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Concrete In Australia : December 2008
factor that reduces the strut’s capacity with increasing tensile strain perpendicular to the strut in the form of Eq. 6-7. v = 1 ee e e q12 2 0.8 170 1 =+ - + xx e1 e2 ex ()/tan e s (6) This increase in horizontal tensile strain significantly reduces (7) = is the major principal strain that is the tension normal to the compression strut = is the minor principal strain parallel to the compression strut = is the strain in the horizontal direction and ? is the angle between the compression strut and the horizontal. The Canadian Code adopts a similar equation. However they tensile strain may be signifi cantly less due to the detailing of the reinforcement. limit the effi ciency factor to 0.85 and have chosen a value of e2 = -0.002. Collins and Mitchell (1986) further proposed that at ultimate limit state the yield strain be taken as the appropriate value of ex Draft Code of AS3600 – DR05252 Following on from the research completed by Collins and Mitchell (1986), Foster and Gilbert (1996) grouped Equations 6-7 together into Equation 8 so that the effi ciency factor was a function of the angle of the strut and the concrete’s compressive strength while keeping the horizontal tensile strain a constant and equal to 0.002. The magnitude of the tensile strain chosen was based on Grade 60 reinforcement (414MPa). In addition to this they modifi ed the peak strains of e2 from -0.002 at 20MPa to -0.003 at 100MPa to accommodate higher strength concrete. v = 1 1 14 0 64.( .++f c / 470)cot q ¢ 2 This equation is outdated as the predominantly specified reinforcement is now 500MPa N Grade. Therefore the yield strain should be equal to 0.0025. Taking this into account Equation 8 and should be updated to Equation 9. kwhere 0.3= = 1.0 bs 111 0.73cot v== 22 10 066.. cot 09. bs 09. + qq = . Table 2. Comparison of normalised collapse loads. Design standard Loads CEB-FIP (1990) ACI 318-02 CSA A23.3-94 DR05252 V*(kN) 54.8 50.8 51.6 50 * Assuming Live Load/Dead Load = 0.25 Concrete in Australia Vol 34 No 4 51 N*(kN) 155.0 262.5 225.0 219.1 + 1 (8) . This is a realistic but conservative assumption as the the strut’s strength. However, it is the lower limit of the strut’s capacity due to the assumption of the corresponding tie yielding. The study by Warwick and Foster (1993) then found that Equation 8 is not sensitive to the variation of strength of the concrete. This is probably due to the equation being based on research of limited scope with respect to the variation of concrete strength, as the panel tests undertaken by Vecchio and Collins (1986) were limited to the range of 12-35MPa. Due to this lack of sensitivity to the strength of concrete Foster and Gilbert (1996) further modifi ed and simplifi ed the Collins and Mitchell (1986) to Equation 10. v = 1 114 0 75 2 + .. cot q (10) However, for the case when cot?= 0 it is assumed that v = 1.0. This is inferred from the modifi ed compression field theory. Therefore a constant is taken out from the equation that is termed in-situ strength factor, k, that is equal to 0.88 (Foster and Malik 2002), though the Draft Code of AS36001 has chosen a value of 0.9. The study by Foster and Malik (2002) tried to substantiate so that it varied linearly Equation 11 with respect to a data set of compression failures. Their study excluded an investigation into the transverse tensile strains. This made it unclear if the sample included specimens that had attained tensile strains close to yielding. Again Equation 11 has to be revised to account for the increase in the yield strain due to the shift from Y grade to N grade reinforcement, shown in Equation 12. kv = 1 225 0 833 2 where k = 0.82 1 .. cot q + Comparison of codified approaches To directly compare the codified approaches1-5 , the design compressive strength of a strut was calculated for each code (11) (12) v = 1 225 0 7225.( . ++ 1 f c / 470)cot q ¢ 2 (9) ULS load Normalised load factor* 1.35G+1.5Q 1.2G+1.6Q 1.25G+1.5Q 1.2G+1.5Q 0.9130 0.9844 0.9692 1.0000 Normalised loads V*(kN) 50.0 50.0 49.9 50 N*(kN) 141.5 258.4 218.1 219.1