Review Article Properties of Concrete at Elevated Temperatures

Review ArticleProperties of Concrete at Elevated Temperatures

Venkatesh Kodur

Department of Civil and Environmental Engineering Michigan State University East Lansing MI 48824 USA

Correspondence should be addressed to Venkatesh Kodur koduregrmsuedu

Received 18 September 2013 Accepted 16 January 2014 Published 13 March 2014

Academic Editors R Kacianauskas I G Raftoyiannis and J Wang

Copyright copy 2014 Venkatesh Kodur 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

Fire response of concrete structural members is dependent on the thermal mechanical and deformation properties of concreteThese properties vary significantly with temperature and also depend on the composition and characteristics of concrete batchmix as well as heating rate and other environmental conditions In this chapter the key characteristics of concrete are outlinedThe various properties that influence fire resistance performance together with the role of these properties on fire resistanceare discussed The variation of thermal mechanical deformation and spalling properties with temperature for different types ofconcrete are presented

1 Introduction

Concrete is widely used as a primary structural material inconstruction due to numerous advantages such as strengthdurability ease of fabrication and noncombustibility proper-ties it possesses over other construction materials Concretestructural members when used in buildings have to satisfyappropriate fire safety requirements specified in buildingcodes [1ndash4] This is because fire represents one of the mostsevere environmental conditions to which structures maybe subjected therefore provision of appropriate fire safetymeasures for structural members is an important aspect ofbuilding design

Fire safety measures to structural members are measuredin terms of fire resistance which is the duration duringwhich a structural member exhibits resistance with respectto structural integrity stability and temperature transmission[5 6] Concrete generally provides the best fire resistanceproperties of any building material [7] This excellent fireresistance is due to concretersquos constituent materials (iecement and aggregates) which when chemically combinedform a material that is essentially inert and has low thermalconductivity high heat capacity and slower strength degrada-tion with temperature It is this slow rate of heat transfer andstrength loss that enables concrete to act as an effective fireshield not only between adjacent spaces but also to protectitself from fire damage

The behaviour of a concrete structural member exposedto fire is dependent in part on thermal mechanical anddeformation properties of concrete of which the memberis composed Similar to other materials the thermophysicalmechanical and deformation properties of concrete changesubstantially within the temperature range associated withbuilding fires These properties vary as a function of temper-ature and depend on the composition and characteristics ofconcrete The strength of concrete has significant influenceon its properties at both room and high temperatures Theproperties of high strength concrete (HSC) vary differentlywith temperature than those of normal strength concrete(NSC) This variation is more pronounced for mechanicalproperties which are affected by strength moisture contentdensity heating rate amount of silica fume and porosity

In practice fire resistance of structural members used tobe evaluated mainly through standard fire tests [8] In recentyears however the use of numerical methods for the calcu-lation of the fire resistance of structural members is gainingacceptance because these calculation methods are far lesscostly and time consuming [9] When a structural memberis subjected to a defined temperature-time exposure during afire this exposure will cause a predictable temperature distri-bution in the member Increased temperatures cause defor-mations and property changes in the constitutive materials ofa structural member With knowledge of deformations andproperty changes the usual methods of structural mechanics

Hindawi Publishing CorporationISRN Civil EngineeringVolume 2014 Article ID 468510 15 pageshttpdxdoiorg1011552014468510

2 ISRN Civil Engineering

can be applied to predict the fire resistance performance of astructural member The availability of material properties atan elevated temperature permits amathematical approach forpredicting fire resistance of structural members [10 11]

Clearly the generic information available on propertiesof concrete at room temperature is seldom applicable in fireresistance design [12] It is imperative therefore that the firesafety practitioner knows how to extend based on a prioriconsiderations the utility of the scanty property data that canbe gathered from the technical literature Also knowledgeof unique characteristics such as fire induced spalling inconcrete is critical to determine the fire performance ofconcrete structural members

2 Properties Influencing Fire Resistance

21 General The fire response of reinforced concrete (RC)members is influenced by the characteristics of constituentmaterials namely concrete and reinforcing steel Theseinclude (a) thermal properties (b) mechanical properties(c) deformation properties and (d) material specific char-acteristics such as spalling in concrete The thermal proper-ties determine the extent of heat transfer to the structuralmember whereas the mechanical properties of constituentmaterials determine the extent of strength loss and stiffnessdeterioration of the member The deformation propertiesin conjunction with mechanical properties determine theextent of deformations and strains in the structural memberIn addition fire induced spalling of concrete can play asignificant role in the fire performance of RC members[13] All these properties vary as a function of tempera-ture and depend on the composition and characteristicsof concrete as well as those of the reinforcing steel [12]The temperature induced variation in properties in concreteis much more complex than that in reinforcing steel dueto moisture migration as well as significant variation ofingredients in different types of concrete Thus the primaryfocus of this chapter is on the effect of temperature onproperties of concrete The effect of temperature on prop-erties of steel reinforcement can be found elsewhere [412]

Concrete is available in various forms and it is oftengrouped under different categories based on weight (as nor-mal weight and light weight concrete) strength (as normalstrength high strength and ultrahigh strength concrete)presence of fibers (as plain and fiber-reinforced concrete)and performance (as conventional and high performanceconcrete) Fire safety practitioners further subdivide normal-weight concretes into silicate (siliceous) and carbonate (lime-stone) aggregate concrete according to the compositionof the principal aggregate Also when a small amount ofdiscontinuous fibers (steel or polypropylene) is added to aconcrete batch mix to improve performance this concrete isreferred to as fiber-reinforced concrete (FRC) In this sectionthe various properties of concrete are mainly discussed forconventional concrete The effect of strength weight andfibers on properties of concrete at elevated temperatures ishighlighted

Traditionally the compressive strength of concrete usedto be around 20 to 50MPa which is classified as normal-strength concrete (NSC) In recent years concrete with acompressive strength in the range of 50 to 120MPa hasbecome widely available and is referred to as high-strengthconcrete (HSC) When compressive strength exceeds120MPa it is often referred to as ultrahigh performanceconcrete (UHP) The strength of concrete degrades withtemperature and the rate of strength degradation is highlyinfluenced by the compressive strength of concrete

22 Thermal Properties The thermal properties that influ-ence temperature rise and distribution in a concrete struc-tural member are thermal conductivity specific heat thermaldiffusivity and mass loss

Thermal conductivity is the property of a material toconduct heat Concrete contains moisture in different formsand the type and the amount of moisture have a significantinfluence on thermal conductivity Thermal conductivity isusuallymeasured bymeans of ldquosteady staterdquo or ldquotransientrdquo testmethods [14] Transient methods are preferred to measurethermal conductivity of moist concrete over steady-statemethods [15ndash17] as physiochemical changes of concrete athigher temperatures cause intermittent direction of heat flowOn average the thermal conductivity of conventional normalstrength concrete at room temperature ranges between 14and 36Wm-∘C [18]

Specific heat is the amount of heat per unit mass requiredto change the temperature of a material by one degree andis often expressed in terms of thermal (heat) capacity whichis the product of specific heat and density Specific heat ishighly influenced by moisture content aggregate type anddensity of concrete [19ndash21] The variation of specific heatwith temperature used to be determined through adiabaticcalorimetry until 1980s Since the 1980s differential scan-ning calorimetry (DSC) has been the most commonly usedtechnique for mapping the curve in a single temperaturesweep at a desired rate of heating [22 23] Unfortunately theaccuracy of the DSC technique in determining the sensibleheat contribution to the apparent specific heat may notbe particularly good (sometimes it may be as low as plusmn20percent) The rate of temperature rise in DSC tests is usually5∘Csdotminminus1 At higher heating rates the peaks in the DSCcurves tend to shift to higher temperatures and becomesharper For temperatures above 600∘C a high-temperaturedifferential thermal analyzer (DTA) is also used to evaluatespecific heat

The thermal diffusivity of amaterial is defined as the ratioof thermal conductivity to the volumetric specific heat of thematerial [24] It measures the rate of heat transfer from anexposed surface of a material to inner layers The larger thediffusivity the faster the temperature rise at a certain depth inthematerial [12] Similar to thermal conductivity and specificheat thermal diffusivity varies with temperature rise in thematerial Thermal diffusivity 120572 can be calculated using therelation

120572 =119896

120588119888119901

(1)

ISRN Civil Engineering 3

where 119896 is thermal conductivity 120588 is density and 119888119901is specific

heat of the materialThedensity in an oven-dry condition is themass of a unit

volume of thematerial comprising the solid itself and the air-filled pores With increasing temperature materials such asconcrete that have high amount of moisture will experienceloss of mass resulting from evaporation of moisture due tochemical reactions Assuming that the material is isotropicwith respect to its dilatometric behavior its density (or mass)at any temperature can be calculated from thermogravimetricand dilatometric curves [24]

23 Mechanical Properties The mechanical properties thatdetermine the fire performance of RC members are com-pressive and tensile strength modulus of elasticity andstress-strain response of constituent materials at elevatedtemperatures

Compressive strength of concrete at an elevated tem-perature is of primary interest in fire resistance designCompressive strength of concrete at ambient temperaturedepends upon water-cement ratio aggregate-paste interfacetransition zone curing conditions aggregated type and sizeadmixture types and type of stress [25] At high temperaturecompressive strength is highly influenced by room tempera-ture strength rate of heating and binders in batch mix (suchas silica fume fly ash and slag) Unlike thermal propertiesat high temperature the mechanical properties of concreteare well researched The strength degradation in HSC is notconsistent and there are significant variations in strength lossas reported by various authors

The tensile strength of concrete is much lower thancompressive strength due to ease with which cracks canpropagate under tensile loads [26] Concrete is weak intension and for NSC tensile strength is only 10 of itscompressive strength and for HSC tensile strength ratio isfurther reduced Thus tensile strength of concrete is oftenneglected in strength calculations at room and elevatedtemperatures However it is an important property becausecracking in concrete is generally due to tensile stresses andthe structural damage of the member in tension is oftengenerated by progression in microcracking [26] Under fireconditions tensile strength of concrete can be even morecrucial in cases where fire induced spalling occurs in aconcrete structural member [27] Tensile strength of concreteis dependent on almost same factors as compressive strengthof concrete [28 29]

Another property that influences fire resistance is themodulus of elasticity of concrete which decreases withtemperature At high temperature disintegration of hydratedcement products and breakage of bonds in themicrostructureof cement paste reduce elastic modulus and the extent ofreduction depends on moisture loss high temperature creepand type of aggregate

24 Deformation Properties Thedeformation properties thatdetermine the fire performance of reinforced concrete mem-bers are thermal expansion and creep of the concrete andreinforcement at elevated temperatures In addition transient

strain that occurs at elevated temperatures in concrete canenhance deformations in fire exposed concrete structuralmembers

Thermal expansion characterizes the expansion (orshrinkage) of a material caused by heating and is definedas the expansion (shrinkage) of unit length of a materialwhen the temperature of concrete is raised by one degreeThecoefficient of thermal expansion is defined as the percentagechange in length of a specimen per degree temperature riseThe expansion is considered to be positive when the materialelongates and is considered negative (shrinkage) when itshortens In general the thermal expansion of a materialis dependent on the temperature and is evaluated throughthe dilatometric curve which is a record of the fractionalchange of a linear dimension of a solid at a steadily increasingor decreasing temperature [24] Thermal expansion is animportant property to predict thermal stresses that get intro-duced in a structural member under fire conditionsThermalexpansion of concrete is generally influenced by cement typewater content aggregate type temperature and age [15 30]

Creep often referred to as creep strain is defined asthe time-dependent plastic deformation of the material Atnormal stresses and ambient temperatures deformationsdue to creep are not significant At higher stress levels andat elevated temperatures however the rate of deformationcaused by creep can be substantial Hence the main factorsthat influence creep are the temperature the stress leveland their duration [31] The creep of concrete is due to thepresence of water in its microstructure [32] There is nosatisfactory explanation for the creep of concrete at elevatedtemperatures

Transient strain occurs during the first time heating ofconcrete and is independent of time It is essentially causedby thermal incompatibilities between the aggregate and thecement paste [6] Transient strain of concrete similar to thatof high temperature creep is a complex phenomenon and isinfluenced by factors such as temperature strength moisturecontent loading and mix proportions

25 Spalling In addition to thermal mechanical and defor-mation properties another property that has a significantinfluence on the fire performance of a concrete structuralmember is spalling [33] This property is unique to concreteand can be a governing factor in determining the fire resis-tance of an RC structural member [34] Spalling is definedas the breaking up of layers (pieces) of concrete from thesurface of a concrete member when it is exposed to highand rapidly rising temperatures such as those encounteredin fires The spalling can occur soon after exposure to rapidheating and can be accompanied by violent explosions orit may happen during later stages of fire when concretehas become so weak after heating such that when cracksdevelop pieces of concrete fall off from the surface of concretemember The consequences are limited as long as the extentof damage is small but extensive spalling may lead to earlyloss of stability and integrity Further spalling exposes deeperlayers of concrete to fire temperatures thereby increasingthe rate of transmission of heat to the inner layers of the


member including the reinforcement When the reinforce-ment is directly exposed to fire the temperatures in thereinforcement rise at a very high rate leading to a fasterdecrease in strength (capacity) of the structural memberTheloss of strength in the reinforcement combined with the lossof concrete due to spalling significantly decreases the fireresistance of a structural member [35 36]

While spalling might occur in all concrete types HSC ismore susceptible to fire induced spalling than NSC becauseof its low permeability and lower water-cement ratio ascompared to NSC The fire induced spalling is furtherdependent on a number of factors including permeabilityof concrete type of fire exposure and tensile strength ofconcrete [34 37ndash40] Thus information on permeability andtensile strength of concrete which vary with temperatureare crucial for predicting fire induced spalling in concretemembers

3 Thermal Properties of Concrete atElevated Temperatures

Thermal properties that govern temperature dependent prop-erties in concrete structures are thermal conductivity specificheat (or heat capacity) and mass loss These propertiesare significantly influenced by the aggregate type moisturecontent and composition of concrete mix There have beennumerous test programs for characterizing thermal prop-erties of concrete at elevated temperatures [16 41ndash44] Adetailed review on the effect of temperature on thermalproperties of different concrete types is given by Khaliq [45]Kodur et al [46] and Flynn [47]

31 Thermal Conductivity Thermal conductivity of concreteat room temperature is in the range of 14 and 36Wm∘K andvaries with temperature [18] Figure 1 illustrates the variationof thermal conductivity of NSC as a function of temperaturebased on published test data and empirical relations Thetest data is compiled by Khaliq [45] from different sourcesbased on experimental data [16 20 21 24 44 48] andempirical relations in different standards [4 15]The variationin measured test data is depicted through the shaded areain Figure 1 and this variation in reported data on thermalconductivity is mainly attributed to moisture content typeof aggregate test conditions and measurement techniquesused in experiments [15 18ndash20 41] It should be notedthat there are very few standardized methods available formeasuring thermal properties Also plotted in Figure 1 is boththe upper and lower bound values of thermal conductivityas per EC2 provisions and this range is for all aggregatetypes However thermal conductivity shown in Figure 1 asper ASCE relations is applicable for carbonate aggregatesconcrete

Overall thermal conductivity decreases gradually withtemperature and this decrease is dependent on the concretemix properties specifically moisture content and permeabil-ity This decreasing trend in thermal conductivity can beattributed to variation of moisture content with increase intemperature [18]

0

05

1

15

2

25

3

0 200 400 600 800 1000

Eurocode (lower)Eurocode (upper)

ASCE (carbonate)Range of reported test

Ther

mal

cond

uctiv

ity (W

m-∘

C)

Temperature (∘C)

Figure 1 Variation in thermal conductivity of normal strengthconcrete as a function of temperature

Thermal conductivity of HSC is higher than that of NSCdue to lowwc ratio and use of different binders in HSC[49] Generally thermal conductivity of HSC is in the rangebetween 24 and 36Wm∘K at room temperature Thermalconductivity for fiber-reinforced concretes (with both steeland polypropylene fibers) almost follow a similar trend as thatof plain concrete and lie closer to that of HSCTherefore it isdeduced that there is no significant effect of fibers on thermalconductivity of concrete in a 20ndash800∘C temperature range[27]

32 Specific Heat The specific heat of concrete at roomtemperature varies in the range of 840 JkgsdotK and 1800 JkgsdotKfor different aggregate types Often specific heat is expressedin terms of thermal capacity which is the product of specificheat and density of concrete The specific heat property issensitive to various physical and chemical transformationsthat take place in concrete at elevated temperatures Thisincludes the vaporization of free water at about 100∘C thedissociation of Ca(OH)

2into CaO and H

2O between 400ndash

500∘C and the quartz transformation of some aggregatesabove 600∘C [24] Specific heat is therefore highly dependenton moisture content and considerably increases with higherwater to cement ratio

Khaliq and Kodur [27] compiled measured specific heatof different concretes from various studies [16 20 24 4144 48] Figure 2 illustrates the variation of specific heat forNSC with temperature as reported in various studies basedon test data and different standards The specific heat ofconcrete type remains almost constant up to 400∘C followedby increases of up to about 700∘C and then remains con-stant between 700 and 800∘C range Of the various factorsaggregate type has a significant influence on the specific heat(thermal capacity) of concreteThis effect is captured inASCEspecified relations for specific heat of concrete [15] Carbonateaggregate concrete has higher specific heat (heat capacity)in 600ndash800∘C temperature range and this is caused by anendothermic reaction which results from decomposition of


0

4

8

12

16

20

0 200 400 600 800 1000

ASCE manualEurocode 2

Kodur and Sultan

Spec

ific h

eat (

MJm

3-∘

C)

