prEN19921-1:2003(E with EN 12390 the compressive strength of concrete at various ages fcm(t) may be estimated from Expressions (3. 1)and (3.2) fam(t=Bcc(t)fcm rith B(t)=exps1 28)2 (3.2) where fcm(t is the mean concrete compressive strength at an age of t days fcm is the mean compressive strength at 28 days according to Table 3.1 Bcc(t) is a coefficient which depends on the age of the concrete t is the age of the concrete in days s is a coefficient which depends on the type of cement 0, 20 for cement of strength Classes CEM 42, 5R, CEM 53, 5N and CEM 53, 5 ( Class R) 0, 35 for cement of strength Classes CEM 32, 5R, CEM 42, 5 N(Class N) 0, 38 for cement of strength Classes CEM 32, 5 N(Class S Where the concrete does not conform with the specification for compressive strength at 28 days the use of Expressions(3. 1)and (3.2)is not appropriate This clause should not be used retrospectively to justify a non conforming reference strength by a later increase of the strength For situations where heat curing is applied to the member see 10.3.1.1( 3) ()P The tensile strength refers to the highest stress reached under concentric tensile loading. For the flexural tensile strength reference should be made to 3. 1. 8(1) (8)Where the tensile strength is determined as the splitting tensile strength, fctsp, an approximate value of the axial tensile strength, fct, may be taken as fat=o, 9fct, sp (9) The development of tensile strength with time is strongly influenced by curing and drying conditions as well as by the dimensions of the structural members. As a first approximation it may be assumed that the tensile strength fctm(t) is equal to fctm(t=(Bcc(t).fctm (34) where Bcc(t) follows from Expression (3.2) and a= 1 for t< 28 a= 2/3 for t2 28. The values for fctm are given in table 3.1 Note: Where the development of the tensile strength with time is important it is recommended that tests are carried out taking into account the exposure conditions and the dimensions of the structural member 3.1.3 Elastic deformation (1)The elastic deformations of concrete largely depend on its composition(especially the 26
prEN 1992-1-1:2003 (E) 26 with EN 12390 the compressive strength of concrete at various ages fcm(t) may be estimated from Expressions (3.1) and (3.2). fcm(t) = βcc(t) fcm (3.1) with ( ) = − 1 2 28 1 / exp t βcc t s (3.2) where: fcm(t) is the mean concrete compressive strength at an age of t days fcm is the mean compressive strength at 28 days according to Table 3.1 βcc(t) is a coefficient which depends on the age of the concrete t t is the age of the concrete in days s is a coefficient which depends on the type of cement: = 0,20 for cement of strength Classes CEM 42,5 R, CEM 53,5 N and CEM 53,5 R (Class R) = 0,35 for cement of strength Classes CEM 32,5 R, CEM 42,5 N (Class N) = 0,38 for cement of strength Classes CEM 32,5 N (Class S) Where the concrete does not conform with the specification for compressive strength at 28 days the use of Expressions (3.1) and (3.2) is not appropriate. This clause should not be used retrospectively to justify a non conforming reference strength by a later increase of the strength. For situations where heat curing is applied to the member see 10.3.1.1 (3). (7)P The tensile strength refers to the highest stress reached under concentric tensile loading. For the flexural tensile strength reference should be made to 3.1.8 (1). (8) Where the tensile strength is determined as the splitting tensile strength, fct,sp, an approximate value of the axial tensile strength, fct, may be taken as: fct = 0,9fct,sp (3.3) (9) The development of tensile strength with time is strongly influenced by curing and drying conditions as well as by the dimensions of the structural members. As a first approximation it may be assumed that the tensile strength fctm(t) is equal to: fctm(t) = (βcc(t))α ⋅ fctm (3.4) where βcc(t) follows from Expression (3.2) and α = 1 for t < 28 α = 2/3 for t ≥ 28. The values for fctm are given in Table 3.1. Note: Where the development of the tensile strength with time is important it is recommended that tests are carried out taking into account the exposure conditions and the dimensions of the structural member. 3.1.3 Elastic deformation (1) The elastic deformations of concrete largely depend on its composition (especially the
