research article structural response to blast loading:...

Research ArticleStructural Response to Blast Loading The Effects of Corrosionon Reinforced Concrete Structures

Hakan Yalciner

Civil Engineering Department Erzincan University Turkey

Correspondence should be addressed to Hakan Yalciner hakanyalcineremuedutr

Received 1 July 2013 Accepted 1 January 2014 Published 2 June 2014

Academic Editor Nuno Maia

Copyright copy 2014 Hakan Yalciner This 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

Structural blast design has become a necessary part of the designwith increasing terrorist attacks Terrorist attacks are not the one tomake the structures important against blast loading where other explosions such as high gas explosions also take an important placein structural safetyThemain objective of this studywas to verify the structural performance levels under the impact of different blastloading scenariosThe blast loads were represented by using triangular pulse for single degree of freedom systemThe effect of blastload on both corroded and uncorroded reinforced concrete buildings was examined for different explosion distances Modifiedplastic hinge properties were used to ensure the effects of corrosion The results indicated that explosion distance and concretestrength were key parameters to define the performance of the structures against blast loading

1 Introduction

Most of the design codes consider essentially the seismicwind rain and snow loads Blast loads have different placein engineering when they are compared with other loadsEven the fundamentals of blast and seismic design dependon dynamic behaviour and energy dissipation approachesthe design of blast and the response of the structures againstblast loads are extremely different than other well-knownloads Unlike seismic and wind loads blast loads have a shortduration generally in milliseconds (ms) With increasingterrorist attacks on military buildings blast design has keptits popularity to develop new design codes From militarybuildings blast design has started to be adopted for residen-tial buildings to resist the gas explosions in huge and closedareas Thus the first blast design code has been developed byFEMA 427 [1] OnMarch 20 2003 the United States attackedIraq Over 4000 US soldiers died in that war Most of thosedeaths occurred with suicide truck bomb that exploded infront of military buildings Figure 1 shows a typical effect ofblast load on Canal Hotel in Baghdad Iraq in 2003 Thebuildingwas heavily damaged by using trinitrotoluene (TNT)which exploded at a nearby distance

If an explosion distance is pretty close and the buildingwalls are not designed by shear walls the blast also affects the

interior side of the buildings Such an explosion was done bycouple car bomb attacks in central Baghdad in 2007 Fifty-nine people died as a result of explosions Twenty peopleout of fifty-nine were located inside of the building Foran explosion outside a building the exterior envelope (iewall reinforced concrete members and glass) is the criticalline of defence that separates the people operations andcontents inside the building from the air-blast effects outsidethe building [2] Unfortunately most of the buildings in Iraqwere ill-suited to resist the blast loads which could have savedthe people that were located inside of the buildings Not onlythe reinforced concrete buildings but also bridges railwaysand roads are under the blast risk Exploded blast load onmajor bridges in Baghdad caused collapse to the whole trusssteel frames and concrete asphalt Within a short period ofexplosion connections of the steel bars were melded withcrushed concrete The released potential energy with blastload is much more effective on steel structures when itis compared with reinforced concrete buildings since steelstructures provide little resistance to thermal energy Whilethe blast load causes the steel structures to melt it turnsthe concrete into sand and dust by exceeding yield strengthof concrete At this point not only the amount of the blastload but also the pressure of the wave to the surface ofconcrete and explosion distance take an important place for

Hindawi Publishing CorporationShock and VibrationVolume 2014 Article ID 529892 7 pageshttpdxdoiorg1011552014529892

2 Shock and Vibration

Figure 1 Destroyed reinforced concrete building by blast load [15]

Hemisphericalshock wave

Drag

Standoff

Ground shock

Center of burst

OverpressureReflected pressurePerimeter protection(fence guards and barriers)