Temperature (∘C)

Figure 2 Variation in specific heat of normal strength concrete as afunction of temperature

dolomite and absorbs a large amount of energy [12] Thishigh heat capacity in carbonate aggregate concrete helps tominimize spalling and enhance fire resistance of structuralmembers

As compared to NSC HSC exhibits slightly lower specificheat throughout the 20ndash800∘C temperature range [41] Thepresence of fibers also has a minor influence on the specificheat of concrete For concrete with polypropylene fibers theburning of polypropylene fibers produces microchannels forrelease of vapor and hence the amount of heat absorbedis less for dehydration of chemically bound water thus itsspecific heat is reduced in the temperature range of 600ndash800∘C However concrete with steel fibers displays a higherspecific heat in the 400ndash800∘C temperature range which canbe attributed to additional heat absorbed for dehydration ofchemically bound water

33 Mass Loss Depending on the density concretes areusually subdivided into two major groups (1) normal-weightconcretes with densities in 2150 to 2450 kgsdotmminus3 range and(2) lightweight concretes with densities between 1350 and1850 kgsdotmminus3 The density or mass of concrete decreaseswith increasing temperature due to loss of moisture Theretention in mass of concrete at elevated temperatures ishighly influenced by the type of aggregate [21 44]

Figure 3 illustrates the variation in mass of concrete asa function of temperature for concretes made with car-bonate and siliceous aggregates The mass loss is minimalfor both carbonate and siliceous aggregate concretes up toabout 600∘C However the type of aggregate has significantinfluence onmass loss in concretes beyond 600∘C In the caseof siliceous aggregate concrete mass loss is insignificant evenabove 600∘C However beyond 600∘C carbonate aggregateconcrete experiences a larger percentage of mass loss as com-pared to siliceous aggregate concrete This higher percentageof mass loss in carbonate aggregate concrete is attributed todissociation of dolomite in carbonate aggregate at around600∘C [12]

60

80

100

0 200 400 600 800 1000

Mas

s (

of o

rigin

al)

Hu et al-carbonateHu et al-siliceousLie and Kodur-carbonate

Lie and Kodur-siliceousKodur and Sultan-carbonateKodur and Sultan-siliceous

Temperature (∘C)

Figure 3 Variation in mass of concrete with different aggregates asa function of temperature

The strength of concrete does not have a significantinfluence on mass loss and hence HSC exhibits a similartrend in mass loss as that of NSC The mass loss for fiber-reinforced concrete is also similar to plain concrete of upto about 800∘C Above 800∘C the mass loss in steel fiber-reinforced HSC is slightly lower than that of plain HSC

4 Mechanical Properties of Concrete atElevated Temperatures

The mechanical properties that are of primary interestin fire resistance design are compressive strength tensilestrength elastic modulus and stress-strain response incompression Mechanical properties of concrete at elevatedtemperatures have been studied extensively in the literaturein comparison to thermal properties [12 39 50ndash52] Hightemperature mechanical property tests are generally carriedout on concrete specimens that are typically cylinders orcubes of different sizes Unlike room temperature propertymeasurements where there are specified specimen sizes asper standards the high temperature mechanical propertiesare usually carried out on a wide range of specimen sizes dueto a lack of standardized test specifications for undertakinghigh temperature mechanical property tests [53 54]

41 Compressive Strength Figures 4 and 5 illustrate thevariation of compressive strength ratio for NSC and HSCat elevated temperatures respectively with upper and lowerbounds (of shaded area) showing range variation in reportedtest data Also plotted in these figures is the variation ofcompressive strength as obtained using Eurocode [4] ASCE[15] and Kodur et al [46] relations Figure 4 shows alarge but uniform variation of the compiled test data forNSC throughout a 20ndash800∘C temperature range HoweverFigure 5 shows a larger variation in compressive strength ofHSC with a temperature in the range of 200∘C to 500∘Cand less variation above 500∘C This is mainly because fewer


0

02

04

06

08

1

12

0 200 400 600 800 1000

Relat

ive c

ompr

essiv

e stre

ngth

ASCE model

Eurocode (siliceous)

Eurocode (carbonate)Range of reported test data

Temperature (∘C)

Figure 4 Variation of relative compressive strength of normalstrength concrete as a function of temperature

0

02

04

06

08

1

12

0 200 400 600 800 1000

Relat

ive c

ompr

essiv

e stre

ngth

Kodur et al model-HSCEurocode-HSC (class 2)Eurocode-HSC (class 3)

Castillo 1990-HSCRange of reported test data

Temperature (∘C)

Figure 5 Variation in relative compressive strength of high strengthconcrete as a function of temperature

test data points were reported for HSC for temperatureshigher than 500∘C either due to the occurrence of spalling inconcrete or due to limitations in the test apparatus Howevera wider variation is observed for NSC in this temperaturerange (above 500∘C) when compared to HSC as seen fromFigures 4 and 5 This is mainly because of the higher numberof test data points reported for NSC in the literature andalso due to the lower tendency of NSC to spall under fireOverall the variation in compressive strength mechanicalproperties of concrete at high-temperatures is quite highThese variations fromdifferent tests can be attributed to usingdifferent heating or loading rates specimen size and curingcondition at testing (moisture content and age of specimen)and the use of admixtures

In the case of NSC the compressive strength of concreteis marginally affected by a temperature of up to 400∘C NSC

is usually highly permeable and allows easy diffusion of porepressure as a result of water vapor On the other hand the useof different binders in HSC produces a superior and densemicrostructure with less amount of calcium hydroxide whichensures a beneficial effect on compressive strength at roomtemperature [55] Binders such as use of slag and silica fumegive the best results to improve compressive strength at roomtemperature which is attributed to a dense microstructureHowever as mentioned earlier the compact microstructureis highly impermeable and under high temperature becomesdetrimental as it does not allow moisture to escape resultingin build-up of pore pressure and rapid development ofmicrocracks in HSC leading to a faster deterioration ofstrength and occurrence of spalling [27 56 57]The presenceof steel fibers in concrete helps to slow down strength loss atelevated temperatures [44 58]

Among the factors that directly affect compressivestrength at elevated temperatures are initial curing moisturecontent at the time of testing and the addition of admixturesand silica fume to the concrete mix [59ndash63]These factors arenot addressed in the literature and there is no test data thatshows the influence of these factors on the high-temperaturemechanical properties of concrete

Another main reasoning for the significant variation inthe high-temperature strength properties of concrete is theuse of different testing conditions (such as heating rate andstrain rate) and test procedures (hot strength test and residualstrength test) due to a lack of standardized test methods forcarrying out property tests [46]

42 Tensile Strength The tensile strength of concrete is muchlower than that of compressive strength and hence tensilestrength of concrete is oftenneglected in strength calculationsat room and elevated temperatures However from fireresistance point of view it is an important property becausecracking in concrete is generally due to tensile stresses andthe structural damage of the member in tension is oftengenerated by progression in microcracking [26] Under fireconditions tensile strength of concrete can be even morecrucial in cases where fire induced spalling occurs in concretemember [27] Thus information on tensile strength of HSCwhich varies with temperature is crucial for predicting fireinduced spalling in HSC members

Figure 6 illustrates the variation of splitting tensilestrength ratio ofNSCandHSCas a function of temperature asreported in previous studies and Eurocode provisions [4 64ndash66] The ratio of tensile strength at a given temperatureto that at room temperature is plotted in Figure 6 Theshaded portion in this plot shows a range of variation insplitting tensile strength as obtained by various researchersfor NSCwith conventional aggregatesThe decrease in tensilestrength of NSC with temperature can be attributed to weakmicrostructure of NSC allowing initiation of microcracks At300∘C concrete loses about 20 of its initial tensile strengthAbove 300∘C the tensile strength of NSC decreases at a rapidrate due to a more pronounced thermal damage in the formofmicrocracks and reaches to about 20 of its initial strengthat 600∘C


0

02

04

06

08

1

0 200 400 600 800

Relat

ive s

plitt

ing

tens

ile st

reng

th

Bahnood 2009 (HSC)Eurocode 2 (NSC)Felicetti 1996 (HSC)

SFPE HB (NSC)Range of test data (NSC and HSC)

Temperature (∘C)

Figure 6 Variation in relative splitting tensile strength of concreteas a function of temperature

HSC experiences a rapid loss of tensile strength at highertemperatures due to development of pore pressure in densemicrostructured HSC [55] The addition of steel fibers toconcrete enhances its tensile strength and the increase can beup to 50 higher at room temperature [67 68] Further thetensile strength of steel fiber-reinforced concrete decreasesat a lower rate than that of plain concrete throughout thetemperature range of 20ndash800∘C [69] This increased tensilestrength can delay the propagation of cracks in steel fiber-reinforced concrete structural members and is highly bene-ficial when the member is subjected to bending stresses

43 Elastic Modulus Themodulus of elasticity (119864) of variousconcretes at room temperature varies over a wide range 50times 103 to 350 times 103MPa and is dependent mainly on thewater-cement ratio in the mixture the age of concrete themethod of conditioning and the amount and nature of theaggregates The modulus of elasticity decreases rapidly withthe rise of temperature and the fractional decline does notdepend significantly on the type of aggregate [70] Fromothersurveys [38 71] it appears however that the modulus ofelasticity of normal-weight concretes decreases at a higherpace with the rise of temperature than that of lightweightconcretes

Figure 7 illustrates variation of ratio of elastic modulus attarget temperature to that at room temperature for NSC andHSC [4 19 72] It can be seen from the figure that the trend ofloss of elastic modulus of both concretes with temperature issimilar but there is a significant variation in the reported testdata The degradation modulus in both NSC and HSC canbe attributed to excessive thermal stresses and physical andchemical changes in concrete microstructure

44 Stress-Strain Response Themechanical response of con-crete is usually expressed in the formof stress-strain relationswhich are often used as input data inmathematicalmodels forevaluating the fire resistance of concrete structural members

0

02

04

06

08

1

12

0 200 400 600 800

Rela

tive e

lasti

c mod

ulus

Phan-HSCCastillo 1990-HSC

EC-NSCRange of reported test data (NSC and HSC)

Temperature (∘C)

Figure 7 Variation in elastic modulus of concrete as a function oftemperature

0

5

10

15

20

25

30

35

40

45

0 0005 001 0015

Stre

ss (M

Pa)

Strain ()

23∘C

200∘C

300∘C

400∘C

500∘C

600∘C

700∘C

800∘C

100∘C

Figure 8 Stress-strain response of normal strength concrete atelevated temperatures

Generally because of a decrease in compressive strength andincrease in ductility of concrete the slope of stress-straincurve decreases with increasing temperature The strength ofconcrete has a significant influence on stress-strain responseboth at room and elevated temperatures

Figures 8 and 9 illustrate stress-strain response of NSCand HSC respectively at various temperatures [72 73] At alltemperatures both NSC and HSC exhibit a linear responsefollowed by a parabolic response till peak stress and thena quick descending portion prior to failure In general it isestablished thatHSChas steeper andmore linear stress-strain


0

10

20

30

40

50

60

70

80

90

100

0 0005 001 0015

Stre

ss (M

Pa)

Strain ()

23∘C

200∘C

300∘C

400∘C

500∘C

600∘C

700∘C

800∘C

100∘C

Figure 9 Stress-strain response of high strength concrete at elevatedtemperatures

curves in comparison to NSC in 20ndash800∘C The temperaturehas a significant effect on the stress-strain response of bothNSC and HSC as with the rate of rise in temperatureThe strain corresponding to peak stress starts to increaseespecially above 500∘C This increase is significant and thestrain at peak stress can reach four times the strain at roomtemperature HSC specimens exhibit a brittle response asindicated by postpeak behavior of stress-strain curves shownin Figure 9 [74] In the case of fiber-reinforced concreteespecially with steel fibers the stress-strain response is moreductile

5 Deformation Properties of Concrete atElevated Temperatures

Deformation properties that include thermal expansioncreep strain and transient strain are highly dependent onthe chemical composition the type of aggregate and thechemical and physical reactions that occur in concrete duringheating [75]

51 Thermal Expansion Concrete generally undergoesexpansion when subjected to elevated temperaturesFigure 10 illustrates the variation of thermal expansion inNSC with temperature [4 15] where the shaded portionindicates the range of test data reported by differentresearchers [46 76] The thermal expansion of concreteincreases from zero at room temperature to about 13 at700∘C and then generally remains constant through 1000∘CThis increase is substantial in the 20ndash700∘C temperaturerange and is mainly due to high thermal expansion resultingfrom constituent aggregates and cement paste in concrete

0

04

08

12

16

0 200 400 600 800 1000

Ther

mal

expa

nsio

n (

)

ASCE modelEurocode carbonate

Eurocode siliceousRange of test data

Temperature (∘C)

Figure 10 Variation in linear thermal expansion of normal strengthconcrete as a function of temperature

Thermal expansion of concrete is complicated by othercontributing factors such as additional volume changescaused by variation in moisture content by chemicalreactions (dehydration change of composition) and bycreep and microcracking resulting from nonuniformthermal stresses [18] In some cases thermal shrinkagecan also result from loss of water due to heating alongwith thermal expansion and this might lead to the overallvolume change to be negative that is shrinkage rather thanexpansion

Eurocodes [4] accounts for the effect of type of aggregateon variation of thermal expansion than of concrete withtemperature Concrete made with siliceous aggregate has ahigher thermal expansion than that of carbonate aggregateconcrete However ASCE provisions [15] provide only onevariation for both siliceous and carbonate aggregate concrete

The strength of concrete and presence of fiber have mod-erate influence on thermal expansion The rate of expansionfor HSC and fiber-reinforced concrete slows down between600ndash800∘C however the rate of thermal expansion increasesagain above 800∘C The slowdown in thermal expansion inthe 600ndash800∘C range is attributed to the loss of chemicallyboundwater in hydrates and the increase in expansion above800∘C is attributed to a softening of concrete and excessivemicro- and macrocrack development [77]

52 Creep and Transient Strains Time-dependent deforma-tions in concrete such as creep and transient strains gethighly enhanced at elevated temperatures under compressivestresses [18] Creep in concrete under high temperaturesincreases due to moisture movement out of concrete matrixThis phenomenon is further intensified by moisture disper-sion and loss of bond in cement gel (CndashSndashH) Thereforethe process of creep is caused and accelerated mainly bytwo processes (1) moisture movement and dehydration ofconcrete due to high temperatures and (2) acceleration in theprocess of breakage of bond


Transient strain occurs during the first time heatingof concrete but it does not occur upon repeated heating[78] Exposure of concrete to high temperature inducescomplex changes in the moisture content and chemicalcomposition of the cement paste Moreover there exists amismatch in the thermal expansion between the cementpaste and the aggregate Therefore factors such as changes inchemical composition of concrete andmismatches in thermalexpansion lead to internal stresses and microcracking inthe concrete constituents (aggregate and cement paste) andresults in transient strain in the concrete [75]

A review of the literature shows that there is limitedinformation on creep and transient strain of concrete atelevated temperatures [46] Some data on the creep ofconcrete at elevated temperatures is available from the workof Cruz [70] MareAchal [79] Gross [80] and Schneideret al [81] Anderberg and Thelandersson [82] carried outtests to evaluate transient and creep strains under elevatedtemperatures They found that predried specimens at 45 and675 of load stress level were less liable to deformation inthe ldquopositive directionrdquo (expansion) under load At 225preload specimens displayed no significant difference ofstrainsThey also found that the influence of water saturationwas not very significant except for free thermal expansion(0 preload) which was found to be smaller for watersaturated specimens

Khoury et al [78] studied creep strain of initially moistconcretes at four load levels measured during first heatingat 1∘Cmin An important feature of these results was that aconsiderable contraction under load was observed as com-pared to free (unloaded) thermal strains This contraction isreferred to as the ldquoload-induced thermal strainrdquo and the actualthermal strain is considered to consist of total thermal strainminus the load-induced thermal strain

Schneider [75] also investigated the effect of transient andcreep restraint on deformation of concrete He concludedthat the transient test for measuring total deformation orrestraint of concrete has the strongest relation to buildingfires and is supposed to give the most realistic data withdirect relevance to fire The important conclusions fromthe study are that (1) water to cement ratio and originalstrength are of little importance on creep deformations undertransient conditions (2) aggregate to cement ratio has a greatinfluence on the strains and critical temperatures the harderthe aggregate the lower the thermal expansion therefore totaldeformation in transient state will be lower and (3) curingconditions are of great importance in the 20ndash300∘C rangeair-cured and oven-dried specimens have lower transient andcreep strains than water cured specimens

Anderberg and Thelandersson [82] developed consti-tutive models for creep and transient strains in concreteat elevated temperatures These equations for creep andtransient strain at elevated temperatures as suggested byAnderberg andThelandersson [82] are

120576cr = 1205731120590

119891119888119879

radic119905119890119889(119879minus293)

120576tr = 1198962120590

11989111988820

120576th

(2)

where 120576cr = creep strain 120576tr = transient strain 1205731= 628 times

10minus6 sminus05 119889 = 2658 times 10minus3 Kminus1 119879 = concrete temperature(∘K) at time 119905 (s) 119891

119888119879= concrete strength at temperature 119879

120590 = stress in the concrete at the current temperature 1198962= a

constant ranges between 18 and 235 120576th = thermal strain and11989111988820

= concrete strength at room temperatureThe above discussed information on high temperature

creep and transient strain is mostly developed for NSCThere is still a lack of test data and models on the effect oftemperature on creep and transient strain in HSC and fiber-reinforced concrete