prEN19921-1:2003(E aggregates). The values given in this standard should be regarded as indicative for general applications. However, they should be specifically assessed if the structure is likely to be sensitive to deviations from these general values (2)The modulus of elasticity of a concrete is controlled by the moduli of elasticity of its components. Approximate values for the modulus of elasticity Ecm(secant value between oc=0 and 0, 4fcm), for concretes with quartzite aggregates, are given in table 3.1. For limestone and sandstone aggregates the value should be reduced by 10%and 30%respectively. For basalt aggregates the value should be increased by 20% Note: A Countrys National Annex may refer to non-contradictory complementary information Table 3.1 Strength and deformation characteristics for concrete 吉a 29到 品8 "8 二 B点 器 点 8 R R 8 t 守 oo2o。0Noo00oNo2 93358 2 8 8 8 2
prEN 1992-1-1:2003 (E) 27 aggregates). The values given in this Standard should be regarded as indicative for general applications. However, they should be specifically assessed if the structure is likely to be sensitive to deviations from these general values. (2) The modulus of elasticity of a concrete is controlled by the moduli of elasticity of its components. Approximate values for the modulus of elasticity Ecm (secant value between σc = 0 and 0,4fcm), for concretes with quartzite aggregates, are given in Table 3.1. For limestone and sandstone aggregates the value should be reduced by 10% and 30% respectively. For basalt aggregates the value should be increased by 20%. Note: A Countryís National Annex may refer to non-contradictory complementary information. Table 3.1 Strength and deformation characteristics for concrete Analytical relation / Explanation fcm = fck+8(MPa) fctm=0,30×fck(2/3) ≤C50/60 fctm=2,12·In(1+(fcm/10)) > C50/60 fctk;0,05 = 0,7×fctm 5% fractile fctk;0,95 = 1,3×fctm 95% fractile Ecm = 22[(fcm)/10]0,3 (fcm in MPa) see Figure 3.2 εc1 ( 0 /00) = 0 7 fcm0,31 <28 see Figure 3.2 for fck ≥ 50 Mpa ε 1( 0 /00)=2 8+27[(98- see Figure 3.3 for fck ≥ 50 Mpa εc2( 0 /00)=2,0+0,085(fck-50)0,53 see Figure 3.3 for fck ≥ 50 Mpa εcu2( 0 /00)=2,6+35[(90- for fck≥ 50 Mpa n=1,4+23,4[(90- fck)/100]4 see Figure 3.4 for fck≥ 50 Mpa εc3( 0 /00)=1,75+0,55[(fck- 50)/40] see Figure 3.4 for fck ≥ 50 Mpa εcu3( 0 /00)=2,6+35[(90- fck)/100] 4 90 105 98 5,0 3,5 6,6 44 2,8 2,8 2,6 2,6 1,4 2,3 2,6 80 95 88 4,8 3,4 6,3 42 2,8 2,8 2, 5 2,6 1,4 2,2 2,6 70 85 78 4,6 3,2 6,0 41 2,7 2,8 2,4 2,7 1,45 2,0 2,7 60 75 68 4,4 3,1 5,7 39 2,6 3,0 2,3 2,9 1,6 1,9 2,9 55 67 63 4,2 3,0 5,5 38 2,5 3,2 2,2 3,1 1,75 1,8 3,1 50 60 58 4,1 2,9 5,3 37 2,45 45 55 53 3,8 2,7 4,9 36 2,4 40 50 48 3,5 2,5 4,6 35 2,3 35 45 43 3,2 2,2 4,2 34 2,25 30 37 38 2,9 2,0 3,8 33 2,2 25 30 33 2,6 1,8 3,3 31 2,1 20 25 28 2,2 1,5 2,9 30 2,0 Stren gth 16 20 24 1,9 1,3 2,5 29 1,9 3,5 2,0 3,5 2,0 1,75 3,5
prEN19921-1:2003 N|:|8 、岂、道山 3 (3) Variation of the modulus of elasticity with time can be estimated by Ecm(t)=(fcm(t)/fcm) Ecm (3.5) where Ecm(t) and fom(t are the values at an age of t days and Ecm and fcm are the values determined at an age of 28 days. The relation between fcm(t) and fom follows from Expression (3.1) (4) Poisson's ratio may be taken equal to 0, 2 for uncracked concrete and 0 for cracked concrete (5) Unless more accurate information is available, the linear coefficient of thermal expansion may be taken equal to 10.10K" 3.1.4 Creep and shrinkage (1)P Creep and shrinkage of the concrete depend on the ambient humidity, the dimensions of the element and the composition of the concrete. Creep is also influenced by the maturity of the concrete when the load is first applied and depends on the duration and magnitude of the loading (2) The creep coefficient, t, to) is related to Ec, the tangent modulus, which may be taken as 1,05 Ecm Where great accuracy is not required, the value found from Figure 3. 1 may be considered as the creep coefficient, provided that the concrete is not subjected to a compressive stress greater than 0, 45 fck(to ) at an age to, the age of concrete at the time of loading Note: For further information, including the development of creep with time, Annex b may be used (3) The creep deformation of concrete Ecc(oo, to)at time t= oo for a constant compressive stress Oc applied at the concrete age to, is given by Ecc(oo, to)=(oo, to).