research article analysis of the seismic performance of...

Research ArticleAnalysis of the Seismic Performance of Isolated Buildingsaccording to Life-Cycle Cost

Yu Dang12 Jian-ping Han2 and Yong-tao Li2

1Key Laboratory of Concrete and Prestressed Concrete Structure Ministry of Education Nanjing 210096 China2School of Civil Engineering Lanzhou University of Technology Lanzhou Gansu 730050 China

Correspondence should be addressed to Yu Dang 601363791qqcom

Received 19 August 2014 Accepted 19 December 2014

Academic Editor Carlos M Travieso-Gonzalez

Copyright copy 2015 Yu Dang et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper proposes an indicator of seismic performance based on life-cycle cost of a building It is expressed as a ratio of lifetimedamage loss to life-cycle cost and determines the seismic performance of isolated buildings Major factors are considered includinguncertainty in hazard demand and structural capacity initial costs and expected loss during earthquakes Thus a high indicatorvalue indicates poor building seismic performance Moreover random vibration analysis is conducted to measure structuralreliability and evaluate the expected loss and life-cycle cost of isolated buildingsThe expected loss of an actual seven-story isolatedhospital building is only 37 of that of a fixed-base building Furthermore the indicator of the structural seismic performance ofthe isolated building is much lower in value than that of the structural seismic performance of the fixed-base building Thereforeisolated buildings are safer and less risky than fixed-base buildings The indicator based on life-cycle cost assists owners andengineers in making investment decisions in consideration of structural design construction and expected loss It also helpsoptimize the balance between building reliability and building investment

1 Introduction

The life-cycle cost of a building is the entire cost over itsexpected life time including initial investment maintenanceand repair costs It also covers loss in occasional cases suchas that incurred during earthquakes The optimum seismicperformance of a building can be considered ldquothe reasonablebalance between the initial investment cost of improvingseismic performance and the prospective loss as a result ofearthquakesrdquo [1] Life-cycle cost can be regarded as an indi-cator of structural seismic performance because the cost ofearthquake damage can be quantified

Many of the following studies determine the optimalseismic design by minimizing life-cycle cost Nathwani et al[2] Pandey and Nathwani [3] and Rackwitz [4] developedoptimal designs simply by minimizing the expected life-cyclecost based on its magnitude of uncertainty Liu et al [5] sug-gested a two-objective optimization procedure to design steelmoment-resisting frame buildings within a performance-based seismic design framework In this procedure the initialmaterial and life time costs of seismic damage are treated

as two separate objectives Lagaros et al [1] adopted thelimit-state cost to compare descriptive and performance-based design procedures Frangopol and Liu [6] reviewed therecent developments in life-cycle maintenance and manage-ment planning for deteriorating civil infrastructures espe-cially bridges Kappos andDimitrakopoulos [7] implementeddecision-making tools namely cost-benefit and life-cyclecost analyses to determine the feasibility of strengtheningreinforced-concrete buildings Pei and van de Lindt [8] alsoproposed a probabilistic framework to estimate long-termearthquake-induced economic loss related to wood-framestructures

Several studies have analyzed the life-cycle cost of isolatedbuildings Lee et al [9] studied the life-cycle cost of astructure with base isolation The results of life-cycle costanalysis indicate that isolators reduced the life-cycle cost byapproximately 16 Moreover Sarkisian et al [10] designed a12-story structure for the Administrative Office of the CourtsLife-cycle cost analysis assisted in informed decision makingand system selection and the final design featured a steel-framed superstructure with an isolation system Chatzidaki

Hindawi Publishing CorporationComputational Intelligence and NeuroscienceVolume 2015 Article ID 495042 7 pageshttpdxdoiorg1011552015495042

2 Computational Intelligence and Neuroscience

[11] optimized the design of and economically evaluated rein-forced-concrete (RC) isolated structures Generally theresearchers have a similar conclusion the life-cycle cost ofisolated buildings is less than that of the fixed-base buildings

In the current study structural seismic performance ismeasured according to indicator-based life-cycle cost Thiscost can synthesize all factors including structural designconstruction and expected loss from earthquakes The indi-cator of an isolated building is analyzed in detail in com-parison with that of a fixed-base building in the followingsections Practical construction complexity important butdifficult to be included in initial cost analysis is taken into dueaccount by a proposed diversity index as another objectivethis approximation data is best used for the preliminarydesign stage and the large pools of alternatives leave to adesign maker much freedom to select the one that best meetshisher goals

2 Indicator-Based Life-Cycle Cost ofStructural Seismic Performance

21 Life-Cycle Cost of Structures The life-cycle cost of astructure may refer either to the design life of a new structureor to the remaining life of an existing or retrofitted structureThis cost can be expressed as a function of time and of thedesign vector [1]

119862tot (119905 119904) = 119862in (119904) + 119890minus120582119905

119862ls (119905 119904) (1)

where 119862tot is the total cost of a structure 119862in is the initial costof a new or retrofitted structure 119862ls is expected loss 119905 is thetime period 119904 is the design vector corresponding to the designloads resistance and material properties that influence theperformance of the structural system and 120582 is the constantannual discount rate and is usually equal to 3 [1]

119862ls can be written as [1]

119862ls (119905 119904) = sum

119895

sum

119894

[119862ls (119861119894) 119875 (119861119894 | 119868)] 119875 (119868119895) (2)

where 119875(119861119894

| 119868) is the conditional probability of failurewhich can be obtained through dynamic reliability analysis119868 is fortification intensity 119875(119868

119895

) is the probability of seismichazard and 119868

119895

denotes the three seismic design levels namelyminor (119868

119904

) moderate (119868119898

) and major earthquakes (119868119897

) Thecumulative distribution function of fortification intensity isa type III extreme value distribution during the design refer-ence period in Mainland China Thus 119875(119868

