CIRIA Spreadsheet EATC - 3 Crack

Crack control Introduction

CIRIA C660 PAGE 1 / 1

C660 - Predicting the risk of cracking and controlling crack widthsThis calculator provides a basis for estimating the likelihood of cracking and for selecting or checking reinforcement to control crack widths

The approach is based on the method of EN1992-1-1 with adjustments where considered appropriate (see Appendix A8)

Three conditions of restraint are dealt with

PAGE 2 Continuous edge restraint. (This includes a calculation to BS8007 / CRIA 91, 1992 for comparative purposes)

PAGE 3 End restraint

PAGE 4 Internal restraint from temperature differentials

Input data are as follows (all other parameters are calculated);

PAGE 2 CONTINUOUS EDGE RESTRAINT

Section thickness mm

Strength class Select from the drop-down menu

Age at cracking days Assumed to be 3 days for early age cracking unless more reliable information is available

Creep factor

Sustained load factor

Coefficient of expansion

Strength of reinforcement This is taken as the characteristic yield strength of the reinforcement = 500 MPa

Early-age strain

Temperature drop

Restraint

Section details and material properties

fck / fck,cube

K1

EN1992-1-1 does not define a creep factor but includes this in the value of restraint R = 0.5 which is the maximum value recommended by EN1992-1-1 and must therefore cover the worst condition of restraint. When this value of R is used, K1 should be assumed to be 1. When R is calculated K1 may be assumed to be 0.65

K2K2 is used in conjunction with K1 to adjust the tensile strain capacity to take account of the change that occurs under conditions of sustained load. A default value of 0.8 is recommended

αcA value of 12 µε / oC is recommended if there is no knowledge of the aggregate type. The recommended value in EN1992-1-1 is 10 µε / oC but many aggregates in the UK produce concrete with higher values

fyk

T1This may be obtained from data in C660, the temperature model (Appendix A2) or by independent validated modelling or measurement

R1

[See note to K1 above] EN1992-1-1 recommends that R = 0.5 but this also includes the coefficient for creep K1.

When following the approach of EN1992-1-1 directly, R = 0.5 and K1 = 1. This will cover the worst case of full restraint for infill bays and is equivalent to R ≈ 0.8 and K1 = 0.65, i.e. R K1 ≈ 0.5. In practice, even infill bays are never subject to full restraint due to some inherent stiffness of the new element and R rarely exceeds about 0.8. EN1992-1-1 will therefore be overly conservative in many situations but permits R to be calculated from the relative stiffness of the element and the member against which it is cast. Where it can be demonstrated that R < 0.8 the calculated value may be used with K1 = 0.65

Crack control Introduction


Long term strains

Long term temperature change

Drying shrinkage

Restraint to drying shrinkage

Bar diameter φ

Bar spacing s

Cover c It is important to include cover as this has a significant effect on the crack spacing and width

Coefficient for bond characteristics

PAGE 3 END RESTRAINT

Section details

Section thickness h

Bar diameter φ

Bar spacing s

Cover c It is important to include cover as this has a significant effect on the crack spacing and width

Strength class Select from the drop-down menu.

Characteristic yield strength This is taken as the characteristic yield strength of the reinforcement = 500 MPa

Elastic modulus 200 GPa

Coefficient for bond characteristics

Age at crackingEarly-age 3 days

Long term 28 days

PAGE 3 INTERNAL RESTRAINT

T2

T2 will only apply when the change in temperature causes differential contraction between the element and the section against which it is cast. It may be ignored if both sections are subject to the same climatic conditions and reduced if the restraining section is affected but to a lesser extent than the section subject to restraint. In the UK values of T2 may be taken as 20oC for summer casting and 10oC for winter casting.

εcdCalculate using the method of EN1992-1-1 unless more reliable information is available. Only apply when causing differential contraction between elements or when the elements acting integrally are subject to external restraint.

