improvingthestructuralreliabilityofsteelframesusing...

Research ArticleImproving the Structural Reliability of Steel Frames UsingPosttensioned Connections

Eden Bojorquez 1 Arturo Lopez-Barraza1 Alfredo Reyes-Salazar 1 Sonia E Ruiz 2

Jorge Ruiz-Garcıa3 Antonio Formisano 4 Francisco Lopez-Almansa5 Julian Carrillo6

and Juan Bojorquez 1

1Facultad de Ingenierıa Universidad Autonoma de Sinaloa Culiacan 80040 Mexico2Instituto de Ingenierıa Universidad Nacional Autonoma de Mexico Mexico City 04510 Mexico3Facultad de Ingenierıa Civil Universidad Michoacana de San Nicolas de Hidalgo Morelia 58040 Mexico4Department of Structures for Engineering and Architecture (DiSt) University of Naples ldquoFederico IIldquo Naples 80125 Italy5Architecture Technology Department Technical University of Catalonia Barcelona 08028 Spain6Ingenierıa Civil Universidad Militar Nueva Granada Bogota Colombia

Correspondence should be addressed to Eden Bojorquez edenuasedumx

Received 23 March 2019 Accepted 2 June 2019 Published 26 June 2019

Academic Editor Rosario Montuori

Copyright copy 2019 Eden Bojorquez 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

In this paper various moment-resisting steel frames (MRSFs) are subjected to 30 narrow-band motions scaled at different groundmotion intensity levels in terms of spectral acceleration at first mode of vibration Sa(T1) in order to perform incremental dynamicanalysis for peak and residual interstory drift demandse results are used to compute the structural reliability of the steel framesby means of hazard curves for peak and residual drifts It is observed that the structures exceed the threshold residual drift of 05which is perceptible to human occupants and it could lead to human discomfort according to recent investigations For thisreason posttensioned connections (PTCs) are incorporated into the steel frames in order to improve the structural reliability eresults suggest that the annual rate of exceedance of peak and residual interstory drift demands are reduced with the use of PTCus the structural reliability of the steel frames with PTC is superior to that of the MRSFs In particular the residual driftdemands tend to be smaller when PTCs are incorporated in the steel structures

1 Introduction

Currently most of the seismic design regulations recommendthe use of maximum interstory drift as the main engineeringdemand parameter Nevertheless earthquake field re-connaissance has evidenced that residual drift demands afteran earthquake play an important role in the seismic per-formance of a structure For example several dozen damagedreinforced concrete structures in Mexico City had to bedemolished after the 1985 Michoacan earthquake because ofthe technical difficulties to straighten and to repair buildingswith large permanent drifts [1] Okada et al [2] reported thatseveral low-rise RC buildings suffered light structural damagebut experienced relatively large residual deformations as aconsequence of the 1995Hyogo-KenNambu earthquake even

though they had sufficient deformation capacity After ex-amining 12 low-to-mid-rise steel office buildings (particularly10 with structural system based on steel moment-resistingframes) structurally damaged and leaned after the sameearthquake Iwata et al [3] highlighted that the cost of repairof leaned steel buildings linearly increased as the maximumand roof residual drift increased Based on their study theauthors suggested that steel buildings should be limited tomaximum and roof residual drift about 14 and 09 re-spectively to satisfy a repairability limit state that meets bothtechnical and economical constraints More recently a fieldinvestigation in Japan indicated that a residual interstory driftof about 05 is perceptible for building occupants [4]Bojorquez and Ruiz-Garcıa [5] by comparing peak and re-sidual drift demand hazard curves have observed that if steel

HindawiAdvances in Civil EngineeringVolume 2019 Article ID 8912390 10 pageshttpsdoiorg10115520198912390

frames exhibit peak drift demands about 3 they couldexperience residual drifts larger than 05 which is thethreshold residual drift that could be tolerable to humanoccupants and it could lead to human discomfort [4] whensubjected to narrow-band earthquake groundmotions of highintensity erefore several researchers have demonstratedthat the estimation of residual drift demands should also playan important role during the design of new buildings [6ndash8]and the evaluation of the seismic structural performance ofexisting buildings [9ndash13]

In the present study motivated by the need to reduce peakand residual interstory drift demands PTCs are incorporatedinto various MRSFs Posttensioned steel moment-resistingframes are structural systems proposed in recent years as anappropriate alternative to welded connections of moment-resisting frames in seismic zones [14ndash27] ey are designedto prevent brittle fractures in the area of the nodes of steelframes which can cause severe reduction in their ductilitycapacity as occurred in many cases during the 1994Northridge and the 1995 Kobe earthquakes e philosophyof structures with PTC is that under an intense earthquakemotion beams and columns remain essentially elastic con-centrating the damage on the energy dissipating elementswhich can be easily replaced at low cost Moreover theyprovide capacity of energy dissipation and self-centeringwhich can significantly reduce the residual demands estructural performance of the selected MRSFs is comparedwith the structures with PTC through incremental dynamicanalysis and the estimation of the structural reliability of theframes in terms of peak and residual interstory drift demandsWith this aim four MRSFs and the same structures with PTC(here named FPTC frames with posttensioned connections)are subjected to 30 long-duration groundmotions recorded atthe lake zone of Mexico City where most of the damages werefound in buildings as a consequence of the 1985 Michoacanearthquake In general it is observed that the structural re-liability of the steel frames with PTC is superior to that of theMRSFs In particular the residual drift demands tend to besmaller than 05 (which is perceptible for building occu-pants) when PTCs are incorporated into the steel structures