Figure 2 Schematic of a blast load [4]

structures When a response of a building from blast loadis considered natural period of vibration of the structure isthe vital parameter for a given explosion Ductile elementsmade of steel and reinforced concrete absorb a lot of strainenergy [3]The effects of blast on reinforced concrete and steelstructures have been widely studied by many researchers Tothe knowledge of the author the effects of corrosion withblast loads on reinforced concrete buildings have not beenstudiedTherefore in this study different blast load scenarioswere performed for uncorroded and corroded reinforcedconcrete buildings to investigate the effect of blast loadswith corrosion Performance levels of the reinforced concretebuildings were obtained under the effect of blast loads Theimpacts of the blast waves on the surface of the structuralmembers were simulated

2 Blast and Loadings

Blast can be defined as a rapid phase of a created pressure by asudden release of energyThis energy provides a blast wave indifferent shapes The general generated blast wave has beenformed in a hemispherical form away from the blast site asshown in Figure 2

In this study the peak static overpressure was calculatedbased on the model developed by Smith and Hetherington[4]

for 119875119904gt 10 bar 119875

119904=

67

1198853+ 1

for 01 lt 119875119904lt 10 bar 119875

119904=

0975

119885+

1455

1198852+

585

1198853

(1)

where 119885 is the scaled distance (ftlb13) and it can becalculated by the following equation In (2) 119877 and 119882 denotethe explosion distance (ft) and the explosives weight (lb) inTNT respectively

119885 =119877

11988213 (2)

Idealized pressure-time history of a blast load and compar-ison between free-field or side-on and reflected pressure-time histories are shown in Figure 3 In Figure 3(a) 119875

119900

is the ambient pressure 119875so is the peak positive side-onoverpressure 119875minusso is the peak negative side-on overpressure119875119904(119905) is the time varying positive overpressure 119875minus

119904(t) is the

time varying negative overpressure 119875119903is the peak reflected

overpressure 119868119904is the positive-phase-specific impulse (the

integration of the positive phase pressure-time history) and119894minus

119904is the negative-phase-specific impulse (the integration of

the negative phase pressure-time history)The velocity of a wave (119880

119904) and the maximum pressure

were calculated based on the model proposed by Smith andHetherington [4] Consider

119880119904= radic

6119875119904+ 7119875119900

7119875119900

sdot 119886119900

119902119904=

51198752

119904

2 (119875119904+ 7119875119900)

(3)

where 119886119900is the ambient air pressure ahead of wave 120574 is the

specific heat ratio and 120588 is the density of air The reflectedpressure 119875

119903 was then calculated by following equations

119875119903= 2119875119904+ (120574 + 1) 119902

119904

119902119904=

1

21205881199041199062

119904

119906119904=

119886119900sdot 119875119904

120574119875119900

[1 + [120574 + 1

2120574]

119875119904

119875119900

]

minus12

119875119903= 2119875119904[7119875119900+ 4119875119904

7119875119900+ 119875119904

]

(4)

In this study four different explosion distances (ie 6m12m 18m and 24m) were defined with having the sameamount of 150 kg TNTThemass specific energy for TNTwasequal to 4520 kJkg

3 Material Modelling

In order to perform the blast load with combined corrosioneffects stress and strain relationships of concrete and rein-forcement bars were defined by user In this study we used the

Shock and Vibration 3

Positivep Negative phase hase

Duration Duration

AmbientPr

essu

re

Time after explosion

Pso

PoPminusso

iminusoPositive impulse

Negative impulse iminuso

tminusotot = 0

Pminuss (t)

Ps(t)

ta + to + tminusotata

ta

+ to

(a)

Pres

sure

Duration Time

Duration

Pso

Po

Pr

Positivep

Negative phase hase

tminuso

to

to

to + tminuso

(b)

