## 8 Conclusions  
In this article, the effectiveness of an energy-based method for the prediction of the dynamic resistance of RC frames was verified through comparing the approximation to more complex non-linear dynamic analyses. First, the performance of the EBM was studied. The influences of damping effects and different column removal scenarios on the performance of the load-bearing capacity prediction were investigated. It was found that the response is not a single deformation mode in the case of an external column removal scenario, which may influence the performance of the EBM and the dynamic amplification factor. Model uncertainties related to the application of the EBM instead of incremental dynamic analyses (IDA) are quantified. The detailed findings are summarized as follows:  
Although no dynamic effects such as damping can be explicitly considered in the EBM, a good performance was found for the EBM to predict the dynamic capacity curve through comparison with results of the IDA. Almost identical results were obtained between the EBM and IDA curve if a damping ratio of 0% was considered, which indicated that the EBM can effectively calculate the maximum dynamic responses. Only a small difference was found between EBM and IDA results if the damping ratio is taken as 5%, which demonstrates that the damping effects have only a limited influence. Moreover, the EBM provides a conservative result for the resistance assessment.  
The EBM assumes that a structure subjected to a column removal scenario deforms in a single deformation mode. An external column removal scenario may influence the performance of the EBM and the dynamic amplification factor as its dynamic response may not be represented by a single deformation mode according to the responses in the frequency domain. However, the internal column removal scenarios were found to behave similar to SDOF dynamic systems, for which the EBM overall has a very good performance. A better performance of the EBM was observed in an internal column loss case rather than for an external column loss case.  
In order to allow for the use of the EBM as part of probabilistic failure analyses and robustness assessments, probabilistic models have been proposed for the model uncertainty of the EBM compared to the IDA. For the different removal scenarios considered as a whole, a lognormal distribution with mean of 0.98 and a standard deviation of 0.02, i.e., LN(0.98,0.02), was fitted for the ratio of the EBM resistance to the IDA resistance, while a lognormal distribution of LN(1.07,0.08) was obtained for the ratio of the EBM to IDA displacements. These values are of particular interest to be included as an additional model uncertainty in probabilistic analyses in case the EBM is applied for the quantification of alternative load path resistances considering dynamic behavior.  
The values of the model uncertainties associated with the resistances indicate a small bias and small standard deviation. This means that the EBM has a good accuracy in calculating the dynamic resistances. In contrast, a larger model uncertainty was found for the computation of the corresponding displacements, as the mean values were slightly larger than one and the standard deviations were considerably larger.  
Conceptualization, L.D., R.V.C., W.B., and R.C.; formal analysis, L.D.; funding acquisition, R.C.; investigation, L.D. and W.B.; methodology, L.D., R.V.C., W.B., and R.C.; project administration, R.V.C. and R.C.; resources, R.V.C., W.B., and R.C.; supervision, R.V.C. and R.C.; writing--original draft preparation, L.D.; writing--review and editing, R.V.C., W.B., and R.C. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the China Scholarship Council (number 201706260259).  
Not applicable.  
The authors declare no conflict of interest.