2 Methodology

21 Structural Steel Frame Models Two groups of fourstructural steel frame models are selected for the study efirst group of structures corresponding to moment-resistingsteel frames was designed according to the Mexico CityBuilding Design Provisions (MCSDPs) [28]e buildings areassumed to be for office occupancy ey have 4 6 8 and 10stories and 3 bays hereafter indicated as F4 F6 F8 and F10respectively e dimensions of the frames are shown inFigure 1 e beams and columns are A36 steel W sections Abilinear hysteretic model for accounting the nonlinear ma-terial behavior with 3 of postyielding stiffness was con-sidered for the analyses and the damping used was 3 ofcritical e fundamental periods of vibration (T1) are 09107 120 and 137 s respectively On the other hand theFPTCs were designed in accordance with the recommen-dations proposed by Garlock et al [21] which basically start

with the design of the steel frames as usually done (consid-ering rigid connections) and then the semirigid post-tensioned connections are designed to satisfy therequirements of the serviceability and resistance conditionse beam-column connections consist of two angles bolted tothe flanges of the beam and to the column flange (top andseat) For the design of posttensioned connections steel grade50 was used for the angles e length of the angles was takenequal to the width of the flange of the beams (bf ) Differentangle sizes were tested but at the end 152times152times13mmangles were used in all the cases Posttensioned cables consistof seven wires with an area of 150mm2 withstanding a load of279 kN they are parallel to the axis of the beam passingthrough the interior columns and fixed to the outer face of thecolumns at the ends of the frame An initial tension of thecables less than 033 times their maximum capacity was usedaccording with the suggestions given by Garlock et al [21]e four FPTC models are identified here as F4PTC F6PTCF8PTC and F10PTC for the frames with 4 6 8 and 10stories respectively e FPTC models have fundamentalperiods of vibration of 089 103 125 and 137 s respectivelye columns of the ground floor are fixed at the base withoutbeing posttensioned e beam and column members usedfor all the frames are illustrated in Table 1 Note that themechanical characteristics and dimensions of beams andcolumns are the same for both theMRSFs and FPTC Figure 2shows a typical assembly of a posttensioned steel frame

22 Connection Model Nonlinear Hysteretic Behaviore hysteretic rules that represent the cyclic behavior of thesemirigid connections of the posttensioned frames are char-acterized by moment-rotation curves (M-θr) with shapessimilar to a flag is representation characterizes the non-linearity self-centering capability and energy dissipationcapacity of the connection Experimental tests with isolatedangles subjected to cyclic and monotonic loads conducted byShen andAstaneh-Asl [29] showed a stable cyclic response andgood capability of hysteretic energy dissipation In generalultimate strength exceeded 3 times the yield strength andductility reached values between 8 and 10 e strength andstiffness in bending of the posttensioned connections is

80m 80m 80m

35m

35m

35m

Variable number of stories

Figure 1 Geometrical characteristics of the MRSFs

2 Advances in Civil Engineering

provided by the contribution of the angles of the PTC and byposttensioned strands Wires and angles work as springs inparallel Posttensioned strands exhibit linear behavior whileconnecting angles behave nonlinearly Figure 3 shows a typicalexample of a hysteretic curve corresponding to a post-tensioned connection is behavior was modeled by mean ofequations (1) and (2) which represent the loading andunloading curves respectively obtained from the superposi-tion of the exponential equation proposed by Richard [30] forsemirigid connections and the linear contribution of thestrands as well as decompression moments (Md) and theclosing moment (Mc) of the connection e first functiongiven by equation (1) corresponds to the initial loading cycletwo types of variables are observed (1) variables dependingonly on geometric and physical properties of angles such asinitial (k) and postyield (kp) stiffnesses the reference moment(Mo) and N that defines the curvature in the transition be-tween the linear and plastic behavior and (2) variablesdepending on the number and type of tendons such as therigidity of the posttensioned tendons (kθS) and the bendingmoment associated with the opening of the connection(named decompression moment Md) which is a function of

the resulting initial tension in the tendons e secondfunction given by equation (2) defines the unloading andreloading process in the connection Ma and θa are themaximum values reached in each cycle and the parameter φdefines the magnitude of the closing moment of the con-nection (Mc) which must be greater than zero in order toinsure complete closure of the connection after gettingcomplete unloading moreover this parameter largely definesthe EH dissipation capacity of the connection (enclosed area)e curves obtained with the modified model exhibit goodaccuracy in comparison with experiment results and theywere modeled in RUAUMOKO [31] as the flag-shaped bi-linear hysteresis [32]

M Md +kminus kp1113872 1113873θr

1 + kminus kp1113872 1113873θr1113872 1113873Mo

11138681113868111386811138681113868

11138681113868111386811138681113868N

1113876 11138771N

+ kp + kθS1113872 1113873θr

(1)

M Ma minuskminus kp1113872 1113873 θa minus θr( 1113857

1 + kminus kp1113872 1113873 θa minus θr( 11138571113872 1113873φMo

11138681113868111386811138681113868

11138681113868111386811138681113868N

1113876 11138771N

minus kp + kθS1113872 1113873 θa minus θr( 1113857

(2)

23 EarthquakeGroundMotions A total of 30 narrow-bandearthquake ground motions recorded at soft soil sites ofMexico City are used for the time story analyses of theMSRFand FPTC e main characteristic of the selected groundmotions recorded on soft soils is that they demand largeenergy on structures in comparison to those recorded onfirm soils [33 34] e ground motions were recorded insites where the period of the soil was close to two secondsand structures were more severely damaged during the 1985Mexico City Earthquake e duration was computedaccording with Trifunac and Brady [35] Table 2 summarizesthe most important characteristics of the records In thetable while PGA and PGV denote the peak ground accel-eration and velocity tD indicates duration

24 Evaluation of Structural Reliability e incrementaldynamic analysis [36] is used to assess the seismic perfor-mance of the steel frames under narrow-band motions atdifferent intensity levels Next the well-known seismicperformance-based assessment procedure suggested by thePacific Earthquake Engineering Center [37] in the UnitedStates was employed in this study which indicates that themean annual frequency of exceedance of an engineeringdemand parameter (EDP) of interest exceeding a certainlevel EDP can be computed as follows

λ(EDPgt edp) 1113946IM

P[EDPgt edp | IM im] middot dλIM(im)1113868111386811138681113868

1113868111386811138681113868

(3)

where IM denotes the ground motion intensity measure(eg peak ground acceleration spectral acceleration at the

Table 1 Relevant characteristics of the steel frames

Frame F4 F6 F8 F10Number ofstories 4 6 8 10

Internal columnsStory 1 W21times 122 W30times173 W36times 210 W36times 280Story 2 W21times 122 W30times173 W36times 210 W36times 280Story 3 W21times 111 W30times148 W36times194 W36times 245Story 4 W21times 111 W30times148 W36times194 W36times 245Story 5 W30times124 W36times170 W36times 210Story 6 W30times124 W36times170 W36times 210Story 7 W36times160 W36times182Story 8 W36times160 W36times182Story 9 W36times150Story 10 W36times150External columnsStory 1 W18times 97 W27times146 W36times194 W36times 280Story 2 W18times 97 W27times146 W36times194 W36times 280Story 3 W18times 86 W27times129 W36times182 W36times 245Story 4 W18times 86 W27times129 W36times182 W36times 245Story 5 W27times114 W36times160 W36times 210Story 6 W27times114 W36times160 W36times 210Story 7 W36times135 W36times182Story 8 W36times135 W36times182Story 9 W36times150Story 10 W36times150BeamsStory 1 W16times 67 W18times 71 W21times 83 W21times 68Story 2 W16times 57 W18times 76 W21times 93 W21times 93Story 3 W16times 45 W18times 76 W21times 93 W21times 101Story 4 W16times 40 W16times 67 W21times 83 W21times 101Story 5 W16times 50 W18times 71 W21times 101Story 6 W16times 45 W18times 65 W21times 93Story 7 W18times 55 W21times 73Story 8 W18times 46 W21times 68Story 9 W21times 57Story 10 W21times 50