Figure 3 (a) Blast wave pressure-time graph (b) Blast load and comparison [4]

model with more than 30 years developed by Kent and Park[5] to model the stress and strain relationships of concreteBasically this model by Kent and Park [5] has two segmentsFor the first segment (A-B) the curve reaches maximumstress level which is equal to 0002 After reaching maximumstress two different other segments occur (B-C B-D) wheretwo straight lines indicate different behaviour of concretefor confined and unconfined concrete Figure 4(a) showsKent and Park [5] model for the stress-strain relationship ofreinforced concrete sections In this studyManderrsquos [6]modelwas used for the modelling of stress-strain relationship ofreinforcement bars Mander [6] proposed a model which canbe used for both softer and harder steel The model includeslinear elastic region up to yield elastic-perfect-plastic regionand strain hardening region Manderrsquos model [6] controlsboth strength and ductility where descending branch of thecurve that first branch increase linearly until yield point

and then the curve continues as constant Figure 4(b) showsthe model proposed by Mander [6] for stress and strainrelationships of reinforcement bars

The steel and concrete classes were selected as S420(420MPa) and C40 (40MPa) respectively Elastic modulusof concrete (119864

119888= 3250radic1198911015840

119888+ 14000MPa) was calculated

according to Turkish standards 500 [7] and the elasticmodu-lus of steel (119864

119904) was taken as 200000MPa A corrosion rate of

040 120583Acm2 was assumed to be used in analyses A corrosionrate in mmyear was converted to 120583Acm2 by consideringthat 1 120583Acm2 is equal to 00116mmyear Three major effects(ie loss in cross-sectional area of reinforcement bars reduc-tion in concrete strength and bond-slip relationships) ofcorrosion were taken into account Reduction in concretestrength was calculated based on the model developed byYalciner et al [8] The model developed by Yalciner et al


D

A

B

C

Unconfined

s

N

Confined

N

N

N

fc

120590c

0002 12057650u 12057650c 12057620c 120576c

lx

ly

12057650h

120579

05fc

02fc

(a)

fsu

fsy

120576sy 120576sp 120576su

(b)

Figure 4 (a) Stress-strain relation of reinforced concrete [5] (b)Stress-strain relation of steel bars [6]

[8] provides calculation of the reduction in concrete strengthas a function of corrosion rate or mass loss The volume ofcorrosion rust is generally 2 to 4 times larger than the volumeof original reinforcement [9] The porous zone around thereinforcing bars is filled with this corrosion product whichresults in internal pressure on the surrounding concrete Asa consequence of volumetric expansion inside of concretethe concrete strengths reduce as a function of corrosion ratewhich occurs due to increased width The model developedby Yalciner et al [8] to calculate the increased width of thestructural members due to corrosion is given in

119887119891minus 1198870

= 119899bars (4120587119889119904(119905)

(1 minus ]119888) (119886119887)

radic120572

+ (1 + ]119888) (119887119886)

radic120572

minus2120587119887119891119905

119864ef)

(5)

In (5) 119887119891is the width increased by corrosion cracking 119887

0

is the section width in the virgin state 119899bars is the numberof the bars in the top layer (compressed bars) 119889

119904(119905) is the

thickness of corrosion product form ]119888is the Poissonrsquos ratio

of concrete 119891119905is the tensile strength of concrete 119864ef is the

effective elastic modulus of concrete (119886 = (119889119887+21198890)2) 119889

119887is

the diameter of reinforcement bars 1198890is the thickness of the

annular layer of concrete pores 119887 is the outer radii of the ofthe thick-wall cylinder (119887 = 1198782) S is the rebar spacing and1198885and 1198886are boundary conditions as proposed by Li et al [10]

Once the corrosion rate is known the reduction in concretestrength can be predicted by using the model developed byYalciner et al [8] Yalciner et al [11] in another study alsodeveloped a corrosion model to predict the ultimate bondstrength of uncorroded and corroded reinforcement bars asa function of three different concrete cover depths and twodifferent concrete strength levels for different given corrosionlevels by using accelerated corrosion method and performedpull-out tests In this study to calculate the ultimate bondstrength of uncorroded structural members the developedmodel by Yalciner et al [11] was used by given (6) In (6) 1198911015840

