# A Parametric Computational Study of RC Building Structures under Corner-Column Removal Situations
## 4 Discussion
### Dynamic Amplification and Load Increase Factors (DAFs and LIFs)  
The scientific community and the international codes [36; 37] proposed different types of factors to simplify building structure calculations in extreme events-accidental situations. These factors multiply the applied load to obtain an equivalent load to avoid more complex calculations such as  
Figure 15: Influence of different parameters on bending moments from P2 to P3 in the second slab: (**a**) tensile strength, (**b**) flexural reinforcement ratio, (**c**) number of floors, (**d**) column removal time, (**e**) superimposed load. those considering dynamic effects and non-linear material behaviour. The present study focused in two groups: (i) factors applied to simplified non-linear static calculations to address dynamic effects and (ii) factors applied to simplified linear static calculations that consider both material nonlinearities and dynamic effects. The former group of factors can be called Dynamic Amplification Factors (DAFs) [36], while the latter are called Load Increase Factors (LIFs) [27; 37]. In this work, both DAFs and LIFs have been computed in the processed models for the parametric study, and both were determined for the displacements and the loads as suggested by codes (e.g., DoD [37]). In displacements, the \(\mathrm{DAF}_{\mathrm{LD}}\) and \(\mathrm{LIF}_{\mathrm{LD}}\) were computed as the difference in the maximum displacement on the top of the removed column (P3) between a static-nonlinear or static-linear and a dynamic-nonlinear FE model, respectively. In the forces, the \(\mathrm{DAF}_{\mathrm{LF}}\) and \(\mathrm{LIF}_{\mathrm{LF}}\) were computed as the difference in the axial force of columns P2/P6 between a static-nonlinear or static-linear and a dynamic-nonlinear FE model, respectively. Table 7 shows the results obtained. DAF\({}_{\mathrm{LD}}\) values in general were between 1.80 and 2.70, which can be considered consistent with test results, theoretical considerations and codes [27; 28; 37]. The lower values obtained within this range are related to stiffer models where the dynamic amplification was lower and where damping was higher; for a single degree of freedom system with 7.3% damping (test value), the theoretical \(\mathrm{DAF}_{\mathrm{LD}}\) is 1.79, which is similar to that obtained in M_Ref. The low value of \(\mathrm{DAF}_{\mathrm{LD}}\) in M_crt0.2 was due to the slow removal of the column (i.e., low dynamic amplification). The higher values obtained for \(\mathrm{DAF}_{\mathrm{LD}}\) were predicted in models with parameter leading to higher deformations, accelerations and lower damping effects. In such cases, \(\mathrm{DAF}_{\mathrm{LD}}\) was larger than 2, which could be justified on (a) undesired overly stiff numerical response predicted by the static nonlinear models and (b) valid theoretical considerations, i.e., as shown in [13], for a single degree of freedom system with nonlinear parabolic response and no damping, the \(\mathrm{DAF}_{\mathrm{LD}}\) is larger than 2 (e.g., 10% or higher depending on the curvature of the parabola). The uncommonly high value of \(\mathrm{DAF}_{\mathrm{LD}}\) in M_q9 was due to the formation of a yield line mechanism in the slab leading to development of plastic deflections captured in the dynamic nonlinear analysis. In this case, the values of DAFs and LIFs are strongly influenced by the flexural capacity of the slab, as shown by the yield lines in Figure 11e. It should be noted that values of \(\mathrm{LIF}_{\mathrm{LD}}\) are always higher because material non-linear effects are included in the factor besides the dynamic effects. The \(\mathrm{DAF}_{\mathrm{LF}}\) and \(\mathrm{LIF}_{\mathrm{LF}}\) values are not significantly different, and they are also relatively constant with changes in the parameters in the study.