Advances in Civil Engineering 3

first-mode period of vibration and inelastic displacementdemand at the buildingrsquos fundamental period of vibration)and P[EDPgt edp | IM im] is the conditional probabilitythat an EDP exceeds a certain level of EDP given that the IMis evaluated at the groundmotion intensity measure level imIn addition dλIM(im) refers to the differential of the groundmotion hazard curve for the IM In this context while thefirst term in the right-hand side of equation (3) can beobtained from probabilistic estimates of the EDP of interestwith incremental dynamic analyses the second term inequation (3) is represented by the seismic hazard curvewhich can be computed from conventional ProbabilisticSeismic Hazard Analysis (PSHA) evaluated at the groundmotion intensity level im Note the importance of the

ground motion intensity measure for assessment of seismicperformance which is the joint between earthquake engi-neering and seismology In this study the spectral accel-eration at first mode of vibration Sa(T1) was selected as IMin such a way that equation (3) can be expressed as

λ(EDPgt edp) 1113946Sa T1( )

P EDPgt edp Sa1113868111386811138681113868 T1( 1113857 sa1113960 1113961

middot dλSa T1( ) sa( 111385711138681113868111386811138681113868

11138681113868111386811138681113868

(4)

where dλSa(T1)(sa) λSa(T1)(sa)minus λSa(T1)(sa + dsa) is thehazard curve differential expressed in terms of Sa(T1)Equation (4) was used to evaluate the structural reliabilityof the study-case frames in terms of two EDPs peak andresidual interstory drift demands For evaluating the firstterm in the integrand for peak and residual drift demands alognormal cumulative probability distribution was used[5] erefore the term P(EDP gt edp | Sa(T1) sa) is an-alytically evaluated as follows

P EDPgt edp Sa1113868111386811138681113868 T1( 1113857 sa1113872 1113873 1minusΦ

ln edpminus 1113954μlnEDP Sa| T1( )sa

1113954σ lnEDP Sa| T1( )sa

⎛⎝ ⎞⎠

(5)

where 1113954μlnEDP|Sa(T1)saand 1113954σlnEDP|Sa(T1)sa

are the geometricmean and standard deviation of the natural logarithm of theEDP respectively and Φ(middot) is the standard normal cumu-lative distribution function It is important to say as Bojorquezet al [38] indicate that the ground motion records used in thepresent study allow the use of spectral acceleration at firstmode of vibration as intensity measure due to its sufficiencywith respect to magnitude and distance and because of thesimilarity of the spectral shape of the records since they havesimilar values of the spectral parameter Np [39]

25 Seismic Performance in terms of Peak and Residual DriftDemands MRSFs vs Steel Frames with PTC e first step to

PT strands

Shimplate

Angle

PTstrands

Reinforcingplate

Figure 2 Angles and posttensioned strands in the FPTC structures

M

M

My

Md

Mc

θrθr (rad)

(θa Ma)

Figure 3 Moment-relative rotation hysteretic curve for theposttensioned connections


evaluate the structural reliability is the computation of theincremental dynamic analysis thus the maximum or residualinterstory drift at different values of the ground motion in-tensity measure which in the present study is Sa(T1) is cal-culated Figure 4 illustrates as an example the incrementaldynamic analysis of the traditional frame F4 under the selectednarrow-band motions It can be observed the increase of themaximum interstory drift as the spectral acceleration at firstmode of vibration tends to increase Likewise notice that theuncertainty in the structural response also tend to increase forlarger values of Sa(T1)en the fragility curves are computedthrough equation (5) which are combined with the seismichazard curves to compute the mean annual rate of exceedancethus the structural reliability via equation (4) in terms of peakand residual interstory drift Note that in this case the spectralacceleration hazard curves corresponding to the first-modeperiod of vibration of each building and for the Secretarıa deComunicaciones y Transportes (SCT) site in Mexico City weredeveloped following the procedure suggested by Alamilla [40]

eMexican City seismic design code takes into accountthe peak interstory drift Recently Bojorquez and Ruiz-Garcıa [5] demonstrated that for MRSFs designed with theMexican City Building Code the control of maximum orpeak interstory drift demands does not necessarily guaranteea good seismic performance in terms of residual drift de-mands In fact by comparing peak and residual drift de-mand hazard curves Bojorquez and Ruiz-Garcıa [5]

concluded that for steel structures that exhibit peak driftdemands of about 3 (the threshold recommended by theMCSDP to avoid collapse) the maximum residual drifts islarger than 05 which is the threshold residual drift thatcould be tolerable to human occupants and it could lead tohuman discomfort identified from recent field investigations[4] when subjected to narrow-band earthquake groundmotions of high intensity For this reason the residualinterstory drift should be considered in future versions of the

Table 2 Narrow-band motions used for the present study

Record Date Magnitude Station PGA (cms2) PGV (cms) tD (s)1 19091985 81 SCT 1780 595 3482 21091985 76 Tlahuac deportivo 487 146 3993 25041989 69 Alameda 450 156 3784 25041989 69 Garibaldi 680 215 6555 25041989 69 SCT 449 128 6586 25041989 69 Sector popular 451 153 7947 25041989 69 Tlatelolco TL08 529 173 5668 25041989 69 Tlatelolco TL55 495 173 5009 14091995 73 Alameda 393 122 53710 14091995 73 Garibaldi 391 106 86811 14091995 73 Liconsa 301 962 60012 14091995 73 Plutarco Elıas Calles 335 937 77813 14091995 73 Sector popular 343 125 101214 14091995 73 Tlatelolco TL08 275 78 85915 14091995 73 Tlatelolco TL55 272 74 68316 09101995 75 Cibeles 144 46 85517 09101995 75 CU Juarez 158 51 97618 09101995 75 Centro urbano Presidente Juarez 157 48 82619 09101995 75 Cordoba 249 86 105120 09101995 75 Liverpool 176 63 104521 09101995 75 Plutarco Elıas Calles 192 79 137522 09101995 75 Sector popular 137 53 98423 09101995 75 Valle Gomez 179 718 62324 11011997 69 CU Juarez 162 59 61125 11011997 69 Centro urbano Presidente Juarez 163 55 85726 11011997 69 Garcıa Campillo 187 69 57027 11011997 69 Plutarco Elıas Calles 222 86 76728 11011997 69 Est 10 Roma A 210 776 74129 11011997 69 Est 11 Roma B 204 71 81630 11011997 69 Tlatelolco TL08 160 72 575