Restraint to T2 R2 Long term restraint will be reduced as the ratio of stiffness of the elements reduces and En / Eo approaches 1 and as elements act integrally.R3

Reinforcement details

k1

EN1992-1-1 gives a value of k1 = 0.8 assuming good bond. As full bond may not be achieved, even when good practice is exercised, it is recommended that a factor of 0.7 (used by EN1992-1-1 when good bond is not guaranteed) be applied and that k1 is increased to 0.8/0.7 = 1.14

fck / fck,cube

Properties of reinforcement

fyk

Es

k1 see ref to k1 above (PAGE 2)

Values of 3 days and 28 days are assumed for the estimation of early age and long term properties. Values derived on this basis are have been shown to be safe in relation to the design of reinforcement for crack control

The input data for dealing with cracking caused by internal restraint is broadly the same as that required for edge restraint with the principal exception that the temperature differential between the centre and the surface ΔT replaces T1. Other changes inherent in the design calculation are the restraint factor R assumed to be 0.42 and the coefficients k and kc which reflect the difference in the stress distribution within the section compared with the condition of external restraint

Crack control Continuous edge restraint


Risk and control of cracking due to continuous edge restraint

Input parameters Symbol Unit Value

Section details and material properties

Section thickness h mm 200 500

Strength class MPa C40/50

Age at cracking days 3 Assume 3 days unless more reliable information is available

Creep factor 0.65 0.5

Sustained load factor 0.80

Coefficient of thermal expansion of concrete 12.0 12

Characteristic yield strength of reinforcement MPa 500 500 Mpa 460

Early age concrete properties

Tensile strength at cracking MPa 2.10 1.61

Elastic modulus GPa 30.2

Tensile strain capacity µε 86 65

Long term concrete properties

Tensile strength MPa 3.51 Mean 28-day value

Elastic modulus GPa 35.2 Mean 28-day value

Tensile strain capacity (sustained loading) µε 123 130

Early-age strain

Temperature drop 21 34

Autogenous shrinkage µε 22

µε 274 408

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 µε 142 204

Risk of early age cracking 2.08 3.14

Early-age crack-inducing strain µε 100 172

CIRIA 91 BS8007

fck / fck,cube

tc

K1 K1 = 0.65 if R is calculated; K1 = 1 if R is assumed to be 0.5 (including creep to EN1992-1-1)

K2

αc µε/oC If aggregate is unknown use 12 µε / oC

fyk

fctm(tc) Mean value of tensile strength fctm(tc)

Ecm(tc) Mean value of elastic modulus Ecm(tc)

εctu(ea) εctu(ea) = [ fctm(tc) / Ecm(tc) ] x [K2 / K1]

fctm

Ecm

εctu(lt) εctu(lt) = [ fctm / Ecm ] x [K2 / K1]

T1oC T1 = Peak temperature - mean ambient temperature

εca(ea) EN1992-1-1 εca(ea) = 2.5 (fck - 10) x (1-exp(- 0.2 tc0.5)

Free contraction εfree(ea) εfree(ea) = T1αc+ εca

εr(ea) εr(ea) = R1 K1 (T1 αc+ εca)

εr(ea)/εctu Low risk of early age cracking if εr(ea)/εctu < 1.

εcr(ea) εc(ea) = R1 K1 (T1αc + εca) - 0.5 εctu




Input parameters Symbol Unit Value CIRIA 91 BS8007

Long term strain (excluding early-age strain)

Autogenous shrinkage (residual up to 28 days) µε 27

Long term temperature change 20 20

Drying shrinkage µε 12 100

Long term free contraction µε 279 340

Restrained long term strain

Restraint to long term thermal strains 0.80 1

Restraint to drying shrinkage 0.80 1

Long term restrained strain µε 145 170

Increase in tensile strain capacity µε 37 65

Long term crack-inducing strain 108 105

Total strain (early-age + long term)

Free contraction µε 553 748

Restrained contraction µε 288 374

Crack-inducing strain µε 208 277


Bar diameter φ mm 16 16

Bar spacing s mm 150 175

Cover c mm 40 40

Area of steel per face per m 1340 1149

Cracking initiated at early age strain

Steel ratio for early age cracking 0.00420 0.0035

Coefficient k 1.00

Coefficient 1

δεca(lt) δεca(lt) = εca(28) - εca(ea)

T2oC T2 and εcd only apply when causing differential contraction or when the

sections acting integrally are subject to external restraint. εcd

εfree(lt) εfree(lt) = δεca + T2 αc + εcd

R2Restraint will reduce as En / Eo approaches 1 in the long term

R3

εfree(lt) εc(lt) = K1 {R2T2αc + R3(δεca + εcd)}

δεctu δεctu = εctu(28) - εctu(ea)

