Uncertainty in shear resistance models of reinforced concrete beams according to fib MC2010

Abstract

Load bearing capacity can be predicted by appropriate modeling of material properties, geometry variables, and uncertainties associated with an applied model for the failure mechanism under consideration. The submitted study investigates shear resistance model uncertainties for reinforced concrete beams with and without shear reinforcement, considering large test databases and various levels of approximation offered by fib Model Code 2010. Model uncertainty is treated as a random variable and its characteristics are obtained by comparing test and model outcomes. The sensitivity of model uncertainty with respect to basic variables is analyzed. For beams with stirrups, Level III is recommended for practical applications. Its predictions are shown to be independent of the amount of shear reinforcement and have reasonable bias and dispersion around test results. For beams without shear reinforcement, the use of Level II is advisable and a distinction between lightly reinforced and moderately to heavily reinforced beams should be made. K E Y W O R D S fib model code 2010, model uncertainty, partial factor, reinforced concrete, shear reinforcement, shear resistance 1 | INTRODUCTIONAdequate description of the uncertainties in resistance models was recognized as one of key issues in reliability investigations of new and existing reinforced concrete (RC) structures. 1 Particularly when description of load effects and structural responses is highly complex, and operational procedures are based on simplified approaches, model uncertainty may dominate structural reliability and its quantification and explicit inclusion in reliability analysis is required. 2 Such cases can be identified by the lack of consensus amongst experts; alternative models used in research studies and practical applications; and different levels of approximation (LoA) 3 introduced in design codes. This is the case with shear resistances of RC structures, recognizing that shear strengths predicted by different design codes for a particular beam or section can vary by factors of more than two. 4 Shear resistances of beams have stimulated an extensive debate over recent decades, as there is not yet an international consensus on which variables are important, 5 which mechanisms govern 6,7 and how to codify existing understanding. 8 Features of several models for shear resistances of beams with and without special shear reinforcement (hereafter referred to as "shear models" for brevity) were investigated and improvements proposed. [9][10][11][12][13][14][15] The complexity of shear transfer actions and modeling was recognized and described in detail in References 16,17.Model uncertainty as an indicator of the difference between model and real structural resistances was explicitly addressed by Russo et al 10 who analyzed the uncertainty associated with the models in EN 1992-1-1 18 and American Concrete Institute (ACI) 318M-08. 19 Bentz et al 4 were focused on the ACI procedure and two approaches belonging to the Modified Compression Field Theory. The recent

Model uncertainties and bias in SHEAR strength predictions of slender stirrup reinforced concrete beams

“…The correlation and regression analysis ( Table 4) reveals that MF MC − 10(III) has a strong decreasing trend with the member depth d (r = − 0.41), evident in Figure 5d and Table 5c. This trend was also identified by other researchers 15,18,21,22,38 (This implies that the MC-10 (III) formulation does not adequately account for the size effect on shear resistance. The risk of insufficient reliability for beams with large depth should be investigated.…”

“…Model factors may be statistically characterized by a probability distribution function with corresponding mean value and variance. In accordance with the MF x associated with a single experiment, x , is calculated from the ratio of the experimentally observed capacity to the best estimate predictions of the analytical model under consideration. …”

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

“…The results in Figures and and in Tables and should be seen against the backdrop of monotonic test‐to‐model comparisons by Sigrist et al and Sykora et al: LoA II and III were found by Sigrist et al to provide median test‐to‐prediction ratios in 243 rectangular or T‐beams with stirrups (79 of which had axial force, normally due to prestress) equal to 1.34 and 1.195, respectively, and corresponding coefficients of variation of 17 and 13%. In Sykora et al 459 beams gave median test‐to‐prediction ratios of 1.58 and 1.125 for LoA II and III, respectively, and corresponding coefficients of variation of 25 and 23%. …”

“…• Of the beneficial contribution of the axial load, outlined in Section 3 • Of the reduction in shear resistance due to cycling of the load, see Section 5.2. Tables 3 and 4 should be seen against the backdrop of monotonic test-tomodel comparisons by Sigrist et al 15 and Sykora et al 16 :…”

Probabilistic studies on mechanics‐based shear capacity models for reinforced concrete beams with stirrups

“…This clearly shows that if filter is not applied COV increases because of diverse shear behavior, for a given a v / d , exhibited by beams in unfiltered database. This is also true for higher order moments like skewness and kurtosis which gets significantly affected by filtering criteria (see Figure ) as pointed out by Sykora et al In the study conducted by Sykora et al, the aim was to address the biases and scatters in the predictions using fib shear capacity equation. Therefore, distribution of shear capacity was not discussed and was considered as an open area of research.…”