(Oc/Ec) (36) (4)When the compressive stress of concrete at an age to exceeds the value 0, 45 fck(to)then creep non-linearity should be considered. Such a high stress can occur as a result of pretensioning, e.g. in precast concrete members at tendon level. In such cases the non-linear notional creep coefficient should be obtained as follows q(∞,t)=g(∞,tb)exp(1,5(k-045) (3.7) Where P(oo, to)is the non-linear notional creep coefficient, which replaces (oo, to) k is the stress-strength ratio ofcm(to), where ac is the compressive stress and fcm(to)is the mean concrete compressive strength at the time of loading
prEN 1992-1-1:2003 (E) 28 12 15 20 1,6 1,1 2,0 27 1,8 fck (MPa) fck,cu be fcm (MPa) fctm (MPa) fctk, 0,05 (MPa) fctk,0,95 (MPa) Ecm (GPa ) εc1 (â) εcu1 (â) εc2 (â) εcu2 (â) n εc3 (â) εcu3 (â) (3) Variation of the modulus of elasticity with time can be estimated by: Ecm(t) = (fcm(t) / fcm) 0,3 Ecm (3.5) where Ecm(t) and fcm(t) are the values at an age of t days and Ecm and fcm are the values determined at an age of 28 days. The relation between fcm(t) and fcm follows from Expression (3.1). (4) Poissonís ratio may be taken equal to 0,2 for uncracked concrete and 0 for cracked concrete. (5) Unless more accurate information is available, the linear coefficient of thermal expansion may be taken equal to 10 ⋅10-6 K -1. 3.1.4 Creep and shrinkage (1)P Creep and shrinkage of the concrete depend on the ambient humidity, the dimensions of the element and the composition of the concrete. Creep is also influenced by the maturity of the concrete when the load is first applied and depends on the duration and magnitude of the loading. (2) The creep coefficient, ϕ(t,t0) is related to Ec, the tangent modulus, which may be taken as 1,05 Ecm. Where great accuracy is not required, the value found from Figure 3.1 may be considered as the creep coefficient, provided that the concrete is not subjected to a compressive stress greater than 0,45 fck (t0 ) at an age t0, the age of concrete at the time of loading. Note: For further information, including the development of creep with time, Annex B may be used. (3) The creep deformation of concrete εcc(∞,t0) at time t = ∞ for a constant compressive stress σc applied at the concrete age t0, is given by: εcc(∞,t0) = ϕ (∞,t0). (σc /Ec) (3.6) (4) When the compressive stress of concrete at an age t0 exceeds the value 0,45 fck(t0) then creep non-linearity should be considered. Such a high stress can occur as a result of pretensioning, e.g. in precast concrete members at tendon level. In such cases the non-linear notional creep coefficient should be obtained as follows: ϕk(∞, t0) = ϕ (∞, t0) exp (1,5 (kσ ñ 0,45)) (3.7) where: ϕk(∞, t0) is the non-linear notional creep coefficient, which replaces ϕ (∞, t0) kσ is the stress-strength ratio σc/fcm(t0), where σc is the compressive stress and fcm(t0) is the mean concrete compressive strength at the time of loading
prEN1992-1-1:2003(E R 10 7,06,050403,02.01,00100300500700900110013001500 inside conditions- RH= 50% Note rsection point between lines 4 and 5 also be above point 1 for to> 100 it is sufficiently accurate to assume to= 100 (and use the tangent line)
prEN 1992-1-1:2003 (E) 29 a) inside conditions - RH = 50% Note: - i n t e rsection point between lines 4 and 5 can also be above point 1 - for t0 > 100 it is sufficiently accurate to assume t0 = 100 (and use the tangent line) 1 4 2 3 5 6,0 5,0 4,0 3,0 2,0 1,0 0 7,0 100 50 30 1 2 3 5 10 20 t 0 ϕ(∞, t 0) S N R 100 300 500 700 900 1100 1300 1500 C20/25 C25/30 C30/37 C35/45 C40/50 C45/55 C50/60 C55/67 C60/75 C70/85 C90/105 C80/95 h 0 (mm)
prEN19921-1:2003(E) N c20/25 25/30 c4050c4555 20 0。5646320-166o0o0so0o001611 p(oo, to o(mm) b)outside conditions-RH=80% Figure 3. 1: Method for determining the creep coefficient p( for concrete under normal environmental conditions
prEN 1992-1-1:2003 (E) 30 b) outside conditions - RH = 80% Figure 3.1: Method for determining the creep coefficient φ(∞, t0) for concrete under normal environmental conditions 6,0 5,0 4,0 3,0 2,0 1,0 0 100 50 30 1 2 3 5 10 20 t 0 ϕ (∞, t 0) S N R 100 300 500 700 900 1100 1300 1500 h 0 (mm) C20/25 C25/30 C30/37 C35/45 C55/67 C70/85 C90/105 C80/95 C45/55 C40/50 C60/75 C50/60