Safety formats for non-linear analysis of concrete structures

Abstract

For realistic modelling of reinforced concrete structures, non-linear models are often inevitable, which raises the question of an appropriate safety format for non-linear analysis. This paper gives an overview of available safety formats and discusses their advantages and disadvantages. An analysis of available round robin tests and modelling competitions shows that current safety formats do not properly account for the modelling uncertainty of non-linear analysis. Based on this observation a new safety format was proposed which allows one to explicitly account for the modelling uncertainty. To avoid any interaction of the modelled response with the safety format, the mean in situ material parameters should be used in the non-linear analysis and a resistance safety factor is used to assure the intended reliability level. The application of the new safety format to beam sections loaded in bending showed that it offers a reliability level that is in good agreement with the target reliability.

Uncertainties in resistance models for sound and corrosion-damaged RC structures according to EN 1992-1-1

“…The experimental data for the latter seem to be rather scattered and inconclusive [44]; this is also the case of punching shear not discussed here. Insights into the uncertainties in models based on the Finite Element Analysis were provided in [38,39,44].…”

Global safety format for non‐linear analysis of reinforced concrete structures

“…where R m and R k are the values of the structural resistance based on the mean and characteristic values of the material resistances respectively. The design resistance is then calculated from (10) Although not included in fib Model Code 2010, the safety format proposed by Schlune et al [5,6] could be considered as an improved ECOV method. Schlune et al present an investigation concerning beam sections subjected to a combination of bending moments and shear forces.…”

“…The coefficient of variation V R is written by Schlune et al [5] as follows: (13) where V g , V m and V f are the coefficients of variation of the geometrical, model and material uncertainties respectively. Suggestions for V g and V m are also proposed in [5,6]. When the main material parameters are the concrete compressive strength and the yield stress of the steel, the coefficient of variation V f can be estimated by means of (14) where σ fc , σ fy standard deviations of the concrete compressive strength and the yield stress of the steel respectively ∆f c , ∆f y finite variations of the material resistances R ∆fc , R ∆fy results of non-linear analyses performed using the values f cm -∆f c for the concrete compressive strength and f ym -∆f y for the yield stress…”

A quantification of the modelling uncertainty of non-linear finite element analyses of large concrete structures

“…By using the Bayesian inference technique suggested by and assuming that θ can be modelled as a log-normally distributed random variable, a mean μ θ = 1.07 and a coefficient of variation V θ = 0.09 was found. This can be regarded as being within the requirements suggested in the literature Schlune, Plos, and Gylltoft, 2012). Engen et al (2017) analysed the same set of benchmark experiments with the same solution strategy as used herein, however using modified Newton-Raphson, a force-based convergence criterion, ||R res ||/||R ext || < 0.01, and not continuously monitoring the fracture criterion during the stress update algorithm for uncracked integration points as mentioned in Section 2.1.2.…”