## 2 Why Strength Reduction for Large RC Structures?
### Strength Reduction
In contrast to ANFEA, SRDM-3D does not use a real constitutive concrete model, as the objective is not to replicate the exact behaviour of concrete. More specifically, the behaviour in tension is disregarded. There is no need for initiation or propagation criteria for the cracking process, as the final objective is to reach an equilibrium configuration where concrete works only in compression, and tension is resisted exclusively by embedded reinforcement. The method inherits the 'lower bound feature' of the S&T method and can be considered as an intermediate approach between ANFEA approach using sophisticated concrete modelling and simplistic 2D approach using the S&T method. The two most important ingredients of the constitutive modelling are the uni-axial stress-strain law in compression and the incompatibility law in tension (relating \(f_{c}\) to \(f_{c}^{\prime}\)). This incompatibility law must be calibrated using a reference S&T solution based on a minimum compatibility angle \(\theta_{min}\) between tension tie and compressive strut [17]. The Todeschini model was used for the uni-axial compressive stress (\(\sigma\))/strain (\(\varepsilon\)) law:  
\[\sigma=\frac{f_{c}^{\prime}\cdot\left(\frac{\varepsilon}{\varepsilon_{0}} \right)}{1+\left(\frac{\varepsilon}{\varepsilon_{0}}\right)^{2}} \tag{2}\]  
where \(\varepsilon_{c0}\) is the strain corresponding to the compressive peak taken as 0.002 in this study. The following compatibility equation from MCFT was suggested in [17], and is retained in this study:  
\[f_{c}=\frac{f_{c}^{\prime}}{0.85-0.27\frac{\varepsilon_{1}}{\varepsilon_{3}}c} \tag{3}\]  
where \(\varepsilon_{1}\) is the local concrete maximum tensile strain, \(\varepsilon_{3}\) is the local concrete minimum compressive strain, and \(c\) is the calibration factor. The value \(c\) = 0.2 was found to be consistent with a limit incompatibility angle \(\theta_{min}\) = 20\({}^{\circ}\) in the previous authors work [17] and is retained in this study. For more details about the algorithm, constitutive equations and the calibration procedure, please refer to [17]. The application of SRDM-3D method yielded compelling results demonstrating comparable robustness and conservativeness to the S&T method, while being notably more straightforward to apply to complex and 3D reinforced concrete (RC) geometries [19]. The extension of this method to the assessment context of an existing RC structure has however shown _three_ main limitations. The first is related to the iterative scheme used to assess the ultimate failure load, in the assessment mode, when non-linear constitutive laws for reinforcement are activated. Several SRDM-3D analyses must be carried out by increasing the load P, to reach a limit equilibrium configuration at the end of the reduction phase. This limit equilibrium corresponds to a critical condition of concrete in compression where the state variable \(\beta\) is close to 1.0 in some critical areas of the model (struts or nodal areas). Secondly, the generalized isotropic strength degradation scenario was more suitable for the context of designing new RC structures. For the assessment context, it is interesting to consider the effect of existing discrete cracks (e.g., originating from temperature gradients) on the final configuration of the flow of stresses. Finally, for the SRDM-3D to be used in a design code or standard, a reliability framework must be developed and should align with the current safety margins implicitly provided by existing conventional design approaches. All of these limitations will be considered in the next section through a new _enhanced Strength Reduction Assessment Methodology_ or SRAM.