Uncertainty in Shear Resistance of Reinforced Concrete Beams With Stirrups – Comparison of EN 1992-1-1 and fib Mc 2010 Approaches

Prior studies point to high model uncertainty in shear prediction. Model factors for various shear prediction models are characterized here, based on a recent and well‐vetted database of shear failures. Characterization includes estimation of main statistical parameters; and importantly also correlation and regression analysis to assess consistency of model factors over ranges of design parameters. The aim of the study is to identify models suitable for use as general probabilistic model (GPM) in future reliability assessments. The Variable Strut Inclination Method (VSIM), shear level of approximation III of the fib Model Code 2010, and ACI 318 displayed high bias, variability and various correlations with shear input parameters which make them unsuitable choices for GPM. The compression chord capacity model and the modified compression field theory displayed low bias and variability with consistent model factors over the ranges of shear design parameters and are thus suitable as GPM. Concerns stem from observed inconsistency in capacity prediction by VSIM and size effect in ACI. Reliability assessment is advised.

Section: Discussion Of Mf Statistical Results and Trendssupporting

confidence: 57%

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

Olalusi

Viljoen

2019

“…Busse et al considered ρ w as the most important parameter instead of ρ w f yw . This makes a marginal difference, as these variables affect the uncertainty of the EC2 model in a similar way . Busse et al obtained μ ≈ 1.35 and V ≈ 0.3 for the EC2 model; μ ≈ 1.12 and a very low V ≈ 0.07 were reported for the model in Reference 45.…”

Section: Discussionmentioning

confidence: 90%

“…The influence of ρ w or ρ w f yw on θ is considerably reduced (| r| ≤ 0.1) for Level III which is its key improvement. Medium correlations θ − d and θ − s are observed ( r ≈ −0.4 to −0.3); detailed results of correlation analysis were provided in Reference .…”

Section: Uncertainty In Shear Models—beams With Stirrupsmentioning

confidence: 99%

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

Sýkora

Krejsa

Mlčoch

et al. 2018

Self Cite

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

“…4 The existing literature on shear capacity of RC beams with stirrups can be broadly classified into three groups: (a) experimental studies conducted to understand the shear behavior 4-34 ; (b) models proposed to determine the shear capacity of RC beams with stirrups 2, [35][36][37][38][39][40][41][42][43] ; and (c) probabilistic studies on shear capacity. [44][45][46][47][48][49][50][51][52][53] The experimental studies were carried out to understand the behavior, crack pattern, failure mode of beams with Discussion on this paper must be submitted within two months of the print publication. The discussion will then be published in print, along with the authors' closure, if any, approximately nine months after the print publication.…”

Section: Introductionmentioning

confidence: 99%

“…This may be due to various unknown factors affecting shear behavior and can be generalized as it is the inherent nature of shear resistance to show large variations. [44][45][46][47][48][49][50][51][52] As a result, the shear capacity should be considered as a random variable, defined by a probability density function (pdf). It is noted that almost every new empirical or mechanics-based model that is proposed is validated using experimental results and COV of modeling error is reported.…”

Section: Introductionmentioning

confidence: 99%

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

Jayakumar

Kanchi

2019

The efficiency of shear capacity models of reinforced concrete beams with stirrups depends on the assumed mechanism and in few cases depends also on critical shear crack angle prediction. In the present study, three mechanics‐based shear capacity models (the limit analysis‐based models presented by Nielsen and Hoang, and the Mari et al. model) are considered covering the range space of shear span to effective depth ratios greater than 2.5. The statistics of modeling error associated with these models are determined using the database created in this study. The database contains limited results of experimental investigations, available in literature, on shear capacity of reinforced concrete beams with stirrups. The randomness in shear capacity is quantified by performing probabilistic analysis of one set of nominally similar beams taken from the database. Based on the shear capacity distribution obtained, characteristic design equations of reinforced concrete beams are proposed. The results of reliability analyses show that the reliability of a beam, for a given mean live to dead load ratio, varies when different shear capacity models are used in the analysis. Thus, calibration studies need to be performed for selecting a model for design.