0

005

01

015

02

025

03

0 500 1000 1500 2000Sa(T1) (cms2)

Max

imum

inte

rsto

ry d

rift

Figure 4 Incremental dynamic analysis of frame F4


Mexican Building Code to guarantee an adequate structuraldynamic behavior of buildings prone to earthquakes Tofurther illustrate the importance of residual drift demands incomparison with peak interstory drift demands via seismicanalysis Two damage indicators are computed e firstdamage parameter is calculated as the ratio of the maximuminterstory drift demand divided by 3 the threshold value ofmaximum drift to avoid collapse according to the MCBC insuch a way that values equal to or larger than one of thismaximum drift damage index (IDmax) indicates the failure ofthe system in terms of peak drift On the other hand thesecond damage index IDres is similar to the first one but theresidual peak drift demand divided by a value of 05 shouldbe considered (the threshold residual drift limit that could beperceptible to human occupants and it could lead to humandiscomfort [4]) Values larger than one of IDres are related tothe structural failure in terms of residual demands Figure 5compares the IDmax and IDres hazard curves for all theMRSFsat different performance levels It is observed that in the case

of the frames F4 F6 F8 and F10 when the damage index isequals to one the mean annual rate of exceedance (MARE)is smaller in terms of peak interstory drift demands incomparison with the residual drift In other words thestructural reliability of the selected MRSFs is larger for peakdrifts indicating that the control of maximum demand doesnot necessarily guarantee the same level of safety in terms ofresidual drift demands For this reason if the parameter toestimate the structural performance of structures is themaximum interstory drift demand it is necessary to obtainlarger structural reliability levels aimed to provide adequatestructural performance in terms of residual drift because it isnecessary to obtain at least the same structural reliability interms of IDmax and IDres For this reason with the aim toincrease the seismic performance for residual drift demandsPTCs are incorporated in the selected MRSFs

e seismic hazard curves in terms of maximuminterstory drift damage index IDmax obtained for the MRSFsand the PTC steel frames are compared in Figure 6 In this

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

Mea

n an

nual

rate

of e

xcee

danc

e

IDmax IDres

IDresIDmax

(a)

Mea

n an

nual

rate

of e

xcee

danc

e

IDresIDmax

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDmax IDres

(b)

Mea

n an

nual

rate

of e

xcee

danc

e

IDresIDmax

IDmax IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(c)

Mea

n an

nual

rate

of e

xcee

danc

e

IDresIDmax

IDmax IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(d)

Figure 5 Comparison of the IDmax and IDres hazard curves for the MRSFs (a) F4 (b) F6 (c) F8 and (d) F10


figure it can be observed that the structural reliability orthe mean annual rate of exceeding a specific value ofmaximum interstory drift is in general smaller for the steelframe with PTC us the seismic performance in terms ofpeak demands is increasing when the PTCs are in-corporated in the traditional MRSFs which also couldrepresent an increase in the structural reliability for theresidual interstory drift demands as will be discussedbelow

e comparison of the structural reliability for theMRSFs and the PTC frames in terms of residual drift de-mands provided by the IDres (damage index in terms ofresidual displacements) is illustrated in Figure 7 As it wasexpected the mean annual rate of exceedance of IDres value isreduced when PTCs are incorporated into the traditionalsteel frames which is valid for all the structures underconsideration In such a way the use of PTC is a goodalternative for example as a solution for rehabilitation of

buildings or in order to reduce peak and residual driftdemands of traditional structural steel systems under severeearthquakes

Finally a comparison of the mean annual rate ofexceedance values when the damage index is equal to one interms of IDmax for the MRSFs and in terms of IDres for thePTC steel frames is provided in Table 3 e aim of using theMARE values for IDmax is because they represent the targetstructural reliability levels obtained buildings designedaccording to the Mexican Building Code us the MAREvalues in terms of IDres for the PTC steel frames should bereduced in comparison to those of peak interstory drift forthe MRSFs to guarantee that by including PTC in the tra-ditional steel frames it is possible to satisfy the structuralreliability for the residual demands provided by the re-quirements of the Mexican Code In Table 3 a column nameratio was used which represents the ratio of MARE of IDres(PTC steel frames) divided by IDmax (MRSFs) and values

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

Mea

n an

nual

rate

of e

xcee

danc

e

IDmax

Frame PTCMRSF

(a)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDmax

(b)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDmax

(c)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDmax

(d)

Figure 6 Comparison of the IDmax curves for the MRSFs and the PTC steel frames with (a) 4 stories (b) 6 stories (c) 8 stories and (d) 10stories


smaller or equal to one indicates that the structural reliabilityis larger in terms of residual drift demands for the PTCframes comparing with the peak drifts of the MRSFs It isobserved that the values of the mean annual rates ofexceedance for the PTC steel frames are in general smaller tothose of the traditional structures when the damage index isequal to one

3 Conclusions

e structural reliability of four moment-resisting steelframes is estimated in terms of peak and residual interstorydrift seismic demands For this aim all the structures aresubjected to 30 narrow-band ground motion records of thesoft soil of Mexico City e numerical results indicates thatthe structural reliability of the traditional steel frames is notadequate in terms of residual interstory drift demands Forthis reason PTCs are incorporated into the selected steelframed buildings in order to increase the structural reliabilitybased on a damage index for the residual interstory drifts Asit was expected for most of the steel framed buildings theability of self-centering for the steel frames incorporating PTCreduces significantly the residual demands in fact for thistype of structural systems the structural reliability is larger interms of residual interstory drifts formost of the frames underconsideration in comparison with peak demands of the

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

Mea

n an

nual

rate

of e

xcee

danc

e

IDres

Frame PTCMRSF

(a)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDres

(b)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(c)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(d)

Figure 7 Comparison of the IDres hazard curves for the MRSFs and the PTC steel frames with (a) 4 stories (b) 6 stories (c) 8 stories and(d) 10 stories