119888

is the concrete compressive strength 119888 is the concrete coverdepth and 119863 is the diameter of a steel bar

120591119887119906

= minus27143 + 036211198911015840

119888+ 23296 (

119888

119863) (MPa) (6)

In order to calculate and predict the ultimate bondstrength of corroded structural members the followingmodel developed by Yalciner et al [11] was used In (7) devel-oped bond strengthmodel by Yalciner et al [11] considers thelimits of corrosion levels for the ascending branchwhen coverto diameter ratios are equal and greater than two Consider

if 119888

119863ge 2

0 le 119862119871le 14 for 119891

1015840

119888= 23MPa

0 le 119862119871le 068 for 119891

1015840

119888= 51MPa

120591119887119906

= 119890(001572119891

1015840

119888+022957(119888119863)+013946119862

119871+175913)

(MPa)

(7)

Calculated bond strengths of structural member were usedto predict the slippage of reinforcement bars For doingthis a well-known slip model developed by Alsiwat andSaatcioglu [12] was used In the model developed by Alsiwatand Saatcioglu [12] the development length was dividedinto four regions based on the state of the steel stress-strain relationship (ie an elastic region a yield plateaua strain hardening region and a pull-out cone region)Alsiwat and Saatcioglu [12] suggested thatonce extension of areinforcement bar is calculated slip rotation can be calculatedby using moment-curvature relationships given by

120579119904=

120575ext119889 minus 119888

(8)

where 119889 is the section depth c is the neutral axis of assessedsection and120575ext is the extension of a bar Calculated reductionin concrete strength (see (5)) loss in cross-sectional area pre-dicted bond strength (see (6) and (7)) and slip rotations (see(8)) were used tomodify themoment-curvature relationshipsof defined structural member


Deformation

Forc

e

A

B IO LS CP C

D E

Figure 5 Force-deformation relationship of a plastic hinge

6m

12m

Shear wall

Figure 6 Modelled reinforced concrete building

4 Blast Analyses and Results

Calculated moment-curvature relationships were usedto define the force-deformation relationships Force-deformation behaviour was defined by using a describedstandard by FEMA-356 [13] Figure 5 shows force-deformation relationships to define the behaviour of aplastic hinge by FEMA-356 [13] On Figure 5 labelled A BC D define force-deformation behaviour which is detailexplained by FEMA-356 [13]

The lengths of the plastic hinges (119871119901) were calculated

according to Park and Paulay [14] by

119871119901= 05119867 (9)

where 119867 is the related section depth of element As men-tioned earlier four different explosion distances (ie 6m12m 18m and 24m) were defined For this purpose areinforced concrete building was modelled The results ofthe blast effect with combined corrosion damage on buildingwere discussed for designed shear wall as shown in Figure 6

The first explosion was done with an explosion distanceof 6m and continued with other distances The resultsclearly indicated that effect of blast regarding the damage ofreinforced concrete building and the resistance of concreteis much more important than the reinforcement bars Atthis point the role of the reinforcement bars on concretewas corrosion If the reinforcement bars were corrodedwith increased cracks within the concrete as a function

Kinetic + strain6660

Damping917

Hysteretic

Total696

Energy contribution as of total

Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

2092

4183

6275

8366

2423

(a)

Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

4530

9060

13590

18120

6770

818

2412

1509

(b)

Figure 7 Blast load with a 6m explosion (a) uncorroded shear walland (b) corroded shear wall

of corrosion rate caused to increase the effect of the blastload After the first explosion the results of the energycontributions of the kinetic + strain damping and hystereticenergies as well as the total energy are shown in Figure 7 InFigure 7 the hysteretic energy was an indication of structuraldamage resulting from the application of the blast load