εcr(lt) εc(lt) = K1 {R2T2αc + R3(δεca + εcd)} - δεctu

εr(total) εfree(total) = εfree(ea) + εfree(lt)

εr(total) εr(total) = εr(ea) + εr(lt)

εcr(total) εcr(total) = εcr(ea) + εcr(lt)

As mm2

Minimum area of reinforcement As,min

fctm/fyk fctm / fyk = ρcrit

k = 1.0 for h ≤ 300mm; k = 0.75 for h ≥ 800mm; intermediate values are interpolated

kc For pure tension kc = 1




Input parameters Symbol Unit Value CIRIA 91 BS8007

mm 100 250

Minimum area of steel per face per m 420 875

Crack spacing and width

mm 100 250

Steel ratio for estimating crack spacing 0.01340 0.00460

Coefficient for bond characteristics 1.14 0.67

Crack spacing mm 714 1166

Early age crack width mm 0.07 0.20

Long term crack width mm 0.15 0.32

Minimum reinforcement requirement for late-life cracking only

Steel ratio for late-life cracking 0.0070 0.0033

Minimum area of steel per face 702 815

Surface zone used in calculating As,min hs,min hs,min = k kc h/2

As,min mm2 As,min = (hs,min x 1000) (fctm / fyk) Highlighted if As < As,min

Surface zone defining the effective area of concrete in tension, Ac,eff

he,ef he,ef = 2.5 (c + φ/2) [NOTE: hs,min and he,ef are not the same]

ρp,eff ρp,eff = As / Ac,eff = As/ (he,ef x 1000)

k1EN1992-1-1 recommends k1= 0.8 but provides a factor of 0.7 where good bond cannot be guaranteed. Hence k1 = 0.8/0.7 = 1.14

Sr,max Sr,max = 3.4c + 0.425 k1 φ/ρp,eff

wk wk = εc(ea) Sr,max

wk wk = εc(total)Sr,max

fctm/fyk fctm / fyk = ρcrit

As,min mm2 Highlighted if As < As,min

Crack Control End restraint


Control of cracking due to end restraint


Section details

Section thickness h mm 200

Bar diameter φ mm 16

Bar spacing S mm 150

Area of steel per face per m 1340

Cover c mm 40


Properties of reinforcement

Characteristic yield strength MPa 500 500 MPa (EN1992-1-1)

Elastic modulus of reinforcement GPa 200

Crack spacing

mm 100

Steel ratio for calculating crack spacing 0.01340

Coefficient for bond characteristics 1.14

Crack spacing mm 714

Early-age crack width

Age at cracking days 3 Use 3 days unless more reliable information is available

Tensile strength of concrete MPa 2.10

Coefficient k 1.00

Coefficient 1

The risk of cracking may be estimated using the calculation for edge restraint (PAGE 2) with an appropriate value for the restraint R. If cracking is predicted then, under conditions of end restraint, the magnitude of the restrained strain will determine the number of cracks which occur but not the individual crack widths, which are determined by the stress transferred to the steel from the concrete. The tensile strength of the concrete at the time of cracking is therefore a principal determinant of the potential crack width. Unless the restrained strain is reduced to the extent that cracking is avoided, reducing the magnitude of restrained strain will only be effective in reducing the number of cracks, but not the crack widths.

As mm2

fck / fck,cube

fyk

Es

Surface zone defining the effective area of concrete in tension Ac,eff

he,ef he,ef = 2.5(c + φ/2) used in calculating crack spacing


k1EN1992-1-1 recommends k1= 0.8 but provides a factor of 0.7 where good bond cannot be guaranteed. Hence k1 = 0.8/0.7 = 1.14

