Ultimate Strain Criteria for RC Members in Monotonic or Cyclic Flexure

Flexural rotation capacity models fitted to test results using different statistical approaches

“…12,13 In that broader context, Equation (12) with parameters from Approach A is the method of choice. In fact, the revision of Eurocode 8 1 adopted the simpler expression, Equation (9), with parameter values from Approach A (which differ little from those of Approach C and are, in general, on the safe side), as well as the physical model of Equations (4), (5), (7), (21), (23), (24) with the ultimate strains from (10). Examples with applications of the proposed models are given in the Appendix.…”

“…The reason is competition between θ pl u and Δθ u,slip , as ϕ u also increases with increasing confinement. This competition explains the markedly larger cov values of the estimates of the confinement parameter β w in Equations (11), (12) than in (8)- (10). Best estimates of factors λ sh , μ sh in Equation (5) The more complex empirical expressions give overall better average fit; for example, in Figure 1j and m lack of fit at the high end of experimental values is less than in Figure 1a, d or g. Table 4 lists medians and covs of the test-to-prediction ratio.…”

Cyclic shear resistance for seismic design, based on monotonic shear models in fib Model Code 2010 and in the 2018 draft of Eurocode 2

“…Biskinis and Fardis 10,11 and Grammatikou et al 12 give a procedure, equations and flowcharts for the calculation of φ u and ξ u at ultimate deformation (conventionally identified with a drop in lateral force resistance of at least 20% of peak resistance), under all possible flexural failure modes of rectangular sections in uniaxial or (16)- (19) in Table 5; (b) Moehle et al, 3 Equations (2b) and (20)- (22) in Table 5; (c) Biskinis et al, 18 Equations (2b), (16a) and (23)-(25) in Table 5 equal biaxial bending and of circular ones. When used together with the ultimate strain criteria for steel and (confined or unconfined) concrete in Grammatikou et al, 12 they give good agreement to experimental ultimate curvatures in hundreds of measurements. 3.…”

“…Their shear resistance, V R , was computed for the inclination θ that gives V R = V R,s (+V R,c ) = V R,max , with ε x computed by applying Equation (6) to the test specimen's end section, for a moment equal to M = V R L s . The experimental resistance was taken equal to the shear force at ultimate deformation, conventionally identified with the point where the lateral force resistance (i.e., the applied shear) drops by at least 20% with respect to the peak resistance reached before (Biskinis and Fardis, 10,11 Grammatikou et al [12][13][14]. Figure 2 compares the experimental cyclic shear resistance to the MC2010 predictions and Table 3 gives the median and the coefficient of variation (cov) of the testto-model ratios.…”

A simplified method to assess seismic behavior of reinforced concrete columns

“…36 It is worth noting that the ultimate strain value cannot consider effects such as the buckling of bars, the statistical effect of the bar number, etc. When the sectional analysis is conducted to design new RC columns, the ultimate strain value should be determined using the method by Grammatikou et al 37 to take the above effects into account, which can ensure that the results of the sectional analysis are conventional and safe for the design of new RC structures. The flowchart of the sectional analysis is given in Figure 4; h and cover thickness a s are proposed for the upper bound c 1 and the lower bound c 2 of the compression zone height c, respectively.…”