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f* As ct Ac f (1) y The area of concrete was taken as the gross cross sectional area unless the section was thicker than 500mm, in which case a surface zone of 250mm at each face is taken.
A further check was then made, to satisfy crack width requirements. f ct* Ac R sh th 0.5 ult As f b 2w
(2)
Although given directly as a required area to control cracking, the equation contains elements relating to crack spacing and crack widths, combined into a single formula. By rearranging Equation (2) to give crack width expressed as the product of crack spacing and crack inducing strain as in Equation (3), comparisons with other standards may be more readily made.
w S r ;max cr
Where:
and
S r ;max
f ct* Ac f ct* A 2 0.5 f f b s b
cr R sh th 0.5 ctu r 0.5 ctu
For comparison, BS8007 had the following calculation procedure: wmax S max
Where:
and
f S r ;max ct fb
2
cs te 100 106 or R T
(3) (4)
(5)
(6) (7)
(8)
Once expressed in this form it can be seen that the requirements of BS8007 and BD28 were reasonably well aligned, with BS8007 presented in a similar style to the method in the Eurocodes and CIRIA C660. There were, however, some differences in the way in which creep and restraint were accounted for in BD28 and BS8007. Notwithstanding these differences, the principles and the overall approach of BS8007 and BD28 were similar. For completeness, comparisons have been drawn in this paper with both BD28 and BS8007 where possible, relative to Eurocodes.
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The Eurocode Design Approach The Eurocode design method comprises two stages. Firstly, the magnitude of free contraction free is estimated and a restraint factor Rax is applied to determine the restrained-strain which, if of sufficient magnitude, may result in cracking. The way in which the restrained-strain is distributed as cracking is then estimated based on the volume and distribution of reinforcement and the nature of the restraint. BS EN 1992-3 deals with two forms of restraint; continuous edge restraint and end restraint. The nature of the restraint is assumed to influence the way in which cracking develops and different approaches are adopted to estimate the magnitude of crack-inducing strain, i.e. that component of strain which is relieved and exhibited as cracking.
Estimating the Risk of Cracking Estimating restrained contraction Similarly to the previous standards, BS EN 1992-3:2006 uses a strain based approach and assumes that all compressive stresses induced during heating are relieved by creep. The restrained contraction r is estimated using the expression;
r = Rax free
(9)
where Rax is the degree of external axial restraint and εfree is the free contraction assuming no restraint. For early-age deformation εr is estimated using the expression (10);
r = (c. T1 +. ca) K. Rax
(10)
T1 is the temperature drop; c is the coefficient of thermal expansion of concrete; ca is autogenous shrinkage; and K is a coefficient for creep. A spreadsheet model for predicting T1 is provided in CIRIA C660 which derives adiabatic temperature rise curves for a variety of UK concretes. It is based on extensive testing at the University of Dundee [7] and was validated against in situ measurements [3]. Autogenous shrinkage is calculated using the expression of BS EN 1992-1-1. Estimating the risk of cracking The risk of cracking is estimated by comparing the restrained strain εr with the tensile strain capacity of the concrete εctu; for no cracking εctu > εr . εctu is estimated from the ratio of the mean tensile strength, fctm(t) and the modulus of elasticity Ecm(t) at early-age (the 3-day value is recommended if the specific time of cracking is not known). fctm(t) and Ecm(t) are estimated using the expressions provided in EN 1992-1-1 and coefficients are applied to the ratio fctm(t)/Ecm(t) which take account of both creep (0.65) and the effect of sustained loading (0.8). The net effect of these coefficients is to increase εctu under short term loading by 0.8/0.65 = 1.27.