As shown in Figure 7(a) structural damage resultingfrom the application of the blast load was less when it wascompared with corroded shear wall due to crack width ofconcrete caused by corrosion The results of exploded TNTfor 18m and 24m for both uncorroded and corroded caseswere given in Figures 8 and 9 respectively

In Figure 8 as it was expected with increased explo-sion distance damage to structure was reduced Moreoverpercentage contribution of the hysteretic energy to the totalenergy was higher for corroded shear wall The recordedrelative percentages of hysteretic energy of uncorroded andcorroded concrete members were 342 and 700 respec-tively These percentages were reduced to zero percentageswith an increased explosion distance by 24m at the sameperiod of 015ms (see Figure 9) Structural damage resultingfrom the application of the blast load having 02ms was 15


Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

941

1882

2823

3764

8702

956

342

309

(a)

Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

1002

2004

3006

4009

8334

967

700

330

(b)

Figure 8 Blast load with 18m explosion distance (a) uncorrodedshear wall and (b) corroded shear wall

and 238 for uncorroded and corroded concrete membersrespectively When two different explosion distances werecompared the recorded 2423 of relative percentage of hys-teretic energy was reduced to zero percentage with increasedexplosion distance from 6m to 24m within 010ms

5 Conclusion

The effects of blast load on corroded and uncorroded rein-forced concrete buildings were studied for different explosiondistancesThe results clearly indicated that structural damagewas reducedwith increased explosion distances by dependingon amount of TNT that was used in current study Performedblast loads and obtained results showed that effect of corro-sion did not play a major role in the percentage contributionof the hysteretic energy to the total energy by reduction incross-sectional area of reinforcement bars Increased crackwidth of concrete due to corrosion played a major rolein the case of corroded structural member Reduction incross-sectional area of reinforcement bars directly causedpremature yielding of reinforcement barsThus a few amountof energy absorption has been lost during blast load Since the

Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

630

1260

1890

2520

9100

900

000

207

(a)

Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

9100

900

000

215

657

1314

1971

2629

(b)

Figure 9 Blast load with a 24m of explosion distance (a) uncor-roded shear wall and (b) corroded shear wall

yield and compressive strength of concrete were vital param-eters slippage of reinforcement bars due to corrosion againstblast load with a very close explosion distance measuredin milliseconds did not influence the performance of thestructure It is believed that the methodology described herewill be a guideline for further studies andnovel investigationsTherefore buckling problems and particularly irregularitiesof buildings under the effect of blast loads do require furtherstudiesThe lessons learned from terrorist events in the recentpast could guide us in the design and in the risk assessmentof buildings considering their vulnerability to blast loading

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] Federal Emergency Management Agency (FEMA) Risk Man-agement Series Primer for Design of Commercial Buildings toMitigate Terrorist Attacks FEMA 427 2003


[2] D O Dusenberry Ed Handbook of Blast Resistant Design ofBuildings John Wiley amp Sons 2010

[3] ldquoDesign of buildings to optimize resistance to blast loadingrdquo inBlast Effects on Buildings G CMays and P D Smith Eds 1995

[4] P D Smith and J G Hetherington Blast and Ballistic Loadingof Structures 2nd edition 1994

[5] D C Kent and R Park ldquoFlexural members with confinedconcreterdquo Journal of Structural Division vol 97 no 7 pp 1969ndash1990 1997

[6] J B Mander Seismic design of bridge piers [PhD thesis]University of Canterbury Canterbury New Zealand 1984

[7] Turkish Standards Institute ldquoRequirements for design andconstruction of reinforced concrete structuresrdquo Tech RepTS500 Turkish Standards Institute Ankara Turkey 2000

[8] H Yalciner S Sensoy and O Eren ldquoTime-dependent seismicperformance assessment of a single-degree-of-freedom framesubject to corrosionrdquo Engineering Failure Analysis vol 19 no 1pp 109ndash122 2012