6 Fire Induced Spalling

A review of the literature presents a conflicting picture onthe occurrence of fire induced spalling and also on the exactmechanism of spalling in concrete While some researchersreported explosive spalling in concrete structural membersexposed to fire a number of other studies reported littleor no significant spalling One possible explanation for thisconfusing trend of observations is the large number of factorsthat influence spalling and their interdependency Howevermost researchers agree that major causes for fire inducedspalling in concrete are low permeability of concrete andmoisture migration in concrete at elevated temperatures

There are two broad theories by which the spallingphenomenon can be explained [83]

(i) Pressure Build-Up Spalling is believed to be causedby the build-up of pore pressure during heating [83ndash85]The extremely high water vapor pressure generated duringexposure to fire cannot escape due to the high density andcompactness (and low permeability) of higher strength con-crete When the effective pore pressure (porosity times porepressure) exceeds the tensile strength of concrete chunksof concrete fall off from the structural member This porepressure is considered to drive progressive failure that isthe lower the permeability of concrete the greater the fireinduced spallingThis falling-off of concrete chunks can oftenbe explosive depending on fire and concrete characteristics[38 86]

(ii) Restrained Thermal DilatationThis hypothesis considersthat spalling results from restrained thermal dilatation closeto the heated surface which leads to the development ofcompressive stresses parallel to the heated surface Thesecompressive stresses are released by brittle fracture of con-crete (spalling) The pore pressure can play a significant roleon the onset of instability in the form of explosive thermalspalling [87]

Although spalling might occur in all concretes high-strength concrete is believed to be more susceptible tospalling thannormal-strength concrete because of its lowper-meability and lowwater-cement ratio [88 89]The highwatervapor pressure generated due to a rapid rise in temperaturecannot escape due to high density (and low permeability) ofHSC and this pressure build-up often reaches the saturationvapor pressure At 300∘C the pore pressure can reach upto 8MPa such internal pressures are often too high to


NSC HSC

Figure 11 Relative spalling in NSC and HSC columns under fireconditions

be resisted by the HSC mix having a tensile strength ofapproximately 5MPa [84] The drained conditions at theheated surface and the low permeability of concrete lead tostrong pressure gradients close to the surface in the formof the so-called ldquomoisture clogrdquo [38 86] When the vaporpressure exceeds the tensile strength of concrete chunks ofconcrete fall off from the structural member In a numberof test observations on HSC columns it has been foundthat spalling is often of an explosive nature [19 90] Hencespalling is one of the major concerns in the use of HSC inbuilding applications and should be properly accounted forin evaluating fire performance [91] Spalling in NSC andHSCcolumns is compared in Figure 11 using data obtained fromfull-scale fire tests on loaded columns [92] It can be seen thatthe spalling is quite significant in fire exposed HSC column

The extent of spalling depends on a number of factorsincluding strength porosity density load level fire intensityaggregate type relative humidity amount of silica fumeand other admixtures [34 93 94] Many of these factorsare interdependent and this makes prediction of spallingquite complex The variation of porosity with temperature isthe most important property needed for predicting spallingperformance of HSC [33] Noumowe et al carried outporosity measurements on NSC and HSC specimens usinga mercury porosimeter at various temperatures [88 95]

Based on limited fire tests researchers have suggested thatspalling in HSC can be minimized by adding polypropylenefibres to the HSC mix [85 96ndash101] The polypropylene fibersmelt when temperatures in concrete reach about 160ndash170∘Cand this creates pores in concrete that are sufficient forrelieving vapor pressure developed in the concrete Anotheralternative for limiting fire induced spalling in HSC columnsis through the use of bent ties where ties are bent at 135∘ intothe concrete core [102]

7 Relations of High TemperatureProperties of Concrete

There are limited constitutive relations for high-temperatureproperties of concrete in codes and standards that canbe used for fire design These relations can be found inthe ASCE manual [15] and Eurocode 2 [4] Kodur et al[46] have compiled different relations that are available forthermal mechanical and deformation of concrete at elevatedtemperatures

There are some differences in the constitutive relation-ships for high-temperature properties of concrete used inEuropean andAmerican standardsThe constitutive relationsin Eurocode are applicable for NSC and HSC while the rela-tions in the ASCE manual of practice are for NSC only Theconstitutive relationships for high-temperature properties ofconcrete specified in the Eurocode and the ASCE manualare summarized in Table 1 In addition to these constitutivemodels Kodur et al [93] proposed constitutive relations forHSC which are an extension to ASCE relations for NSCThese relations for HSC are also included in Table 1

A major difference between the European and the ASCEhigh-temperature constituent relations for concrete is theeffect of aggregate type on concrete propertiesThe Eurocodedoes not specifically account for the effect of aggregate typeon the thermal capacity of concrete at high-temperaturesIn the Eurocode properties such as specific heat densitychanges and hence heat capacity are considered to bethe same for all aggregate types used in concrete For thethermal conductivity of concrete the Eurocode proposesupper and lower bound limits without indicating which limitto use for a given aggregate type in concrete FurthermoreEurocode classifies HSC into three classes depending on itscompressive strength namely

(i) class 1 for concretewith compressive strength betweenC5567 and C6075

(ii) class 2 for concrete with compressive strengthbetween C7085 and C8095

(iii) class 3 for concrete with compressive strength higherthan C90105

8 Summary

Concrete at elevated temperatures undergoes significantphysicochemical changes These changes cause propertiesto deteriorate at elevated temperatures and introduce addi-tional complexities such as spalling in HSC Thus thermalmechanical and deformation properties of concrete changesubstantially within the temperature range associated withbuilding fires Furthermore many of these properties aretemperature dependent and sensitive to testing (method)parameters such as heating rate strain rate temperaturegradient and so on

Based on information presented in this chapter it isevident that high temperature properties of concrete arecrucial for modeling fire response of reinforced concretestructures A good amount of data exists on high temperaturethermal mechanical and deformation properties of NSC

ISRN Civil Engineering 11Ta

ble1Con

stitu

tiver

elationships

ofhigh

-temperature

prop

ertie

sofcon

crete

NSC

mdashASC

EManual1992

HSC

mdashKo

dure

tal2004

[10]

NSC

andHSC

mdashEN

1992-1-

22004

[4]

Stress-strain

relatio

nships

120590119888

=

1198911015840

119888119879

[1minus(

120576minus120576max119879

120576max119879

)

2

]120576le120576max119879

1198911015840

119888119879

[1minus(

120576max119879

minus120576

3120576max119879

)

2

]120576gt120576max119879

1198911015840

119888119879

=

1198911015840

119888

20∘

Cle119879le450∘

C

1198911015840

119888

[2011minus2353(119879minus20

1000

)]450∘

Clt119879le874∘

C

0

874∘

Clt119879

120576max119879

=00025+(60119879+0041198792

)times10minus6

120590119888

=

1198911015840

119888119879

[1minus(

120576max119879

minus120576

120576max119879

)

119867

]

120576le120576max119879

1198911015840

119888119879

[1minus(

30(120576minus120576max119879

)

(130minus1198911015840

119888

)120576max119879

)

2

]120576gt120576max119879

1198911015840

119888119879

=

1198911015840

119888

[10minus0003125(119879minus20)]119879lt100∘

C0751198911015840

119888

100∘

Cle119879le400∘

C1198911015840

119888

[133minus000145119879]

400∘

Clt119879

120576max119879

=00018+(671198911015840

119888

+60119879+0031198792

)times10minus6

119867=228minus00121198911015840

119888

120590119888

=

31205761198911015840

119888119879

1205761198881119879

(2+(1205761205761198881119879

)3

)

120576le120576cu1119879

For1205761198881(119879)

lt120576le120576cu1(119879)

the

Eurocode

perm

itsthe

useo

flineara

swellasn

onlin

eard

escend

ing

branch

inthen

umericalanalysis

Forthe

parametersinthisequatio

nreferto

Table2

Thermal

capacity

Siliceous

aggregatec

oncrete

120588119888=

0005119879+1720∘

Cle119879le200∘

C27

200∘

Clt119879le400∘

C0013119879minus25400∘

Clt119879le500∘

C105minus0013119879500∘

Clt119879le600∘

C27

600∘

Clt119879

Carbon

atea

ggregateconcrete

120588119888=

2566

20∘

Cle119879le400∘

C01765119879minus68034

400∘

Clt119879le410∘

C2500671minus005043119879

410∘

Clt119879le445∘

C2566

445∘

Clt119879le500∘

C001603119879minus544881

500∘

Clt119879le635∘

C016635119879minus10090225635∘

Clt119879le715∘

C17607343minus022103119879715∘

Clt119879le785∘

C2566

785∘

Clt119879

Siliceous

aggregatec

oncrete

120588119888=

0005119879+17

20∘

Cle119879le200∘

C27

200∘

Clt119879le400∘

C0013119879minus25

400∘

Clt119879le500∘

Cminus0013119879+105500∘

Clt119879le600∘

C27

600∘

Clt119879le635∘

CCa

rbon

atea

ggregateconcrete

120588119888=

245

20∘

Cle119879le400∘

C0026119879minus1285

400∘

Clt119879le475∘

C00143119879minus6295

475∘

Clt119879le650∘

C01894119879minus12011650∘

Clt119879le735∘

Cminus0263119879+2124735∘

Clt119879le800∘

C2

800∘

Clt119879le1000∘

C

Specifich

eat(Jk

gC)

119888=900

for2

0∘Cle119879le100∘

C119888=900+(119879minus100)

for100∘

Clt119879le200∘C

119888=1000+(119879minus200)2

for2

00∘

Clt119879le400∘

C119888=1100

for4

00∘

Clt119879le1200∘

CDensitychange

(kgm

3 )120588=120588(20∘

C)=Re

ferenced

ensity

for2

0∘Cle119879le115∘C

120588=120588(20∘

C)(1minus002(119879minus115)85)

for115∘

Clt119879le200∘C

120588=120588(20∘

C)(098minus003(119879minus200)200)

for2

00∘

Clt119879le40

0∘C

120588=120588(20∘

C)(095minus007(119879minus400)800)

for4

00∘

Clt119879le1200∘

CTh

ermalcapacity=120588times119888

Thermal

cond

uctiv

ity

Siliceous

aggregatec

oncrete

119896119888

=minus0000625119879+1520∘

Cle119879le800∘

C10

800∘

Clt119879

Carbon

atea

ggregateconcrete

119896119888

=1355

20∘

Cle119879le293∘

Cminus0001241119879+17162293∘

Clt119879

Siliceous

aggregatec

oncrete

119896119888

=085(2minus00011119879)20∘

Clt119879le1000∘

C

Carbon

atea

ggregateconcrete

119896119888

=085(2minus00013119879)

20∘

Cle119879le300∘

C085(221minus0002119879)300∘

Clt119879

Alltypes

Upp

erlim

it119896119888

=2minus02451(119879100)+00107(119879100)2

for2

0∘Cle119879le1200∘

CLo

wer

limit

119896119888

=136minus0136(119879100)+00057(119879100)2

for2

0∘Cle119879le1200∘

C

Thermal

strain

Alltypes

120576th=[0004(1198792

minus400)+6(119879minus20)]times10minus6

Alltypes

120576th=[0004(1198792


Siliceous

aggregates

120576th=minus18times10minus4

+9times10minus6

119879+23times10minus11

1198793

for2

0∘Cle119879le700∘C

120576th=14times10minus3

for7

00∘

Clt119879le1200∘

CCalcareou

saggregates


+6times10minus6


1198793

for2

0∘Cle119879le805∘C


for8

05∘

Clt119879le1200∘

C


Table 2 Values of themain parameters of the stress-strain relationships of NSC andHSC at elevated temperatures as specified in EN1992-1-22004 [4]

Temp ∘F Temp ∘CNSC HSC

Siliceous agg Calcareous agg 1198911015840

119888119879

1198911015840

119888

(20∘C)

1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879

120576cu1119879 1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879

120576cu1119879 Class 1 Class 2 Class 368 20 1 00025 002 1 00025 002 1 1 1212 100 1 0004 00225 1 0004 0023 09 075 075392 200 095 00055 0025 097 00055 0025 09 075 070572 300 085 0007 00275 091 0007 0028 085 075 065752 400 075 001 003 085 001 003 075 075 045932 500 06 0015 00325 074 0015 0033 060 060 0301112 600 045 0025 0035 06 0025 0035 045 045 0251292 700 03 0025 00375 043 0025 0038 030 030 0201472 800 015 0025 004 027 0025 004 015 015 0151652 900 008 0025 00425 015 0025 0043 008 0113 0081832 1000 004 0025 0045 006 0025 0045 004 0075 0042012 1100 001 0025 00475 002 0025 0048 001 0038 0012192 1200 0 mdash mdash 0 mdash mdash 0 0 0The Eurocode classifies HSC into three classeslowast depending on its compressive strength namely(i) class 1 for concrete with compressive strength between C5567 and C6075(ii) class 2 for concrete with compressive strength between C7085 and C8095(iii) class 3 for concrete with compressive strength higher than C90105The strength notation of C5567 refers to a concrete grade with a characteristic cylinder and cube strength of 55Nmm2 and 67Nmm2 respectivelylowastNote where the actual characteristic strength of concrete is likely to be of a higher class than that specified in the design the relative reduction in strength forthe higher class should be used for fire design

and HSC However there is very limited property data onhigh temperature properties of new types of concrete suchas self-consolidated concrete and fly ash concrete at elevatedtemperatures

The review on material properties provided in this chap-ter is a broad outline of currently available information Addi-tional details related to specific conditions on which theseproperties are developed can be found in cited referencesAlso when using the material properties presented in thischapter due consideration should be given to batch mixproperties and other characteristics such as heating rate andloading level because the properties at elevated temperaturesdepend on a number of factors

Disclaimer

Certain commercial products are identified in this paper inorder to adequately specify the experimental procedure Inno case does such identification imply recommendations orendorsement by the author nor does it imply that the productor material identified is the best available for the purpose

Conflict of Interests

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

References

[1] ACI 2161 ldquoCode requirements for determining fire resistanceof concrete and masonry construction assembliesrdquo ACI 2161-07TMS-0216-07 American Concrete Institute FarmingtonHills Mich USA 2007

[2] ACI-318 Building Code Requirements For ReinForced Concreteand Commentary American Concrete Institute FarmingtonHills Mich USA 2008

[3] ldquoEN 1991-1-2 actions on structures Part 1-2 general actionsmdashactions on structures exposed to firerdquo Eurocode 1 EuropeanCommittee for Standardization Brussels Belgium 2002

[4] ldquoEN 1992-1-2 design of concrete structures Part 1-2 generalrulesmdashstructural fire designrdquo Eurocode 2 European Commit-tee for Standardization Brussels Belgium 2004

[5] A H Buchanan Structural Design For Fire Safety John Wileyand Sons Chichester UK 2002

[6] J A Purkiss Fire Safety Engineering Design of StructuresButterworth-Heinemann Elsevier Oxoford UK 2007

[7] V R Kodur and N Raut ldquoPerformance of concrete structuresunder fire hazard emerging trendsrdquo The Indian Concrete Jour-nal vol 84 no 2 pp 23ndash31 2010

[8] ldquoStandard test methods for fire tests of building constructionand materialsrdquo ASTM E119-08b ASTM International WestConshohocken Pa USA 2008

[9] ldquoFire design of concrete structuresmdashmaterials structures andmodellingrdquo FIB Bulletin 38 The International Federation forStructural Concrete Lausanne Switzerland 2007

[10] V K R Kodur T C Wang and F P Cheng ldquoPredicting thefire resistance behaviour of high strength concrete columnsrdquo


Cement and Concrete Composites vol 26 no 2 pp 141ndash1532004

[11] V Kodur M Dwaikat and N Raut ldquoMacroscopic FE modelfor tracing the fire response of reinforced concrete structuresrdquoEngineering Structures vol 31 no 10 pp 2368ndash2379 2009

[12] V R Kodur and T Z Harmathy ldquoProperties of buildingmaterialsrdquo in SFPE Handbook of Fire Protection Engineering PJ DiNenno Ed National Fire Protection Association QuincyMass USA 2008

[13] M BDwaikat andV K R Kodur ldquoFire induced spalling in highstrength concrete beamsrdquo Fire Technology vol 46 no 1 pp 251ndash274 2010

[14] ldquoStandard test method for evaluating the resistance to thermaltransmission of materials by the guarded heat flow metertechniquerdquo ASTM E1530 ASTM International West Con-shohocken Pa USA 2011

[15] ASCE Structural Fire Protection ASCE Committee on FireProtection Structural Division American Society of CivilEngineers New York NY USA 1992

[16] K-Y Shin S-B Kim J-H Kim M Chung and P-S JungldquoThermo-physical properties and transient heat transfer ofconcrete at elevated temperaturesrdquo Nuclear Engineering andDesign vol 212 no 1ndash3 pp 233ndash241 2002

[17] B Adl-Zarrabi L Bostrom and U Wickstrom ldquoUsing the TPSmethod for determining the thermal properties of concrete andwood at elevated temperaturerdquo Fire andMaterials vol 30 no 5pp 359ndash369 2006

[18] Z P Bazant and M F Kaplan Concrete at High TemperaturesMaterial Properties and Mathematical Models Longman GroupLimited Essex UK 1996

[19] L T Phan ldquoFire performance of high-strength concrete areport of the state-of-the-artrdquo Tech Rep National Institute ofStandards and Technology Gaithersburg Md USA 1996

[20] T Z Harmathy and LW Allen ldquoThermal properties of selectedmasonry unit concretesrdquo Journal American Concrete Institutionvol 70 no 2 pp 132ndash142 1973

