Chapter 4: Parametric Study of the EN 1992-1-1 & 3 and Corresponding Codes BS 8007 & BS
4.2 Design Parameters
The parametric study was deterministic in nature, meaning that the inherent variability and uncertainty in each input variable were disregarded. Instead, each input variable was regarded as
having a fixed value. A list of both the material and physical parameters used in this study are given below:
4.2.1 Material parameters
Concrete compressive strength (characteristic value)
A survey of South African water retaining structures revealed that typical concrete grade used included either C25/30 OPC concrete or otherwise grade C30/37(Holicky, Retief & Wium, 2009).
The latter of the two was chosen as the concrete grade of choice. A concrete grade of C30/37 was selected.
Concrete tensile strength (mean value)
For C30/37 concrete at 3 days fctm (3) = 1.73 MPa (fctm = fct,eff ). The tensile strength taken at 28 days is fctm (28) = 2.9 MPa for C30/37.Values are for concrete tensile strength are taken from CIRIA C660, table 3.2 (Bamforth, 2007).
Reinforcement yield strength (characteristic value)
The reinforcement yield strength common in South Africa is 450 MPa.
Modulus of elasticity of steel
The modulus of elasticity of steel is 200 GPa.
Modular ratio
The modular ratio is αe = Es/Ec, where Es denotes the modulus of elasticity of the steel and Ec
relates to the modulus of elasticity of concrete at the appropriate age. This value can be estimated by from EN 1992-1-1:2004 equation (under clause 3.1.3):
Ecm (t) = (fctm (t)/fcm)0.3 Ecm, where,
Ecm (t) is the modulus of elasticity at ‘t’ days
fcm (t) is the mean concrete compressive strength at ‘t’ days (EN 1992-1-1 (2004), clause 3.1.2, equation 3.1)
Ecm is the modulus of elasticity at 28 days
fcm is the mean concrete compressive strength at 28 days (taken from table 3.1 of EN 1992-1-1:2004)
Ecm (3) = (22.8/38)0.3x33 = 28 GPa, This makes the modular ratio for C30/37 concrete αe = 200/28=
7.14 for concrete at 3 days. At 28 days Ecm = (38/38)0.3x33 = 33 GPa, making αe = 200/33 = 6.06 for C30/37 concrete.
Coefficient of thermal expansion, αc,T
The most used aggregate in South African concrete is quartzite and sandstone (Addis and Owens, 2001) and thus reading from table 4.4 in CIRIA C660 (Bamforth, 2007), the coefficient of thermal expansion for quartzite containing concrete was (wasαT,c = 14µɛ/˚C, which acted as the reference thermal expansion coefficient for calculations). This was a proposed conservative design value on the high-end of the observed range of concrete thermal expansion coefficients (after Browne 1972 as cited by Bamforth, 2007 in CIRIA C660).
Autogenous shrinkage, εca
The values for autogenous shrinkage strain obtained from table 4.5 of CIRIA C660 were ɛca = 15µɛ (at 3 days) for C30/37 concrete and ɛca = 33µɛ (28 days) – used in calculations, taking into consideration long term effects. Or otherwise the autogenous shrinkage may be obtained via the formulae for autogenous shrinkage in EN 1992-1-1:2004, under clause 3.1.4:
εca(t) = βas(t)εca(∞) where,
εca(∞) = 2.5(fck – 10)x10-6 and
βas(t) = 1-exp(-0.2t0.5).
The time, t, input is given in days. Using these formulae it may be found that:
For t = 3 days, εca(3)=(1-exp(-0.2(3)0.5)x2.5(30-10)10-6 = 14.64με (≈15με)
For t = 28 days, εca(28)=(1-exp(-0.2(28)0.5)x2.5(30-10)10-6 = 32.65με (≈33με)
T1
The most common formwork used in South Africa is steel formwork (Addis and Owens, 2001).
Table 4.2 of CIRIA C660 gives 340kg/m3 binder content for C30/37 CEM I (ordinary Portland cement) concrete. Figure 4.5 from CIRIA C660 (this value is based on a mean ambient temperature of 15°C and placing temperature of 20°C) gives, T1 value of 15°C.
T2
Considering the concrete placement in summer, the T2 fall in temperature selected for the analysis was 23°C (estimating from data obtained by SouthAfrica.info, 2015 and the Climate Change Knowledge Portal, 2009).
Drying shrinkage strain, εcd
For relative humidity was said to be 80% for coastal areas (Addis and Owens, 2001) where the section thickness h = 250 mm and the width of the section considered is b = 1000 mm. The effective section thickness h0 may then be obtained by dividing twice the concrete cross-sectional area by the perimeter of the parts of the cross-section that would be exposed to the drying (2Ac/u).
Applying this formula in this context gave the following result:
2Ac/u=2(250 x 1000)/ (2x1000) = 250 mm (considering a section of wall, top and bottom of cross section not exposed)
Reading from figure 8.20 from Fulton’s Concrete Technology (Addis and Owens, 2001), the drying shrinkage strain is interpolate between values for h0 = 150 and 300 in this instance where h0 = 250 mm, yielding ɛcd = 220µɛ (30 year shrinkage) - this was the value to be adopted in the subsequent parametric calculations. For inland areas, the relative humidity in South Africa is 60%.
For h0 of 250 mm lying between 150 mm and 300 mm, as before, the drying shrinkage read for 60% relative humidity was ɛcd = 340µɛ (30-year shrinkage).
Tensile strain capacity, εctu
The tensile strain capacity represents the maximum amount of strain that the concrete can sustain before the formation of a crack (Bamforth, 2007). This value may be obtained by dividing the mean tensile strength of the concrete by the mean modulus of elasticity of the concrete. The values of the tensile strain capacity were taken from table 4.11 of CIRIA C660 (Bamforth, 2007) where the effects of creep and sustained loading were accounted for.
εctu = 76 με for C30/37 concrete at 3 days.
εctu = 108 με for C30/37 concrete at 28 days.
4.2.2 Physical parameters Section thickness, h
The typical section thickness in South Africa for water retaining structures was found to be 250mm (Holicky, Retief & Wium, 2009).
Cover, c
The concrete cover was taken to be 40mm (this value takes into consideration the minimum concrete covers for the durability of water retaining structures in accordance with BS 8007. It was also found to be the typical choice for engineers in South Africa (Holicky, Retief & Wium, 2009)).
Diameter of reinforcement, φ
This value may vary depending on the parameter being studied, a reinforcing steel diameter of 16 mm was selected as the reference case.
Area of tension reinforcement, As
Varies as required in the comparisons considered. The maximum amount of area of steel reinforcement (As) allowed in South Africa as stipulated by SANS10100-1 (clause 4.11.5.3) is 4% of the gross cross-sectional area of concrete (Ac). A feasible minimum limit of 75 mm spacing for single bars of reinforcement was used.
Restraint degree, R
A maximum restraint degree, with creep accounted for, will be used. Otherwise, the reference value for the restraint factor is taken to be 0.5 (for a concrete member under full restraint with the effects of creep accounted for).