119904

) 119875(119868119898

) and 119875(119868119897

)

are approximately equal to 70 252 and 45 respectively[12]

119861 represents structural damage and can be divided intofive levels that is none slight moderate severe and col-lapsed These structural damage states are defined by specificquantities Interstory drift can be a reliable limit-state cri-terion according to which expected damage can be deter-mined Thus maximum interstory drift (120579) is considered theresponse parameter that best characterizes structural dam-age The damage index limits of isolated superstructures aresimilar to those of fixed-base buildings however these limitshave not been determined for the isolated layer The damage

Table 1 Damage index limits for RC frames

Damage state None Slight Moderate Severe CollapsedDriftratio

Superstructure 0002 0004 0008 002 005Isolated layer 051 090 128 179 205

states are quantitatively defined in terms of interstory driftgiven that the isolator may be damaged when its shear strainexceeds the acceptable value as shown in Table 1

119862ls corresponds to the limit-state economic and noneco-nomic loss from earthquakes The economic loss consistsof direct and indirect economic loss relief costs and long-term investment Noneconomic loss mainly involves the lossof human life The economic quantification of these lossesdepends on several socioeconomic parameters and the mostdifficult cost to quantify is that which corresponds to theloss of human life This loss can be estimated using variousapproaches that range from purely economic reasoning tomore sensitive concepts that consider human loss to be irre-placeable These cost components are related to RC buildingdamage 119862 is initial building cost 119875 is the total number ofhuman beings in the building and 119886 119890 and 119889 are the ratiosof indirect economic loss relief cost and structural contentrespectively These data are derived from [13] as shown inTable 2Thus119862ls can be determined based on initial cost andbuilding function

22 Indicator of Structural Seismic Performance As with thecoefficient of investment risk the indicator of structural seis-mic performance can be expressed as

120593 = 1 minus119862in (119904)

119862tot (119905 119904)= 1 minus

119862in (119904)

119862in (119904) + 119890minus120582119905119862ls (119905 119904)

=119890minus120582119905

119862ls (119905 119904)

119862tot (119905 119904)

(3)

where 120593 is the indicator of structural seismic performancebased on life-cycle cost It represents the proportion ofexpected damage to life-cycle cost A high 120593 value increasesthe risk of the expected economic loss and indicates the poorseismic performance of a building

3 Conditional Failure Probability ofIsolated Buildings

The calculation of conditional failure probability is key tolife-cycle cost evaluation Thus random dynamic analysis isalso conducted in this study to determine dynamic reliabilityConsequently the conditional failure probability of isolatedbuildings can be calculated

31 Random Dynamic Analysis of Isolated Buildings Thenonlinear behavior of isolated buildings is presented in aBouc-Wen model The equivalent linearization method isapplied and the equations of motion can thus be obtained

MY + CY + KY + Kh120592 = minusMEug

+ CeqY + Keq120592 = 0(4)

Computational Intelligence and Neuroscience 3

Table 2 Limit-state parameters for cost evaluation (10000 yuan)

Damage state None Slight Moderate Severe CollapsedEconomic loss 0 01(1 + 119886 + 119890) times 119862 04(1 + 119886 + 119890) times 119862 [07(1 + 119886 + 119890) + 03119889] times 119862 (1 + 119886 + 119890 + 095119889) times 119862

Noneconomic loss 0 00011 times 119875 00268 times 119875 02050 times 119875 22350 times 119875

where

M =[[[

[

1198981

0 0 0

1198982

1198982

0 0

sdot sdot sdot

119898119899

119898119899

119898119899

119898119899

]]]

]

C =

[[[[[[[

[

1198881

minus1198882

0

1198882

minus1198883

1198883

minus1198884

sdot sdot sdot

119888119899minus1

minus119888119899

0 119888119899

]]]]]]]

]

K =

[[[[[[[

[

1205721

1198961

minus1205722

1198962

0

1205722

1198962

minus1205723

1198963

1205723

1198963

minus1205724

1198964

sdot sdot sdot

120572119899minus1

119896119899minus1

minus120572119899

119896119899

0 120572119899

119896119899

]]]]]]]

]

Kh =

[[[[[[[

[

(1 minus 1205721

) 1198961

minus (1 minus 1205722

) 1198962

0

(1 minus 1205722

) 1198962


) 1198963

(1 minus 1205723

) 1198963


) 1198964

sdot sdot sdot

(1 minus 120572119899minus1

) 119896119899minus1

minus (1 minus 120572119899

) 119896119899

0 (1 minus 120572119899

) 119896119899

]]]]]]]

]

Ceq =[[[

[

119862eq1 0

119862eq2d

0 119862eq119899

]]]

]

Keq =[[[

[

119870eq1 0

119870eq2d

0 119870eq119899

]]]

]

(5)

When the parameters of the Bouc-Wen model are 119860 = 1 119899 =2 then

119862eq119894 = minus1 +2

120587120573119894

1205902

120592119894

[120601 minus1

2sin (2120601) minus 120587

2] + 120574119894

1205902

120592119894

119870eq119894 =4

120587120573119894

120590119909119894120590120592119894 (1 minus 120588

2

119909119894120592119894

)15

+120588119909119894120592119894[120601 minus

1

2sin (2120601) minus 120587

2]

+ 2120574119894

119864 [119894

120592119894

]

120601 = arctg(radic1 minus 120588

2

119909119894120592119894

120588119909119894120592119894

) 120588119909119894119911119894=119864 [119894

120592119894

]

120590119909119894120590120592119894

(6)

whereE = 1 0 sdot sdot sdot 0119879 119888119894

= 2119898119894

120596120577119894

and120596 and 120577119894

are thefundamental frequencies and the damping ratio of a buildingrespectively Consider 120577