[21] V R Kodur and M A Sultan ldquoThermal propeties of highstrength concrete at elevated temperaturesrdquo American ConcreteInstitute Special Publication SP-179 pp 467ndash480 1998

[22] ldquoStandard test method for determining specific heat capacityby differential scanning calorimetryrdquo ASTM C1269 ASTMInternational West Conshohocken Pa USA 2011

[23] ISODIS22007-22008 ldquoDetermination of thermal conductivityand thermal diffusivity Part 2 transient plane heat source (hotdisc) methodrdquo ISO Geneva Switzerland 2008

[24] T Z Harmathy ldquoThermal properties of concrete at elevatedtemperaturesrdquo ASTM Journal of Materials vol 5 no 1 pp 47ndash74 1970

[25] P K Mehta and P J M Monteiro Concrete MicrostructureProperties and Materials McGraw-Hill New York NY USA2006

[26] S Mindess J F Young and D Darwin Concrete PearsonEducation Upper Saddle River NJ USA 2003

[27] W Khaliq and V Kodur ldquoHigh temperature mechanical prop-erties of high strength fly ash concrete with and without fibersrdquoACI Materials Journal vol 109 no 6 pp 665ndash674 2012

[28] A M Neville Properties of Concrete Pearson Education EssexUK 2004

[29] S P Shah ldquoDo fibers increase the tensile strength of cement-based matrixesrdquo ACI Materials Journal vol 88 no 6 pp 595ndash602 1991

[30] Z P Bazant and J-C Chern ldquoStress-induced thermal andshrinkage strains in concreterdquo Journal of EngineeringMechanicsvol 113 no 10 pp 1493ndash1511 1987

[31] T ZHarmathy ldquoA comprehensive creepmodelrdquo Journal of BasicEngineering vol 89 no 3 pp 496ndash502 1967

[32] F H Wittmann Ed Fundamental Research on Creep andShrinkage of Concrete Martinus Nijhoff The Hague Nether-lands 1982

[33] M B Dwaikat and V K R Kodur ldquoHydrothermal model forpredicting fire-induced spalling in concrete structural systemsrdquoFire Safety Journal vol 44 no 3 pp 425ndash434 2009

[34] V K R Kodur and L Phan ldquoCritical factors governing thefire performance of high strength concrete systemsrdquo Fire SafetyJournal vol 42 no 6-7 pp 482ndash488 2007

[35] X Yu X Zha and Z Huang ldquoThe influence of spalling on thefire resistance of RC structuresrdquo Advanced Materials Researchvol 255ndash260 pp 519ndash523 2011

[36] V K R Kodur and M Dwaikat ldquoEffect of fire induced spallingon the response of reinforced concrete beamsrdquo InternationalJournal of Concrete Structures and Materials vol 2 no 2 pp71ndash82 2008

[37] T Z Harmathy ldquoMoisture and heat transport with particu-lar reference to concreterdquo NRCC 12143 National Council ofCanada 1971

[38] T Z Harmathy Fire Safety Design and Concrete John Wiley ampSons New York NY USA 1993

[39] G A Khoury ldquoConcrete spalling assessment methodologiesand polypropylene fibre toxicity analysis in tunnel firesrdquo Struc-tural Concrete vol 9 no 1 pp 11ndash18 2008

[40] P Kalifa G Chene and C Galle ldquoHigh-temperaturebehaviour of HPC with polypropylene fibresmdashfrom spalling tomicrostructurerdquo Cement and Concrete Research vol 31 no 10pp 1487ndash1499 2001

[41] V K R Kodur and M A Sultan ldquoEffect of temperatureon thermal properties of high-strength concreterdquo Journal ofMaterials in Civil Engineering vol 15 no 2 pp 101ndash107 2003

[42] M G Van Geem J Gajda and K Dombrowski ldquoThermalproperties of commercially available high-strength concretesrdquoCement Concrete and Aggregates vol 19 no 1 pp 38ndash54 1997

[43] T T Lie and V R Kodur ldquoThermal properties of fibre-reinforced concrete at elevated temperaturesrdquo IR 683 IRCNational Research Council of Canada Ottawa Canada 1995

[44] T T Lie and V K R Kodur ldquoThermal and mechanical proper-ties of steel-fibre-reinforced concrete at elevated temperaturesrdquoCanadian Journal of Civil Engineering vol 23 no 2 pp 511ndash5171996

[45] W Khaliq Performance characterization of high performanceconcretes under fire conditions [PhD thesis] Michigan StateUniversity 2012

[46] V K R Kodur M M S Dwaikat and M B Dwaikat ldquoHigh-temperature properties of concrete for fire resistance modelingof structuresrdquoACIMaterials Journal vol 105 no 5 pp 517ndash5272008

[47] D R Flynn ldquoResponse of high performance concrete to fireconditions review of thermal property data and measurementtechniquesrdquo Tech Rep National Institute of Standards andTechnology Millwood Va USA 1999

[48] T Harada J Takeda S Yamane and F Furumura ldquoStrengthelasticity and thermal properties of concrete subjected toelevated temperaturesrdquo ACI Concrete For Nuclear Reactor SPvol 34 no 2 pp 377ndash406 1972


[49] V Kodur and W Khaliq ldquoEffect of temperature on thermalproperties of different types of high-strength concreterdquo Journalof Materials in Civil Engineering ASCE vol 23 no 6 pp 793ndash801 2011

[50] W C Tang and T Y Lo ldquoMechanical and fracture properties ofnormal-and high-strength concretes with fly ash after exposureto high temperaturesrdquo Magazine of Concrete Research vol 61no 5 pp 323ndash330 2009

[51] A Noumowe ldquoMechanical properties and microstructure ofhigh strength concrete containing polypropylene fibres exposedto temperatures up to 200∘Crdquo Cement and Concrete Researchvol 35 no 11 pp 2192ndash2198 2005

[52] M Li C Qian and W Sun ldquoMechanical properties of high-strength concrete after firerdquo Cement and Concrete Research vol34 no 6 pp 1001ndash1005 2004

[53] RILEMTC 129-MHT ldquoTest methods for mechanical propertiesof concrete at high temperaturesmdashcompressive strength forservice and accident conditionsrdquo Materials and Structures vol28 no 3 pp 410ndash414 1995

[54] RILEMTC 129-MHT ldquoTest methods for mechanical propertiesof concrete at high temperatures Part 4mdashtensile strength forservice and accident conditionsrdquo Materials and Structures vol33 pp 219ndash223 2000

[55] Y N Chan G F Peng and M Anson ldquoResidual strength andpore structure of high-strength concrete and normal strengthconcrete after exposure to high temperaturesrdquo Cement andConcrete Composites vol 21 no 1 pp 23ndash27 1999

[56] C-S Poon S Azhar M Anson and Y-L Wong ldquoComparisonof the strength and durability performance of normal- andhigh-strength pozzolanic concretes at elevated temperaturesrdquoCement andConcrete Research vol 31 no 9 pp 1291ndash1300 2001

[57] B Chen and J Liu ldquoResidual strength of hybrid-fiber-reinforcedhigh-strength concrete after exposure to high temperaturesrdquoCement and Concrete Research vol 34 no 6 pp 1065ndash10692004

[58] A Lau andM Anson ldquoEffect of high temperatures on high per-formance steel fibre reinforced concreterdquo Cement and ConcreteResearch vol 36 no 9 pp 1698ndash1707 2006

[59] W P S Dias G A Khoury and P J E Sullivan ldquoMechanicalproperties of hardened cement paste exposed to temperaturesup to 700∘Crdquo ACI Materials Journal vol 87 no 2 pp 160ndash1661990

[60] F Furumura T Abe and Y Shinohara ldquoMechanical propertiesof high strength concrete at high temperaturesrdquo in Proceedingsof the 4th Weimar Workshop on High Performance ConcreteMaterial Properties and Design pp 237ndash254 1995

[61] R Felicetti and P G Gambarova ldquoEffects of high temperatureon the residual compressive strength of high-strength siliceousconcretesrdquo ACI Materials Journal vol 95 no 4 pp 395ndash4061998

[62] K K Sideris ldquoMechanical characteristics of self-consolidatingconcretes exposed to elevated temperaturesrdquo Journal of Materi-als in Civil Engineering vol 19 no 8 pp 648ndash654 2007

[63] H Fares S Remond A Noumowe and A CoustureldquoHigh temperature behaviour of self-consolidating concreteMicrostructure and physicochemical propertiesrdquo Cement andConcrete Research vol 40 no 3 pp 488ndash496 2010

[64] A Behnood and M Ghandehari ldquoComparison of compressiveand splitting tensile strength of high-strength concrete with andwithout polypropylene fibers heated to high temperaturesrdquo FireSafety Journal vol 44 no 8 pp 1015ndash1022 2009

[65] G G Carette K E Painter andVMMalhotra ldquoSustained hightemperature effect on concretes made with normal portlandcement normal portland cement and slag or normal portlandcement and fly ashrdquo Concrete International vol 4 no 7 pp 41ndash51 1982

[66] R Felicetti P G Gambarova G P Rosati F Corsi andG Giannuzzi ldquoResidual mechanical properties of high-strength concretes subjected to high-temperature cyclesrdquo inProceedings of the International Symposium of Utilization ofHigh-StrengthHigh-Performance Concrete pp 579ndash588 ParisFrance 1996

[67] J A Purkiss ldquoSteel fibre reinforced concrete at elevated tem-peraturesrdquo International Journal of Cement Composites andLightweight Concrete vol 6 no 3 pp 179ndash184 1984

[68] P Rossi ldquoSteel fiber reinforced concretes (SFRC) an example ofFrench researchrdquo ACI Materials Journal vol 91 no 3 pp 273ndash279 1994

[69] V R Kodur ldquoFibre-reinforced concrete for enhancing struc-tural fire resistance of columnsrdquo Fibre-Structural Applications ofFibre-Reinforced Concrete ACI SP-182 pp 215ndash234 1999

[70] C R Cruz ldquoElastic properties of concrete at high temperaturesrdquoJournat of the PCA Research and Development Laboratories vol8 pp 37ndash45 1966

[71] I D Bennetts Tech Rep MRLPS2381001 BHP MelbourneResearch Laboratories Clayton Australia 1981

[72] C Castillo and A J Durrani ldquoEffect of transient high temper-ture on high-strength concreterdquo ACI Materials Journal vol 87no 1 pp 47ndash53 1990

[73] F P ChengVK R Kodur andTCWang ldquoStress-strain curvesfor high strength concrete at elevated temperaturesrdquo Tech RepNRCC-46973 National Research Council of Canada 2004

[74] Y F Fu Y L Wong C S Poon and C A Tang ldquoStress-strainbehaviour of high-strength concrete at elevated temperaturesrdquoMagazine of Concrete Research vol 57 no 9 pp 535ndash544 2005

[75] U Schneider ldquoConcrete at high temperaturesmdasha generalreviewrdquo Fire Safety Journal vol 13 no 1 pp 55ndash68 1988

[76] N Raut Response of high strength concrete columns under fire-induced biaxial bending [PhD thesis] Michigan State Univer-sity East Lansing Mich USA 2011

[77] Y-F Fu Y-L Wong C-S Poon C-A Tang and P LinldquoExperimental study of micromacro crack development andstress-strain relations of cement-based composite materials atelevated temperaturesrdquo Cement and Concrete Research vol 34no 5 pp 789ndash797 2004

[78] G A Khoury B N Grainger and P J E Sullivan ldquoStrain ofconcrete during fire heating to 600∘Crdquo Magazine of ConcreteResearch vol 37 no 133 pp 195ndash215 1985

[79] J C MareAchal ACI SP 34 American Concrete InstituteDetroit Mich USA 1972

[80] H Gross ldquoHigh-temperature creep of concreterdquo Nuclear Engi-neering and Design vol 32 no 1 pp 129ndash147 1975

[81] U Schneider U Diedrichs W Rosenberger and R WeissSonderforschungsbereich 148 Arbeitsbericht 1978ndash1980 Teil IIB 3 Technical University of Braunschweig Germany 1980

[82] Y Anderberg and S Thelandersson ldquoStress and deforma-tion characteristics of concrete at high temperatures 2-Experimental investigation and material behaviour modelrdquoBulletin 54 Lund Institute of Technology Lund Sweden 1976

[83] V K R Kodur ldquoSpalling in high strength concrete exposed tofiremdashconcerns causes critical parameters and curesrdquo in Pro-ceedings of the ASCE Structures Congress Advanced Technologyin Structural Engineering pp 1ndash9 May 2000


[84] U Diederichs U Jumppanen and U Schneider ldquoHigh tem-perature properties and spalling behaviour of high strengthconcreterdquo in Proceedings of the 4th Weimar Workshop on HighPerformance Concrete HAB Weimar Germany 1995

[85] K D Hertz ldquoLimits of spalling of fire-exposed concreterdquo FireSafety Journal vol 38 no 2 pp 103ndash116 2003

[86] Y Anderberg ldquoSpalling phenomenon of HPC and OCrdquo inProceedings of the InternationalWorkshop onFire Performance ofHigh Strength Concrete NIST SP 919 NIST Gaithersburg MdUSA 1997

[87] Z P Bazant ldquoAnalysis of pore pressure thermal stress andfracture in rapidly heated concreterdquo in Proceedings of theInternational Workshop on Fire Performance of High StrengthConcrete NIST SP 919 pp 155ndash164 Gaithersburg Md USA1997

[88] A N Noumowe R Siddique and G Debicki ldquoPermeability ofhigh-performance concrete subjected to elevated temperature(600∘C)rdquo Construction and BuildingMaterials vol 23 no 5 pp1855ndash1861 2009

[89] V Boel K Audenaert and G De Schutter ldquoGas permeabilityand capillary porosity of self-compacting concreterdquo Materialsand StructuresMateriaux et Constructions vol 41 no 7 pp1283ndash1290 2008

[90] U Danielsen ldquoMarine concrete structures exposed to hydro-carbon firesrdquo Tech Rep SINTEF-TheNorwegian Fire ResearchInstitute Trondheim Norway 1997

[91] V R Kodur and M A Sultan ldquoStructural behaviour of highstrength concrete columns exposed to firerdquo in Proceedings ofthe International Symposium on High Performance and ReactivePowder Concrete pp 217ndash232 1998

[92] V Kodur and R McGrath ldquoFire endurance of high strengthconcrete columnsrdquo Fire Technology vol 39 no 1 pp 73ndash872003

[93] V K R Kodur F-P Cheng T-C Wang and M A SultanldquoEffect of strength and fiber reinforcement on fire resistanceof high-strength concrete columnsrdquo Journal of Structural Engi-neering vol 129 no 2 pp 253ndash259 2003

[94] L T Phan ldquoSpalling and mechanical properties of highstrength concrete at high temperaturerdquo in Proceedings of the 5thInternational Conference on Concrete under Severe ConditionsEnvironment amp Loading (CONSEC rsquo07) CONSEC CommitteeTours France 2007

[95] A Noumowe P Clastres G Debicki and J Costaz ldquoThermalstresses and water vapor pressure of high performance concreteat high temperaturerdquo in Proceedings of the 4th InternationalSymposium on Utilization of High-StrengthHigh-PerformanceConcrete Paris France 1996

[96] V K R Kodur ldquoFiber reinforcement for minimizing spallingin High Strength Concrete structural members exposed tofirerdquo ACI Special Publication Innovations in Fibre-ReinForcedConcrete For Value 216-14 pp 221ndash236 2003

[97] V K R Kodur ldquoDesign solutions for enhancing the fireresistance of high strength concrete columnsrdquo Indian ConcreteJournal vol 81 no 10 pp 9ndash20 2007

[98] V Kodur Fire Resistance Design Guidelines for High StrengthConcrete Columns National Research Council OntarioCanada 2003

[99] A Bilodeau V M Malhotra and G C Hoff ldquoHydrocarbonfire resistance of high strength normal weight and light weightconcrete incorporating polypropylene fibresrdquo in Proceedings ofthe International Symposium on High Performance and ReactivePowder Concrete Sherbrooke Canada 1998

[100] A Bilodeau V K R Kodur and G C Hoff ldquoOptimization ofthe type and amount of polypropylene fibres for preventing thespalling of lightweight concrete subjected to hydrocarbon firerdquoCement and Concrete Composites vol 26 no 2 pp 163ndash1742004

[101] D P Bentz ldquoFibers percolation and spelling of high-performance concreterdquoACI Structural Journal vol 97 no 3 pp351ndash359 2000

[102] V K R Kodur and R McGrath ldquoEffect of silica fume andlateral confinement on fire endurance of high strength concretecolumnsrdquo Canadian Journal of Civil Engineering vol 33 no 1pp 93ndash102 2006

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



can be applied to predict the fire resistance performance of astructural member The availability of material properties atan elevated temperature permits amathematical approach forpredicting fire resistance of structural members [10 11]

Clearly the generic information available on propertiesof concrete at room temperature is seldom applicable in fireresistance design [12] It is imperative therefore that the firesafety practitioner knows how to extend based on a prioriconsiderations the utility of the scanty property data that canbe gathered from the technical literature Also knowledgeof unique characteristics such as fire induced spalling inconcrete is critical to determine the fire performance ofconcrete structural members