Table 3 Mean annual rate of exceedance values when the damageindex is equal to one in terms of IDmax for the MRSFs and in termsof IDres for the PTC steel frames

Steelframe

MARE forIDmax 1

Steelframe

MARE forIDres 1 Ratio

F4 000024 F4 000019 079F6 000046 F6 000024 052F8 000089 F8 000057 064F10 000067 F10 000072 107


MRSFs Moreover the seismic performance in terms of peakdemands is also increasing when PTCs are incorporated intothe traditional MRSFs It is concluded that the use of PTC is agood alternative as a solution for rehabilitation of buildings orin order to reduce peak and residual interstory drift seismicdemands of traditional structural steel systems under severeearthquakes Furthermore PTC in steel frames could be aninteresting solution toward structural systems with highseismic resilience

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

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

Acknowledgments

e financial support given by the Universidad Autonomade Sinaloa under grant PROFAPI and the UniversidadMichoacana de San Nicolas de Hidalgo is appreciated eauthors express their gratitude to the Consejo Nacional deCiencia y Tecnologıa (CONACYT) inMexico for funding theresearch reported in this paper under grant Ciencia BasicaFinancial support also was given by DGAPA-UNAM undergrant PAPIIT IN10351 In addition Julian Carrillo thanksthe Vicerrectorıa de Investigaciones at Universidad MilitarNueva Granada for providing research grants

References

[1] E Rosenblueth and R Meli ldquoe 1985 Mexico earthquakecauses and effects in Mexico Cityrdquo Concrete International(ACI) vol 8 no 5 pp 23ndash34 1986

[2] T Okada T Kabeyasawa T Nakano M Maeda andT Nakamura ldquoImprovement of seismic performance ofreinforced concrete school buildings in Japan-Part 1 Damagesurvey and performance evaluation after the 1995 Hyogo-KenNambu earthquakerdquo in Proceedings of the 12th World Con-ference on Earthquake Engineering vol 2421 Auckland NewZealand February 2000

[3] Y Iwata H Sugimoto and H Kuguamura ldquoReparability limitof steel structural buildings based on the actual data of theHyogoken-Nanbu earthquakerdquo in Proceedings of the 38thJoint Panel vol 1057 pp 23ndash32 Wind and Seismic effectsNIST Special Publication Gaithersburg MD USA May 2006

[4] J McCormick H Aburano M Ikenaga and M NakashimaldquoPermissible residual deformation levels for building struc-tures considering both safety and human elementsrdquo in Pro-ceedings of the 14th World Conference on EarthquakeEngineering Beijing China October 2008

[5] E Bojorquez and J Ruiz-Garcıa ldquoResidual drift demands inmoment-resisting steel frames subjected to narrow-bandearthquake ground motionsrdquo Earthquake Engineering andStructural Dynamics vol 42 no 11 pp 1583ndash1598 2013

[6] S Pampanin C Christopoulos and M J Nigel PriestleyldquoPerformance-based seismic response of frame structuresincluding residual deformations part II multi-degree of

freedom systemsrdquo Journal of Earthquake Engineering vol 7no 1 pp 119ndash147 2003

[7] D Pettinga C Christopoulos S Pampanin and N PriestleyldquoEffectiveness of simple approaches in mitigating residualdeformations in buildingsrdquo Earthquake Engineering ampStructural Dynamics vol 36 no 12 pp 1763ndash1783 2006

[8] J Erochko C Christopoulos R Tremblay and H ChoildquoResidual drift response of SMRFs and BRB frames in steelbuildings designed according to ASCE 7-05rdquo Journal ofStructural Engineering vol 137 no 5 pp 589ndash599 2011

[9] J Ruiz-Garcıa and EMiranda ldquoPerformance-based assessmentof existing structures accounting for residual displacementsrdquoJohn A Blume Earthquake Engineering Center TechnicalReport 153 Stanford University Stanford CA USA 2005httpblumestanfordeduBlumeTechnicalReportshtm

[10] J Ruiz-Garcıa and E Miranda ldquoEvaluation of residual driftdemands in regular multi-storey frames for performance-based seismic assessmentrdquo Earthquake Engineering ampStructural Dynamics vol 35 no 13 pp 1609ndash1629 2006

[11] J Ruiz-Garcıa and E Miranda ldquoProbabilistic estimation ofresidual drift demands for seismic assessment of multi-storyframed buildingsrdquo Engineering Structures vol 32 no 1pp 11ndash20 2010

[12] S R Uma S Pampanin and C Christopoulos ldquoDevelopmentof probabilistic framework for performance-based seismicassessment of structures considering residual deformationsrdquoJournal of Earthquake Engineering vol 14 no 7 pp 1092ndash1111 2010

[13] U Yazgan and A Dazio ldquoPost-earthquake damage assess-ment using residual displacementsrdquo Earthquake Engineeringamp Structural Dynamics vol 41 no 8 pp 1257ndash1276 2012

[14] J M Ricles R Sause M M Garlock and C Zhao ldquoPost-tensioned seismic-resistant connections for steel framesrdquoJournal of Structural Engineering vol 127 no 2 pp 113ndash1212001

[15] J M Ricles R Sause S W Peng and LW Lu ldquoExperimentalevaluation of earthquake resistant posttensioned steel con-nectionsrdquo Journal of Structural Engineering vol 128 no 7pp 850ndash859 2002

[16] J M Ricles R Sause Y C Lin and C Y Seo ldquoSelf-centeringmoment connections for damage-free seismic response ofsteel MRFsrdquo in Proceedings of the Structures Congressvol 2010 Orlando FL USA May 2010

[17] C Christopoulos A Filiatrault and C M Uang ldquoSelf-centering post-tensioned energy dissipating (PTED) steelframes for seismic regionsrdquo Report no SSRP-200206 Uni-versity of California Oakland CA USA 2002

[18] C Christopoulos and A Filiatrault ldquoSeismic response ofposttensioned energy dissipating moment resisting steelframesrdquo in Proceedings of the 12th European Conference onEarthquake Engineering London UK September 2002

[19] C Christopoulos A Filiatrault and C M Uang ldquoSeismicdemands on post-tensioned energy dissipating moment-resisting steel framesrdquo in Proceedings of the Steel Structuresin Seismic Areas (STESSA) Naples Italy June 2003

[20] M M Garlock J M Ricles and R Sause ldquoExperimentalstudies of full-scale posttensioned steel connectionsrdquo Journalof Structural Engineering vol 131 no 3 pp 438ndash448 2005

