal ofEarthquake Engineering vol 9 no 6 pp 831ndash854 2005

[22] C Bhatt and R Bento ldquo+e extended adaptive capacityspectrum method for the seismic assessment of plan-asymmetric buildingsrdquo Earthquake Spectra vol 30 no 2pp 683ndash703 2014

[23] S A Anagnostopoulos M T Kyrkos and K G StathopoulosldquoEarthquake induced torsion in buildings critical review andstate of the artrdquo Earthquakes and Structures vol 8 no 2pp 305ndash377 2015

[24] ASCE Minimum Design Loads for Buildings and OtherStructures ASCESEI 7 American Society of Civil EngineersReston VA USA 2010

[25] European Committee for Standardization Eurocode 8 DesignProvisions for Earthquake Resistance of Structures Part 1-2General RulesmdashGeneral Rules for Building European Com-mittee for Standardization Brussels Belgium 1993

[26] Associate Committee on the National Building Code Na-tional Building Code of Canada National Research CouncilOttawa ON Canada 1995

[27] European Committee for Standardization Eurocode 8 Designof Structures for Earthquake ResistancemdashPart 1 General RulesSeismic Actions and Rules for Buildings Eurocode EuropeanCommittee for Standardization Brussels Belgium 2004


[29] SAP2000 CSI Integrated Software for Structural Analysis ampDesign Computer and Structures Inc Berkeley CA USA2007

[30] DMLLPP2018 17 Gennaio 2018 Norme Tecniche Per LeCostruzioni (NTC) GU n 42 del 20 febbraio 2018

[31] F Pugi and S Galassi ldquoSeismic analysis of masonry voussoirarches according to the Italian building coderdquo InternationalJournal of Earthquake and Impact Engineering vol 30 no 3pp 33ndash55 Patron Bologna Italy 2013

[32] ASCE Seismic Evaluation and Retrofit of Existing Buildings(ASCE 41-13) ASCESEI 4 American Society of Civil Engi-neers Reston VA USA 2014


International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

[17ndash22] +en an important contribution that deals withtorsion issue and plan regularity of building structures isprovided by Anagnostopoulos et al [23]

+is paper is focused on the evaluation of the ASCEtorsional provision (ASCE Standard 7-10) [24] +e re-sponse of a case study building is investigated in order toevaluate the torsional irregularity provided by the code andthe corresponding uneven distribution of inelastic demandwhich is detected using the nonlinear dynamic analysismethod

2 Torsional Provisions

+e previous generation of seismic codes was providingdesign eccentricities for equivalent static analysis as follows

ed α middot e0 + β middot b (1)

where ed is the design eccentricity e0 is the distance betweenthe centre of mass (CM) and the centre of rigidity (CR)measured orthogonally to the loading direction b is thebuilding dimension perpendicular to the loading direction αis a coefficient accounting for dynamic amplification of thetorsional response and β is a coefficient accounting foraleatoric position of the CM

In Table 1 coefficients α and β are provided according toEurocode 8 1993 (EC8-93) [25] National Building Code ofCanada 1995 (NBCC-95) [26] and ASCE Standard 7-10(ASCE 7-10) [24] where Ax is the amplification factorprovided by ASCE 7-10 (defined in the following) and e2 isthe additional eccentricity provided by EC8-93 equal to thesmaller of the following values

e2 min

01 middot (L + B) middot

10 middot e0

L

1113970

le 01 middot (L + B)

12 middot e0

middot ℓ2s minus e20 minus r

2+

ℓ2s minus e20 minus r2( 11138572

+ 4 middot e20 middot r21113969

1113876 1113877

⎧⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎩

(2)

where ℓs is the radius of gyration of the floor mass in-plan(square root of the ratio of the polar moment of inertia of thefloor mass in-plan (a) with respect to the centre of mass ofthe floor to (b) the floor mass (b)) and r is the square root ofthe ratio of the torsional stiffness to the lateral stiffness in theloading direction (ldquotorsional radiusrdquo)

In current code provisions such as Eurocode 8 2004(EC8-04) [27] and National Building Code of Canada 2010(NBCC-10) [28] in the case of torsional irregularity only a3D dynamic analysis is allowed Even when adopting aspatial model and the CQC modal combination the acci-dental eccentricity is considered accounting for the randomposition of CM and the design eccentricity is computed bythe following equation

ed e0 + β middot b (3)

However criteria for assessing in-plan irregularity arestill very important indeed it affects the choice of themethod of analysis and the definition of the behaviourfactor

Qualitatively in-plan irregularity is due to asymmetricdistributions of mass and stiffness but quantitatively adefinition universally shared does not exist Eurocode 8 2004(EC8-04) provides a list of conditions to classify a building asregular in-plan