Sr,max Sr,max = 3.4 c + 0.425 k1 φ / ρp,eff

tc

fctm(tc) Mean value of tensile strength fctm(t)

k = 1.0 for h ≤ 300mm; k= 0.75 for h ≥ 800mm; intermediate values are interpolated

kc For pure tension kc = 1

Crack Control End restraint


Control of cracking due to end restraint


mm 100

Minimum area of reinforcement 420

Elastic modulus of concrete GPa 30.2

Modular ratio 6.6

ρ 0.013404

Crack-inducing strain µε 426

MPa 171

Crack width mm 0.30

Long term crack width

Age at cracking days 28 28 day properties provide safe values

Tensile strength of concrete MPa 3.51

Minimum area of reinforcement mm2 702

Elastic modulus of concrete GPa 35.2

Modular ratio 5.7

Crack-inducing strain µε 704

MPa 282

Crack width mm 0.50

Surface zone used in calculating As,min hs,min hs,min = k kc h/2

As,min mm2 As,min = (hs,min x 1000) (fctm / fyk) Highlighted if As < As,min

Ecm Mean value of elastic modulus Ecm(t)

αe

Steel ratio for calculating crack-inducing strain (εsm - εcm)Based on full section thickness (coefficients k and kc are included in expression for (εsm - εcm)

(εsm - εcm) (εsm - εcm) = 0.5 αe kc k kcr fctm(tc) (1+1/(αeρ))/Es

Stress in steel (should not exceed fyk) σs σs = 2 x Es x (εsm - εcm) Highlighted if σs > fky

wk wk = (εsm-εcm) sr,max

tc

fctm Mean value of tensile strength fctm

As,min

Ecm Mean value of elastic modulus Ecm

αe

(εsm - εcm) (εsm - εcm) = 0.5 αe kc k fctm(tc) (1+1/(αeρ))/Es

Stress in steel (should not exceed fky) σs σs = 2 x Es x (εsm - εcm) Highlighted if σs > fky

wk wk = (εsm-εcm) Sr,max

Crack control Internal restraint


Control of cracking due to internal restraint (temperature differential)


Concrete and steel properties

Section thickness h mm 2000


Age at cracking days 3 Assume 3 days unless more reliable information is available

Creep factor 0.65 Default = 0.65

Sustained load factor 0.80 Default = 0.8

Coefficient of thermal expansion 12.0 If aggregate is unknown use 12

Characteristic yield strength of reinforcement MPa 500 500 MPa (EN1992-1-1)

Early-age concrete properties

Tensile strength MPa 2.10

Elastic modulus GPa 30.2

Tensile strain capacity under sustained loading µε 86

Early-age strain

Temperature differential ΔT 21

Free differential strain µε 252

Restraint R 0.42

Restrained differential strain µε 69

Risk of early-age cracking 0.80

Crack-inducing differential strain µε 26


Bar diameter φ mm 16

Bar spacing S mm 150

Cover c mm 50

Area of steel per face per m 1340

Early-age cracking

0.0042

fck/fck,cube

tc

K1

K2

αc µε/oC

fky

fct,eff Mean value of tensile strength, fctm(tc)

Ec Mean value of elastic modulus Ecm(tc)

εctu εctu = [ fctm(tc) / Ecm(tc) ] x [K2 / K1]

oC ΔT = Peak temperature - surface temperature

Δεfree Δεfree = ΔT αc

Δεr Δεr(ea) = R1 K1 ΔT αc

Δεr/εctu Low risk of early-age cracking if Δεr / εctu < 1.

Δεcr Δεcr= R1 K1 ΔT αc- 0.5 εctu

As mm2

Steel ratio for estimating As,min fctm/fyk fctm/fyk = ρcrit

Crack control Internal restraint


Control of cracking due to internal restraint (temperature differential)


Coefficient k 1.0

Coefficient 0.5

mm 400

Minimum area of steel per face 840

mm 145

Steel ratio for calculating early-age crack spacing 0.00924

Coefficient for bond characteristics 1.14

Crack spacing mm 1009

Crack width mm 0.03

kc

Surface zone defining the area of concrete in the tensile zone Act hs,min hs,min = 0.2 h

As,min mm2 Highlighted if As < As,min

Surface zone defining the effective area of concrete in tension, Ac,eff he,ef he,ef = 2.5 (c + φ/2) [NB hs,min and he,ef are not the same]


k1

sr,max sr,max = 3.4 c + 0.425 k1 φ / ρp,eff)

wk wk = Δεcr Sr,max

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CIRIA Spreadsheet EATC - 3 Crack