[21] M M Garlock R Sause and J M Ricles ldquoBehavior anddesign of posttensioned steel frame systemsrdquo Journal ofStructural Engineering vol 133 no 3 pp 389ndash399 2007

[22] M M Garlock J M Ricles and R Sause ldquoInfluence of designparameters on seismic response of post-tensioned steel MRF


systemsrdquo Engineering Structures vol 30 no 4 pp 1037ndash10472008

[23] H-J Kim and C Christopoulos ldquoSeismic design procedureand seismic response of post-tensioned self-centering steelframesrdquo Earthquake Engineering amp Structural Dynamicsvol 38 no 3 pp 355ndash376 2009

[24] C C Chung K C Tsai and W C Yang ldquoSelf-centering steelconnection with steel bars and a discontinuous compositeslabrdquo Earthquake Engineering amp Structural Dynamics vol 38no 4 pp 403ndash422 2009

[25] M Wolski J M Ricles and R Sause ldquoExperimental study ofself-centering beam-column connection with bottom flangefriction devicerdquo ASCE Journal of Structural Engineeringvol 135 no 5 2009

[26] G Tong S Lianglong and Z Guodong ldquoNumerical simu-lation of the seismic behavior of self-centering steel beam-column connections with bottom flange friction devicesrdquoEarthquake Engineering and Engineering Vibration vol 10no 2 pp 229ndash238 2011

[27] Z Zhou X T He J Wu C L Wang and S P MengldquoDevelopment of a novel self-centering buckling-restrainedbrace with BFRP composite tendonsrdquo Steel and CompositeStructures vol 16 no 5 pp 491ndash506 2014

[28] Mexico City Building Code Normas Tecnicas Com-plementarias para el Disentildeo por Sismo Departamento del-Distrito Federal Mexico City Mexico 2004 in Spanish

[29] J Shen and A Astaneh-Asl ldquoHysteretic behavior of bolted-angle connectionsrdquo Journal of Constructional Steel Researchvol 51 no 3 pp 201ndash218 1999

[30] R M Richard PRCONN Moment-Rotation Curves for Par-tially Restrained Connections RMR Design Group TucsonArizona 1993

[31] A Carr RUAUMOKO Inelastic Dynamic Analysis ProgramUniversity of Cantenbury Department of Civil EngineeringChristchurch New Zealand 2011

[32] A Lopez-Barraza E Bojorquez S E Ruiz and A Reyes-Salazar ldquoReduction of maximum and residual drifts onposttensioned steel frames with semirigid connectionsrdquoAdvances in Materials Science and Engineering vol 2013Article ID 192484 11 pages 2013

[33] E Bojorquez and S E Ruiz ldquoStrength reduction factors forthe valley of Mexico taking into account low cycle fatigueeffectsrdquo in Proceedings of the 13deg World Conference onEarthquake Engineering Vancouver Canada August 2004

[34] A Teran-Gilmore and J O Jirsa ldquoEnergy demands for seismicdesign against low-cycle fatiguerdquo Earthquake Engineering ampStructural Dynamics vol 36 no 3 pp 383ndash404 2007

[35] M D Trifunac and A G Brady ldquoA study of the duration ofstrong earthquake ground motionrdquo Bulletin of the Seismo-logical Society of America vol 65 no 3 pp 581ndash626 1975

[36] D Vamvatsikos and C A Cornell ldquoIncremental dynamicanalysisrdquo Earthquake Engineering and Structural Dynamicsvol 26 no 3 pp 701ndash716 2002

[37] G G Deierlein ldquoOverview of a comprehensive framework forperformance earthquake assessmentrdquo Report PEER 200405Pacific Earthquake Engineering Center Berkeley California2004

[38] E Bojorquez A Teran-Gilmore S E Ruiz and A Reyes-Salazar ldquoEvaluation of structural reliability of steel framesinterstory drift versus plastic hysteretic energyrdquo EarthquakeSpectra vol 27 no 3 pp 661ndash682 2011

[39] E Bojorquez and I Iervolino ldquoSpectral shape proxies andnonlinear structural responserdquo Soil Dynamics and EarthquakeEngineering vol 31 no 7 pp 996ndash1008 2011

[40] J L Alamilla Reliability-based seismic design criteria forframed structures PhD thesis Universidad NacionalAutonoma de Mexico UNAM Mexico City Mexico 2001 inSpanish


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

frames exhibit peak drift demands about 3 they couldexperience residual drifts larger than 05 which is thethreshold residual drift that could be tolerable to humanoccupants and it could lead to human discomfort [4] whensubjected to narrow-band earthquake groundmotions of highintensity erefore several researchers have demonstratedthat the estimation of residual drift demands should also playan important role during the design of new buildings [6ndash8]and the evaluation of the seismic structural performance ofexisting buildings [9ndash13]

In the present study motivated by the need to reduce peakand residual interstory drift demands PTCs are incorporatedinto various MRSFs Posttensioned steel moment-resistingframes are structural systems proposed in recent years as anappropriate alternative to welded connections of moment-resisting frames in seismic zones [14ndash27] ey are designedto prevent brittle fractures in the area of the nodes of steelframes which can cause severe reduction in their ductilitycapacity as occurred in many cases during the 1994Northridge and the 1995 Kobe earthquakes e philosophyof structures with PTC is that under an intense earthquakemotion beams and columns remain essentially elastic con-centrating the damage on the energy dissipating elementswhich can be easily replaced at low cost Moreover theyprovide capacity of energy dissipation and self-centeringwhich can significantly reduce the residual demands estructural performance of the selected MRSFs is comparedwith the structures with PTC through incremental dynamicanalysis and the estimation of the structural reliability of theframes in terms of peak and residual interstory drift demandsWith this aim four MRSFs and the same structures with PTC(here named FPTC frames with posttensioned connections)are subjected to 30 long-duration groundmotions recorded atthe lake zone of Mexico City where most of the damages werefound in buildings as a consequence of the 1985 Michoacanearthquake In general it is observed that the structural re-liability of the steel frames with PTC is superior to that of theMRSFs In particular the residual drift demands tend to besmaller than 05 (which is perceptible for building occu-pants) when PTCs are incorporated into the steel structures