(i) With respect to the lateral stiffness and mass dis-tribution the building structure shall be approxi-mately symmetrical in plan with respect to twoorthogonal axes

(ii) +e plan configuration shall be compact ie eachfloor shall be delimited by a polygonal convex line Ifin-plan setbacks (ie reentrant corners or edgerecesses) exist regularity in plan may still be con-sidered as being satisfied provided that these set-backs do not affect the floor in-plan stiffness andthat for each setback the area between the outline ofthe floor and a convex polygonal line enveloping thefloor does not exceed 5 of the floor area

(iii) +e in-plan stiffness of the floors shall be sufficientlylarge in comparison with the lateral stiffness of thevertical structural elements so that the deformationof the floor shall have a small effect on the distri-bution of the forces among the vertical structuralelements In this respect the L C H I and X planshapes should be carefully examined notably asconcerns the stiffness of the lateral branches whichshould be comparable to that of the central part inorder to satisfy the rigid diaphragm condition +eapplication of this paragraph should be consideredfor the global behaviour of the building

(iv) +e slenderness λ LmaxLmin of the building in-plan shall not be higher than 4 where Lmax and Lminare respectively the larger in-plan and smallerdimension of the building measured in two or-thogonal directions

(v) At each level and for each direction of analysis thestructural eccentricity e0 and the torsional radius r

shall conform to the following conditions

eo le 030 middot r

rge ℓs(4)

+e first four criteria are almost qualitative while thefifth one if strictly applied is valid only for single-storybuildings For multistory buildings only approximate def-initions of the centre of stiffness and the torsional radius arepossible [27] Similarly ASCE Standard 7-10 [24] provides a

Table 1 Design eccentricity coefficients

Analyzed elements Flexible-side elements Stiff-sideelements

Code α β α βEC8-93 10 + e2e0 005 10 minus005NBCC-95 15 010 05 minus010ASCE 7-10 10 005 middot Ax 10 minus005 middot Ax















3 Case Study





δA

δB









E + G1 + G2 + 06 middot Q (7)



gmiddot λ (8)









(a) (b) (c)






025 times 030m

670

m

132

0m

345m 345m 375m 345m 345m 345m 345m 345m 345m 345m 345m 375m 345m 345m

650

m

Raer012 times 040m

(a)

Beam 080 times 022m

Frame X3

Frame X2

Frame X1

Fram

e Y2

Fram

e Y1

Beam 025 times 090m


025 times 030m

035 times 025m

670

m

132

0 m

345m 345m 375m 345m 345m 345m 345m 345m 345m 345m 345m 375m 345m 345m

650

m

(b)

X

Y

670

m

132

0 m

345m 345m 375m 345m 345m 345m 345m

4890m

345m 345m 345m 345m 375m

025 times 030m

025 times 055m

040 times 025m

345m 345m

650

m

(c)














000005010015020025030035040045050

Spec

tral

acce

lera

tion

(g)

05 1 15 2 25 3 35 40Period (s)



000005010015020025

Gro

und

acce

lera

tion

(g)

2 4 6 8 10 12 14 16 180Time (s)


000010020030040050060070080

0 05 1 15 2 25 3 35 4

Spec

tral

acce

lera

tion

(g)

Period (s)


A

BC

D E

IOPS LS

P S CPP S

Deformation

Nor

mal

ized

forc

e












10

11

12

13

14

15

δ max

δav

g





000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)








5 Conclusions


000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)



000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)



000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)



00010102020303040405

1 105 11 115 12 125 13 135 14Dem

and-

to-c

apac

ity ra

tios (

DC

)

dmaxdavg

Stiff side

Flexible side


Stiff side

Flexible side

00

05

10

15

20

25

30

1 105 11 115 12 125 13 135 14Nor

mal

ized

dem

and-

to-c

apac

ityra

tios (

DC

)

dmaxdavg




Data Availability




Acknowledgments


References










10

11

12

13

14

15

1 105 11 115 12 125 13 135 14

Nor

mal

ized

ratio

s (D

C) m

ax(

DC

) avg

dmaxdavg

1

2

34

2

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


3

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


4

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


1

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia















3 Case Study





δA

δB









E + G1 + G2 + 06 middot Q (7)



gmiddot λ (8)









(a) (b) (c)






025 times 030m

670

m

132

0m

345m 345m 375m 345m 345m 345m 345m 345m 345m 345m 345m 375m 345m 345m

650

m

Raer012 times 040m

(a)