[9] Z P Bazant ldquoPhysical model for steel corrosion in concretesea structuresmdashapplicationrdquo ASCE Journal of the StructureDivision vol 105 no 6 pp 1155ndash1166 1979

[10] C Q Li J J Zheng W Lawanwisut and R E Melchers ldquoCon-crete delamination caused by steel reinforcement corrosionrdquoJournal of Materials in Civil Engineering vol 19 no 7 pp 591ndash600 2007

[11] H Yalciner O Eren and S Sensoy ldquoAn experimental studyon the bond strength between reinforcement bars and concreteas a function of concrete cover strength and corrosion levelrdquoCement and Concrete Research vol 42 no 5 pp 643ndash655 2012

[12] J M Alsiwat and M Saatcioglu ldquoReinforcement anchorageslip under monotonic loadingrdquo ASCE Journal of StructuralEngineering vol 118 no 9 pp 2421ndash2438 1992

[13] Federal Emergency Management Agency Pre-Standard andCommentary for the Seismic Rehabilitation of Buildings TheAmerican Society of Civil Engineers for the Federal EmergencyManagement Agency (FEMA) Washington DC USA 2000Publications no 356

[14] R Park and T Paulay Reinforced Concrete Structures JohnWiley amp Sons New York NY USA 1975

[15] BBC news 2012 httpwwwbbccouknewsworld-middle-east-18422636

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Figure 1 Destroyed reinforced concrete building by blast load [15]

Hemisphericalshock wave

Drag

Standoff

Ground shock

Center of burst

OverpressureReflected pressurePerimeter protection(fence guards and barriers)

Figure 2 Schematic of a blast load [4]

structures When a response of a building from blast loadis considered natural period of vibration of the structure isthe vital parameter for a given explosion Ductile elementsmade of steel and reinforced concrete absorb a lot of strainenergy [3]The effects of blast on reinforced concrete and steelstructures have been widely studied by many researchers Tothe knowledge of the author the effects of corrosion withblast loads on reinforced concrete buildings have not beenstudiedTherefore in this study different blast load scenarioswere performed for uncorroded and corroded reinforcedconcrete buildings to investigate the effect of blast loadswith corrosion Performance levels of the reinforced concretebuildings were obtained under the effect of blast loads Theimpacts of the blast waves on the surface of the structuralmembers were simulated

2 Blast and Loadings

Blast can be defined as a rapid phase of a created pressure by asudden release of energyThis energy provides a blast wave indifferent shapes The general generated blast wave has beenformed in a hemispherical form away from the blast site asshown in Figure 2

In this study the peak static overpressure was calculatedbased on the model developed by Smith and Hetherington[4]

for 119875119904gt 10 bar 119875

119904=

67

1198853+ 1

for 01 lt 119875119904lt 10 bar 119875

119904=

0975

119885+

1455

1198852+

585

1198853

(1)

where 119885 is the scaled distance (ftlb13) and it can becalculated by the following equation In (2) 119877 and 119882 denotethe explosion distance (ft) and the explosives weight (lb) inTNT respectively

119885 =119877

11988213 (2)

Idealized pressure-time history of a blast load and compar-ison between free-field or side-on and reflected pressure-time histories are shown in Figure 3 In Figure 3(a) 119875

119900

is the ambient pressure 119875so is the peak positive side-onoverpressure 119875minusso is the peak negative side-on overpressure119875119904(119905) is the time varying positive overpressure 119875minus

119904(t) is the

time varying negative overpressure 119875119903is the peak reflected

overpressure 119868119904is the positive-phase-specific impulse (the

integration of the positive phase pressure-time history) and119894minus

119904is the negative-phase-specific impulse (the integration of

the negative phase pressure-time history)The velocity of a wave (119880

119904) and the maximum pressure

were calculated based on the model proposed by Smith andHetherington [4] Consider