Estimating Minimum Area of Reinforcement The minimum area of reinforcement As,min is that which ensures that, if all of the tension in the concrete prior to cracking is assumed to be transferred to the steel immediately after cracking,
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then the stress in the steel will be below its yield strength. Expressions used by BS 8007 and BS EN 1992-1-1 are shown in Table 1. In the design approach of BD28 and BS 8007 it was assumed that cracking is initiated from the surface [8]. In practice however, it is more likely that, under conditions of external restraint in which there is tension across the full section, cracking will be initiated at the point where the temperature drop is the greatest, i.e. at the centre of the section (see Figure 1). Stress will therefore be transferred from the full section to the reinforcement when a crack occurs. Hence the underlying assumption regarding the surface zone may not be valid. BD28 f ct* As Ac fy Ac is the gross cross section or a surface zone of 250mm at either edge 0.7 f ct 0.12 f cu fy is the yield strength of the steel
BS 8007 fct As Ac Ac ρcrit fy
EN 1992-1-1 fct, eff As, min kc k Act (kc k Act ρcrit) fky
Ac is the gross cross section or a surface zone of 250mm at either edge
Act is the area of concrete in tension
fct is the tensile strength of the concrete fy is the yield strength of the steel
fct,eff is the tensile strength of the concrete fyk is the yield strength of the steel
k allows for non-uniform and selfequilibrating stress which leads to a reduction in restraint forces k = 1 for h ≤ 300mm k = 0.65 for h ≥ 800mm intermediate values are interpolated kc takes account of the stress distribution in the section = 1 for pure tension Table 1. Expressions for estimating the minimum area of reinforcement t3
Temperature profile
t2 t0 Cracking propagated from the centre where temperature change is greatest
Restraint
Restraint
t1
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Figure 1. Cross-section through a thick wall subject to external restraint
This revised view of crack development is reflected in the change in EN 1992-1-1 and has been extended for the case of EATC in CIRIA C660 which has increased the coefficient k (see Table 1) from 0.65 to 0.75 for h ≥ 800mm to take account of both the (generally) parabolic temperature profile and the fact that in practice some compressive stresses must be relieved by a drop in temperature before tensile stress are generated. A comparison of the effective surface zones is shown in Figure 2.
Figure 2. Surface zones used in estimating the minimum area of reinforcement in sections that are dominated by external restraint
The difference is most significant in thick sections that are at risk of cracking due to external restraint, where the methods of EN 1992-1-1 and C660 assume that stress is transferred from a much higher proportion of the section thickness (i.e. a much higher effective surface zone) and hence lead to the requirements for more minimum reinforcement compared with BS 8007 and BD28.
Estimating Crack Spacing and Crack Width The characteristic crack width wk (expected to be about 30% higher than the mean value [9], [10] ) is estimated from the product of the crack-inducing strain εcr and the crack spacing Sr,max. Crack spacing The expressions for calculating crack spacing are given in Table 2. The same expressions apply for both edge restraint and end restraint. The second term in the BS EN 1992-1-1:2004
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expression appears to be very similar to that of BS 8007. However, the way in which ρe,eff is calculated leads to very different results. Consider a 500mm thick wall; if c = 40mm and φ = 20mm, the effective surface zone, he,ef = 2.5(40 +20/2) = 125mm. For a 500mm wall this is only half the value of 250mm used by BD28 and BS 8007. As the value of ρp,eff is inversely proportional to he,ef this will result in ρp,eff being double the value used by BD 28 and BS8007, thus halving the value of the second term in the crack width expression. This difference is partially offset by a cover term (3.4c) but the net effect is that, in this example, the crack spacing estimated using EN 1992-1-1 will be significantly lower than the crack spacing estimated using BS 8007. With no other changes this would lead to a significant reduction in crack control reinforcement compared with BS 8007 as shown in Figure 3 (a). BS 8007 and BD28/87 S r,max 0.5
EN 1992-1-1
f ct φ fb ρ
S r,max 3.4c 0.425
k1 φ ρ p,eff
NO cover term
c is the cover (mm)
fct/fb is the ratio of the tensile strength of the concrete to the bond strength, which for type 2 deformed bars = 0.67