Beam 080 times 022m

Frame X3

Frame X2

Frame X1

Fram

e Y2

Fram

e Y1

Beam 025 times 090m


025 times 030m

035 times 025m

670

m

132

0 m

345m 345m 375m 345m 345m 345m 345m 345m 345m 345m 345m 375m 345m 345m

650

m

(b)

X

Y

670

m

132

0 m

345m 345m 375m 345m 345m 345m 345m

4890m

345m 345m 345m 345m 375m

025 times 030m

025 times 055m

040 times 025m

345m 345m

650

m

(c)














000005010015020025030035040045050

Spec

tral

acce

lera

tion

(g)

05 1 15 2 25 3 35 40Period (s)



000005010015020025

Gro

und

acce

lera

tion

(g)

2 4 6 8 10 12 14 16 180Time (s)


000010020030040050060070080

0 05 1 15 2 25 3 35 4

Spec

tral

acce

lera

tion

(g)

Period (s)


A

BC

D E

IOPS LS

P S CPP S

Deformation

Nor

mal

ized

forc

e












10

11

12

13

14

15

δ max

δav

g





000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)








5 Conclusions


000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)



000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)



000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)



00010102020303040405

1 105 11 115 12 125 13 135 14Dem

and-

to-c

apac

ity ra

tios (

DC

)

dmaxdavg

Stiff side

Flexible side


Stiff side

Flexible side

00

05

10

15

20

25

30

1 105 11 115 12 125 13 135 14Nor

mal

ized

dem

and-

to-c

apac

ityra

tios (

DC

)

dmaxdavg




Data Availability




Acknowledgments


References










10

11

12

13

14

15

1 105 11 115 12 125 13 135 14

Nor

mal

ized

ratio

s (D

C) m

ax(

DC

) avg

dmaxdavg

1

2

34

2

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


3

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


4

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


1

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








E + G1 + G2 + 06 middot Q (7)



gmiddot λ (8)









(a) (b) (c)






025 times 030m

670

m

132

0m

345m 345m 375m 345m 345m 345m 345m 345m 345m 345m 345m 375m 345m 345m

650

m

Raer012 times 040m

(a)

Beam 080 times 022m

Frame X3

Frame X2

Frame X1

Fram

e Y2

Fram

e Y1

Beam 025 times 090m


025 times 030m

035 times 025m

670

m

132

0 m

345m 345m 375m 345m 345m 345m 345m 345m 345m 345m 345m 375m 345m 345m

650

m

(b)

X

Y

670

m

132

0 m

345m 345m 375m 345m 345m 345m 345m

4890m

345m 345m 345m 345m 375m

025 times 030m

025 times 055m

040 times 025m

345m 345m

650

m

(c)














000005010015020025030035040045050

Spec

tral

acce

lera

tion

(g)

05 1 15 2 25 3 35 40Period (s)



000005010015020025

Gro

und

acce

lera

tion

(g)

2 4 6 8 10 12 14 16 180Time (s)


000010020030040050060070080

0 05 1 15 2 25 3 35 4

Spec

tral

acce

lera

tion

(g)

Period (s)


A

BC

D E

IOPS LS

P S CPP S

Deformation

Nor

mal

ized

forc

e












10

11

12

13

14

15

δ max

δav

g





000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)








5 Conclusions


000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)



000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)



000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)



00010102020303040405

1 105 11 115 12 125 13 135 14Dem

and-

to-c

apac

ity ra

tios (

DC

)

dmaxdavg

Stiff side

Flexible side


Stiff side

Flexible side

00

05

10

15

20

25

30

1 105 11 115 12 125 13 135 14Nor

mal

ized

dem

and-

to-c

apac

ityra

tios (

DC

)

dmaxdavg




Data Availability




Acknowledgments


References










10

11

12

13

14

15

1 105 11 115 12 125 13 135 14

Nor

mal

ized

ratio

s (D

C) m

ax(

DC

) avg

dmaxdavg

1

2

34

2

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


3

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


4

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


1

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





025 times 030m

670

m

132

0m

345m 345m 375m 345m 345m 345m 345m 345m 345m 345m 345m 375m 345m 345m

650

m

Raer012 times 040m

(a)

Beam 080 times 022m

Frame X3

Frame X2

Frame X1

Fram

e Y2

Fram

e Y1

Beam 025 times 090m


025 times 030m

035 times 025m

670

m

132

0 m

345m 345m 375m 345m 345m 345m 345m 345m 345m 345m 345m 375m 345m 345m

650

m

(b)

X

Y

670

m

132

0 m

345m 345m 375m 345m 345m 345m 345m

4890m

345m 345m 345m 345m 375m

025 times 030m

025 times 055m

040 times 025m

345m 345m

650

m

(c)














000005010015020025030035040045050

Spec

tral

acce

lera

tion

(g)