119880119904= radic

6119875119904+ 7119875119900

7119875119900

sdot 119886119900

119902119904=

51198752

119904

2 (119875119904+ 7119875119900)

(3)

where 119886119900is the ambient air pressure ahead of wave 120574 is the

specific heat ratio and 120588 is the density of air The reflectedpressure 119875

119903 was then calculated by following equations

119875119903= 2119875119904+ (120574 + 1) 119902

119904

119902119904=

1

21205881199041199062

119904

119906119904=

119886119900sdot 119875119904

120574119875119900

[1 + [120574 + 1

2120574]

119875119904

119875119900

]

minus12

119875119903= 2119875119904[7119875119900+ 4119875119904

7119875119900+ 119875119904

]

(4)

In this study four different explosion distances (ie 6m12m 18m and 24m) were defined with having the sameamount of 150 kg TNTThemass specific energy for TNTwasequal to 4520 kJkg

3 Material Modelling

In order to perform the blast load with combined corrosioneffects stress and strain relationships of concrete and rein-forcement bars were defined by user In this study we used the



Duration Duration

AmbientPr

essu

re


Pso

PoPminusso



tminusotot = 0

Pminuss (t)

Ps(t)


ta

+ to

(a)

Pres

sure

Duration Time

Duration

Pso

Po

Pr

Positivep

Negative phase hase

tminuso

to

to

to + tminuso

(b)





119888= 3250radic1198911015840






D

A

B

C

Unconfined

s

N

Confined

N

N

N

fc

120590c

0002 12057650u 12057650c 12057620c 120576c

lx

ly

12057650h

120579

05fc

02fc

(a)

fsu

fsy

120576sy 120576sp 120576su

(b)



119887119891minus 1198870

= 119899bars (4120587119889119904(119905)

(1 minus ]119888) (119886119887)

radic120572

+ (1 + ]119888) (119887119886)

radic120572

minus2120587119887119891119905

119864ef)

(5)


0


119904(119905) is the




119887is




119888


120591119887119906

= minus27143 + 036211198911015840

119888+ 23296 (

119888

119863) (MPa) (6)


if 119888

119863ge 2

0 le 119862119871le 14 for 119891

1015840

119888= 23MPa

0 le 119862119871le 068 for 119891

1015840

119888= 51MPa

120591119887119906

= 119890(001572119891

1015840

119888+022957(119888119863)+013946119862

119871+175913)

(MPa)

(7)


120579119904=

120575ext119889 minus 119888

(8)



Deformation

Forc

e

A

B IO LS CP C

D E


6m

12m

Shear wall






119871119901= 05119867 (9)




Damping917

Hysteretic

Total696


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

2092

4183

6275

8366

2423

(a)

Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

4530

9060

13590

18120

6770

818

2412

1509

(b)






Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

941

1882

2823

3764

8702

956

342

309

(a)

Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

1002

2004

3006

4009

8334

967

700

330

(b)



5 Conclusion


Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

630

1260

1890

2520

9100

900

000

207

(a)

Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

9100

900

000

215

657

1314

1971

2629

(b)





References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Duration Duration

AmbientPr

essu

re


Pso

PoPminusso



tminusotot = 0

Pminuss (t)

Ps(t)


ta

+ to

(a)

Pres

sure

Duration Time

Duration

Pso

Po

Pr

Positivep

Negative phase hase

tminuso

to

to

to + tminuso

(b)





119888= 3250radic1198911015840






D

A

B

C

Unconfined

s

N

Confined

N

N

N

fc

120590c

0002 12057650u 12057650c 12057620c 120576c

lx

ly

12057650h

120579

05fc

02fc

(a)

fsu

fsy

120576sy 120576sp 120576su

(b)



119887119891minus 1198870

= 119899bars (4120587119889119904(119905)

(1 minus ]119888) (119886119887)

radic120572

+ (1 + ]119888) (119887119886)

radic120572

minus2120587119887119891119905

119864ef)

