## 2 Probabilistic Non-Linear Computation
### Limit State Design  
As requested by the current codes [8; 27]_Serriccability Limit State (SLS)_ verifications must be performed as post-analysis checks. For the load level corresponding to the SLS, derived from the SLS combinations imposed by the current codes, the stress state, crack opening and deflections controls must be performed. Regarding the _Ultimate Limit State (ULS)_, verifications must be performed in order to obtain an adequate level of resistance against the loads imposed on the structures. The MC2010 proposes (a) the probabilistic method, (b) global resistance factor format (GRF) and (c) the partial safety factor format (PF). The Estimate of Coefficient of Variation of Resistance (ECOV) method is a particular method within the global resistance format. The forthcoming fib Model Code 2020, although its content and formats are still under discussion, should also encompass this concept.  
_Global Resistance Factor format (GRF)_: According to this format, the global resistance of the structure is a random variable. The effects of various uncertainties are integrated in the global design resistance and can be expressed by a global safety factor. The global safety coefficient is equal to the product of the safety and the model coefficients.  
_Partial Safety Factor format (PF)_: According to the Partial Safety Factor format, the basis variables are deterministic quantities representing values related to a level of confidence for each parameter. In that sense, the treatment of uncertainties and variabilities originating from various causes is distributed to the individual input parameters by means of design values assigned to variables. The variable design values are obtained by calibrating their characteristic values with corresponding partial factor. Design material properties, derived from the characteristic ones, are then used in the analysis. Understandably, the non-linear analysis is carried out for extremely low strength input parameters which can lead to a non-realistic structural response or global failure mechanism. For this reason, it is not advised to rely solely on the PF format for the design.  
_Estimation of Coefficient of Variation of Resistance method (ECOV)_: In this case, one estimation of the mean and one of the characteristic resistances are calculated using the respective set of values of the material parameters. The random distribution of resistance of reinforced concrete members can be described in a first approximation by a two-parameter lognormal distribution (the use of other distributions is possible but needs an adjustment of the following equations) while these two parameters are the mean resistance and the coefficient of variation of the material property, \(V_{R}\). \(V_{R}\) is calculated according to [27] by:  
\[V_{R}=\frac{1}{1.65}\cdot ln\left(\frac{R_{m}}{R_{k}}\right) \tag{5}\]  
where \(R_{m}\) is the mean resistance value and \(R_{k}\) is the characteristic value of resistance corresponding to 5% exceedance probability. The respective global safety factor \(\gamma_{R}\) is calculated as:  
\[\gamma_{R}=\mathrm{e}^{\alpha_{R}\cdot\beta\cdot V_{R}} \tag{6}\]  
where \(\alpha_{R}\) is a constant value and is assumed to be 0.8. The safety index \(\beta\) is to be taken in accordance with the target reliability index and applicable standards.  
In this approach, the sensitivity factor of the resistance side \(\alpha_{R}\), the coefficient of variation \(V_{R}\) of the resistance side and the reliability index \(\beta\) are considered. The descriptive elements of the action side (e.g., partial safety factor \(\gamma_{E}\)) influences the consideration only indirectly via the interrelation between \(\alpha_{E}\), \(\alpha_{R}\) and \(\beta\).