k1 is a coefficient which takes account of the bond properties of the reinforcement = 0.8 (and increased in C660 to 1.14)
φ is the bar diameter (mm) ρ is the steel ratio based on a surface zone of 250mm or h/2, whichever is less Hence,
S r,max 0.335
ρe,eff is the effective steel ratio based on an effective surface zone he.eff to a depth of 2.5 (c + φ/2) or h/2, whichever is less
φ ρ
and, S r,max 3.4c 0.34
φ ρ p,eff
200
200 180
Cover
160 140
70 mm
120
60 mm
100 50 mm
80
40 mm 30 mm
60 40 20
0 300 400 500 600 700 800 900 1000
Percent steel relative to BS8007
Percent steel relative to BS8007
Table 2. Expressions for the calculation of crack spacing 70 mm
180 60 mm
160 140
50 mm
120 40 mm
100 80
30 mm
60
Cover
40 20 0 300 400 500 600 700 800 900 1000
Thickness (mm)
Thickness (mm)
(a) k1 = 0.8 (EN 1992-1-1)
(b) k1 = 1.14 (CIRIA C660)
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Figure 3. The ratio of reinforcement requirements for design to EN 1992 and BS8007 (C30/37 concrete; plywood formwork; limiting early-age crack width to 0.15 mm; cover as shown)
Observations by the authors suggest that the requirements of BD28 and BS 8007, while having been generally applicable, have occasionally led to excessive crack widths and that it would be unsafe to adopt a design that significantly reduces the current requirements. The design parameters were therefore investigated. BS EN 1992-1-1:2004 recommends a factor of 0.7 is applied to bond stress in cases when “good” bond cannot be guaranteed. In C660, this factor has been considered applicable to k1 in cases of EATC, so the bond coefficient k1 is increased from 0.8 to 1.14, since 0.8/0.7 = 1.14. Calculations using the increased value of k1 are shown in Figure 3 (b) and lead to steel requirements that are closer to those of BS 8007 within the normal range of cover. Higher steel ratios than those suggested by BS 8007 are generally associated with high cover. Crack width Up to this point in the design the nature of the restraint has not been considered. However, in estimating crack width, BS EN 1992-3:2006 uses different expressions for estimating the magnitude of crack-inducing strain εcr. For continuous edge restraint informative Annex M of BS EN 1992-3:2006 assumes εcr = εr i.e. the restrained-strain. CIRIA C660 proposes the expression εcr = εr – 0.5εctu i.e. εr less the residual strain in the concrete after cracking. (This approach is also taken by BD28.) In each case the assumption is that the crack width is strain limited. For end restraint only a different expression is used as follows;
cr
0.5αe.kc.k.fct.eff 1 1 Es αeρ
Es is the modulus of elasticity of the steel; αe is the modular ratio; fct,eff is the tensile stress in the concrete immediately prior to cracking; ρ is the steel ratio based on the full area of concrete in tension [N.B. This is not the same as ρp,eff used in the calculation of crack spacing]; k and kc are area coefficients described in Table 1. This expression assumes that the crack width is limited by the stress transferred to the steel. Under conditions of end restraint, even when the minimum steel ratio is exceeded, crack widths may be significantly wider than achieved under conditions of edge restraint, although fewer cracks may occur. For example, in a 400mm section with 16mm bars at 250mm centres using C30/37, the crack width resulting from end restraint is estimated to be 1mm, while under conditions of edge restraint the estimated crack width is in the order of 0.15mm.
The Influence of Cover The net effect on crack width of cover alone is shown in Figure 4. This has been recognised for many years. For example, Campbell-Allen & Hughes [11] recommended that “the placing of such reinforcement shall be as near to the surface of the concrete as is consistent with the
P Bamforth, J Shave, S Denton
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requirements of adequate cover”. However, in relation to control of EATC, the effect of cover has not previously been quantified. Furthermore, recognising that the crack profile may differ significantly from that of a crack developed by an element in flexure, it may be inappropriate to adopt a similar expression to derive crack spacing and further research is recommended in this area to avoid unnecessarily high volumes of reinforcement being used when high cover is specified. 2000
Area of reinforcement (mm 2)
Crack width (mm)
0.25 0.20 0.15 0.10 0.05 0.00 30
40
50
60
1500 1000 500 0 30
70
40
50
60
70
Cover (mm)
Cover (mm)
(b) Area of reinforcement (mm2/m/face) required to achieve a crack width of 0.15mm
(a) Effect of cover on crack width