119894

= 005Assuming that the ground motion is stationary with

zero mean and that the power spectral density of groundacceleration is expressed as the Kanai-Tajimi spectrum the


pseudoexcitation method can then be used to analyze therandom response of a building

Given pseudoexcitation 119906119892

= radic119878119892(120596)119890119894120596119905 the response

of (4) can be written as

Y = B119890119894120596119905 Y = 119894120596B119890119894120596119905 Y = minus1205962B119890119894120596119905

= B1015840119890119894120596119905(7)

where B is the amplitude vector of the pseudoresponse Con-sider

B = Br + 119894Bi

Br =minusGr

G2r + G2iEradic119878119892(120596) Bi =

GiG2r + G2i

Eradic119878119892(120596)

Gr = Mminus1K minus 1205962I + 120596Mminus1KhTiCeq

Gi = 120596Mminus1C minus 120596Mminus1KhTrCeq

(8)

where Ti and Tr are the diagonal matrices The respectivediagonal elements are then obtained by

119879119894119895=

minus120596

1198702

eq119895 + 1205962

119879119903119895=

119870eq119895

1198702

eq119895 + 1205962

119895 = 1 2 119899

B1015840 = (120596Ti minus 119894120596Tr)CeqB

(9)

If a set of 120596 can be generated then the pseudoresponsecan be determined Finally the power spectral density of theresponse is written as

119878

119884

(120596) =Ylowast

sdotY119879

119878120592

(120596) = lowast

sdot 119879

119878

119884120592

(120596) =Ylowast

sdot 119879

(10)

If the input is a stationary process with zero mean thenthe response is a stationary process with zero mean as wellThus

120583119910

= 0 1205902

119910

= 119864 [ 1199102

] = int

+infin

minusinfin

119878

119884

(120596) 119889120596

120583120592

= 0 1205902

120592

= 119864 [1205922

] = int

+infin

minusinfin

119878120592

(120596) 119889120596

119864 [ 119910120592] = int

+infin

minusinfin

119878

119884120592

(120596) 119889120596

(11)

The power spectral density of the structural responseis computed using (4)sim(11) Iteration may be required toproduce a solution We therefore obtain the mean squarevalue of the displacement in each layer with

1205902

119910

= 119864 [1199102

] = int

+infin

minusinfin

119878119884

(120596) 119889120596 (12)

Themean variance and coefficient variation of themaxi-mum interstory drift may be calculated using

120583120579119898119894

=120583119910119898119894

ℎ119894

120590120579119898119894

=120590119910119898119894

ℎ119894

120575120579119898119894

=120590119910119898119894

120583119910119898119894

(13)

where ℎ119894

is the height of each story and 120583119910119898119894

and 120590119910119898119894

are themean and variance of the maximum displacement in eachstory respectively 120583

119910119898119894and 120590

119910119898119894can be written as [14]

120583119910119898119894

= 119901119894

120590119910119894 120590

119910119898119894= 119891119894

120590119910119894 (14)

119901119894

and119891119894

are the factors of maximum earthquake accelerationand are expressed as

119901119894

= radic2 ln (]119894

120591) +05772

radic2 ln (]119894

120591)

119891119894

=120587

radic12 ln (]119894

120591)

(15)

]119894

is the zero rate of earthquake response ]119894

= 120590119910119894120587120590119910119894 120591 is

the characteristic value of earthquake groundmotion 120591 = 55

for hard soil [12]

32 Conditional Probability of Failure in Isolated BuildingsThe limit-state equation of isolated buildings can be ex-pressed as

119885 = 120579 minus 120579119898

= 0 (16)

The conditional failure probability is computed by

119875119891

= 119875 (119885 lt 0) = 119875 (120579 lt 120579119898

| 119868 = 1198680

120591) = 1 minus Φ (120573) (17)

where 1198680

and 120573120579119894

are the seismic fortification intensity and thereliability of the structure respectively The seismic responseof the structuremeets log-normal distribution if the structureis an RC frame As per the JC method 120573

120579119894

is written as

120573120579119894

=

ln [120583120579119894radic1 + 120575

2

120579119898119894

120583120579119898119894radic1 + 120575

2

120579119894

]

radicln (1 + 1205752120579119894

) (1 + 1205752

120579119898119894

)

(18)

where 120583120579119894is the mean value of the seismic isolation layer and

120583120579119894= 120579119894

and 120575120579119894is the variation coefficient of the maximum

interstory drift ratio 1205751205790

= 035 for the isolation layer and120575120579119894= 03642 for the 119894th story 120583

120579119898119894and 120575

120579119898119894can be computed

with (13)An isolated building fails if any floor fails therefore the

reliability of this building can be determined using

120573 =

119899

prod

119894=1

120573120579119894

(19)

4 Numerical Example and Analysis

The structural seismic performance of isolated buildings iscompared with that of fixed-base buildings by taking theisolated building as a numerical example


Table 3 Structural parameters of the numerical example

119896 (kNm) 120573 120574 Mass (103 kg) ℎ (m)Isolation Fixed-base Isolation Fixed-base Isolation Fixed-base

Isolation layer 1513071 mdash 05 mdash 05 mdash 21429 031 1390000 1946000 3729 3729 minus1243 minus1243 20464 422 1470000 2058000 5302 5302 minus1767 minus1767 19572 333 1370000 1918000 6848 6848 minus2283 minus2283 18388 334 1290000 1806000 8237 8237 minus2746 minus2746 14887 335 1070000 1498000 11191 11191 minus3730 minus3730 8788 336 1660000 2324000 93468 93468 minus31156 minus31156 4354 157 204000 285600 30632 30632 minus10211 minus10211 1354 3

Table 4 Economic and noneconomic losses in different damage states (10000 yuan)