2 Properties Influencing Fire Resistance

21 General The fire response of reinforced concrete (RC)members is influenced by the characteristics of constituentmaterials namely concrete and reinforcing steel Theseinclude (a) thermal properties (b) mechanical properties(c) deformation properties and (d) material specific char-acteristics such as spalling in concrete The thermal proper-ties determine the extent of heat transfer to the structuralmember whereas the mechanical properties of constituentmaterials determine the extent of strength loss and stiffnessdeterioration of the member The deformation propertiesin conjunction with mechanical properties determine theextent of deformations and strains in the structural memberIn addition fire induced spalling of concrete can play asignificant role in the fire performance of RC members[13] All these properties vary as a function of tempera-ture and depend on the composition and characteristicsof concrete as well as those of the reinforcing steel [12]The temperature induced variation in properties in concreteis much more complex than that in reinforcing steel dueto moisture migration as well as significant variation ofingredients in different types of concrete Thus the primaryfocus of this chapter is on the effect of temperature onproperties of concrete The effect of temperature on prop-erties of steel reinforcement can be found elsewhere [412]

Concrete is available in various forms and it is oftengrouped under different categories based on weight (as nor-mal weight and light weight concrete) strength (as normalstrength high strength and ultrahigh strength concrete)presence of fibers (as plain and fiber-reinforced concrete)and performance (as conventional and high performanceconcrete) Fire safety practitioners further subdivide normal-weight concretes into silicate (siliceous) and carbonate (lime-stone) aggregate concrete according to the compositionof the principal aggregate Also when a small amount ofdiscontinuous fibers (steel or polypropylene) is added to aconcrete batch mix to improve performance this concrete isreferred to as fiber-reinforced concrete (FRC) In this sectionthe various properties of concrete are mainly discussed forconventional concrete The effect of strength weight andfibers on properties of concrete at elevated temperatures ishighlighted

Traditionally the compressive strength of concrete usedto be around 20 to 50MPa which is classified as normal-strength concrete (NSC) In recent years concrete with acompressive strength in the range of 50 to 120MPa hasbecome widely available and is referred to as high-strengthconcrete (HSC) When compressive strength exceeds120MPa it is often referred to as ultrahigh performanceconcrete (UHP) The strength of concrete degrades withtemperature and the rate of strength degradation is highlyinfluenced by the compressive strength of concrete

22 Thermal Properties The thermal properties that influ-ence temperature rise and distribution in a concrete struc-tural member are thermal conductivity specific heat thermaldiffusivity and mass loss

Thermal conductivity is the property of a material toconduct heat Concrete contains moisture in different formsand the type and the amount of moisture have a significantinfluence on thermal conductivity Thermal conductivity isusuallymeasured bymeans of ldquosteady staterdquo or ldquotransientrdquo testmethods [14] Transient methods are preferred to measurethermal conductivity of moist concrete over steady-statemethods [15ndash17] as physiochemical changes of concrete athigher temperatures cause intermittent direction of heat flowOn average the thermal conductivity of conventional normalstrength concrete at room temperature ranges between 14and 36Wm-∘C [18]

Specific heat is the amount of heat per unit mass requiredto change the temperature of a material by one degree andis often expressed in terms of thermal (heat) capacity whichis the product of specific heat and density Specific heat ishighly influenced by moisture content aggregate type anddensity of concrete [19ndash21] The variation of specific heatwith temperature used to be determined through adiabaticcalorimetry until 1980s Since the 1980s differential scan-ning calorimetry (DSC) has been the most commonly usedtechnique for mapping the curve in a single temperaturesweep at a desired rate of heating [22 23] Unfortunately theaccuracy of the DSC technique in determining the sensibleheat contribution to the apparent specific heat may notbe particularly good (sometimes it may be as low as plusmn20percent) The rate of temperature rise in DSC tests is usually5∘Csdotminminus1 At higher heating rates the peaks in the DSCcurves tend to shift to higher temperatures and becomesharper For temperatures above 600∘C a high-temperaturedifferential thermal analyzer (DTA) is also used to evaluatespecific heat

The thermal diffusivity of amaterial is defined as the ratioof thermal conductivity to the volumetric specific heat of thematerial [24] It measures the rate of heat transfer from anexposed surface of a material to inner layers The larger thediffusivity the faster the temperature rise at a certain depth inthematerial [12] Similar to thermal conductivity and specificheat thermal diffusivity varies with temperature rise in thematerial Thermal diffusivity 120572 can be calculated using therelation

120572 =119896

120588119888119901

(1)






















0

05

1

15

2

25

3

0 200 400 600 800 1000



Ther

mal

cond

uctiv

ity (W

m-∘

C)

Temperature (∘C)




2into CaO and H

2O between 400ndash




0

4

8

12

16

20

0 200 400 600 800 1000


Kodur and Sultan

Spec

ific h

eat (

MJm

3-∘

C)

Temperature (∘C)






60

80

100

0 200 400 600 800 1000

Mas

s (

of o

rigin

al)



Temperature (∘C)







0

02

04

06

08

1

12

0 200 400 600 800 1000

Relat

ive c

ompr

essiv

e stre

ngth

ASCE model



Temperature (∘C)


0

02

04

06

08

1

12

0 200 400 600 800 1000

Relat

ive c

ompr

essiv

e stre

ngth



Temperature (∘C)










0

02

04

06

08

1

0 200 400 600 800

Relat

ive s

plitt

ing

tens

ile st

reng

th



Temperature (∘C)






0

02

04

06

08

1

12

0 200 400 600 800

Rela

tive e

lasti

c mod

ulus



Temperature (∘C)


0

5

10

15

20

25

30

35

40

45

0 0005 001 0015

Stre

ss (M

Pa)

Strain ()

23∘C

200∘C

300∘C

400∘C

500∘C

600∘C

700∘C

800∘C

100∘C





0

10

20

30

40

50

60

70

80

90

100

0 0005 001 0015

Stre

ss (M

Pa)

Strain ()

23∘C

200∘C

300∘C

400∘C

500∘C

600∘C

700∘C

800∘C

100∘C






0

04

08

12

16

0 200 400 600 800 1000

Ther

mal

expa

nsio

n (

)



Temperature (∘C)












120576cr = 1205731120590

119891119888119879

radic119905119890119889(119879minus293)

120576tr = 1198962120590

11989111988820

120576th

(2)















NSC HSC












8 Summary




ble1Con

stitu

tiver

elationships

ofhigh

-temperature

prop

ertie

sofcon

crete

NSC

mdashASC

EManual1992

HSC

mdashKo

dure

tal2004

[10]

NSC

andHSC

mdashEN

1992-1-

22004

[4]

Stress-strain

relatio

nships

120590119888

=

1198911015840

119888119879

[1minus(

120576minus120576max119879

120576max119879

)

2

]120576le120576max119879

1198911015840

119888119879

[1minus(

120576max119879

minus120576

3120576max119879

)

2

]120576gt120576max119879

1198911015840

119888119879

=

1198911015840

119888

20∘

Cle119879le450∘

C

1198911015840

119888

[2011minus2353(119879minus20

1000

)]450∘

Clt119879le874∘

C

0

874∘

Clt119879

120576max119879

=00025+(60119879+0041198792

)times10minus6

120590119888

=

1198911015840

119888119879

[1minus(

120576max119879

minus120576

120576max119879

)

119867

]

120576le120576max119879

1198911015840

119888119879

[1minus(

30(120576minus120576max119879

)

(130minus1198911015840

119888

)120576max119879

)

2

]120576gt120576max119879

1198911015840

119888119879

=

1198911015840

119888

[10minus0003125(119879minus20)]119879lt100∘

C0751198911015840

119888

100∘

Cle119879le400∘

C1198911015840

119888

[133minus000145119879]

400∘

Clt119879

120576max119879

=00018+(671198911015840

119888

+60119879+0031198792

)times10minus6

119867=228minus00121198911015840

119888

120590119888

=

31205761198911015840

119888119879

1205761198881119879

(2+(1205761205761198881119879

)3

)

120576le120576cu1119879

For1205761198881(119879)

lt120576le120576cu1(119879)

the

Eurocode

perm

itsthe

useo

flineara

swellasn

onlin

eard

escend

ing

branch

inthen

umericalanalysis

Forthe


nreferto

Table2

Thermal

capacity

Siliceous

aggregatec

oncrete

120588119888=

0005119879+1720∘

Cle119879le200∘

C27

200∘

Clt119879le400∘

C0013119879minus25400∘

Clt119879le500∘

C105minus0013119879500∘

Clt119879le600∘

C27

600∘

Clt119879

Carbon

atea

ggregateconcrete

120588119888=

2566

20∘

Cle119879le400∘

C01765119879minus68034

400∘

Clt119879le410∘

C2500671minus005043119879

410∘

Clt119879le445∘

C2566

445∘

Clt119879le500∘

C001603119879minus544881

500∘

Clt119879le635∘

C016635119879minus10090225635∘

Clt119879le715∘

C17607343minus022103119879715∘

Clt119879le785∘

C2566

785∘

Clt119879

Siliceous

aggregatec

oncrete

120588119888=

0005119879+17

20∘

Cle119879le200∘

C27

200∘

Clt119879le400∘

C0013119879minus25

400∘

Clt119879le500∘

Cminus0013119879+105500∘

Clt119879le600∘

C27

600∘

Clt119879le635∘

CCa

rbon

atea

ggregateconcrete

120588119888=

245

20∘

Cle119879le400∘

C0026119879minus1285

400∘

Clt119879le475∘

C00143119879minus6295

475∘

Clt119879le650∘

C01894119879minus12011650∘

Clt119879le735∘

Cminus0263119879+2124735∘

Clt119879le800∘

C2

800∘

Clt119879le1000∘

C

Specifich

eat(Jk

gC)

119888=900

for2

0∘Cle119879le100∘

C119888=900+(119879minus100)

for100∘

Clt119879le200∘C

119888=1000+(119879minus200)2

for2

00∘

Clt119879le400∘

C119888=1100

for4

00∘

Clt119879le1200∘

CDensitychange

(kgm

3 )120588=120588(20∘

C)=Re

ferenced

ensity

for2

0∘Cle119879le115∘C

120588=120588(20∘

C)(1minus002(119879minus115)85)

for115∘

Clt119879le200∘C

120588=120588(20∘

C)(098minus003(119879minus200)200)

for2

00∘

Clt119879le40

0∘C

120588=120588(20∘

C)(095minus007(119879minus400)800)

for4

00∘

Clt119879le1200∘

CTh


Thermal

cond

uctiv

ity

Siliceous

aggregatec

oncrete

119896119888

=minus0000625119879+1520∘

Cle119879le800∘

C10

800∘

Clt119879

Carbon

atea

ggregateconcrete

119896119888

=1355

20∘

Cle119879le293∘

Cminus0001241119879+17162293∘

Clt119879

Siliceous

aggregatec

oncrete

119896119888

=085(2minus00011119879)20∘

Clt119879le1000∘

C

Carbon

atea

ggregateconcrete

119896119888

=085(2minus00013119879)

20∘

Cle119879le300∘

C085(221minus0002119879)300∘

Clt119879

Alltypes

Upp

erlim

it119896119888

=2minus02451(119879100)+00107(119879100)2

for2

0∘Cle119879le1200∘

CLo

wer

limit

119896119888

=136minus0136(119879100)+00057(119879100)2

for2

0∘Cle119879le1200∘

C

Thermal

strain

Alltypes

120576th=[0004(1198792


Alltypes

120576th=[0004(1198792


Siliceous

aggregates


+9times10minus6


1198793

for2

0∘Cle119879le700∘C


for7

00∘

Clt119879le1200∘

CCalcareou

saggregates


+6times10minus6


1198793

for2

0∘Cle119879le805∘C


for8

05∘

Clt119879le1200∘

C





119888119879

1198911015840

119888

(20∘C)

1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879

120576cu1119879 1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879




Disclaimer




References













































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






























0

05

1

15

2

25

3

0 200 400 600 800 1000



Ther

mal

cond

uctiv

ity (W

m-∘

C)

Temperature (∘C)




2into CaO and H

2O between 400ndash




0

4

8

12

16

20

0 200 400 600 800 1000


Kodur and Sultan

Spec

ific h

eat (

MJm

3-∘

C)

Temperature (∘C)






60

80

100

0 200 400 600 800 1000

Mas

s (

of o

rigin

al)



Temperature (∘C)







0

02

04

06

08

1

12

0 200 400 600 800 1000

Relat

ive c

ompr

essiv

e stre

ngth

ASCE model



Temperature (∘C)


0

02

04

06

08

1

12

0 200 400 600 800 1000

Relat

ive c

ompr

essiv

e stre

ngth



Temperature (∘C)










0

02

04

06

08

1

0 200 400 600 800

Relat

ive s

plitt

ing

tens

ile st

reng

th



Temperature (∘C)






0

02

04

06

08

1

12

0 200 400 600 800

Rela

tive e

lasti

c mod

ulus



Temperature (∘C)


0

5

10

15

20

25

30

35

40

45

0 0005 001 0015

Stre

ss (M

Pa)

Strain ()

23∘C

200∘C

300∘C

400∘C

500∘C

600∘C

700∘C

800∘C

100∘C





0

10

20

30

40

50

60

70

80

90

100

0 0005 001 0015

Stre

ss (M

Pa)

Strain ()

23∘C

200∘C

300∘C

400∘C

500∘C

600∘C

700∘C

800∘C

100∘C






0

04

08

12

16

0 200 400 600 800 1000

Ther

mal

expa

nsio

n (

)



Temperature (∘C)












120576cr = 1205731120590

119891119888119879

radic119905119890119889(119879minus293)

120576tr = 1198962120590

11989111988820

120576th

(2)















NSC HSC












8 Summary




ble1Con

stitu

tiver

elationships

ofhigh

-temperature

prop

ertie

sofcon

crete

NSC

mdashASC

EManual1992

HSC

mdashKo

dure

tal2004

[10]

NSC

andHSC

mdashEN

1992-1-

22004

[4]

Stress-strain

relatio

nships

120590119888

=

1198911015840

119888119879

[1minus(

120576minus120576max119879

120576max119879

)

2

]120576le120576max119879

1198911015840

119888119879

[1minus(

120576max119879

minus120576

3120576max119879

)

2

]120576gt120576max119879

1198911015840

119888119879

=

1198911015840

119888

20∘

Cle119879le450∘

C

1198911015840

119888

[2011minus2353(119879minus20

1000

)]450∘

Clt119879le874∘

C

0

874∘

Clt119879

120576max119879

=00025+(60119879+0041198792

)times10minus6

120590119888

=

1198911015840

119888119879

[1minus(

120576max119879

minus120576

120576max119879

)

119867

]

120576le120576max119879

1198911015840

119888119879

[1minus(

30(120576minus120576max119879

)

(130minus1198911015840

119888

)120576max119879

)

2

]120576gt120576max119879

1198911015840

119888119879

=

1198911015840

119888

[10minus0003125(119879minus20)]119879lt100∘

C0751198911015840

119888

100∘

Cle119879le400∘

C1198911015840

119888

[133minus000145119879]

400∘

Clt119879

120576max119879

=00018+(671198911015840

119888

+60119879+0031198792

)times10minus6

119867=228minus00121198911015840

119888

120590119888

=

31205761198911015840

119888119879

1205761198881119879

(2+(1205761205761198881119879

)3

)

120576le120576cu1119879

For1205761198881(119879)

lt120576le120576cu1(119879)

the

Eurocode

perm

itsthe

useo

flineara

swellasn

onlin

eard

escend

ing

branch

inthen

umericalanalysis

Forthe


nreferto

Table2

Thermal

capacity

Siliceous

aggregatec

oncrete

120588119888=

0005119879+1720∘

Cle119879le200∘

C27

200∘

Clt119879le400∘

C0013119879minus25400∘

Clt119879le500∘

C105minus0013119879500∘

Clt119879le600∘

C27

600∘

Clt119879

Carbon

atea

ggregateconcrete

120588119888=

2566

20∘

Cle119879le400∘

C01765119879minus68034

400∘

Clt119879le410∘

C2500671minus005043119879

410∘

Clt119879le445∘

C2566

445∘

Clt119879le500∘

C001603119879minus544881

500∘

Clt119879le635∘

C016635119879minus10090225635∘

Clt119879le715∘

C17607343minus022103119879715∘

Clt119879le785∘

C2566

785∘

Clt119879

Siliceous

aggregatec

oncrete

120588119888=

0005119879+17

20∘

Cle119879le200∘

C27

200∘

Clt119879le400∘

C0013119879minus25

400∘

Clt119879le500∘

Cminus0013119879+105500∘

Clt119879le600∘

C27

600∘

Clt119879le635∘

CCa

rbon

atea

ggregateconcrete

120588119888=

245

20∘

Cle119879le400∘

C0026119879minus1285

400∘

Clt119879le475∘

C00143119879minus6295

475∘

Clt119879le650∘

C01894119879minus12011650∘

Clt119879le735∘

Cminus0263119879+2124735∘

Clt119879le800∘

C2

800∘

Clt119879le1000∘

C

Specifich

eat(Jk

gC)

119888=900

for2

0∘Cle119879le100∘

C119888=900+(119879minus100)

for100∘

Clt119879le200∘C

119888=1000+(119879minus200)2

for2

00∘

Clt119879le400∘

C119888=1100

for4

00∘

Clt119879le1200∘

CDensitychange

(kgm

3 )120588=120588(20∘

C)=Re

ferenced

ensity

for2

0∘Cle119879le115∘C

120588=120588(20∘

C)(1minus002(119879minus115)85)

for115∘

Clt119879le200∘C

120588=120588(20∘

C)(098minus003(119879minus200)200)

for2

00∘

Clt119879le40

0∘C

120588=120588(20∘

C)(095minus007(119879minus400)800)

for4

00∘

Clt119879le1200∘

CTh


Thermal

cond

uctiv

ity

Siliceous

aggregatec

oncrete

119896119888

=minus0000625119879+1520∘

Cle119879le800∘

C10

800∘

Clt119879

Carbon

atea

ggregateconcrete

119896119888

=1355

20∘

Cle119879le293∘

Cminus0001241119879+17162293∘

Clt119879

Siliceous

aggregatec

oncrete

119896119888

=085(2minus00011119879)20∘

Clt119879le1000∘

C

Carbon

atea

ggregateconcrete

119896119888

=085(2minus00013119879)

