# A Durability Prediction Method for Historical Square Rebar Reinforced Concrete Buildings
## 3 The Method for Determination of Critical Components
### The Finite Element Method for Components Importance Analysis  
According to the theory given above, [PERSON] et al. [29] adopted the removing component method to analyze some examples. The method proposed by them requires manual calculation or code calculation for each different case; thus, it is highly inefficient. Besides, the requirement for redistribution of the load in each calculation process for the demolition of a single component can pose negative importance values for some beam components, which causes uncertainty in identifying the engineering significance of components. In this study, the finite element method is adopted to develop the abovementioned method based on the conversion of the single complete component demolition to an element demolition, via the commercial finite element software, ANSYS. The method of reducing elastic modulus was adopted, which depends on the reduction of the concretes' elastic modulus with a considerably small coefficient. The calculation is achieved by reducing the elastic modulus of every element of the finite element, rather than a whole structural component. Many durability problems (such as local spalling of concrete, local cracking of concrete components, etc.) are local damages of structural components, rather than the total destruction of the structural component. The proposed reducing elastic modulus method based on the finite element model can much better simulate the local damage. For the removing component method, it has to handle the load redistribution as if the disappearance of a component changes the load condition of the structure locally. For the proposed reducing elastic modulus based on finite element model, it only changes the elastic modulus of a part of a structural component, which does not change the load condition of the structure locally, thus, the load redistribution can be ignored in the calculation process. The advantages of this methodology are as follows: (1) the calculation efficiency can be significantly improved by finite element software; (2) the same finite element model can be utilized for structural analyzes and component importance analysis, besides the use of finite element model can also improve the efficiency of the overall evaluation works of the building; (3) the finite element method can eliminate the negative values of some beam components, and clarify each component's importance, which is analyzed in detail in previous texts. In this paper, the calculation is achieved by the finite element model; hence, the expression should be as follows:  
\[\Gamma=\left(1-\frac{U_{0}}{U_{f}}\right)/v_{e} \tag{2}\]  
where, \(\Gamma\) is the unit volume change rate of the total strain energy of the structure, and \(v_{e}\) is the element volume. The calculation procedure is as follows: (i) constructing a finite element model of the structure according to the in-site investigation results, with the realistic cross-sectional dimensions of members and the tested material strength; (ii) calculating the total strain energy of the entire structure in the normal condition; (iii) reducing the elastic modulus of one element, and calculating the new value of total strain energy of the entire structure, obtaining the importance value of the element according to Equation (2); (iv) traveling the step (iii) to obtain the importance value for each element of the model. Figure 2 illustrates the computation procedure in detail. Figure 3 presents a calculation example from the study performed by [PERSON] et al. [29], while Figure 4 illustrates the results from the finite element method used in the current study. It is obviously shown in Figure 4 that negative importance values (in Figure 3) can be eliminated through the method of reducing elastic modulus based on the finite element model.