Damage state None Slight Moderate Severe CollapsedEconomic loss 0 0106 times 119862 0424 times 119862 1192 times 119862 2485 times 119862

Noneconomic loss 0 308 7504 574 6258

41 Numerical Example Aseven-story hospital buildingwitha reinforced-concrete frame is designed for Gulang ChinaThe following design parameters are applied seismic pre-cautionary intensity 9 basic acceleration of ground motion040 g site class II and total building area of 778951m2 Table3 shows the other parameters for both isolated and fixed-base buildings In addition the parameters of the Bouc-Wenmodel for a superstructure are as follows

119860119894

= 1 119899119894

= 2 120572119894

= 002 (20)

The parameter of the Bouc-Wen model for an isolatedlayer is

120572 = 01 (21)

42 Seismic Performance of Isolated Buildings Based onLife-Cycle Cost

421 Initial Costs The initial cost of the isolated buildingis 13278 million yuan Specifically the isolators cost 810000yuan This initial cost is higher than that of a fixed-basebuilding because the seismic measures of the superstructurehospital building are strengthened by the requirements ofChinese seismic design provisions The initial cost of a fixed-base building is reduced by 1 of that of an isolated buildingthat is 13145 million yuan as per the statistical data [13]

422 Expected Loss from Earthquakes The building housesapproximately 2800 people Table 4 depicts the economiclosses and the casualties under different situations accordingto the analysis above 119862 is the initial cost of the structure

When the precautionary seismic intensity of the buildingis grade 9 the peak accelerations of the different earthquakelevels that is minor moderate and strong earthquakes are14 40 and 62mS2 respectively Table 5 displays the condi-tional probability of failures in the isolated and the fixed-basebuildings at various earthquake-risk levels

Assuming that the lifetime of the building is 50 yearsthe probabilities of exceeding this lifetime are 70 252and 45 given the varied earthquake levels Table 6 exhibitsthe expected loss at these levels The total expected loss isexpressed as the sum of the losses at the different risk levelsthus

the expected loss of the isolated building 119862ls = 0 +

31471 + 20059 = 51530 (10000 yuan)the expected loss of the fixed-base building 119862ls =

10946 + 23534 + 105069 = 139549 (10000 yuan)

423 Life-Cycle Costs Life-cycle cost is the sum of the initialcost and the expected loss Given the discounted factor overtime 119905 = 50 and annual constant discount rate 120582 = 003 then

the life-cycle cost of the isolation building is 119862tot =

13278 + 26436119890minus003times50

= 13337 (10000 yuan)the life-cycle cost of the fixed-base building is 119862tot =

13145 + 139549119890minus003times50

= 13456 (10000 yuan)

424 Indicator of Structural Seismic Performance By sub-stituting the initial and the life-cycle costs into (3) we candetermine the seismic performance of the isolated and thefixed-base buildings

Isolated building

120593 = 1 minus119862in (119904)

119862tot (119905 119904)= 1 minus

13278

13337= 00044 (22)

Fixed-base building

120593 = 1 minus119862in (119904)

119862tot (119905 119904)= 1 minus

13145

13456= 00231 (23)

The indicator of the structural seismic performance of theisolated building ismuch lower in value than that of the struc-tural seismic performance of the fixed-base building There-fore isolated buildings are safer and less risky than fixed-basebuildings


Table 5 Conditional probability of failure

119861119894

Minor earthquake Moderate earthquake Strong earthquakeSeismic isolation Not isolated Seismic isolation Not isolated Seismic isolation Not isolated

None 00489 00015 02710 1 04643 1Slight 0 01098 08683 03427 09965 1Moderate 0 0 0 00705 04740 1Severe 0 0 0 0 0 07287Collapsed 0 0 0 0 0 0

Table 6 Lifetime losses from damage in isolated and fixed-base buildings (10000 yuan)

119861119894

Minor earthquake Moderate earthquake Major earthquakeSeismic isolation Not isolated Seismic isolation Seismic isolation Not isolated Seismic isolation

None 0000 0000 0000 0000 0000 0000Slight 0000 10946 31471 12299 6450 6409Moderate 0000 0000 0000 11235 13609 28457Severe 0000 0000 0000 0000 0000 70203Collapsed 0000 0000 0000 0000 0000 0000Total 0000 10946 31471 23534 20059 105069

5 Conclusion

This paper proposes an indicator of structural seismic per-formance based on life-cycle cost The indicator is expressedas a ratio of lifetime damage loss to life-cycle cost Thusmajor factors are considered including the uncertainty inhazard demand and structural capacity nonlinear structuralresponse behavior balance of costs and loss from earth-quakes Therefore a high indicator value indicates the poorseismic performance of a building We take an actual seven-story isolated hospital building during an earthquake atGulang Gansu China as an example and conduct a randomvibration analysis to determine the dynamic reliability andconditional failure probability By substituting the dynamicreliability of the building we evaluate the expected loss andlife-cycle cost of the isolated building The study conclusionscan be summarized as follows

(1) The initial costs in the isolated case are higher by 1than those in the corresponding fixed-base case Thesample building is a hospital thus the superstructureseismic measures are strengthened by the require-ments of Chinese seismic design provisions

(2) Base isolation reduces conditional failure probabilitytherefore the expected loss of the isolated building isonly 37 of that of the fixed-base building Moreoverthe life-cycle cost of the isolated building decreases tonearly 1 of that of the fixed-base building The baseisolation reduces earthquake response and protectsagainst such calamities Hence the isolated buildingeffectively withstands future earthquakes

(3) The optimum design balances building reliability andbuilding investment The indicator based on life-cycle cost assists owners and engineers in makinginvestment decisions in consideration of structuraldesign construction and expected loss