20∘

Cle119879le300∘

C085(221minus0002119879)300∘

Clt119879

Alltypes

Upp

erlim

it119896119888

=2minus02451(119879100)+00107(119879100)2

for2

0∘Cle119879le1200∘

CLo

wer

limit

119896119888

=136minus0136(119879100)+00057(119879100)2

for2

0∘Cle119879le1200∘

C

Thermal

strain

Alltypes

120576th=[0004(1198792


Alltypes

120576th=[0004(1198792


Siliceous

aggregates


+9times10minus6


1198793

for2

0∘Cle119879le700∘C


for7

00∘

Clt119879le1200∘

CCalcareou

saggregates


+6times10minus6


1198793

for2

0∘Cle119879le805∘C


for8

05∘

Clt119879le1200∘

C





119888119879

1198911015840

119888

(20∘C)

1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879

120576cu1119879 1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879




Disclaimer




References













































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
















0

05

1

15

2

25

3

0 200 400 600 800 1000



Ther

mal

cond

uctiv

ity (W

m-∘

C)

Temperature (∘C)




2into CaO and H

2O between 400ndash




0

4

8

12

16

20

0 200 400 600 800 1000


Kodur and Sultan

Spec

ific h

eat (

MJm

3-∘

C)

Temperature (∘C)






60

80

100

0 200 400 600 800 1000

Mas

s (

of o

rigin

al)



Temperature (∘C)







0

02

04

06

08

1

12

0 200 400 600 800 1000

Relat

ive c

ompr

essiv

e stre

ngth

ASCE model



Temperature (∘C)


0

02

04

06

08

1

12

0 200 400 600 800 1000

Relat

ive c

ompr

essiv

e stre

ngth



Temperature (∘C)










0

02

04

06

08

1

0 200 400 600 800

Relat

ive s

plitt

ing

tens

ile st

reng

th



Temperature (∘C)






0

02

04

06

08

1

12

0 200 400 600 800

Rela

tive e

lasti

c mod

ulus



Temperature (∘C)


0

5

10

15

20

25

30

35

40

45

0 0005 001 0015

Stre

ss (M

Pa)

Strain ()

23∘C

200∘C

300∘C

400∘C

500∘C

600∘C

700∘C

800∘C

100∘C





0

10

20

30

40

50

60

70

80

90

100

0 0005 001 0015

Stre

ss (M

Pa)

Strain ()

23∘C

200∘C

300∘C

400∘C

500∘C

600∘C

700∘C

800∘C

100∘C






0

04

08

12

16

0 200 400 600 800 1000

Ther

mal

expa

nsio

n (

)



Temperature (∘C)












120576cr = 1205731120590

119891119888119879

radic119905119890119889(119879minus293)

120576tr = 1198962120590

11989111988820

120576th

(2)















NSC HSC












8 Summary




ble1Con

stitu

tiver

elationships

ofhigh

-temperature

prop

ertie

sofcon

crete

NSC

mdashASC

EManual1992

HSC

mdashKo

dure

tal2004

[10]

NSC

andHSC

mdashEN

1992-1-

22004

[4]

Stress-strain

relatio

nships

120590119888

=

1198911015840

119888119879

[1minus(

120576minus120576max119879

120576max119879

)

2

]120576le120576max119879

1198911015840

119888119879

[1minus(

120576max119879

minus120576

3120576max119879

)

2

]120576gt120576max119879

1198911015840

119888119879

=

1198911015840

119888

20∘

Cle119879le450∘

C

1198911015840

119888

[2011minus2353(119879minus20

1000

)]450∘

Clt119879le874∘

C

0

874∘

Clt119879

120576max119879

=00025+(60119879+0041198792

)times10minus6

120590119888

=

1198911015840

119888119879

[1minus(

120576max119879

minus120576

120576max119879

)

119867

]

120576le120576max119879

1198911015840

119888119879

[1minus(

30(120576minus120576max119879

)

(130minus1198911015840

119888

)120576max119879

)

2

]120576gt120576max119879

1198911015840

119888119879

=

1198911015840

119888

[10minus0003125(119879minus20)]119879lt100∘

C0751198911015840

119888

100∘

Cle119879le400∘

C1198911015840

119888

[133minus000145119879]

400∘

Clt119879

120576max119879

=00018+(671198911015840

119888

+60119879+0031198792

)times10minus6

119867=228minus00121198911015840

119888

120590119888

=

31205761198911015840

119888119879

1205761198881119879

(2+(1205761205761198881119879

)3

)

120576le120576cu1119879

For1205761198881(119879)

lt120576le120576cu1(119879)

the

Eurocode

perm

itsthe

useo

flineara

swellasn

onlin

eard

escend

ing

branch

inthen

umericalanalysis

Forthe


nreferto

Table2

Thermal

capacity

Siliceous

aggregatec

oncrete

120588119888=

0005119879+1720∘

Cle119879le200∘

C27

200∘

Clt119879le400∘

C0013119879minus25400∘

Clt119879le500∘

C105minus0013119879500∘

Clt119879le600∘

C27

600∘

Clt119879

Carbon

atea

ggregateconcrete

120588119888=

2566

20∘

Cle119879le400∘

C01765119879minus68034

400∘

Clt119879le410∘

C2500671minus005043119879

410∘

Clt119879le445∘

C2566

445∘

Clt119879le500∘

C001603119879minus544881

500∘

Clt119879le635∘

C016635119879minus10090225635∘

Clt119879le715∘

C17607343minus022103119879715∘

Clt119879le785∘

C2566

785∘

Clt119879

Siliceous

aggregatec

oncrete

120588119888=

0005119879+17

20∘

Cle119879le200∘

C27

200∘

Clt119879le400∘

C0013119879minus25

400∘

Clt119879le500∘

Cminus0013119879+105500∘

Clt119879le600∘

C27

600∘

Clt119879le635∘

CCa

rbon

atea

ggregateconcrete

120588119888=

245

20∘

Cle119879le400∘

C0026119879minus1285

400∘

Clt119879le475∘

C00143119879minus6295

475∘

Clt119879le650∘

C01894119879minus12011650∘

Clt119879le735∘

Cminus0263119879+2124735∘

Clt119879le800∘

C2

800∘

Clt119879le1000∘

C

Specifich

eat(Jk

gC)

119888=900

for2

0∘Cle119879le100∘

C119888=900+(119879minus100)

for100∘

Clt119879le200∘C

119888=1000+(119879minus200)2

for2

00∘

Clt119879le400∘

C119888=1100

for4

00∘

Clt119879le1200∘

CDensitychange

(kgm

3 )120588=120588(20∘

C)=Re

ferenced

ensity

for2

0∘Cle119879le115∘C

120588=120588(20∘

C)(1minus002(119879minus115)85)

for115∘

Clt119879le200∘C

120588=120588(20∘

C)(098minus003(119879minus200)200)

for2

00∘

Clt119879le40

0∘C

120588=120588(20∘

C)(095minus007(119879minus400)800)

for4

00∘

Clt119879le1200∘

CTh


Thermal

cond

uctiv

ity

Siliceous

aggregatec

oncrete

119896119888

=minus0000625119879+1520∘

Cle119879le800∘

C10

800∘

Clt119879

Carbon

atea

ggregateconcrete

119896119888

=1355

20∘

Cle119879le293∘

Cminus0001241119879+17162293∘

Clt119879

Siliceous

aggregatec

oncrete

119896119888

=085(2minus00011119879)20∘

Clt119879le1000∘

C

Carbon

atea

ggregateconcrete

119896119888

=085(2minus00013119879)

20∘

Cle119879le300∘

C085(221minus0002119879)300∘

Clt119879

Alltypes

Upp

erlim

it119896119888

=2minus02451(119879100)+00107(119879100)2

for2

0∘Cle119879le1200∘

CLo

wer

limit

119896119888

=136minus0136(119879100)+00057(119879100)2

for2

0∘Cle119879le1200∘

C

Thermal

strain

Alltypes

120576th=[0004(1198792


Alltypes

120576th=[0004(1198792


Siliceous

aggregates


+9times10minus6


1198793

for2

0∘Cle119879le700∘C


for7

00∘

Clt119879le1200∘

CCalcareou

saggregates


+6times10minus6


1198793

for2

0∘Cle119879le805∘C


for8

05∘

Clt119879le1200∘

C





119888119879

1198911015840

119888

(20∘C)

1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879

120576cu1119879 1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879




Disclaimer




References













































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

4

8

12

16

20

0 200 400 600 800 1000


Kodur and Sultan

Spec

ific h

eat (

MJm

3-∘

C)

Temperature (∘C)






60

80

100

0 200 400 600 800 1000

Mas

s (

of o

rigin

al)



Temperature (∘C)







0

02

04

06

08

1

12

0 200 400 600 800 1000

Relat

ive c

ompr

essiv

e stre

ngth

ASCE model



Temperature (∘C)


0

02

04

06

08

1

12

0 200 400 600 800 1000

Relat

ive c

ompr

essiv

e stre

ngth



Temperature (∘C)










0

02

04

06

08

1

0 200 400 600 800

Relat

ive s

plitt

ing

tens

ile st

reng

th



Temperature (∘C)






0

02

04

06

08

1

12

0 200 400 600 800

Rela

tive e

lasti

c mod

ulus



Temperature (∘C)


0

5

10

15

20

25

30

35

40

45

0 0005 001 0015

Stre

ss (M

Pa)

Strain ()

23∘C

200∘C

300∘C

400∘C

500∘C

600∘C

700∘C

800∘C

100∘C





0

10

20

30

40

50

60

70

80

90

100

0 0005 001 0015

Stre

ss (M

Pa)

Strain ()

23∘C

200∘C

300∘C

400∘C

500∘C

600∘C

700∘C

800∘C

100∘C






0

04

08

12

16

0 200 400 600 800 1000

Ther

mal

expa

nsio

n (

)



Temperature (∘C)












120576cr = 1205731120590

119891119888119879

radic119905119890119889(119879minus293)

120576tr = 1198962120590

11989111988820

120576th

(2)















NSC HSC












8 Summary




ble1Con

stitu

tiver

elationships

ofhigh

-temperature

prop

ertie

sofcon

crete

NSC

mdashASC

EManual1992

HSC

mdashKo

dure

tal2004

[10]

NSC

andHSC

mdashEN

1992-1-

22004

[4]

Stress-strain

relatio

nships

120590119888

=

1198911015840

119888119879

[1minus(

120576minus120576max119879

120576max119879

)

2

]120576le120576max119879

1198911015840

119888119879

[1minus(

120576max119879

minus120576

3120576max119879

)

2

]120576gt120576max119879

1198911015840

119888119879

=

1198911015840

119888

20∘

Cle119879le450∘

C

1198911015840

119888

[2011minus2353(119879minus20

1000

)]450∘

Clt119879le874∘

C

0

874∘

Clt119879

120576max119879

=00025+(60119879+0041198792

)times10minus6

120590119888

=

1198911015840

119888119879

[1minus(

120576max119879

minus120576

120576max119879

)

119867

]

120576le120576max119879

1198911015840

119888119879

[1minus(

30(120576minus120576max119879

)

(130minus1198911015840

119888

)120576max119879

)

2

]120576gt120576max119879

1198911015840

119888119879

=

1198911015840

119888

[10minus0003125(119879minus20)]119879lt100∘

C0751198911015840

119888

100∘

Cle119879le400∘

C1198911015840

119888

[133minus000145119879]

400∘

Clt119879

120576max119879

=00018+(671198911015840

119888

+60119879+0031198792

)times10minus6

119867=228minus00121198911015840

119888

120590119888

=

31205761198911015840

119888119879

1205761198881119879

(2+(1205761205761198881119879

)3

)

120576le120576cu1119879

For1205761198881(119879)

lt120576le120576cu1(119879)

the

Eurocode

perm

itsthe

useo

flineara

swellasn

onlin

eard

escend

ing

branch

inthen

umericalanalysis

Forthe


nreferto

Table2

Thermal

capacity

Siliceous

aggregatec

oncrete

120588119888=

0005119879+1720∘

Cle119879le200∘

C27

200∘

Clt119879le400∘

C0013119879minus25400∘

Clt119879le500∘

C105minus0013119879500∘

Clt119879le600∘

C27

600∘

Clt119879

Carbon

atea

ggregateconcrete

120588119888=

2566

20∘

Cle119879le400∘

C01765119879minus68034

400∘

Clt119879le410∘

C2500671minus005043119879

410∘

Clt119879le445∘

C2566

445∘

Clt119879le500∘

C001603119879minus544881

500∘

Clt119879le635∘

C016635119879minus10090225635∘

Clt119879le715∘

C17607343minus022103119879715∘

Clt119879le785∘

C2566

785∘

Clt119879

Siliceous

aggregatec

oncrete

120588119888=

0005119879+17

20∘

Cle119879le200∘

C27

200∘

Clt119879le400∘

C0013119879minus25

400∘

Clt119879le500∘

Cminus0013119879+105500∘

Clt119879le600∘

C27

600∘

Clt119879le635∘

CCa

rbon

atea

ggregateconcrete

120588119888=

245

20∘

Cle119879le400∘

C0026119879minus1285

400∘

Clt119879le475∘

C00143119879minus6295

475∘

Clt119879le650∘

C01894119879minus12011650∘

Clt119879le735∘

Cminus0263119879+2124735∘

Clt119879le800∘

C2

800∘

Clt119879le1000∘

C

Specifich

eat(Jk

gC)

119888=900

for2

0∘Cle119879le100∘

C119888=900+(119879minus100)

for100∘

Clt119879le200∘C

119888=1000+(119879minus200)2

for2

00∘

Clt119879le400∘

C119888=1100

for4

00∘

Clt119879le1200∘

CDensitychange

(kgm

3 )120588=120588(20∘

C)=Re

ferenced

ensity

for2

0∘Cle119879le115∘C

120588=120588(20∘

C)(1minus002(119879minus115)85)

for115∘

Clt119879le200∘C

120588=120588(20∘

C)(098minus003(119879minus200)200)

for2

00∘

Clt119879le40

0∘C

120588=120588(20∘

C)(095minus007(119879minus400)800)

for4

00∘

Clt119879le1200∘

CTh


Thermal

cond

uctiv

ity

Siliceous

aggregatec

oncrete

119896119888

=minus0000625119879+1520∘

Cle119879le800∘

C10

800∘

Clt119879

Carbon

atea

ggregateconcrete

119896119888

=1355

20∘

Cle119879le293∘

Cminus0001241119879+17162293∘

Clt119879

Siliceous

aggregatec

oncrete

119896119888

=085(2minus00011119879)20∘

Clt119879le1000∘

C

Carbon

atea

ggregateconcrete

119896119888

=085(2minus00013119879)

20∘

Cle119879le300∘

C085(221minus0002119879)300∘

Clt119879

Alltypes

Upp

erlim

it119896119888

=2minus02451(119879100)+00107(119879100)2

for2

0∘Cle119879le1200∘

CLo

wer

limit

119896119888

=136minus0136(119879100)+00057(119879100)2

for2

0∘Cle119879le1200∘

C

Thermal

strain

Alltypes

120576th=[0004(1198792


Alltypes

120576th=[0004(1198792


Siliceous

aggregates


+9times10minus6


1198793

for2

0∘Cle119879le700∘C


for7

00∘

Clt119879le1200∘

CCalcareou

saggregates


+6times10minus6


1198793

for2

0∘Cle119879le805∘C


for8

05∘

Clt119879le1200∘

C





119888119879

1198911015840

119888

(20∘C)

1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879

120576cu1119879 1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879




Disclaimer




References













































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

02

04

06

08

1

12

0 200 400 600 800 1000

Relat

ive c

ompr

essiv

e stre

ngth

ASCE model



Temperature (∘C)


0

02

04

06

08

1

12

0 200 400 600 800 1000

Relat

ive c

ompr

essiv

e stre

ngth



Temperature (∘C)










0

02

04

06

08

1

0 200 400 600 800

Relat

ive s

plitt

ing

tens

ile st

reng

th



Temperature (∘C)






0

02

04

06

08

1

12

0 200 400 600 800

Rela

tive e

lasti

c mod

ulus



Temperature (∘C)


0

5

10

15

20

25

30

35

40

45

0 0005 001 0015

Stre

ss (M

Pa)

Strain ()

23∘C

200∘C

300∘C

400∘C

500∘C

600∘C

700∘C

800∘C

100∘C





0

10

20

30

40

50

60

70

80

90

100

0 0005 001 0015

Stre

ss (M

Pa)

Strain ()

23∘C

200∘C

300∘C

400∘C

500∘C

600∘C

700∘C

800∘C

100∘C






0

04

08

12

16

0 200 400 600 800 1000

Ther

mal

expa

nsio

n (

)



Temperature (∘C)












120576cr = 1205731120590

119891119888119879

radic119905119890119889(119879minus293)

120576tr = 1198962120590

11989111988820

120576th

(2)















NSC HSC












8 Summary




ble1Con

stitu

tiver

elationships

ofhigh

-temperature

prop

ertie

sofcon

crete

NSC

mdashASC

EManual1992

HSC

mdashKo

dure

tal2004

[10]

NSC

andHSC

mdashEN

1992-1-

22004

[4]