Figure 4. The Effect of Cover in a 300mm Wall Subject to a 30oC Temperature Drop and 70% Restraint
Comparison Between Estimated and Observed Crack Widths Comparisons between observed crack widths and predictions using current methods are shown in Figure 5. These graphs are based on back analysis of measured data, as explained by Bamforth[12]. It is clear that both BS 8007 and BS EN 1992 (without extension as recommended in C660) lead to unsafe predictions of crack width for many of the examples. In some cases the difference was as much as 50%. The method of CIRIA C660, which is based on the method of BS EN 1992 but extended as described, shows a much better correlation with the reported crack widths. BS8007
EN1992-3 0.5
Estimated crack width (mm)
Estimated crack width (mm)
0.5 0.4 0.3 0.2 0.1 0.0 0.2
0.25
0.3
0.35
Measured crack w idth (m m )
0.4
0.4 0.3 0.2 0.1 0.0 0.2
0.25
0.3
0.35
Measured crack w idth (m m )
0.4
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CIRIA C660 Estimated crack width (mm)
0.5 0.4 0.3 0.2 0.1 0.0 0.2
0.25
0.3
0.35
0.4
Measured crack w idth (m m )
Figure 5. Comparison of observed and predicted crack widths using the methods of BS 8007, BS EN 1992-3:2006 (without extension for EATC) and CIRIA C660[12]
Conclusions The design approach for early-age thermal cracking adopted by BS EN 1992-3:2006 is broadly similar to that of BD 28 and BS 8007 but there are some significant and important differences as follows; 1) Different values of surface zone are used to estimate the minimum area of reinforcement 2) Different surface zones are used to estimated the steel ratio for calculating crack width 3) BS EN 1992-1-1:2004 includes cover in the expressions for crack spacing and width. This was not included in BS 8007 of BD 28 4) The term fct / fb (tensile strength/bond strength) has been replaced by the coefficient k1 5) Crack development and crack widths depend on whether the element is subject to edge restraint or end restraint and this is reflected in different expressions for calculating crack width 6) Autogenous shrinkage is assumed to occur in all grades of structural concrete CIRIA C660 has recognised these changes and has proposed modifications to the design parameters to complement EN 1992 and ensure that estimated crack widths reflect more reliably those observed in practice.
Acknowledgements The authors wish to thank the Construction Industry Research and Information Association for their permission to publish this paper.
References [1] [2] [3]
BD28/87 Early Thermal Cracking of Concrete, Design Manual for Roads and Bridges Vol 1 Section 3, Incorporating Amendment No 1, 1989, TSO British Standards Institution, 1987, Design of Concrete Structures for Retaining Aqueous Liquids, BS8007:1987. Bamforth, P B, 2007, Early-age Thermal Crack Control in Concrete, CIRIA Report C660, Construction Industry Research and Information Association, London.
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[8]
[9]
[10]
[11]
[12]
11
Harrison, T A, 1992, Early-age Thermal Crack Control in Concrete, CIRIA Report 91, Construction Industry Research and Information Association, London. British Standards Institution, 1985, Structural Use of Concrete. BS8110:1985 British Standards Institution , 1990, BS 5400-4:1990, Steel, concrete and composite bridges. Code of practice for design of concrete bridges. Dhir, R K, Paine, K A and Zheng, L, 2006, Design data for low heat and very low heat special cements, University of Dundee, Research Contract No. CTU/I53), Report CTU/4006, September 2006 Anchor, R D, Hill, A W and Hughes, B P, 1979, Handbook on BS 5337:1976 (The structural use of concrete for retaining aqueous liquids) Viewpoint Publications, Cement & Concrete Association, Slough. Narayanan, R S and Beeby, A W, Designers’ Guide to EN 1992-1-1 and EN 1992-1-2 Eurocode 2: Design of Concrete Structures. General rules and rules for buildings and structural fire design, Thomas Telford. Beeby, A W, 1990, Fixings in cracked concrete – The Probability of Coincident Occurrence and Likely Crack Width, CIRIA Technical Note 136, Construction Industry Research and Information Association, London. Campbell-Allen, D and Hughes, G W, 1981, Reinforcement to Control Thermal and Shrinkage Cracking. Transaction of the Institution of Engineers, Australia, Civil Engineering, August, Vol. CE23. No. 3. Bamforth, P B, 2008, A revised approach for the design of reinforcement to control cracking in concrete resulting from restrained contraction - Case studies and validation, ICE Research Project 0706, Project Report ICE/0706/007. Institution of Civil Engineers, London. Project Report ICE/0706/007.