Conflict of Interests

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

Acknowledgments

This project was funded by the National Natural ScienceFoundation of China (Grant no 61262016) the NationalNatural Science Foundation of China (Grant no 51368039)and the Open Grant of the Key Laboratory of Concrete andPrestressed Concrete Structure Ministry of Education

References

[1] N D Lagaros A D Fotis and S A Krikos ldquoAssessment ofseismic design procedures based on the total costrdquo EarthquakeEngineering and Structural Dynamics vol 35 no 11 pp 1381ndash1401 2006

[2] J S Nathwani N C Lind and M D Pandey Affordable Safetyby Choice The Life Quality Method Institute for Risk ResearchUniversity of Waterloo Waterloo Canada 1997

[3] M D Pandey and J S Nathwani ldquoLife quality index for the esti-mation of societal willingness-to-pay for safetyrdquo StructuralSafety vol 26 no 2 pp 181ndash199 2004

[4] R Rackwitz ldquoOptimizationmdashthe basis of code-making andreliability verificationrdquo Structural Safety vol 22 no 1 pp 27ndash60 2000

[5] M Liu Y K Wen and S A Burns ldquoLife cycle cost orientedseismic design optimization of steel moment frame structureswith risk-taking preferencerdquo Engineering Structures vol 26 no10 pp 1407ndash1421 2004

[6] D M Frangopol and M Liu ldquoMaintenance and managementof civil infrastructure based on condition safety optimizationand life-cycle costrdquo Structure and Infrastructure Engineeringvol 3 no 1 pp 29ndash41 2007


[7] A J Kappos and E G Dimitrakopoulos ldquoFeasibility of pre-earthquake strengthening of buildings based on cost-benefitand life-cycle cost analysis with the aid of fragility curvesrdquoNatural Hazards vol 45 no 1 pp 33ndash54 2008

[8] S Pei and J W van de Lindt ldquoMethodology for earthquake-induced loss estimation an application to woodframe build-ingsrdquo Structural Safety vol 31 no 1 pp 31ndash42 2009

[9] C S Lee K Goda and H P Hong ldquoCost-effectiveness of tunedmass damper and base isolationrdquo in Proceedings of the 14thWorld Conference on Earthquake Engineering Beijing China2008

[10] M Sarkisian P Lee L Hu and C Doo ldquoEnhanced seismicdesign of the New San Bernardino Courtrdquo in Proceedings of theStructures Congress (ASCE rsquo11) pp 994ndash1006 April 2011

[11] F Chatzidaki Optimum design of base isolated RC structures[Postgraduate diploma thesis] National Technical University ofAthens Athens Greece 2013

[12] Code for Seismic Design of Buildings GB 50010-2010 2010[13] E M Lapointe An Investigation of the Principles and Practices

of Seismic Isolation in Bridge Structures Massachusetts Instituteof Technology 2004

[14] F Naeim The Seismic Design Handbook Kluwer AcademicBoston Mass USA 2nd edition 2001

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Distributed Sensor Networks


Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications


Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia


Biomedical Imaging


ArtificialNeural Systems

Advances in


RoboticsJournal of



Computational Intelligence and Neuroscience

Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



[11] optimized the design of and economically evaluated rein-forced-concrete (RC) isolated structures Generally theresearchers have a similar conclusion the life-cycle cost ofisolated buildings is less than that of the fixed-base buildings

In the current study structural seismic performance ismeasured according to indicator-based life-cycle cost Thiscost can synthesize all factors including structural designconstruction and expected loss from earthquakes The indi-cator of an isolated building is analyzed in detail in com-parison with that of a fixed-base building in the followingsections Practical construction complexity important butdifficult to be included in initial cost analysis is taken into dueaccount by a proposed diversity index as another objectivethis approximation data is best used for the preliminarydesign stage and the large pools of alternatives leave to adesign maker much freedom to select the one that best meetshisher goals

2 Indicator-Based Life-Cycle Cost ofStructural Seismic Performance

21 Life-Cycle Cost of Structures The life-cycle cost of astructure may refer either to the design life of a new structureor to the remaining life of an existing or retrofitted structureThis cost can be expressed as a function of time and of thedesign vector [1]

119862tot (119905 119904) = 119862in (119904) + 119890minus120582119905

119862ls (119905 119904) (1)

where 119862tot is the total cost of a structure 119862in is the initial costof a new or retrofitted structure 119862ls is expected loss 119905 is thetime period 119904 is the design vector corresponding to the designloads resistance and material properties that influence theperformance of the structural system and 120582 is the constantannual discount rate and is usually equal to 3 [1]

119862ls can be written as [1]

119862ls (119905 119904) = sum

119895

sum

119894

[119862ls (119861119894) 119875 (119861119894 | 119868)] 119875 (119868119895) (2)

where 119875(119861119894

| 119868) is the conditional probability of failurewhich can be obtained through dynamic reliability analysis119868 is fortification intensity 119875(119868

119895

) is the probability of seismichazard and 119868

119895

denotes the three seismic design levels namelyminor (119868

119904

) moderate (119868119898

) and major earthquakes (119868119897

) Thecumulative distribution function of fortification intensity isa type III extreme value distribution during the design refer-ence period in Mainland China Thus 119875(119868

119904

) 119875(119868119898

) and 119875(119868119897

)

are approximately equal to 70 252 and 45 respectively[12]

119861 represents structural damage and can be divided intofive levels that is none slight moderate severe and col-lapsed These structural damage states are defined by specificquantities Interstory drift can be a reliable limit-state cri-terion according to which expected damage can be deter-mined Thus maximum interstory drift (120579) is considered theresponse parameter that best characterizes structural dam-age The damage index limits of isolated superstructures aresimilar to those of fixed-base buildings however these limitshave not been determined for the isolated layer The damage