05 1 15 2 25 3 35 40Period (s)



000005010015020025

Gro

und

acce

lera

tion

(g)

2 4 6 8 10 12 14 16 180Time (s)


000010020030040050060070080

0 05 1 15 2 25 3 35 4

Spec

tral

acce

lera

tion

(g)

Period (s)


A

BC

D E

IOPS LS

P S CPP S

Deformation

Nor

mal

ized

forc

e












10

11

12

13

14

15

δ max

δav

g





000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)








5 Conclusions


000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)



000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)



000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)



00010102020303040405

1 105 11 115 12 125 13 135 14Dem

and-

to-c

apac

ity ra

tios (

DC

)

dmaxdavg

Stiff side

Flexible side


Stiff side

Flexible side

00

05

10

15

20

25

30

1 105 11 115 12 125 13 135 14Nor

mal

ized

dem

and-

to-c

apac

ityra

tios (

DC

)

dmaxdavg




Data Availability




Acknowledgments


References










10

11

12

13

14

15

1 105 11 115 12 125 13 135 14

Nor

mal

ized

ratio

s (D

C) m

ax(

DC

) avg

dmaxdavg

1

2

34

2

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


3

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


4

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


1

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia











000005010015020025030035040045050

Spec

tral

acce

lera

tion

(g)

05 1 15 2 25 3 35 40Period (s)



000005010015020025

Gro

und

acce

lera

tion

(g)

2 4 6 8 10 12 14 16 180Time (s)


000010020030040050060070080

0 05 1 15 2 25 3 35 4

Spec

tral

acce

lera

tion

(g)

Period (s)


A

BC

D E

IOPS LS

P S CPP S

Deformation

Nor

mal

ized

forc

e












10

11

12

13

14

15

δ max

δav

g





000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)








5 Conclusions


000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)



000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)



000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)



00010102020303040405

1 105 11 115 12 125 13 135 14Dem

and-

to-c

apac

ity ra

tios (

DC

)

dmaxdavg

Stiff side

Flexible side


Stiff side

Flexible side

00

05

10

15

20

25

30

1 105 11 115 12 125 13 135 14Nor

mal

ized

dem

and-

to-c

apac

ityra

tios (

DC

)

dmaxdavg




Data Availability




Acknowledgments


References










10

11

12

13

14

15

1 105 11 115 12 125 13 135 14

Nor

mal

ized

ratio

s (D

C) m

ax(

DC

) avg

dmaxdavg

1

2

34

2

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


3

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


4

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


1

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia











10

11

12

13

14

15

δ max

δav

g





000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)








5 Conclusions


000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)



000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)



000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)



00010102020303040405

1 105 11 115 12 125 13 135 14Dem

and-

to-c

apac

ity ra

tios (

DC

)

dmaxdavg

Stiff side

Flexible side


Stiff side

Flexible side

00

05

10

15

20

25

30

1 105 11 115 12 125 13 135 14Nor

mal

ized

dem

and-

to-c

apac

ityra

tios (

DC

)

dmaxdavg




Data Availability




Acknowledgments


References










10

11

12

13

14

15

1 105 11 115 12 125 13 135 14

Nor

mal

ized

ratio

s (D

C) m

ax(

DC

) avg

dmaxdavg

1

2

34

2

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


3

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


4

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


1

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






5 Conclusions


000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)



000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)



000010020030040050

Dem

and-

to-c

apac

ity ra

tios (

DC

)



00010102020303040405

1 105 11 115 12 125 13 135 14Dem

and-

to-c

apac

ity ra

tios (

DC

)

dmaxdavg

Stiff side

Flexible side


Stiff side

Flexible side

00

05

10

15

20

25

30

1 105 11 115 12 125 13 135 14Nor

mal

ized

dem

and-

to-c

apac

ityra

tios (

DC

)

dmaxdavg




Data Availability




Acknowledgments


References










10

11

12

13

14

15

1 105 11 115 12 125 13 135 14

Nor

mal

ized

ratio

s (D

C) m

ax(

DC

) avg

dmaxdavg

1

2

34

2

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


3

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


4

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


1

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Data Availability




Acknowledgments


References










10

11

12

13

14

15

1 105 11 115 12 125 13 135 14

Nor

mal

ized

ratio

s (D

C) m

ax(

DC

) avg

dmaxdavg

1

2

34

2

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


3

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


4

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)


1

000010020030040050

Dem

and-

to-c

apac

ityra

tios (

DC

)






























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

EvaluationoftheAmericanApproachforDetecting PlanIrregularitydownloads.hindawi.com/journals/ace/2019/2861093.pdf · 2019. 7. 30. · buildings, as follows: (i) Torsional irregularity: