Recommendation of RILEM TC 200HTC: mechanical concrete properties at high temperatures—modelling and applications
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Compressive Strength Steady State Creep Thermal Strain Restraint Stress Transient Creep1 Preface
The present set of RILEM recommendations specifies test methodologies for determining the different mechanical properties of concrete at high temperatures. It applies to all types of concrete used in construction, including high strength concrete, but excluding refractory concrete [1].
This document, Introduction—General Presentation, is the umbrella providing the general intentions of all the subsequent ten parts, each one being a specific recommendation (see Ref. 2, parts 2–11).
2 Background
According to their function, concrete structures may be subjected to very different mechanical, thermal and environmental conditions.
Under service conditions, they are generally exposed to limited temperatures (below 200°C) for longer periods of time, the prestressed concrete pressure vessels of gascooled reactors are designed to sustain high pressure and temperatures around 65°C.

the fire resistance of buildings and tunnels

the behaviour of nuclear reactor containments in case of an accident.
In order to be able to design concrete structures as well as to assess the safety with regard to some design thermal events or after a real accident, it is necessary to have detailed knowledge of the properties of concrete for temperatures ranging from 20°C to at least 750°C. In some cases, the data of concrete properties are needed up to melting.
In the future, the development of new innovative concretes requires concise knowledge about their behaviour and properties, under various environmental conditions including fire and high temperatures.
When heating concrete, different physical processes and chemical reactions occur, which highly depend on the specific material composition, on the loading and on the environmental conditions. The temperature rise causes temperature gradients and water migration. Besides, moisture loss, dehydration and crystal transformations take place. These reactions lead to significant changes in the micro and macro structure of concrete like changes in porosity and permeability.
Macroscopically large modifications of the mechanical concrete behaviour are observed. The respective material properties vary with temperature, for example loss of strength and thermal strain.
In order to enable accurate predictions of the behaviour of concrete structures under high temperatures, full scale experimental investigations have been carried out, which led to the needs for the development of analytical models and to the determination of material properties. These properties vary with temperatures, like e.g. the modulus of elasticity, compressive and tensile strength, thermal strain, creep e.c. and their determination requires well determined test procedures.
The present set of recommendations provides a framework of standards which describes the tests procedures for mechanical properties of concrete at high temperature.
3 Scope
This document specifies the environmental and testing conditions associated with service or accident conditions of structural concrete at high temperature. The recommendations are applicable to concrete in the temperature range of 20°C to at least 750°C.
The document contains also a list of symbols and definitions used in the different recommendations (parts 2–11).

Part 2 Stress–strain relation

Part 3 Compressive strengh for service and accident conditions

Part 4 Tensile strength for service and accident conditions

Part 5 Modulus of elasticity for service and accident conditions

Part 6 Thermal strain

Part 7 Transient creep for service and accident conditions

Part 8 Steadystate creep and creep recovery for service and accident conditions

Part 9 Shrinkage for service and accident conditions

Part 10 Restraint stress

Part 11 Relaxation
4 Test conditions

Properties, obtained during a transient heating process should be differenciated from those obtained under steady state conditions. Table 1 shows the recommended test procedures according to the heating regimes.

In certain test procedures, the measured values are influenced by the applied loadtemperature sequence. For example, steadystate creep is derived either from specimens heated before loading or from specimens loaded before heating.

Some properties are determined either in hot state or at ambient temperature after heating and cooling (the latters are marked as residual). The results obtained by the different test regimes are usually not the same. This applies to the properties of stress–strain relation, compressive strength, tensile strength and modulus of elasticity. In the respective test results the subscript “res” is added for residual properties.
 The moisture transport during a test influences the material behaviour. Two boundary conditions have been selected to represent the extreme cases of the moisture states in concrete structures:

Boundary condition ‘d’: drying (unsealed) concrete

Boundary condition ‘nd’: nondrying (moisture saturated or sealed) concrete
The first case characterizes the moisture state of thin concrete elements or in the surface layer of thick members, while the second case characterizes the moisture state in the core of concrete of thick members. In general, boundary condition ‘d’ applies to drying structures in air with a maximum thickness d < 400mm, or structures with no point which is farther than 200 mm away from a surface exposed to air. Boundary condition ‘nd’ is defined for the following wet structures:
Sealed structures independent of their dimensions.

Zones of structures with a distance > 200 mm from the surface exposed to air.

Structures under water.
The moisture states during the tests are also related to the initial moisture content prior to heating. To obtain reproducible results, the recommendations propose on the one hand specifications for moulds, casting, curing and storage and on the other hand the use of specimens with identical mix design and identical curing conditions. Usually the tests are carried out during or after the first heating of specimens.

 Two situations for the design have been identified where concrete is exposed to elevated temperature:

Service conditions normally involve longterm exposure in the range 20–200°C and moisture states between the two boundary conditions defined above.

Accident conditions normally involve shortterm exposure in the range 20–750°C and transient moisture states.
These two conditions represent the framework which allows to link the range of maximum temperature, the heating rate and the moisture boundary conditions, as indicated in Table 2.

Recommended test procedures and related heating regimes
Heating regimes  Comments  

Steady state  Transient  
Stress–strain relation  –  – 
Compressive strength  –  – 
Tensile strength  –  – 
Modulus of elasticity  –  – 
Shrinkage  Thermal strain  Strain variation without external load 
Creep and creep recovery  Transient creep  Strain variation, at constant stress 
Relaxation  Restraint stress  Stress variation, at constant strain 
Test conditions included in the recommendations
Conditions  Range of temperature  Regime of temperature (Rate of heating: R)  Boundary condition  

Drying concrete  Moisture sealed or satured concrete  
Service conditions  \(20^{\circ}\hbox{C} < T < 200^{\circ}\hbox{C}\)  Transient  suitable R  “d”  “nd” 
Steady state  R = 0  
Accident conditions  \(20^{\circ}\hbox{C} < T < 750^{\circ}\hbox{C}\)  Transient  suitable R  “d”  
Steady state  R = 0 
5 Symbols and notations
In order to identify the test conditions and the physical parameters for measured values, a system of notations is proposed. Some subscripts and superscripts have been added to the symbols, that define the material testing parameters and properties (see Table 3). Generally, the superscripts are related to the test conditions during the heating phase, while the subscripts are related to the physical nature of the parameter, to the special conditions during a mechanical test, or to the location of the measured temperature value.

\(\varepsilon _{tot({t_1 t_0})}^{T_{max },\,\sigma,\,d}\) represents the total strain (tot) of a drying (d) concrete, determined on a loaded (σ) specimen maintained at constant temperature (T _{ max }), between the time period \({t}_{1}{t}_{0}\).

\(\varepsilon _{tr,tot}^{T,0,nd}\) represents the total strain (tot) of a nondrying (nd) concrete, determined during heating (T and tr) without load (σ = 0).
List of symbols and notations
Superscripts  
Four superscripts, separated by a comma, are used when relevant. They are placed in the following order  
first  T  specifies the concrete temperature 
T _{ max }  specifies the maximum reference test temperature (constant)  
second  σ  specifies that a load has been applied during the hold time period of heating and cooling if relevant 
0  stands for a zero stress (σ = 0)  
third  \(\dot{\varepsilon}\)  strainrate controlled 
\(\dot {\sigma}\)  stressrate controlled  
fourth  d  specifies the drying moisture boundary condition 
nd  specifies the nondrying moisture boundary condition  
Subscripts  
first  co  describes the constant temperature regime 
tr  describes the transient temperature regime  
cr1  indicates steady state creep measurements which commence at t _{0}, the number “1” denotes a heating without loading  
cr2  indicates steady state creep measurements which commence at t _{0}, the number “2” denotes a loading before heating  
second  cr  creep 
el  elastic  
rc  recovery  
res  residual  
sh  shrinkage  
th  thermal  
tot  total  
third  t _{ k }  the presence of a subscript indicates a defined time; k = 0, 1, 2 or i (for initial) 
\(({t}_{2}\,\,{t}_{1})\)  refers to the time step \(\Updelta{t} = {t}_{2}  {t}_{1}\) associated with the strain under consideration 
α  stress ratio 
ɛ  strain (\(LL_{i})/{L}_{i}\) 
\(\dot{\varepsilon}\)  strain rate 
ɛ_{ c1}  strain at the peak of a stress–strain relation 
ɛ_{ cu }  strain at the end of the descending branch of a stress–strain relation 
Δɛ  strain increment 
σ  stress or stress level 
\(\dot {\sigma}\)  stress rate 
σ_{0}  initial stress 
Δσ  stress increment 
Ψ  relaxation 
A  cross sectional area of the specimen before heating 
D  thermal diffusivity of concrete 
E  modulus of elasticity 
f  strength 
\({f}_{t}^{T}\)  tensile strength at temperature T _{ max } 
\({f}_{t,res}^{T}\)  residual tensile strength after cooling from temperature T _{ max } 
\({f}_{c}^{T}\)  compressive strength at temperature T _{ max } 
\({f}_{c,res}^{T}\)  residual compressive strength after cooling from temperature T _{ max } 
\({f}_{c}^{\sigma,{T}}\)  compressive strength at temperature T _{ max }, for a specimen subjected to heating with load 
\({f}_{c,res}^{\sigma,{T}}\)  residual compressive strength after cooling from temperature T _{ max }, for a specimen subjected to heating with load 
F  applied force 
maxF  maximum force applied on the specimen during strength test 
F _{ r,tot }  measured total restraint force 
L  measured length (variable) 
L _{ i }  initial reference length of the specimen at ambient temperature (constant) 
r  radius of the specimen before heating 
R  constant heating rate \((\hbox{d}T_{s}/\hbox{d}t)\) 
RH  relative humidity 
t  time (variable) 
t _{ i }  time at initiation of test 
t _{ b }  time at beginning of shrinkage measurements 
\({t}_{T_{max}}\)  time, when T reaches T _{ max } 
t _{0}  time at beginning of steady state regime, (e.g. time of start of steady state creep) 
t _{1}  time of unloading 
t _{2}  time at end of test 
T  reference temperature (variable or constant in the parts related to compressive and tensile strength) 
T _{ ca }  temperature at central axis of rotation of specimen (variable) 
T _{ max }  maximum reference test temperature (constant) 
T _{ n }  standard reference condition of temperature at ambient 
T _{ s }  temperature at the surface of specimen (variable) 
\({T}_{s}^{*}\)  surface temperature at which \(\hbox{d}T_{s}/\hbox{d}t\) starts to reduce from “R” 
ΔT  temperature difference \({T}_{s}  {T}_{ca}\) 
TTP  transitional thermal period 
Superscript index  
d  superscript index for drying (unsealed concrete) 
nd  superscript index for nondrying (sealed concrete) 
0  superscript index for zero stress (σ = 0) 
T  superscript index for thermal 
Subscript index  
b  subscript index for before 
c  subscript index for compressive 
ca  subscript index for location at central axis of rotation of the specimen 
co  subscript index for constant temperature regime 
cr  subscript index for creep 
cr1  subscript index for creep according to case 1 
cr2  subscript index for creep according to case 2 
c1  subscript index for strain at compression peak 
cu  subscript index for maximum strain 
el  subscript index for elastic 
i  subscript index for initial 
max  subscript index for maximum 
n  subscript index for normal 
o  subscript index for start 
r  subscript index for restraint 
res  subscript index for residual 
rc  subscript index for creep recovery 
s  subscript index for location at the surface of the specimen 
sh  subscript index for drying shrinkage 
t  subscript index for tensile 
th  subscript index for thermal 
tot  subscript index for total 
tr  subscript index for transient temperature regime 
6 Definitions of individual properties and relationships
6.1 Stress–strain relation (Part 2)
The stress–strain relation of concrete may be determined for specimens which are loaded or nonloaded prior to testing and during the thermal exposure. Because the stress level σ during heating influences the stress–strain relation of concrete, it is proposed to distinguish the two cases: specimen unstressed during the temperature exposure and specimen stressed (at a constant load level) during the temperature exposure.
6.2 Compressive strength (Part 3)
The compressive strength of concrete (\({f}_{c}^{T}\)) is determined either in the hot state, i.e. at test temperature T _{ max }, or after cooling down to ambient temperature (\({f}_{c,res}^{T}\) : residual compressive strength).
After reaching the maximum test temperature the specimen temperature shall be kept constant for a defined period of time to ensure a uniform temperature distribution in the specimen.
The compressive strength of concrete may be determined from specimens with or without a sustained load during the total period of temperature exposure. The sustained load level influences the compressive strength of the concrete. The load level (percentage of the reference strength at ambient temperature) must be kept constant during heating (\({f}_{c}^{{T},\sigma}\)) or heating and cooling (\({f}_{c,res}^{{T},\sigma}\)).
6.3 Tensile strength (Part 4)
The tensile strength of concrete is defined as the strength of concrete under direct axial tension. The tensile strength is determined either in the hot state (\({f}_{t}^{T}\)), i.e. at test temperature T, or after heating and cooling down to ambient temperature (\({f}_{t,res}^{T}\)). The specimens are usually not loaded during heating or cooling.
6.4 Modulus of elasticity (Part 5)
Because the stress level σ, during thermal treatment, influences the modulus of elasticity of concrete, two separate cases are considered: the modulus of elasticity of specimens may be determined without load during heating or heating and cooling (E ^{ T } or \(E_{res}^T\)), or by applying a constant load during heating or heating and cooling (E ^{ T,σ} or \(E_{res}^{T,\sigma}\)).
6.5 Thermal strain (Part 6)
Thermal strain of concrete is defined as the strain determined during heating without load.
Thermal strain \(\varepsilon _{tr,th}^{T,0,nd}\) of nondrying concrete is the total strain \(\varepsilon _{tr,tot}^{T,0,nd}\) determined during heating at a constant rate without external load and without moisture loss (\(\varepsilon _{tr,th}^{T,0,nd}\,=\,\varepsilon _{tr,tot}^{T,0,nd}\)).
Under transient temperature conditions, the drying shrinkage part of the strain cannot be determined easily by a single test. Therefore, in practice the thermal strains and shrinkage strains are determined together and are normally not separable. In practice the thermal strain of drying concrete is taken as the total strain, although it contains a drying shrinkage component: (\(\varepsilon _{tr,th}^{T,0,d}\,=\,\varepsilon _{tr,tot}^{T,0,d}\)).
6.6 Transient creep (Part 7)
Transient creep of concrete is defined as the creep that occurs during the first heating period under load.
 for the nondrying case:$$ \varepsilon _{tr,cr}^{T, \sigma,nd}\,=\,\varepsilon _{tr,tot}^{T,\sigma,nd}\,\,\varepsilon _{tr,th}^{T,0,nd}\,\,\varepsilon _{co,el}^{T, \sigma,nd} $$(1)
 for the drying case:$$ \varepsilon _{tr,cr}^{T, \sigma,d}\,=\,\varepsilon _{tr,tot}^{T,\sigma,d}\,\,\varepsilon _{tr,th}^{T,0,d}\,\,\varepsilon _{co,el}^{T, \sigma,d} $$(2)
These equations are strictly valid only in the elastic range. If the applied load leads to plastic strain, it should be measured and substracted as well.
The elastic strain is determined in accordance with recommendation for the modulus of elasticity, as indicated in Sect. 6.4.
6.7 Steady state creep and creep recovery (Part 8)
 In the case 1 (subscript: cr1), the specimen is first heated without load to T _{ max } as in the thermal strain test and then loaded at t _{0} (see Fig. 4). Steady state creep is determined as follows:
 for nondrying case:$$ \varepsilon _{cr1({t_1 t_0 })}^{T_{max},\sigma,nd}\,=\,\varepsilon _{tot({t_1 t_0})}^{T_{max},\sigma,nd}\,\,\varepsilon _{el({t_0})}^{T_{max },\sigma,nd} $$(3)
 for drying case:$$ \varepsilon _{cr1({t_1 t_0})}^{T_{max},\sigma,d}\,=\,\varepsilon _{tot({t_1 t_0})}^{T_{max},\sigma,d}\,\,\varepsilon _{sh({t_1 t_0})}^{T_{max},0,d}\,\,\varepsilon _{el({t_0})}^{T_{max},\sigma,d} $$(4)

 In the case 2 (subscript: cr2), the specimen is loaded at t _{ i } before heating to T _{ max } as in the transient creep test and the steadystate creep measurements commence at t _{0} (see Fig. 5).
 for nondrying case:$$ \varepsilon _{cr2({t_1 t_0 })}^{T_{max},\sigma,nd} =\varepsilon _{tot({t_1 t_0})}^{T_{max},\sigma,nd} $$(5)
 for drying case:$$ \varepsilon _{cr2({t_1 t_0})}^{T_{max},\sigma,d} =\varepsilon _{tot({t_1 t_0})}^{T_{max},\sigma,d}\,\,\varepsilon _{sh({t_1 t_0})}^{T_{max},0,d} $$(6)

 for the nondrying case:$$ \varepsilon _{cr,rc({t_2 t_1})}^{T_{max},0,nd} =\varepsilon _{tot,rc({t_2 t_1})}^{T_{max},0,nd} \varepsilon _{el({t_1})}^{T_{max},\sigma,nd} $$(7)
 for the drying case:$$ \varepsilon _{cr,rc({t_2 t_1})}^{T_{max},0,d}\,=\,\varepsilon _{tot,rc({t_2 t_1})}^{T_{max},0,d}\,\,\varepsilon _{el({t_1})}^{T_{max},\sigma,d} $$(8)
6.8 Shrinkage (Part 9)
Shrinkage is the drying induced strain of specimen without load at constant temperature.
For nondrying concrete, shrinkage is not considered.
6.9 Restraint stress (Part 10)
 for the nondrying case:$$ \sigma _r^{T,\alpha_i,nd} =\frac{F_{r,tot}}{A} $$(11)
 for the drying case:$$ \sigma_r^{T,\alpha _i,d} =\frac{F_{r,tot}}{A} $$(12)
6.10 Relaxation (Part 11)
Relaxation of concrete is defined as the time dependent stress reduction which occurs at constant temperature and constant strain.

Regime 1: The specimem is first heated without load to T _{ max } as in the thermal strain tests and then loaded at t _{0}.

Regime 2: The specimen is first loaded at t _{ i } before heating to T _{ max } as in the transient creep tests and relaxation measurements commence at t _{0}.

Regime 3: The specimen is loaded at t _{ i } before heating to T _{ max } as in the restraint stress tests and relaxation measurements commence at t _{0}.
 for the nondrying case:$$ \Uppsi_{(tt_0)}^{T_{max},\alpha _0,nd} =\frac{\Updelta\alpha _{(tt_0)}^{T_{max},nd}}{\alpha _0 }=\frac{\Updelta\sigma _{(tt_0)}^{T_{max},nd}}{\sigma _0}$$(13)
 for the drying case:$$ \Uppsi _{(tt_0)}^{T_{max},\alpha _0,d} =\frac{\Updelta\alpha _{(tt_0)}^{T_{max},d}}{\alpha _0 }=\frac{\Updelta \sigma _{(tt_0)}^{T_{max},d}}{\sigma _0} $$(14)
7 Test management
7.1 The notion of standard test parameters
Each recommendation proposes standards for test parameters, test procedures and the degree of accuracy of the measurements.
However, other values for the test parameters and procedures may be used when information is required for special applications. Any deviation from the recommended test parameters and procedures shall be reported separately as nonstandard.
7.2 Material
The behaviour of concrete depends mainly on the nature, size and shape of aggregates and the cement paste type and content. The mix proportions should be fixed according to the concrete design in practice. The maximum aggregates size of ordinary concrete should not be less than 8 mm.
The recommendations may be applied to all types of concrete used in constructions and to cement mortar.
7.3 Test operations
List of experimental operations
Step  Operations  Comments 

1  Basic choices and controls  Control of the testing equipments 
The boundary condition drying or sealed concrete  
Slenderness of specimens between 3 and 5  
Location of temperature measuring points on specimen  
2  Reference tests Test preparations  Before testing the specimens should be cured and stored according to the recommandation 
Reference measurements should be performed (compressive strength, moisture determination...)  
Installation of the specimen according to the recommendations (centering control, preload...)  
3  Loading at T _{ n }  Application of a preload or a defined strain before heating according to the recommendation 
4  Transient test (with heating)  During the first stage, the heating rate increases progressively to the prescribed value 
During the second stage, the heating rate is constant  
During the third stage, the device reduces progressively the heating rate to maintain a constant temperature T _{ max }. This period is called TTP (Transitional Thermal Period)  
During the fourth stage T _{ max } is maintained constant until the temperature inside the center of the specimen reaches T _{ max }  
5  Loading at T _{ max }  According to the recommendation 
6  Steadystate test at constant temperature T _{ max }  Control the measurement and recording system 
7  Unloading at T _{ max }  According to the recommendation 
8  Cooling  The specimens intended for residual testing shall be cooled within the heating device at an appropiate rate to avoid significant cracking due to thermal stresses or significant moisture absorption 
9  Residual tests  Tests after cooling 
8 Tables giving tests results and materials properties
The tests results and materials properties
Title of the test recommendation  Options  Mechanical tests  Properties, relationships derived  Other tests required (partreference)  

Reference  Moisture condition  Stress sustained during heating  Compatibility with other procedure (partreference)  Under temperature (T _{ s })  After cooling (T _{ n })  
Part 2: Stress–strain relation  1  nd  0  (6–2)  \(\sigma =\sigma ^{{T},\dot{\sigma},nd}(\varepsilon)\)  \(f_c^{T,nd},\quad \varepsilon _{C1} \)  
2  nd  σ  (7–2)  \(\sigma =\sigma ^{T,\sigma,\dot {\sigma},nd}(\varepsilon)\)  \(f_c^{T,\sigma,nd},\quad \varepsilon _{C1} \)  
3  nd  0  (6–2)  \(\sigma =\sigma _{res}^{T_{max},\dot {\sigma },nd} (\varepsilon)\)  \(f_{c,res}^{T,nd},\quad \varepsilon _{C1,res} \)  
4  nd  σ  (7–2)  \(\sigma =\sigma _{res}^{T_{max},\sigma,\dot {\sigma },nd} (\varepsilon)\)  \(f_{c,res}^{T,\sigma,nd}, \quad \varepsilon _{C1,res}\)  
5  d  0  (6–1)  \(\sigma =\sigma ^{T,\dot {\sigma},d}(\varepsilon)\)  \(f_c^{T,d},\quad \varepsilon _{C1} \)  
6  d  σ  (7–1)  \(\sigma =\sigma ^{T,\sigma,\dot {\sigma},d}(\varepsilon)\)  \(f_c^{T,\sigma,d}, \quad \varepsilon _{C1} \)  
7  d  0  (6–1)  \(\sigma =\sigma _{res}^{T_{max},\dot {\sigma },d} (\varepsilon)\)  \(f_{c,res}^{T,d},\quad \varepsilon _{C1,res}\)  
8  d  σ  (7–1)  \(\sigma =\sigma _{res}^{T_{max},\sigma,\dot {\sigma},d} (\varepsilon)\)  \(f_{c,res}^{T,\sigma,d},\quad \varepsilon_{C1,res}\)  
9  nd  0  (6–2)  \(\sigma =\sigma ^{T,\dot {\varepsilon},nd}(\varepsilon)\)  \(f_c^{T,nd},\quad \varepsilon _{C1} \)  
10  nd  σ  (7–2)  \(\sigma =\sigma ^{T,\sigma,\dot {\varepsilon},nd}(\varepsilon)\)  \(f_c^{T,\sigma nd},\quad \varepsilon _{C1} \)  
11  nd  0  (6–2)  \(\sigma =\sigma _{res}^{T_{max},\dot {\varepsilon},nd} (\varepsilon)\)  \(f_{c,res}^{T,nd}, \quad \varepsilon _{C1,res}\)  
12  nd  σ  (7–2)  \(\sigma =\sigma _{res}^{T_{ max},\sigma,\dot {\varepsilon},nd} (\varepsilon)\)  \(f_{c,res}^{T,\sigma,nd},\quad \varepsilon _{C1,res}\)  
13  d  0  (6–1)  \(\sigma =\sigma ^{T,\dot {\varepsilon},d}(\varepsilon)\)  \(f_c^{T,d},\quad \varepsilon _{C1} \)  
14  d  σ  (7–1)  \(\sigma =\sigma ^{T,\sigma,\dot {\varepsilon},d}(\varepsilon)\)  \(f_c^{T,\sigma, d},\quad \varepsilon _{C1} \)  
15  d  0  (6–1)  \(\sigma =\sigma _{res}^{T_{max},\dot {\varepsilon},d} (\varepsilon)\)  \(f_{c,res}^{T,d},\quad \varepsilon _{C1,res}\)  
16  d  σ  (7–1)  \(\sigma =\sigma _{res}^{T_{max },\sigma,\dot {\varepsilon},d} (\varepsilon)\)  \(f_{c,res}^{T,\sigma,d},\quad \varepsilon _{C1,res}\)  
Part 3: Compressive strength  1  d  0  (6–1)  \(f_c^{T,d} \)  
2  nd  0  (6–2)  \(f_c^{T,nd} \)  
3  d  0  (6–1)  \(f_{c,res}^{T,d} \)  
4  nd  0  (6–2)  \(f_{c,res}^{T,nd} \)  
5  d  σ  (7–1)  \(f_c^{T,\sigma,d} \)  
6  nd  σ  (7–2)  \(f_c^{T,\sigma,nd} \)  
7  d  σ  (7–1)  \(f_{c,res}^{T,\sigma,nd} \)  
8  nd  σ  (7–2)  \(f_{c,res}^{T, \sigma,nd} \)  
Part 4: Tensile Strength  1  d  0  (6–1)  \(f_t^{T,d} \)  
2  nd  0  (6–2)  \(f_t^{T,nd} \)  
3  d  0  (6–1)  \(f_{t,res}^{T,d} \)  
4  nd  0  (6–2)  \(f_{c,res}^{T,nd} \)  
Part 5: Modulus of elasticity  1  d  0  (6–1)  E ^{ T,d }  (3–1)  
2  nd  0  (6–2)  E ^{ T,nd }  (3–2)  
3  d  0  (5–1)  \(E_{res}^{T,nd} \)  (3–3)  
4  nd  0  (5–2)  \(E_{res}^{T,nd} \)  (3–4)  
5  d  σ  (7–1)  \(E^{T,\sigma,d}\)  (3–5)  
6  nd  σ  (7–2)  \(E^{T,\sigma,nd}\)  (3–6)  
7  d  σ  (5–5)  \(E_{res}^{T,\sigma, nd} \)  (3–7)  
8  nd  σ  (5–6)  \(E_{res}^{T,\sigma, nd} \)  (3–8)  
Part 6: Thermal srain  1  d  0  \(\varepsilon _{tr,th}^{T,0,d} \quad = \quad \varepsilon _{tr,tot}^{T,0,d} \)  
2  nd  0  \(\varepsilon _{tr,th}^{T,0,nd} \quad = \quad \varepsilon _{tr,tot}^{T,0,nd} \)  
Part 7: Transient creep  1  d  σ  \(\varepsilon _{tr,cr}^{T,\sigma,d} \)  \(\varepsilon _{tr,tot}^{T,0,d},\quad \varepsilon _{co,el}^{T,\sigma,d} \)  (6–1) + (5–5)  
2  nd  σ  \(\varepsilon _{tr,cr}^{T,\sigma,nd} \)  \(\varepsilon _{tr,th}^{T,0,nd},\quad \varepsilon _{co,el}^{T,\sigma,nd} \)  (6–2) + (5–6)  
Part 8: Steady state creep and creep recovery  1  d  0  (6–1)  \(\varepsilon _{cr1({t_1t_0})}^{T_{max},\sigma,d} \)  \(\varepsilon _{el(t_0)}^{T_{max },\sigma,d},\varepsilon _{tr,tot}^{T,0,d} \)  
2  nd  0  (6–2)  \(\varepsilon _{cr1({t_1t_0})}^{T_{max},\sigma,nd} \)  \(\varepsilon _{el(t_0)}^{T_{max},\sigma,nd},\varepsilon _{tr,th}^{T,0,nd}\)  
3  d  σ  (7–1)  \(\varepsilon _{cr2({t_1t_0})}^{T_{max},\sigma,d} \)  
4  nd  σ  (7–2)  \(\varepsilon _{cr2({t_1t_0})}^{T_{max},\sigma,d} \)  
5  d  0  (8–1)  \(\varepsilon _{cr1,rc({t_2t_1 })}^{T_{max},0,d} \)  \(\varepsilon _{el(t_1)}^{T_{max},\sigma,d} \)  
6  nd  0  (8–2)  \(\varepsilon _{cr1,rc({t_2t_1})}^{T_{max},0,nd} \)  \(\varepsilon _{el(t_1)}^{T_{max},\sigma,nd} \)  
7  d  0  (8–3)  \(\varepsilon _{cr2,rc({t_2t_1 })}^{T_{max},0,d} \)  \(\varepsilon _{el(t_1)}^{T_{max},\sigma,d} \)  
8  nd  0  (8–4)  \(\varepsilon _{cr2,rc({t_2t_1})}^{T_{max},0,nd} \)  \(\varepsilon _{el(t_1)}^{T_{max},\sigma,nd} \)  
Part 9: Shrinkage  1  d  0  (6–1)  \(\varepsilon _{sh({tt_0})}^{T_{max},0,d} \)  
Part 10: Restraint stress  1  d  ɛ  \(\sigma_r^{T,\alpha _i,d} \)  
2  nd  ɛ  \(\sigma _r^{T,\alpha _i,nd} \)  
Part 11: Relaxation  1  d  0  (6–1)  \(\Uppsi _{(tt_0)}^{T_{max},\alpha _0,d} \)  
2  nd  0  (6–2)  \(\Uppsi _{(tt_0)}^{T_{max},\alpha _0,nd} \)  
3  d  σ  (7–1)  \(\Uppsi _{(tt_0)}^{T_{max},\alpha _0,d} \)  
4  nd  σ  (7–2)  \(\Uppsi _{(tt_0)}^{T_{max},\alpha _0,nd} \)  
5  d  ɛ  (10–1)  \(\Uppsi _{(tt_0)}^{T_{max},\alpha _0,d} \)  
6  nd  ɛ  (10–2)  \(\Uppsi _{(tt_0)}^{T_{max},\alpha _0,nd} \) 
References
 1.Schneider U, Schwesinger P (eds) (1990) Mechanical testing of concrete at high temperatures. RILEM Transaction 1, February 1990, ISBN: 388122565X, 72Google Scholar
 2.RILEM TC 129 MHT: Test methods for mechanical properties of concrete at high temperatures and RILEM TC 200HTC: Mechanical Concrete Properties at High Temperature—Modelling and Applications. Part 1: Introduction Materials und Structures doi: 10.1617/s1152700792852; Part 2: Stress–strain relation Materials und Structures doi: 10.1617/s1152700792861; Part 3: Compressive strength for service and accident conditions (1995) Materials and Structures 28:410–414; Part 4: Tensile strength for service and accident conditions (2000) Materials and Structures 33:219–223; Part 5: Modulus of elasticity for service and accident conditions (2004) Materials and Structures 37:139–144; Part 6: Thermal strain (1997) Materials and Structures, Supplement March, 17–21; Part 7: Transient creep for service and accident conditions (1998) Materials and Structures 31:290–295; Part 8: Steadystate creep and creep recovery for service and accident conditions (2000) Materials and Structures 33:6–13; Part 9: Shrinkage for service and accident conditions (2000) Materials and Structures 33:224–228; Part 10: Restraint stress (2005) Materials und Structures 38:913–919; Part 11: Relaxation (2007) Materials und Structures 40:449–458