Crack control Continuous edge restraint
Risk and control of cracking due to continuous edge restraint
CIRIA 91
Input parameters Symbol Unit Value
BS8007
Section details and material properties
Section thickness h mm 800 500
Strength class f ck / f ck,cube MPa C30/37
Age at cracking tc days 3 Assume 3 days unless more reliable information is available
K 1 = 0.65 if R is calculated; K 1 = 1 if R is assumed to be 0.5
Creep factor K1 0.65 0.5
(including creep to EN1992-1-1)
Sustained load factor K2 0.80
Coefficient of thermal expansion of concrete αc µε/oC 12.0 If aggregate is unknown use 12 µε / oC 12
Characteristic yield strength of reinforcement f yk MPa 500 500 Mpa 460
Early age concrete properties
Tensile strength at cracking f ctm (t c ) MPa 1.73 Mean value of tensile strength f ctm (t c ) 1.61
Elastic modulus E cm (t c ) GPa 28.1 Mean value of elastic modulus E cm (t c )
Tensile strain capacity ε ctu(ea) µε 76 ε ctu(ea) = [ f ctm (t c ) / E cm (t c ) ] x [K 2 / K 1 ] 65
Long term concrete properties
Tensile strength f ctm MPa 2.90 Mean 28-day value
Elastic modulus E cm GPa 32.8 Mean 28-day value
Tensile strain capacity (sustained loading) ε ctu(lt) µε 109 ε ctu(lt) = [ f ctm / E cm ] x [K 2 / K 1 ] 130
Early-age strain
T1 o T 1 = Peak temperature - mean ambient temperature
Temperature drop C 15 34
Autogenous shrinkage ε ca(ea) µε 15 EN1992-1-1 ε ca(ea) = 2.5 (f ck - 10) x (1-exp(- 0.2 t c 0.5 )
Free contraction ε free(ea) µε 195 ε free(ea) = T 1 α c + ε ca 408
Restrained early-age strain and risk of cracking
Restraint R 0.80 Use restraint calculator for walls or adjacent slabs; or historical data 1
Early-age restrained contraction ε r(ea) µε 101 ε r(ea) = R 1 K 1 (T 1 α c + ε ca ) 204
Risk of early age cracking ε r(ea) /ε ctu 1.67 Low risk of early age cracking if ε r(ea) /ε ctu < 1 . 3.14
Early-age crack-inducing strain ε cr(ea) µε 63 ε c(ea) = R 1 K 1 (T 1 α c + ε ca ) - 0.5 ε ctu 172
CIRIA C660 PAGE 2 / 1
Crack control Continuous edge restraint
Risk and control of cracking due to continuous edge restraint
CIRIA 91
Input parameters Symbol Unit Value
BS8007
Long term strain (excluding early-age strain)
Autogenous shrinkage (residual up to 28 days) δε ca(lt) µε 18 δεca(lt) = ε ca(28) - ε ca(ea)
T2 o
Long term temperature change C 15 T 2 and ε cd only apply when causing differential contraction or when the 20
Drying shrinkage ε cd µε 150 sections acting integrally are subject to external restraint. 100
Long term free contraction ε free(lt) µε 348 ε free(lt) = δε ca + T 2 α c + ε cd 340
Restrained long term strain
Restraint to long term thermal strains R2 0.80 1
Restraint will reduce as E n / E o approaches 1 in the long term
Restraint to drying shrinkage R3 0.80 1
Long term restrained strain ε free(lt) µε 181 ε c(lt) = K 1 {R 2 T 2 α c + R 3 ( δεca + ε cd )} 170
Increase in tensile strain capacity δε ctu µε 33 δε ctu = ε ctu(28) - ε ctu(ea) 65
Long term crack-inducing strain ε cr(lt) 148 ε c(lt) = K 1 {R 2 T 2 α c + R 3 ( δεca + ε cd )} - δε ctu 105
Total strain (early-age + long term)
Free contraction ε r(total) µε 543 ε free(total) = ε free(ea) + ε free(lt) 748
Restrained contraction ε r(total) µε 282 ε r(total) = ε r(ea) + ε r(lt) 374
Crack-inducing strain ε cr(total) µε 211 ε cr(total) = ε cr(ea) + ε cr(lt) 277
Reinforcement details
Bar diameter φ mm 45 16
Bar spacing s mm 135 175
Cover c mm 100 40
Area of steel per face per m As mm2 11781 1149
Cracking initiated at early age strain
Minimum area of reinforcement A s,min