2 Methodology

21 Structural Steel Frame Models Two groups of fourstructural steel frame models are selected for the study efirst group of structures corresponding to moment-resistingsteel frames was designed according to the Mexico CityBuilding Design Provisions (MCSDPs) [28]e buildings areassumed to be for office occupancy ey have 4 6 8 and 10stories and 3 bays hereafter indicated as F4 F6 F8 and F10respectively e dimensions of the frames are shown inFigure 1 e beams and columns are A36 steel W sections Abilinear hysteretic model for accounting the nonlinear ma-terial behavior with 3 of postyielding stiffness was con-sidered for the analyses and the damping used was 3 ofcritical e fundamental periods of vibration (T1) are 09107 120 and 137 s respectively On the other hand theFPTCs were designed in accordance with the recommen-dations proposed by Garlock et al [21] which basically start

with the design of the steel frames as usually done (consid-ering rigid connections) and then the semirigid post-tensioned connections are designed to satisfy therequirements of the serviceability and resistance conditionse beam-column connections consist of two angles bolted tothe flanges of the beam and to the column flange (top andseat) For the design of posttensioned connections steel grade50 was used for the angles e length of the angles was takenequal to the width of the flange of the beams (bf ) Differentangle sizes were tested but at the end 152times152times13mmangles were used in all the cases Posttensioned cables consistof seven wires with an area of 150mm2 withstanding a load of279 kN they are parallel to the axis of the beam passingthrough the interior columns and fixed to the outer face of thecolumns at the ends of the frame An initial tension of thecables less than 033 times their maximum capacity was usedaccording with the suggestions given by Garlock et al [21]e four FPTC models are identified here as F4PTC F6PTCF8PTC and F10PTC for the frames with 4 6 8 and 10stories respectively e FPTC models have fundamentalperiods of vibration of 089 103 125 and 137 s respectivelye columns of the ground floor are fixed at the base withoutbeing posttensioned e beam and column members usedfor all the frames are illustrated in Table 1 Note that themechanical characteristics and dimensions of beams andcolumns are the same for both theMRSFs and FPTC Figure 2shows a typical assembly of a posttensioned steel frame

22 Connection Model Nonlinear Hysteretic Behaviore hysteretic rules that represent the cyclic behavior of thesemirigid connections of the posttensioned frames are char-acterized by moment-rotation curves (M-θr) with shapessimilar to a flag is representation characterizes the non-linearity self-centering capability and energy dissipationcapacity of the connection Experimental tests with isolatedangles subjected to cyclic and monotonic loads conducted byShen andAstaneh-Asl [29] showed a stable cyclic response andgood capability of hysteretic energy dissipation In generalultimate strength exceeded 3 times the yield strength andductility reached values between 8 and 10 e strength andstiffness in bending of the posttensioned connections is

80m 80m 80m

35m

35m

35m

Variable number of stories

Figure 1 Geometrical characteristics of the MRSFs





1 + kminus kp1113872 1113873θr1113872 1113873Mo

11138681113868111386811138681113868

11138681113868111386811138681113868N

1113876 11138771N

+ kp + kθS1113872 1113873θr

(1)



11138681113868111386811138681113868

11138681113868111386811138681113868N

1113876 11138771N


(2)





1113868111386811138681113868

(3)









P EDPgt edp Sa1113868111386811138681113868 T1( 1113857 sa1113960 1113961

middot dλSa T1( ) sa( 111385711138681113868111386811138681113868

11138681113868111386811138681113868

(4)





⎛⎝ ⎞⎠

(5)




PT strands

Shimplate

Angle

PTstrands

Reinforcingplate


M

M

My

Md

Mc

θrθr (rad)

(θa Ma)








0

005

01

015

02

025

03

0 500 1000 1500 2000Sa(T1) (cms2)

Max

imum

inte

rsto

ry d

rift






0000001

000001

00001

0001

001

01

1

0 05 1 15 2

Mea

n an

nual

rate

of e

xcee

danc

e

IDmax IDres

IDresIDmax

(a)

Mea

n an

nual

rate

of e

xcee

danc

e

IDresIDmax

0000001

000001

00001

0001

001

01

1


(b)

Mea

n an

nual

rate

of e

xcee

danc

e

IDresIDmax

IDmax IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(c)

Mea

n an

nual

rate

of e

xcee

danc

e

IDresIDmax

IDmax IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(d)







0000001

000001

00001

0001

001

01

1

0 05 1 15 2

Mea

n an

nual

rate

of e

xcee

danc

e

IDmax

Frame PTCMRSF

(a)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDmax

(b)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDmax

(c)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDmax

(d)




3 Conclusions


0000001

000001

00001

0001

001

01

1

0 05 1 15 2

Mea

n an

nual

rate

of e

xcee

danc

e

IDres

Frame PTCMRSF

(a)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDres

(b)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(c)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(d)



Steelframe

MARE forIDmax 1

Steelframe


F4 000024 F4 000019 079F6 000046 F6 000024 052F8 000089 F8 000057 064F10 000067 F10 000072 107



Data Availability




Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





1 + kminus kp1113872 1113873θr1113872 1113873Mo

11138681113868111386811138681113868

11138681113868111386811138681113868N

1113876 11138771N

+ kp + kθS1113872 1113873θr

(1)



11138681113868111386811138681113868

11138681113868111386811138681113868N

1113876 11138771N


(2)





1113868111386811138681113868

(3)









P EDPgt edp Sa1113868111386811138681113868 T1( 1113857 sa1113960 1113961

middot dλSa T1( ) sa( 111385711138681113868111386811138681113868

11138681113868111386811138681113868

(4)





⎛⎝ ⎞⎠

(5)




PT strands

Shimplate

Angle

PTstrands

Reinforcingplate


M

M

My

Md

Mc

θrθr (rad)

(θa Ma)








0

005

01

015

02

025

03

0 500 1000 1500 2000Sa(T1) (cms2)

Max

imum

inte

rsto

ry d

rift






0000001

000001

00001

0001

001

01

1

0 05 1 15 2

Mea

n an

nual

rate

of e

xcee

danc

e

IDmax IDres

IDresIDmax

(a)

Mea

n an

nual

rate

of e

xcee

danc

e

IDresIDmax

0000001

000001

00001

0001

001

01

1


(b)

Mea

n an

nual

rate

of e

xcee

danc

e

IDresIDmax

IDmax IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(c)

Mea

n an

nual

rate

of e

xcee

danc

e

IDresIDmax

IDmax IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(d)







0000001

000001

00001

0001

001

01

1

0 05 1 15 2

Mea

n an

nual

rate

of e

xcee

danc

e

IDmax

Frame PTCMRSF

(a)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDmax

(b)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDmax

(c)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDmax

(d)




