Assessment of reliability of EN 1992‐1‐1 variable strut inclination method of shear design provisions for stirrup failure

Abstract

The best estimate shear strength predictions of the operational EN 1992‐1‐1 (EC2) variable strut inclination method (VSIM) have been shown to underestimate shear capacity at low stirrup quantities. Conversely, the model overestimates shear capacity at high stirrup quantities (Cladera and Mari, 2007; Olalusi and Viljoen, 2019). Sufficient safety performance of the design formulation should be confirmed at high levels of stirrup reinforcement, and over conservatism at low stirrup reinforcement is not ideal. This contribution assesses the consistency and uniformity of the reliability index of EC2 shear design formulation over the range of practical design situations. Prediction model uncertainty is an important parameter in the assessment (Olalusi and Viljoen, 2019). The principal reliability assessment was performed using as general probabilistic model (GPM), the probabilistic representation of the modified compression field theory (MCFT) as implemented in analysis program Response 2000 (R2k), which was shown to provide the most accurate estimates of shear capacity (Bentz, 2000). This was validated by means of a similar reliability analysis using the compression chord capacity model (CCC) as GPM. The outcome of EC2 reliability analysis indicated uneconomically high reliability at low levels of shear reinforcement, high concrete strength and large beam depth, and actively reducing reliability with increased levels of shear reinforcement, reduced concrete strength and reduced beam depth for both rectangular and I‐shaped beam cross‐sections. Reliability indices of all the test sections investigated meet the target reliability requirements for Reliability Class 2 structures prescribed by basis of design standards SANS 10160 and EN 1990, for the design range considered.

Probabilistic Studies on the Shear Strength of Slender Steel Fiber Reinforced Concrete Structures

“…Model uncertainty is described as the deficiency of a model to accurately represent a physical phenomenon due to lack of comprehension of the phenomenon, conservative assumptions and mathematical simplifications [30,31]. The model uncertainties related to the MC-10, DAfStB and the Bernat et al [27] shear models are investigated in this section.…”

“…The influence of such uncertainties is quantified and accounted for using statistical and probabilistic approaches [28,29]. In reliability analysis, uncertainties must be adequately considered in order to predict the probability of failure under prescribed limit states [29,30]. Uncertainties in structural engineering can be classified into two sources, namely aleatory (inherent random variability) and epistemic [28].…”

“…Model uncertainty is a random variable describing the effects neglected in the representation of the actual structures and the simplifications in the mathematical expressions. Model uncertainty in shear prediction is significant and has been shown to dominate shear reliability performance [30]. The mean (bias) and variability of the model uncertainty are used as inputs in reliability analysis and thus, will affect the reliability performance [30].…”

“…Model uncertainty in shear prediction is significant and has been shown to dominate shear reliability performance [30]. The mean (bias) and variability of the model uncertainty are used as inputs in reliability analysis and thus, will affect the reliability performance [30]. Reliability analysis is usually performed based on a particular design situation, i.e., specific geometry, material strength and reinforcement ratio.…”

“…Reliability analysis is usually performed based on a particular design situation, i.e., specific geometry, material strength and reinforcement ratio. Thus, trends in the model uncertainty bias or variability may render the overall model uncertainty not to be representative for a specific design situation, which will result in an erroneous evaluation of reliability [30].…”