(5)


0


119904(119905) is the




119887is




119888


120591119887119906

= minus27143 + 036211198911015840

119888+ 23296 (

119888

119863) (MPa) (6)


if 119888

119863ge 2

0 le 119862119871le 14 for 119891

1015840

119888= 23MPa

0 le 119862119871le 068 for 119891

1015840

119888= 51MPa

120591119887119906

= 119890(001572119891

1015840

119888+022957(119888119863)+013946119862

119871+175913)

(MPa)

(7)


120579119904=

120575ext119889 minus 119888

(8)



Deformation

Forc

e

A

B IO LS CP C

D E


6m

12m

Shear wall






119871119901= 05119867 (9)




Damping917

Hysteretic

Total696


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

2092

4183

6275

8366

2423

(a)

Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

4530

9060

13590

18120

6770

818

2412

1509

(b)






Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

941

1882

2823

3764

8702

956

342

309

(a)

Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

1002

2004

3006

4009

8334

967

700

330

(b)



5 Conclusion


Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

630

1260

1890

2520

9100

900

000

207

(a)

Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

9100

900

000

215

657

1314

1971

2629

(b)





References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










D

A

B

C

Unconfined

s

N

Confined

N

N

N

fc

120590c

0002 12057650u 12057650c 12057620c 120576c

lx

ly

12057650h

120579

05fc

02fc

(a)

fsu

fsy

120576sy 120576sp 120576su

(b)



119887119891minus 1198870

= 119899bars (4120587119889119904(119905)

(1 minus ]119888) (119886119887)

radic120572

+ (1 + ]119888) (119887119886)

radic120572

minus2120587119887119891119905

119864ef)

(5)


0


119904(119905) is the




119887is




119888


120591119887119906

= minus27143 + 036211198911015840

119888+ 23296 (

119888

119863) (MPa) (6)


if 119888

119863ge 2

0 le 119862119871le 14 for 119891

1015840

119888= 23MPa

0 le 119862119871le 068 for 119891

1015840

119888= 51MPa

120591119887119906

= 119890(001572119891

1015840

119888+022957(119888119863)+013946119862

119871+175913)

(MPa)

(7)


120579119904=

120575ext119889 minus 119888

(8)



Deformation

Forc

e

A

B IO LS CP C

D E


6m

12m

Shear wall






119871119901= 05119867 (9)




Damping917

Hysteretic

Total696


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

2092

4183

6275

8366

2423

(a)

Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

4530

9060

13590

18120

6770

818

2412

1509

(b)






Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

941

1882

2823

3764

8702

956

342

309

(a)

Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

1002

2004

3006

4009

8334

967

700

330

(b)



5 Conclusion


Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

630

1260

1890

2520

9100

900

000

207

(a)

Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

9100

900

000

215

657

1314

1971

2629

(b)





References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Deformation

Forc

e

A

B IO LS CP C

D E


6m

12m

Shear wall






119871119901= 05119867 (9)




Damping917

Hysteretic

Total696


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

2092

4183

6275

8366

2423

(a)

Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

4530

9060

13590

18120

6770

818

2412

1509

(b)






Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

941

1882

2823

3764

8702

956

342

309

(a)

Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

1002

2004

3006

4009

8334

967

700

330

(b)



5 Conclusion


Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

630

1260

1890

2520

9100

900

000

207

(a)

Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

9100

900

000

215

657

1314

1971

2629

(b)





References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

941

1882

2823

3764

8702

956

342

309

(a)

Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

1002

2004

3006

4009

8334

967

700

330

(b)



5 Conclusion


Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

630

1260

1890

2520

9100

900

000

207

(a)

Kinetic + strain

Damping

Hysteretic

Total


Ener

gy (m

-kN

)

00 01 01 02 02 03 03 04 04 05

Time (s)05

9100

900

000

215

657

1314

1971

2629

(b)





References



















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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