Table 1 Damage index limits for RC frames

Damage state None Slight Moderate Severe CollapsedDriftratio

Superstructure 0002 0004 0008 002 005Isolated layer 051 090 128 179 205

states are quantitatively defined in terms of interstory driftgiven that the isolator may be damaged when its shear strainexceeds the acceptable value as shown in Table 1

119862ls corresponds to the limit-state economic and noneco-nomic loss from earthquakes The economic loss consistsof direct and indirect economic loss relief costs and long-term investment Noneconomic loss mainly involves the lossof human life The economic quantification of these lossesdepends on several socioeconomic parameters and the mostdifficult cost to quantify is that which corresponds to theloss of human life This loss can be estimated using variousapproaches that range from purely economic reasoning tomore sensitive concepts that consider human loss to be irre-placeable These cost components are related to RC buildingdamage 119862 is initial building cost 119875 is the total number ofhuman beings in the building and 119886 119890 and 119889 are the ratiosof indirect economic loss relief cost and structural contentrespectively These data are derived from [13] as shown inTable 2Thus119862ls can be determined based on initial cost andbuilding function

22 Indicator of Structural Seismic Performance As with thecoefficient of investment risk the indicator of structural seis-mic performance can be expressed as

120593 = 1 minus119862in (119904)

119862tot (119905 119904)= 1 minus

119862in (119904)

119862in (119904) + 119890minus120582119905119862ls (119905 119904)

=119890minus120582119905

119862ls (119905 119904)

119862tot (119905 119904)

(3)

where 120593 is the indicator of structural seismic performancebased on life-cycle cost It represents the proportion ofexpected damage to life-cycle cost A high 120593 value increasesthe risk of the expected economic loss and indicates the poorseismic performance of a building

3 Conditional Failure Probability ofIsolated Buildings

The calculation of conditional failure probability is key tolife-cycle cost evaluation Thus random dynamic analysis isalso conducted in this study to determine dynamic reliabilityConsequently the conditional failure probability of isolatedbuildings can be calculated

31 Random Dynamic Analysis of Isolated Buildings Thenonlinear behavior of isolated buildings is presented in aBouc-Wen model The equivalent linearization method isapplied and the equations of motion can thus be obtained

MY + CY + KY + Kh120592 = minusMEug

+ CeqY + Keq120592 = 0(4)





where

M =[[[

[

1198981

0 0 0

1198982

1198982

0 0

sdot sdot sdot

119898119899

119898119899

119898119899

119898119899

]]]

]

C =

[[[[[[[

[

1198881

minus1198882

0

1198882

minus1198883

1198883

minus1198884

sdot sdot sdot

119888119899minus1

minus119888119899

0 119888119899

]]]]]]]

]

K =

[[[[[[[

[

1205721

1198961

minus1205722

1198962

0

1205722

1198962

minus1205723

1198963

1205723

1198963

minus1205724

1198964

sdot sdot sdot

120572119899minus1

119896119899minus1

minus120572119899

119896119899

0 120572119899

119896119899

]]]]]]]

]

Kh =

[[[[[[[

[

(1 minus 1205721

) 1198961


) 1198962

0

(1 minus 1205722

) 1198962


) 1198963

(1 minus 1205723

) 1198963


) 1198964

sdot sdot sdot

(1 minus 120572119899minus1

) 119896119899minus1

minus (1 minus 120572119899

) 119896119899

0 (1 minus 120572119899

) 119896119899

]]]]]]]

]

Ceq =[[[

[

119862eq1 0

119862eq2d

0 119862eq119899

]]]

]

Keq =[[[

[

119870eq1 0

119870eq2d

0 119870eq119899

]]]

]

(5)


119862eq119894 = minus1 +2

120587120573119894

1205902

120592119894

[120601 minus1

2sin (2120601) minus 120587

2] + 120574119894

1205902

120592119894

119870eq119894 =4

120587120573119894

120590119909119894120590120592119894 (1 minus 120588

2

119909119894120592119894

)15

+120588119909119894120592119894[120601 minus

1

2sin (2120601) minus 120587

2]

+ 2120574119894

119864 [119894

120592119894

]


2

119909119894120592119894

120588119909119894120592119894

) 120588119909119894119911119894=119864 [119894

120592119894

]

120590119909119894120590120592119894

(6)


= 2119898119894

120596120577119894

and120596 and 120577119894


119894








Y = B119890119894120596119905 Y = 119894120596B119890119894120596119905 Y = minus1205962B119890119894120596119905

= B1015840119890119894120596119905(7)


B = Br + 119894Bi

Br =minusGr

G2r + G2iEradic119878119892(120596) Bi =

GiG2r + G2i

Eradic119878119892(120596)



(8)


119879119894119895=

minus120596

1198702

eq119895 + 1205962

119879119903119895=

119870eq119895

1198702

eq119895 + 1205962

119895 = 1 2 119899

B1015840 = (120596Ti minus 119894120596Tr)CeqB

(9)


119878

119884

(120596) =Ylowast

sdotY119879

119878120592

(120596) = lowast

sdot 119879

119878

119884120592

(120596) =Ylowast

sdot 119879

(10)


120583119910

= 0 1205902

119910

= 119864 [ 1199102

] = int

+infin

minusinfin

119878

119884

(120596) 119889120596

120583120592

= 0 1205902

120592

= 119864 [1205922

] = int

+infin

minusinfin

119878120592

(120596) 119889120596

119864 [ 119910120592] = int

+infin

minusinfin

119878

119884120592

(120596) 119889120596

(11)


1205902

119910

= 119864 [1199102

] = int

+infin

minusinfin

119878119884

(120596) 119889120596 (12)


120583120579119898119894

=120583119910119898119894

ℎ119894

120590120579119898119894

=120590119910119898119894

ℎ119894

120575120579119898119894

=120590119910119898119894

120583119910119898119894

(13)

where ℎ119894


and 120590119910119898119894


119910119898119894and 120590

119910119898119894can be written as [14]

120583119910119898119894

= 119901119894

120590119910119894 120590

119910119898119894= 119891119894

120590119910119894 (14)

119901119894

and119891119894


119901119894

= radic2 ln (]119894

120591) +05772

radic2 ln (]119894

120591)

119891119894

=120587

radic12 ln (]119894

120591)

(15)

]119894


= 120590119910119894120587120590119910119894 120591 is


for hard soil [12]


119885 = 120579 minus 120579119898

= 0 (16)


119875119891

= 119875 (119885 lt 0) = 119875 (120579 lt 120579119898

| 119868 = 1198680

120591) = 1 minus Φ (120573) (17)

where 1198680

and 120573120579119894


120579119894

is written as

120573120579119894

=

ln [120583120579119894radic1 + 120575

2

120579119898119894

120583120579119898119894radic1 + 120575

2

120579119894

]

radicln (1 + 1205752120579119894

) (1 + 1205752

120579119898119894

)

(18)


120583120579119894= 120579119894




120579119898119894and 120575

120579119898119894can be computed



120573 =

119899

prod

119894=1

120573120579119894

(19)











119860119894

= 1 119899119894

= 2 120572119894

= 002 (20)


120572 = 01 (21)








10946 + 23534 + 105069 = 139549 (10000 yuan)



13278 + 26436119890minus003times50


13145 + 139549119890minus003times50

= 13456 (10000 yuan)


Isolated building

120593 = 1 minus119862in (119904)

119862tot (119905 119904)= 1 minus

13278

13337= 00044 (22)

Fixed-base building

120593 = 1 minus119862in (119904)

119862tot (119905 119904)= 1 minus

13145

13456= 00231 (23)




119861119894




119861119894



5 Conclusion







Acknowledgments


References























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in







where

M =[[[

[

1198981

0 0 0

1198982

1198982

0 0

sdot sdot sdot

119898119899

119898119899

119898119899

119898119899

]]]

]

C =

[[[[[[[

[

1198881

minus1198882

0

1198882

minus1198883

1198883

minus1198884

sdot sdot sdot

119888119899minus1

minus119888119899

0 119888119899

]]]]]]]

]

K =

[[[[[[[

[

1205721

1198961

minus1205722

1198962

0

1205722

1198962

minus1205723

1198963

1205723

1198963

minus1205724

1198964

sdot sdot sdot

120572119899minus1

119896119899minus1

minus120572119899

119896119899

0 120572119899

119896119899

]]]]]]]

]

Kh =

[[[[[[[

[

(1 minus 1205721

) 1198961


) 1198962

0

(1 minus 1205722

) 1198962


) 1198963

(1 minus 1205723

) 1198963


) 1198964

sdot sdot sdot

(1 minus 120572119899minus1

) 119896119899minus1

minus (1 minus 120572119899

) 119896119899

0 (1 minus 120572119899

) 119896119899

]]]]]]]

]

Ceq =[[[

[

119862eq1 0

119862eq2d

0 119862eq119899

]]]

]

Keq =[[[

[

119870eq1 0

119870eq2d

0 119870eq119899

]]]

]

(5)


119862eq119894 = minus1 +2

120587120573119894

1205902

120592119894

[120601 minus1

2sin (2120601) minus 120587

2] + 120574119894

1205902

120592119894

119870eq119894 =4

120587120573119894

120590119909119894120590120592119894 (1 minus 120588

2

119909119894120592119894

)15

+120588119909119894120592119894[120601 minus

1

2sin (2120601) minus 120587

2]

+ 2120574119894

119864 [119894

120592119894

]


2

119909119894120592119894

120588119909119894120592119894

) 120588119909119894119911119894=119864 [119894

120592119894

]

120590119909119894120590120592119894

(6)


= 2119898119894

120596120577119894

and120596 and 120577119894


119894








Y = B119890119894120596119905 Y = 119894120596B119890119894120596119905 Y = minus1205962B119890119894120596119905

= B1015840119890119894120596119905(7)


B = Br + 119894Bi

Br =minusGr

G2r + G2iEradic119878119892(120596) Bi =

GiG2r + G2i

Eradic119878119892(120596)



(8)


119879119894119895=

minus120596

1198702

eq119895 + 1205962

119879119903119895=

119870eq119895

1198702

eq119895 + 1205962

119895 = 1 2 119899

B1015840 = (120596Ti minus 119894120596Tr)CeqB

(9)


119878

119884

(120596) =Ylowast

sdotY119879

119878120592

(120596) = lowast

sdot 119879

119878

119884120592

(120596) =Ylowast

sdot 119879

(10)


120583119910

= 0 1205902

119910

= 119864 [ 1199102

] = int

+infin

minusinfin

119878

119884

(120596) 119889120596

120583120592

= 0 1205902

120592

= 119864 [1205922

] = int

+infin

minusinfin

119878120592

(120596) 119889120596

119864 [ 119910120592] = int

+infin

minusinfin

119878

119884120592

(120596) 119889120596

(11)


1205902

119910

= 119864 [1199102

] = int

+infin

minusinfin

119878119884

(120596) 119889120596 (12)


120583120579119898119894

=120583119910119898119894

ℎ119894

120590120579119898119894

=120590119910119898119894

ℎ119894

120575120579119898119894

=120590119910119898119894

120583119910119898119894

(13)

where ℎ119894


and 120590119910119898119894


119910119898119894and 120590

119910119898119894can be written as [14]

120583119910119898119894

= 119901119894

120590119910119894 120590

119910119898119894= 119891119894

120590119910119894 (14)

119901119894

and119891119894


119901119894

= radic2 ln (]119894

120591) +05772

radic2 ln (]119894

120591)

119891119894

=120587

radic12 ln (]119894

120591)

(15)

]119894


= 120590119910119894120587120590119910119894 120591 is


for hard soil [12]


119885 = 120579 minus 120579119898

= 0 (16)


119875119891

= 119875 (119885 lt 0) = 119875 (120579 lt 120579119898

| 119868 = 1198680

120591) = 1 minus Φ (120573) (17)

where 1198680

and 120573120579119894


120579119894

is written as

120573120579119894

=

ln [120583120579119894radic1 + 120575

2

120579119898119894

120583120579119898119894radic1 + 120575

2

120579119894

]

radicln (1 + 1205752120579119894

) (1 + 1205752

120579119898119894

)

(18)


120583120579119894= 120579119894




120579119898119894and 120575

120579119898119894can be computed



120573 =

119899

prod

119894=1

120573120579119894

(19)











119860119894

= 1 119899119894

= 2 120572119894

= 002 (20)


120572 = 01 (21)








10946 + 23534 + 105069 = 139549 (10000 yuan)



13278 + 26436119890minus003times50


13145 + 139549119890minus003times50

= 13456 (10000 yuan)


Isolated building

120593 = 1 minus119862in (119904)

119862tot (119905 119904)= 1 minus

13278

13337= 00044 (22)

Fixed-base building

120593 = 1 minus119862in (119904)

119862tot (119905 119904)= 1 minus

13145

13456= 00231 (23)




119861119894




119861119894



5 Conclusion







Acknowledgments


References























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in








Y = B119890119894120596119905 Y = 119894120596B119890119894120596119905 Y = minus1205962B119890119894120596119905

= B1015840119890119894120596119905(7)


B = Br + 119894Bi

Br =minusGr

G2r + G2iEradic119878119892(120596) Bi =

GiG2r + G2i

Eradic119878119892(120596)



(8)


119879119894119895=

minus120596

1198702

eq119895 + 1205962

119879119903119895=

119870eq119895

1198702

eq119895 + 1205962

119895 = 1 2 119899

B1015840 = (120596Ti minus 119894120596Tr)CeqB

(9)


119878

119884

(120596) =Ylowast

sdotY119879

119878120592

(120596) = lowast

sdot 119879

119878

119884120592

(120596) =Ylowast

sdot 119879

(10)


120583119910

= 0 1205902

119910

= 119864 [ 1199102

] = int

+infin

minusinfin

119878

119884

(120596) 119889120596

120583120592

= 0 1205902

120592

= 119864 [1205922

] = int

+infin

minusinfin

119878120592

(120596) 119889120596

119864 [ 119910120592] = int

+infin

minusinfin

119878

119884120592

(120596) 119889120596

(11)


1205902

119910

= 119864 [1199102

] = int

+infin

minusinfin

119878119884

(120596) 119889120596 (12)


120583120579119898119894

=120583119910119898119894

ℎ119894

120590120579119898119894

=120590119910119898119894

ℎ119894

120575120579119898119894

=120590119910119898119894

120583119910119898119894

(13)

where ℎ119894


and 120590119910119898119894


119910119898119894and 120590

119910119898119894can be written as [14]

120583119910119898119894

= 119901119894

120590119910119894 120590

119910119898119894= 119891119894

120590119910119894 (14)

119901119894

and119891119894


119901119894

= radic2 ln (]119894

120591) +05772

radic2 ln (]119894

120591)

119891119894

=120587

radic12 ln (]119894

120591)

(15)

]119894


= 120590119910119894120587120590119910119894 120591 is


for hard soil [12]


119885 = 120579 minus 120579119898

= 0 (16)


119875119891

= 119875 (119885 lt 0) = 119875 (120579 lt 120579119898

| 119868 = 1198680

120591) = 1 minus Φ (120573) (17)

where 1198680

and 120573120579119894


120579119894

is written as

120573120579119894

=

ln [120583120579119894radic1 + 120575

2

120579119898119894

120583120579119898119894radic1 + 120575

2

120579119894

]

radicln (1 + 1205752120579119894

) (1 + 1205752

120579119898119894

)

(18)


120583120579119894= 120579119894




120579119898119894and 120575

120579119898119894can be computed



120573 =

119899

prod

119894=1

120573120579119894

(19)











119860119894

= 1 119899119894

= 2 120572119894

= 002 (20)


120572 = 01 (21)








10946 + 23534 + 105069 = 139549 (10000 yuan)



13278 + 26436119890minus003times50


13145 + 139549119890minus003times50

= 13456 (10000 yuan)


Isolated building

120593 = 1 minus119862in (119904)

119862tot (119905 119904)= 1 minus

13278

13337= 00044 (22)

Fixed-base building

120593 = 1 minus119862in (119904)

119862tot (119905 119904)= 1 minus

13145

13456= 00231 (23)




119861119894




119861119894



5 Conclusion







Acknowledgments


References























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in











119860119894

= 1 119899119894

= 2 120572119894

= 002 (20)


120572 = 01 (21)








10946 + 23534 + 105069 = 139549 (10000 yuan)



13278 + 26436119890minus003times50


13145 + 139549119890minus003times50

= 13456 (10000 yuan)


Isolated building

120593 = 1 minus119862in (119904)

119862tot (119905 119904)= 1 minus

13278

13337= 00044 (22)

Fixed-base building

120593 = 1 minus119862in (119904)

119862tot (119905 119904)= 1 minus

13145

13456= 00231 (23)




119861119894




119861119894



5 Conclusion







Acknowledgments


References























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





119861119894




119861119894



5 Conclusion







Acknowledgments


References























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



















Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



research article analysis of the seismic performance of...

Documents