3 Conclusions


0000001

000001

00001

0001

001

01

1

0 05 1 15 2

Mea

n an

nual

rate

of e

xcee

danc

e

IDres

Frame PTCMRSF

(a)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDres

(b)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(c)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(d)



Steelframe

MARE forIDmax 1

Steelframe


F4 000024 F4 000019 079F6 000046 F6 000024 052F8 000089 F8 000057 064F10 000067 F10 000072 107



Data Availability




Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





P EDPgt edp Sa1113868111386811138681113868 T1( 1113857 sa1113960 1113961

middot dλSa T1( ) sa( 111385711138681113868111386811138681113868

11138681113868111386811138681113868

(4)





⎛⎝ ⎞⎠

(5)




PT strands

Shimplate

Angle

PTstrands

Reinforcingplate


M

M

My

Md

Mc

θrθr (rad)

(θa Ma)








0

005

01

015

02

025

03

0 500 1000 1500 2000Sa(T1) (cms2)

Max

imum

inte

rsto

ry d

rift






0000001

000001

00001

0001

001

01

1

0 05 1 15 2

Mea

n an

nual

rate

of e

xcee

danc

e

IDmax IDres

IDresIDmax

(a)

Mea

n an

nual

rate

of e

xcee

danc

e

IDresIDmax

0000001

000001

00001

0001

001

01

1


(b)

Mea

n an

nual

rate

of e

xcee

danc

e

IDresIDmax

IDmax IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(c)

Mea

n an

nual

rate

of e

xcee

danc

e

IDresIDmax

IDmax IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(d)







0000001

000001

00001

0001

001

01

1

0 05 1 15 2

Mea

n an

nual

rate

of e

xcee

danc

e

IDmax

Frame PTCMRSF

(a)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDmax

(b)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDmax

(c)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDmax

(d)




3 Conclusions


0000001

000001

00001

0001

001

01

1

0 05 1 15 2

Mea

n an

nual

rate

of e

xcee

danc

e

IDres

Frame PTCMRSF

(a)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDres

(b)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(c)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(d)



Steelframe

MARE forIDmax 1

Steelframe


F4 000024 F4 000019 079F6 000046 F6 000024 052F8 000089 F8 000057 064F10 000067 F10 000072 107



Data Availability




Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







0

005

01

015

02

025

03

0 500 1000 1500 2000Sa(T1) (cms2)

Max

imum

inte

rsto

ry d

rift






0000001

000001

00001

0001

001

01

1

0 05 1 15 2

Mea

n an

nual

rate

of e

xcee

danc

e

IDmax IDres

IDresIDmax

(a)

Mea

n an

nual

rate

of e

xcee

danc

e

IDresIDmax

0000001

000001

00001

0001

001

01

1


(b)

Mea

n an

nual

rate

of e

xcee

danc

e

IDresIDmax

IDmax IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(c)

Mea

n an

nual

rate

of e

xcee

danc

e

IDresIDmax

IDmax IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(d)







0000001

000001

00001

0001

001

01

1

0 05 1 15 2

Mea

n an

nual

rate

of e

xcee

danc

e

IDmax

Frame PTCMRSF

(a)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDmax

(b)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDmax

(c)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDmax

(d)




3 Conclusions


0000001

000001

00001

0001

001

01

1

0 05 1 15 2

Mea

n an

nual

rate

of e

xcee

danc

e

IDres

Frame PTCMRSF

(a)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDres

(b)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(c)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(d)



Steelframe

MARE forIDmax 1

Steelframe


F4 000024 F4 000019 079F6 000046 F6 000024 052F8 000089 F8 000057 064F10 000067 F10 000072 107



Data Availability




Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





0000001

000001

00001

0001

001

01

1

0 05 1 15 2

Mea

n an

nual

rate

of e

xcee

danc

e

IDmax IDres

IDresIDmax

(a)

Mea

n an

nual

rate

of e

xcee

danc

e

IDresIDmax

0000001

000001

00001

0001

001

01

1


(b)

Mea

n an

nual

rate

of e

xcee

danc

e

IDresIDmax

IDmax IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(c)

Mea

n an

nual

rate

of e

xcee

danc

e

IDresIDmax

IDmax IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(d)







0000001

000001

00001

0001

001

01

1

0 05 1 15 2

Mea

n an

nual

rate

of e

xcee

danc

e

IDmax

Frame PTCMRSF

(a)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDmax

(b)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDmax

(c)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDmax

(d)




3 Conclusions


0000001

000001

00001

0001

001

01

1

0 05 1 15 2

Mea

n an

nual

rate

of e

xcee

danc

e

IDres

Frame PTCMRSF

(a)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDres

(b)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(c)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(d)



Steelframe

MARE forIDmax 1

Steelframe


F4 000024 F4 000019 079F6 000046 F6 000024 052F8 000089 F8 000057 064F10 000067 F10 000072 107



Data Availability




Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






0000001

000001

00001

0001

001

01

1

0 05 1 15 2

Mea

n an

nual

rate

of e

xcee

danc

e

IDmax

Frame PTCMRSF

(a)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDmax

(b)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDmax

(c)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDmax

(d)




3 Conclusions


0000001

000001

00001

0001

001

01

1

0 05 1 15 2

Mea

n an

nual

rate

of e

xcee

danc

e

IDres

Frame PTCMRSF

(a)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDres

(b)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(c)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(d)



Steelframe

MARE forIDmax 1

Steelframe


F4 000024 F4 000019 079F6 000046 F6 000024 052F8 000089 F8 000057 064F10 000067 F10 000072 107



Data Availability




Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



3 Conclusions


0000001

000001

00001

0001

001

01

1

0 05 1 15 2

Mea

n an

nual

rate

of e

xcee

danc

e

IDres

Frame PTCMRSF

(a)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

0000001

000001

00001

0001

001

01

1

0 05 1 15 2IDres

(b)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(c)

Mea

n an

nual

rate

of e

xcee

danc

e

Frame PTCMRSF

IDres

0000001

000001

00001

0001

001

01

1

0 05 1 15 2

(d)



Steelframe

MARE forIDmax 1

Steelframe


F4 000024 F4 000019 079F6 000046 F6 000024 052F8 000089 F8 000057 064F10 000067 F10 000072 107



Data Availability




Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Data Availability




Acknowledgments


References















































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia
























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


improvingthestructuralreliabilityofsteelframesusing...

Documents