Stress-strain

relatio

nships

120590119888

=

1198911015840

119888119879

[1minus(

120576minus120576max119879

120576max119879

)

2

]120576le120576max119879

1198911015840

119888119879

[1minus(

120576max119879

minus120576

3120576max119879

)

2

]120576gt120576max119879

1198911015840

119888119879

=

1198911015840

119888

20∘

Cle119879le450∘

C

1198911015840

119888

[2011minus2353(119879minus20

1000

)]450∘

Clt119879le874∘

C

0

874∘

Clt119879

120576max119879

=00025+(60119879+0041198792

)times10minus6

120590119888

=

1198911015840

119888119879

[1minus(

120576max119879

minus120576

120576max119879

)

119867

]

120576le120576max119879

1198911015840

119888119879

[1minus(

30(120576minus120576max119879

)

(130minus1198911015840

119888

)120576max119879

)

2

]120576gt120576max119879

1198911015840

119888119879

=

1198911015840

119888

[10minus0003125(119879minus20)]119879lt100∘

C0751198911015840

119888

100∘

Cle119879le400∘

C1198911015840

119888

[133minus000145119879]

400∘

Clt119879

120576max119879

=00018+(671198911015840

119888

+60119879+0031198792

)times10minus6

119867=228minus00121198911015840

119888

120590119888

=

31205761198911015840

119888119879

1205761198881119879

(2+(1205761205761198881119879

)3

)

120576le120576cu1119879

For1205761198881(119879)

lt120576le120576cu1(119879)

the

Eurocode

perm

itsthe

useo

flineara

swellasn

onlin

eard

escend

ing

branch

inthen

umericalanalysis

Forthe


nreferto

Table2

Thermal

capacity

Siliceous

aggregatec

oncrete

120588119888=

0005119879+1720∘

Cle119879le200∘

C27

200∘

Clt119879le400∘

C0013119879minus25400∘

Clt119879le500∘

C105minus0013119879500∘

Clt119879le600∘

C27

600∘

Clt119879

Carbon

atea

ggregateconcrete

120588119888=

2566

20∘

Cle119879le400∘

C01765119879minus68034

400∘

Clt119879le410∘

C2500671minus005043119879

410∘

Clt119879le445∘

C2566

445∘

Clt119879le500∘

C001603119879minus544881

500∘

Clt119879le635∘

C016635119879minus10090225635∘

Clt119879le715∘

C17607343minus022103119879715∘

Clt119879le785∘

C2566

785∘

Clt119879

Siliceous

aggregatec

oncrete

120588119888=

0005119879+17

20∘

Cle119879le200∘

C27

200∘

Clt119879le400∘

C0013119879minus25

400∘

Clt119879le500∘

Cminus0013119879+105500∘

Clt119879le600∘

C27

600∘

Clt119879le635∘

CCa

rbon

atea

ggregateconcrete

120588119888=

245

20∘

Cle119879le400∘

C0026119879minus1285

400∘

Clt119879le475∘

C00143119879minus6295

475∘

Clt119879le650∘

C01894119879minus12011650∘

Clt119879le735∘

Cminus0263119879+2124735∘

Clt119879le800∘

C2

800∘

Clt119879le1000∘

C

Specifich

eat(Jk

gC)

119888=900

for2

0∘Cle119879le100∘

C119888=900+(119879minus100)

for100∘

Clt119879le200∘C

119888=1000+(119879minus200)2

for2

00∘

Clt119879le400∘

C119888=1100

for4

00∘

Clt119879le1200∘

CDensitychange

(kgm

3 )120588=120588(20∘

C)=Re

ferenced

ensity

for2

0∘Cle119879le115∘C

120588=120588(20∘

C)(1minus002(119879minus115)85)

for115∘

Clt119879le200∘C

120588=120588(20∘

C)(098minus003(119879minus200)200)

for2

00∘

Clt119879le40

0∘C

120588=120588(20∘

C)(095minus007(119879minus400)800)

for4

00∘

Clt119879le1200∘

CTh


Thermal

cond

uctiv

ity

Siliceous

aggregatec

oncrete

119896119888

=minus0000625119879+1520∘

Cle119879le800∘

C10

800∘

Clt119879

Carbon

atea

ggregateconcrete

119896119888

=1355

20∘

Cle119879le293∘

Cminus0001241119879+17162293∘

Clt119879

Siliceous

aggregatec

oncrete

119896119888

=085(2minus00011119879)20∘

Clt119879le1000∘

C

Carbon

atea

ggregateconcrete

119896119888

=085(2minus00013119879)

20∘

Cle119879le300∘

C085(221minus0002119879)300∘

Clt119879

Alltypes

Upp

erlim

it119896119888

=2minus02451(119879100)+00107(119879100)2

for2

0∘Cle119879le1200∘

CLo

wer

limit

119896119888

=136minus0136(119879100)+00057(119879100)2

for2

0∘Cle119879le1200∘

C

Thermal

strain

Alltypes

120576th=[0004(1198792


Alltypes

120576th=[0004(1198792


Siliceous

aggregates


+9times10minus6


1198793

for2

0∘Cle119879le700∘C


for7

00∘

Clt119879le1200∘

CCalcareou

saggregates


+6times10minus6


1198793

for2

0∘Cle119879le805∘C


for8

05∘

Clt119879le1200∘

C





119888119879

1198911015840

119888

(20∘C)

1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879

120576cu1119879 1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879




Disclaimer




References













































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

02

04

06

08

1

0 200 400 600 800

Relat

ive s

plitt

ing

tens

ile st

reng

th



Temperature (∘C)






0

02

04

06

08

1

12

0 200 400 600 800

Rela

tive e

lasti

c mod

ulus



Temperature (∘C)


0

5

10

15

20

25

30

35

40

45

0 0005 001 0015

Stre

ss (M

Pa)

Strain ()

23∘C

200∘C

300∘C

400∘C

500∘C

600∘C

700∘C

800∘C

100∘C





0

10

20

30

40

50

60

70

80

90

100

0 0005 001 0015

Stre

ss (M

Pa)

Strain ()

23∘C

200∘C

300∘C

400∘C

500∘C

600∘C

700∘C

800∘C

100∘C






0

04

08

12

16

0 200 400 600 800 1000

Ther

mal

expa

nsio

n (

)



Temperature (∘C)












120576cr = 1205731120590

119891119888119879

radic119905119890119889(119879minus293)

120576tr = 1198962120590

11989111988820

120576th

(2)















NSC HSC












8 Summary




ble1Con

stitu

tiver

elationships

ofhigh

-temperature

prop

ertie

sofcon

crete

NSC

mdashASC

EManual1992

HSC

mdashKo

dure

tal2004

[10]

NSC

andHSC

mdashEN

1992-1-

22004

[4]

Stress-strain

relatio

nships

120590119888

=

1198911015840

119888119879

[1minus(

120576minus120576max119879

120576max119879

)

2

]120576le120576max119879

1198911015840

119888119879

[1minus(

120576max119879

minus120576

3120576max119879

)

2

]120576gt120576max119879

1198911015840

119888119879

=

1198911015840

119888

20∘

Cle119879le450∘

C

1198911015840

119888

[2011minus2353(119879minus20

1000

)]450∘

Clt119879le874∘

C

0

874∘

Clt119879

120576max119879

=00025+(60119879+0041198792

)times10minus6

120590119888

=

1198911015840

119888119879

[1minus(

120576max119879

minus120576

120576max119879

)

119867

]

120576le120576max119879

1198911015840

119888119879

[1minus(

30(120576minus120576max119879

)

(130minus1198911015840

119888

)120576max119879

)

2

]120576gt120576max119879

1198911015840

119888119879

=

1198911015840

119888

[10minus0003125(119879minus20)]119879lt100∘

C0751198911015840

119888

100∘

Cle119879le400∘

C1198911015840

119888

[133minus000145119879]

400∘

Clt119879

120576max119879

=00018+(671198911015840

119888

+60119879+0031198792

)times10minus6

119867=228minus00121198911015840

119888

120590119888

=

31205761198911015840

119888119879

1205761198881119879

(2+(1205761205761198881119879

)3

)

120576le120576cu1119879

For1205761198881(119879)

lt120576le120576cu1(119879)

the

Eurocode

perm

itsthe

useo

flineara

swellasn

onlin

eard

escend

ing

branch

inthen

umericalanalysis

Forthe


nreferto

Table2

Thermal

capacity

Siliceous

aggregatec

oncrete

120588119888=

0005119879+1720∘

Cle119879le200∘

C27

200∘

Clt119879le400∘

C0013119879minus25400∘

Clt119879le500∘

C105minus0013119879500∘

Clt119879le600∘

C27

600∘

Clt119879

Carbon

atea

ggregateconcrete

120588119888=

2566

20∘

Cle119879le400∘

C01765119879minus68034

400∘

Clt119879le410∘

C2500671minus005043119879

410∘

Clt119879le445∘

C2566

445∘

Clt119879le500∘

C001603119879minus544881

500∘

Clt119879le635∘

C016635119879minus10090225635∘

Clt119879le715∘

C17607343minus022103119879715∘

Clt119879le785∘

C2566

785∘

Clt119879

Siliceous

aggregatec

oncrete

120588119888=

0005119879+17

20∘

Cle119879le200∘

C27

200∘

Clt119879le400∘

C0013119879minus25

400∘

Clt119879le500∘

Cminus0013119879+105500∘

Clt119879le600∘

C27

600∘

Clt119879le635∘

CCa

rbon

atea

ggregateconcrete

120588119888=

245

20∘

Cle119879le400∘

C0026119879minus1285

400∘

Clt119879le475∘

C00143119879minus6295

475∘

Clt119879le650∘

C01894119879minus12011650∘

Clt119879le735∘

Cminus0263119879+2124735∘

Clt119879le800∘

C2

800∘

Clt119879le1000∘

C

Specifich

eat(Jk

gC)

119888=900

for2

0∘Cle119879le100∘

C119888=900+(119879minus100)

for100∘

Clt119879le200∘C

119888=1000+(119879minus200)2

for2

00∘

Clt119879le400∘

C119888=1100

for4

00∘

Clt119879le1200∘

CDensitychange

(kgm

3 )120588=120588(20∘

C)=Re

ferenced

ensity

for2

0∘Cle119879le115∘C

120588=120588(20∘

C)(1minus002(119879minus115)85)

for115∘

Clt119879le200∘C

120588=120588(20∘

C)(098minus003(119879minus200)200)

for2

00∘

Clt119879le40

0∘C

120588=120588(20∘

C)(095minus007(119879minus400)800)

for4

00∘

Clt119879le1200∘

CTh


Thermal

cond

uctiv

ity

Siliceous

aggregatec

oncrete

119896119888

=minus0000625119879+1520∘

Cle119879le800∘

C10

800∘

Clt119879

Carbon

atea

ggregateconcrete

119896119888

=1355

20∘

Cle119879le293∘

Cminus0001241119879+17162293∘

Clt119879

Siliceous

aggregatec

oncrete

119896119888

=085(2minus00011119879)20∘

Clt119879le1000∘

C

Carbon

atea

ggregateconcrete

119896119888

=085(2minus00013119879)

20∘

Cle119879le300∘

C085(221minus0002119879)300∘

Clt119879

Alltypes

Upp

erlim

it119896119888

=2minus02451(119879100)+00107(119879100)2

for2

0∘Cle119879le1200∘

CLo

wer

limit

119896119888

=136minus0136(119879100)+00057(119879100)2

for2

0∘Cle119879le1200∘

C

Thermal

strain

Alltypes

120576th=[0004(1198792


Alltypes

120576th=[0004(1198792


Siliceous

aggregates


+9times10minus6


1198793

for2

0∘Cle119879le700∘C


for7

00∘

Clt119879le1200∘

CCalcareou

saggregates


+6times10minus6


1198793

for2

0∘Cle119879le805∘C


for8

05∘

Clt119879le1200∘

C





119888119879

1198911015840

119888

(20∘C)

1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879

120576cu1119879 1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879




Disclaimer




References













































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

10

20

30

40

50

60

70

80

90

100

0 0005 001 0015

Stre

ss (M

Pa)

Strain ()

23∘C

200∘C

300∘C

400∘C

500∘C

600∘C

700∘C

800∘C

100∘C






0

04

08

12

16

0 200 400 600 800 1000

Ther

mal

expa

nsio

n (

)



Temperature (∘C)












120576cr = 1205731120590

119891119888119879

radic119905119890119889(119879minus293)

120576tr = 1198962120590

11989111988820

120576th

(2)















NSC HSC












8 Summary




ble1Con

stitu

tiver

elationships

ofhigh

-temperature

prop

ertie

sofcon

crete

NSC

mdashASC

EManual1992

HSC

mdashKo

dure

tal2004

[10]

NSC

andHSC

mdashEN

1992-1-

22004

[4]

Stress-strain

relatio

nships

120590119888

=

1198911015840

119888119879

[1minus(

120576minus120576max119879

120576max119879

)

2

]120576le120576max119879

1198911015840

119888119879

[1minus(

120576max119879

minus120576

3120576max119879

)

2

]120576gt120576max119879

1198911015840

119888119879

=

1198911015840

119888

20∘

Cle119879le450∘

C

1198911015840

119888

[2011minus2353(119879minus20

1000

)]450∘

Clt119879le874∘

C

0

874∘

Clt119879

120576max119879

=00025+(60119879+0041198792

)times10minus6

120590119888

=

1198911015840

119888119879

[1minus(

120576max119879

minus120576

120576max119879

)

119867

]

120576le120576max119879

1198911015840

119888119879

[1minus(

30(120576minus120576max119879

)

(130minus1198911015840

119888

)120576max119879

)

2

]120576gt120576max119879

1198911015840

119888119879

=

1198911015840

119888

[10minus0003125(119879minus20)]119879lt100∘

C0751198911015840

119888

100∘

Cle119879le400∘

C1198911015840

119888

[133minus000145119879]

400∘

Clt119879

120576max119879

=00018+(671198911015840

119888

+60119879+0031198792

)times10minus6

119867=228minus00121198911015840

119888

120590119888

=

31205761198911015840

119888119879

1205761198881119879

(2+(1205761205761198881119879

)3

)

120576le120576cu1119879

For1205761198881(119879)

lt120576le120576cu1(119879)

the

Eurocode

perm

itsthe

useo

flineara

swellasn

onlin

eard

escend

ing

branch

inthen

umericalanalysis

Forthe


nreferto

Table2

Thermal

capacity

Siliceous

aggregatec

oncrete

120588119888=

0005119879+1720∘

Cle119879le200∘

C27

200∘

Clt119879le400∘

C0013119879minus25400∘

Clt119879le500∘

C105minus0013119879500∘

Clt119879le600∘

C27

600∘

Clt119879

Carbon

atea

ggregateconcrete

120588119888=

2566

20∘

Cle119879le400∘

C01765119879minus68034

400∘

Clt119879le410∘

C2500671minus005043119879

410∘

Clt119879le445∘

C2566

445∘

Clt119879le500∘

C001603119879minus544881

500∘

Clt119879le635∘

C016635119879minus10090225635∘

Clt119879le715∘

C17607343minus022103119879715∘

Clt119879le785∘

C2566

785∘

Clt119879

Siliceous

aggregatec

oncrete

120588119888=

0005119879+17

20∘

Cle119879le200∘

C27

200∘

Clt119879le400∘

C0013119879minus25

400∘

Clt119879le500∘

Cminus0013119879+105500∘

Clt119879le600∘

C27

600∘

Clt119879le635∘

CCa

rbon

atea

ggregateconcrete

120588119888=

245

20∘

Cle119879le400∘

C0026119879minus1285

400∘

Clt119879le475∘

C00143119879minus6295

475∘

Clt119879le650∘

C01894119879minus12011650∘

Clt119879le735∘

Cminus0263119879+2124735∘

Clt119879le800∘

C2

800∘

Clt119879le1000∘

C

Specifich

eat(Jk

gC)

119888=900

for2

0∘Cle119879le100∘

C119888=900+(119879minus100)

for100∘

Clt119879le200∘C

119888=1000+(119879minus200)2

for2

00∘

Clt119879le400∘

C119888=1100

for4

00∘

Clt119879le1200∘

CDensitychange

(kgm

3 )120588=120588(20∘

C)=Re

ferenced

ensity

for2

0∘Cle119879le115∘C

120588=120588(20∘

C)(1minus002(119879minus115)85)

for115∘

Clt119879le200∘C

120588=120588(20∘

C)(098minus003(119879minus200)200)

for2

00∘

Clt119879le40

0∘C

120588=120588(20∘

C)(095minus007(119879minus400)800)

for4

00∘

Clt119879le1200∘

CTh


Thermal

cond

uctiv

ity

Siliceous

aggregatec

oncrete

119896119888

=minus0000625119879+1520∘

Cle119879le800∘

C10

800∘

Clt119879

Carbon

atea

ggregateconcrete

119896119888

=1355

20∘

Cle119879le293∘

Cminus0001241119879+17162293∘

Clt119879

Siliceous

aggregatec

oncrete

119896119888

=085(2minus00011119879)20∘

Clt119879le1000∘

C

Carbon

atea

ggregateconcrete

119896119888

=085(2minus00013119879)

20∘

Cle119879le300∘

C085(221minus0002119879)300∘

Clt119879

Alltypes

Upp

erlim

it119896119888

=2minus02451(119879100)+00107(119879100)2

for2

0∘Cle119879le1200∘

CLo

wer

limit

119896119888

=136minus0136(119879100)+00057(119879100)2

for2

0∘Cle119879le1200∘

C

Thermal

strain

Alltypes

120576th=[0004(1198792


Alltypes

120576th=[0004(1198792


Siliceous

aggregates


+9times10minus6


1198793

for2

0∘Cle119879le700∘C


for7

00∘

Clt119879le1200∘

CCalcareou

saggregates


+6times10minus6


1198793

for2

0∘Cle119879le805∘C


for8

05∘

Clt119879le1200∘

C





119888119879

1198911015840

119888

(20∘C)

1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879

120576cu1119879 1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879




Disclaimer




References













































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















120576cr = 1205731120590

119891119888119879

radic119905119890119889(119879minus293)

120576tr = 1198962120590

11989111988820

120576th

(2)















NSC HSC












8 Summary




ble1Con

stitu

tiver

elationships

ofhigh

-temperature

prop

ertie

sofcon

crete

NSC

mdashASC

EManual1992

HSC

mdashKo

dure

tal2004

[10]

NSC

andHSC

mdashEN

1992-1-

22004

[4]

Stress-strain

relatio

nships

120590119888

=

1198911015840

119888119879

[1minus(

120576minus120576max119879

120576max119879

)

2

]120576le120576max119879

1198911015840

119888119879

[1minus(

120576max119879

minus120576

3120576max119879

)

2

]120576gt120576max119879

1198911015840

119888119879

=

1198911015840

119888

20∘

Cle119879le450∘

C

1198911015840

119888

[2011minus2353(119879minus20

1000

)]450∘

Clt119879le874∘

C

0

874∘

Clt119879

120576max119879

=00025+(60119879+0041198792

)times10minus6

120590119888

=

1198911015840

119888119879

[1minus(

120576max119879

minus120576

120576max119879

)

119867

]

120576le120576max119879

1198911015840

119888119879

[1minus(

30(120576minus120576max119879

)

(130minus1198911015840

119888

)120576max119879

)

2

]120576gt120576max119879

1198911015840

119888119879

=

1198911015840

119888

[10minus0003125(119879minus20)]119879lt100∘

C0751198911015840

119888

100∘

Cle119879le400∘

C1198911015840

119888

[133minus000145119879]

400∘

Clt119879

120576max119879

=00018+(671198911015840

119888

+60119879+0031198792

)times10minus6

119867=228minus00121198911015840

119888

120590119888

=

31205761198911015840

119888119879

1205761198881119879

(2+(1205761205761198881119879

)3

)

120576le120576cu1119879

For1205761198881(119879)

lt120576le120576cu1(119879)

the

Eurocode

perm

itsthe

useo

flineara

swellasn

onlin

eard

escend

ing

branch

inthen

umericalanalysis

Forthe


nreferto

Table2

Thermal

capacity

Siliceous

aggregatec

oncrete

120588119888=

0005119879+1720∘

Cle119879le200∘

C27

200∘

Clt119879le400∘

C0013119879minus25400∘

Clt119879le500∘

C105minus0013119879500∘

Clt119879le600∘

C27

600∘

Clt119879

Carbon

atea

ggregateconcrete

120588119888=

2566

20∘

Cle119879le400∘

C01765119879minus68034

400∘

Clt119879le410∘

C2500671minus005043119879

410∘

Clt119879le445∘

C2566

445∘

Clt119879le500∘

C001603119879minus544881

500∘

Clt119879le635∘

C016635119879minus10090225635∘

Clt119879le715∘

C17607343minus022103119879715∘

Clt119879le785∘

C2566

785∘

Clt119879

Siliceous

aggregatec

oncrete

120588119888=

0005119879+17

20∘

Cle119879le200∘

C27

200∘

Clt119879le400∘

C0013119879minus25

400∘

Clt119879le500∘

Cminus0013119879+105500∘

Clt119879le600∘

C27

600∘

Clt119879le635∘

CCa

rbon

atea

ggregateconcrete

120588119888=

245

20∘

Cle119879le400∘

C0026119879minus1285

400∘

Clt119879le475∘

C00143119879minus6295

475∘

Clt119879le650∘

C01894119879minus12011650∘

Clt119879le735∘

Cminus0263119879+2124735∘

Clt119879le800∘

C2

800∘

Clt119879le1000∘

C

Specifich

eat(Jk

gC)

119888=900

for2

0∘Cle119879le100∘

C119888=900+(119879minus100)

for100∘

Clt119879le200∘C

119888=1000+(119879minus200)2

for2

00∘

Clt119879le400∘

C119888=1100

for4

00∘

Clt119879le1200∘

CDensitychange

(kgm

3 )120588=120588(20∘

C)=Re

ferenced

ensity

for2

0∘Cle119879le115∘C

120588=120588(20∘

C)(1minus002(119879minus115)85)

for115∘

Clt119879le200∘C

120588=120588(20∘

C)(098minus003(119879minus200)200)

for2

00∘

Clt119879le40

0∘C

120588=120588(20∘

C)(095minus007(119879minus400)800)

for4

00∘

Clt119879le1200∘

CTh


Thermal

cond

uctiv

ity

Siliceous

aggregatec

oncrete

119896119888

=minus0000625119879+1520∘

Cle119879le800∘

C10

800∘

Clt119879

Carbon

atea

ggregateconcrete

119896119888

=1355

20∘

Cle119879le293∘

Cminus0001241119879+17162293∘

Clt119879

Siliceous

aggregatec

oncrete

119896119888

=085(2minus00011119879)20∘

Clt119879le1000∘

C

Carbon

atea

ggregateconcrete

119896119888

=085(2minus00013119879)

20∘

Cle119879le300∘

C085(221minus0002119879)300∘

Clt119879

Alltypes

Upp

erlim

it119896119888

=2minus02451(119879100)+00107(119879100)2

for2

0∘Cle119879le1200∘

CLo

wer

limit

119896119888

=136minus0136(119879100)+00057(119879100)2

for2

0∘Cle119879le1200∘

C

Thermal

strain

Alltypes

120576th=[0004(1198792


Alltypes

120576th=[0004(1198792


Siliceous

aggregates


+9times10minus6


1198793

for2

0∘Cle119879le700∘C


for7

00∘

Clt119879le1200∘

CCalcareou

saggregates


+6times10minus6


1198793

for2

0∘Cle119879le805∘C


for8

05∘

Clt119879le1200∘

C





119888119879

1198911015840

119888

(20∘C)

1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879

120576cu1119879 1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879




Disclaimer




References













































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










NSC HSC












8 Summary




ble1Con

stitu

tiver

elationships

ofhigh

-temperature

prop

ertie

sofcon

crete

NSC

mdashASC

EManual1992

HSC

mdashKo

dure

tal2004

[10]

NSC

andHSC

mdashEN

1992-1-

22004

[4]

Stress-strain

relatio

nships

120590119888

=

1198911015840

119888119879

[1minus(

120576minus120576max119879

120576max119879

)

2

]120576le120576max119879

1198911015840

119888119879

[1minus(

120576max119879

minus120576

3120576max119879

)

2

]120576gt120576max119879

1198911015840

119888119879

=

1198911015840

119888

20∘

Cle119879le450∘

C

1198911015840

119888

[2011minus2353(119879minus20

1000

)]450∘

Clt119879le874∘

C

0

874∘

Clt119879

120576max119879

=00025+(60119879+0041198792

)times10minus6

120590119888

=

1198911015840

119888119879

[1minus(

120576max119879

minus120576

120576max119879

)

119867

]

120576le120576max119879

1198911015840

119888119879

[1minus(

30(120576minus120576max119879

)

(130minus1198911015840

119888

)120576max119879

)

2

]120576gt120576max119879

1198911015840

119888119879

=

1198911015840

119888

[10minus0003125(119879minus20)]119879lt100∘

C0751198911015840

119888

100∘

Cle119879le400∘

C1198911015840

119888

[133minus000145119879]

400∘

Clt119879

120576max119879

=00018+(671198911015840

119888

+60119879+0031198792

)times10minus6

119867=228minus00121198911015840

119888

120590119888

=

31205761198911015840

119888119879

1205761198881119879

(2+(1205761205761198881119879

)3

)

120576le120576cu1119879

For1205761198881(119879)

lt120576le120576cu1(119879)

the

Eurocode

perm

itsthe

useo

flineara

swellasn

onlin

eard

escend

ing

branch

inthen

umericalanalysis

Forthe


nreferto

Table2

Thermal

capacity

Siliceous

aggregatec

oncrete

120588119888=

0005119879+1720∘

Cle119879le200∘

C27

200∘

Clt119879le400∘

C0013119879minus25400∘

Clt119879le500∘

C105minus0013119879500∘

Clt119879le600∘

C27

600∘

Clt119879

Carbon

atea

ggregateconcrete

120588119888=

2566

20∘

Cle119879le400∘

C01765119879minus68034

400∘

Clt119879le410∘

C2500671minus005043119879

410∘

Clt119879le445∘

C2566

445∘

Clt119879le500∘

C001603119879minus544881

500∘

Clt119879le635∘

C016635119879minus10090225635∘

Clt119879le715∘

C17607343minus022103119879715∘

Clt119879le785∘

C2566

785∘

Clt119879

Siliceous

aggregatec

oncrete

120588119888=

0005119879+17

20∘

Cle119879le200∘

C27

200∘

Clt119879le400∘

C0013119879minus25

400∘

Clt119879le500∘

Cminus0013119879+105500∘

Clt119879le600∘

C27

600∘

Clt119879le635∘

CCa

rbon

atea

ggregateconcrete

120588119888=

245

20∘

Cle119879le400∘

C0026119879minus1285

400∘

Clt119879le475∘

C00143119879minus6295

475∘

Clt119879le650∘

C01894119879minus12011650∘

Clt119879le735∘

Cminus0263119879+2124735∘

Clt119879le800∘

C2

800∘

Clt119879le1000∘

C

Specifich

eat(Jk

gC)

119888=900

for2

0∘Cle119879le100∘

C119888=900+(119879minus100)

for100∘

Clt119879le200∘C

119888=1000+(119879minus200)2

for2

00∘

Clt119879le400∘

C119888=1100

for4

00∘

Clt119879le1200∘

CDensitychange

(kgm

3 )120588=120588(20∘

C)=Re

ferenced

ensity

for2

0∘Cle119879le115∘C

120588=120588(20∘

C)(1minus002(119879minus115)85)

for115∘

Clt119879le200∘C

120588=120588(20∘

C)(098minus003(119879minus200)200)

for2

00∘

Clt119879le40

0∘C

120588=120588(20∘

C)(095minus007(119879minus400)800)

for4

00∘

Clt119879le1200∘

CTh


Thermal

cond

uctiv

ity

Siliceous

aggregatec

oncrete

119896119888

=minus0000625119879+1520∘

Cle119879le800∘

C10

800∘

Clt119879

Carbon

atea

ggregateconcrete

119896119888

=1355

20∘

Cle119879le293∘

Cminus0001241119879+17162293∘

Clt119879

Siliceous

aggregatec

oncrete

119896119888

=085(2minus00011119879)20∘

Clt119879le1000∘

C

Carbon

atea

ggregateconcrete

119896119888

=085(2minus00013119879)

20∘

Cle119879le300∘

C085(221minus0002119879)300∘

Clt119879

Alltypes

Upp

erlim

it119896119888

=2minus02451(119879100)+00107(119879100)2

for2

0∘Cle119879le1200∘

CLo

wer

limit

119896119888

=136minus0136(119879100)+00057(119879100)2

for2

0∘Cle119879le1200∘

C

Thermal

strain

Alltypes

120576th=[0004(1198792


Alltypes

120576th=[0004(1198792


Siliceous

aggregates


+9times10minus6


1198793

for2

0∘Cle119879le700∘C


for7

00∘

Clt119879le1200∘

CCalcareou

saggregates


+6times10minus6


1198793

for2

0∘Cle119879le805∘C


for8

05∘

Clt119879le1200∘

C





119888119879

1198911015840

119888

(20∘C)

1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879

120576cu1119879 1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879




Disclaimer




References













































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










ble1Con

stitu

tiver

elationships

ofhigh

-temperature

prop

ertie

sofcon

crete

NSC

mdashASC

EManual1992

HSC

mdashKo

dure

tal2004

[10]

NSC

andHSC

mdashEN

1992-1-

22004

[4]

Stress-strain

relatio

nships

120590119888

=

1198911015840

119888119879

[1minus(

120576minus120576max119879

120576max119879

)

2

]120576le120576max119879

1198911015840

119888119879

[1minus(

120576max119879

minus120576

3120576max119879

)

2

]120576gt120576max119879

1198911015840

119888119879

=

1198911015840

119888

20∘

Cle119879le450∘

C

1198911015840

119888

[2011minus2353(119879minus20

1000

)]450∘

Clt119879le874∘

C

0

874∘

Clt119879

120576max119879

=00025+(60119879+0041198792

)times10minus6

120590119888

=

1198911015840

119888119879

[1minus(

120576max119879

minus120576

120576max119879

)

119867

]

120576le120576max119879

1198911015840

119888119879

[1minus(

30(120576minus120576max119879

)

(130minus1198911015840

119888

)120576max119879

)

2

]120576gt120576max119879

1198911015840

119888119879

=

1198911015840

119888

[10minus0003125(119879minus20)]119879lt100∘

C0751198911015840

119888

100∘

Cle119879le400∘

C1198911015840

119888

[133minus000145119879]

400∘

Clt119879

120576max119879

=00018+(671198911015840

119888

+60119879+0031198792

)times10minus6

119867=228minus00121198911015840

119888

120590119888

=

31205761198911015840

119888119879

1205761198881119879

(2+(1205761205761198881119879

)3

)

120576le120576cu1119879

For1205761198881(119879)

lt120576le120576cu1(119879)

the

Eurocode

perm

itsthe

useo

flineara

swellasn

onlin

eard

escend

ing

branch

inthen

umericalanalysis

Forthe


nreferto

Table2

Thermal

capacity

Siliceous

aggregatec

oncrete

120588119888=

0005119879+1720∘

Cle119879le200∘

C27

200∘

Clt119879le400∘

C0013119879minus25400∘

Clt119879le500∘

C105minus0013119879500∘

Clt119879le600∘

C27

600∘

Clt119879

Carbon

atea

ggregateconcrete

120588119888=

2566

20∘

Cle119879le400∘

C01765119879minus68034

400∘

Clt119879le410∘

C2500671minus005043119879

410∘

Clt119879le445∘

C2566

445∘

Clt119879le500∘

C001603119879minus544881

500∘

Clt119879le635∘

C016635119879minus10090225635∘

Clt119879le715∘

C17607343minus022103119879715∘

Clt119879le785∘

C2566

785∘

Clt119879

Siliceous

aggregatec

oncrete

120588119888=

0005119879+17

20∘

Cle119879le200∘

C27

200∘

Clt119879le400∘

C0013119879minus25

400∘

Clt119879le500∘

Cminus0013119879+105500∘

Clt119879le600∘

C27

600∘

Clt119879le635∘

CCa

rbon

atea

ggregateconcrete

120588119888=

245

20∘

Cle119879le400∘

C0026119879minus1285

400∘

Clt119879le475∘

C00143119879minus6295

475∘

Clt119879le650∘

C01894119879minus12011650∘

Clt119879le735∘

Cminus0263119879+2124735∘

Clt119879le800∘

C2

800∘

Clt119879le1000∘

C

Specifich

eat(Jk

gC)

119888=900

for2

0∘Cle119879le100∘

C119888=900+(119879minus100)

for100∘

Clt119879le200∘C

119888=1000+(119879minus200)2

for2

00∘

Clt119879le400∘

C119888=1100

for4

00∘

Clt119879le1200∘

CDensitychange

(kgm

3 )120588=120588(20∘

C)=Re

ferenced

ensity

for2

0∘Cle119879le115∘C

120588=120588(20∘

C)(1minus002(119879minus115)85)

for115∘

Clt119879le200∘C

120588=120588(20∘

C)(098minus003(119879minus200)200)

for2

00∘

Clt119879le40

0∘C

120588=120588(20∘

C)(095minus007(119879minus400)800)

for4

00∘

Clt119879le1200∘

CTh


Thermal

cond

uctiv

ity

Siliceous

aggregatec

oncrete

119896119888

=minus0000625119879+1520∘

Cle119879le800∘

C10

800∘

Clt119879

Carbon

atea

ggregateconcrete

119896119888

=1355

20∘

Cle119879le293∘

Cminus0001241119879+17162293∘

Clt119879

Siliceous

aggregatec

oncrete

119896119888

=085(2minus00011119879)20∘

Clt119879le1000∘

C

Carbon

atea

ggregateconcrete

119896119888

=085(2minus00013119879)

20∘

Cle119879le300∘

C085(221minus0002119879)300∘

Clt119879

Alltypes

Upp

erlim

it119896119888

=2minus02451(119879100)+00107(119879100)2

for2

0∘Cle119879le1200∘

CLo

wer

limit

119896119888

=136minus0136(119879100)+00057(119879100)2

for2

0∘Cle119879le1200∘

C

Thermal

strain

Alltypes

120576th=[0004(1198792


Alltypes

120576th=[0004(1198792


Siliceous

aggregates


+9times10minus6


1198793

for2

0∘Cle119879le700∘C


for7

00∘

Clt119879le1200∘

CCalcareou

saggregates


+6times10minus6


1198793

for2

0∘Cle119879le805∘C


for8

05∘

Clt119879le1200∘

C





119888119879

1198911015840

119888

(20∘C)

1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879

120576cu1119879 1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879




Disclaimer




References













































































































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













119888119879

1198911015840

119888

(20∘C)

1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879

120576cu1119879 1198911015840

119888119879

1198911015840

119888

(20∘C) 120576

1198881119879




Disclaimer




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



































































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











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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