Steel ratio for early age cracking f ctm /f yk 0.00347 f ctm / f yk = ρ crit 0.0035
k = 1.0 for h ≤ 300mm; k = 0.75 for h ≥ 800mm; intermediate values
Coefficient k 0.75
are interpolated
Coefficient kc 1 For pure tension k c = 1
Surface zone used in calculating A s,min h s,min mm 300 h s,min = k k c h/2 250
Minimum area of steel per face per m A s,min mm2 1040 A s,min = (h s,min x 1000) (f ctm / f yk ) Highlighted if A s < A s,min 875
Crack spacing and width
Surface zone defining the effective area of
h e,ef mm 306.25 h e,ef = 2.5 (c + φ/2) [NOTE: h s,min and h e,ef are not the same] 250
concrete in tension, A c,eff
Steel ratio for estimating crack spacing ρ p,eff 0.03847 ρ p,eff = A s / A c,eff = A s / (h e,ef x 1000) 0.00460
EN1992-1-1 recommends k 1 = 0.8 but provides a factor of 0.7 where
Coefficient for bond characteristics k1 1.14 0.67
good bond cannot be guaranteed. Hence k 1 = 0.8/0.7 = 1.14
Crack spacing S r,max mm 907 S r,max = 3.4c + 0.425 k 1 φ/ρ p,eff 1166
Early age crack width wk mm 0.06 w k = ε c(ea) S r,max 0.20
Long term crack width wk mm 0.19 w k = ε c(total) S r,max 0.32
Minimum reinforcement requirement for late-life cracking only
Steel ratio for late-life cracking f ctm /f yk 0.0058 f ctm / f yk = ρ crit 0.0033
Minimum area of steel per face A s,min mm2 1738 Highlighted if A s < A s,min 815
CIRIA C660 PAGE 2 / 2
Control of cracking due to internal restraint (temperature differential)
Input parameters Symbol Unit Value
Concrete and steel properties
Section thickness h mm 800
Strength class f ck /f ck,cube MPa C30/37
Age at cracking tc days 3 Assume 3 days unless more reliable information is available
Creep factor K1 0.65 Default = 0.65
Sustained load factor K2 0.80 Default = 0.8
Coefficient of thermal expansion αc µε /oC 12.0 If aggregate is unknown use 12
Characteristic yield strength of reinforcement f ky MPa 500 500 MPa (EN1992-1-1)
Early-age concrete properties
Tensile strength f ct,eff MPa 1.73 Mean value of tensile strength, f ctm (t c )
Elastic modulus Ec GPa 28.1 Mean value of elastic modulus E cm (t c )
Tensile strain capacity under sustained loading ε ctu µε 76 ε ctu = [ f ctm (t c ) / E cm (t c ) ] x [K 2 / K 1 ]
Early-age strain
o
Temperature differential ΔT C 46 ΔT = Peak temperature - surface temperature
Free differential strain Δε free µε 552 Δε free = ΔT α c
Restraint R 0.42
Restrained differential strain Δε r µε 151 Δε r(ea) = R 1 K 1 ΔT α c
Risk of early-age cracking Δε r /ε ctu 1.99 Low risk of early-age cracking if Δε r / ε ctu < 1 .
Crack-inducing differential strain Δε cr µε 113 Δε cr = R 1 K 1 ΔT α c - 0.5 ε ctu
Reinforcement details
Bar diameter φ mm 45
Bar spacing S mm 135
Cover c mm 100
As 2
Area of steel per face per m mm 11781
Early-age cracking
Steel ratio for estimating A s,min f ctm /f yk 0.0035 f ctm /f yk = ρ crit
Control of cracking due to internal restraint (temperature differential)
Input parameters Symbol Unit Value
Coefficient k 1.0
Coefficient kc 0.5
Surface zone defining the area of concrete in the tensile zone A ct h s,min mm 160 h s,min = 0.2 h
A s,min 2 Highlighted if A s < A s,min
Minimum area of steel per face mm 277
Surface zone defining the effective area of concrete in tension, A c,eff h e,ef mm 306.25 h e,ef = 2.5 (c + φ/2) [NB h s,min and h e,ef are not the same]
Steel ratio for calculating early-age crack spacing ρ p,eff 0.03847 ρ p,eff = A s / A c,eff = A s / (h e,ef x 1000)
Coefficient for bond characteristics k1 1.14
Crack spacing s r,max mm 907 s r,max = 3.4 c + 0.425 k 1 φ / ρ p,eff)
Crack width wk mm 0.10 w k = Δε cr S r,max
