Abstract
The alternative load path method is widely used to assess the progressive collapse performance of reinforced concrete structures. As an alternative to an accurate non–linear dynamic analysis, an energy–based method (EBM) can also be adopted to approximately calculate the dynamic load–bearing capacity curve or the dynamic resistance based on a static capacity curve. However, dynamic effects cannot be explicitly taken into account in the EBM. The model uncertainty associated with the use of the EBM for evaluating the dynamic ultimate capacity of structural frames has not yet been quantified. Knowledge of this model uncertainty is however necessary when applying EBM as part of reliability calculations, for example, in relation to structural robustness quantification. Hence, this article focuses on the evaluation of the performance of the EBM and the quantification of its model uncertainty in the context of reliability–based assessments of progressive or disproportionate collapse. The influences of damping effects and different column removal scenarios are investigated. As a result, it is found that damping effects have a limited influence on the performance of the EBM. In the case of an external column removal scenario, the performance of the EBM is lower as the response is not a single deformation mode according to the results in the frequency domain. However, a good performance is found in the case of an internal column removal scenario in which the assumption of a single deformation mode is found to be sufficiently adequate. Probabilistic models for the model uncertainties related to the use of the EBM compared to direct dynamic analyses are proposed in relation to both the resistances and the associated displacements. Overall, the EBM shows to be an adequate approximation, resulting in a small bias and small standard deviation for its associated model uncertainty.
Highlights
Progressive collapse triggered by extreme events is often accompanied by catastrophic losses in terms of human lives and the economy, e.g., as experienced in the 1995 Alfred P
The effectiveness of an energy–based method for the prediction of the dynamic resistance of reinforced concrete (RC) frames was verified through comparing the approximation to more complex non–linear dynamic analyses
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 energy–based method (EBM) and the dynamic amplification factor
Summary
Progressive collapse triggered by extreme events is often accompanied by catastrophic losses in terms of human lives and the economy, e.g., as experienced in the 1995 Alfred P. Considering that the EBM is an approximate approach, the quantitative assessment of the model uncertainty associated to the EBM becomes important when the EBM is applied to quantify the reliability or robustness of a RC building structure following a sudden column removal scenario. Such information regarding RC frames is currently lacking in. Sci. 2021, 11, 7492 quantitative assessment of the model uncertainty associated to the EBM becomes important when the EBM is applied to quantify the reliability or robustness of a RC buil3doifn2g3 structure following a sudden column removal scenario Such information regarding RC frames is currently lacking in the literature [19]. F y, f u, and εu are the modulus of elasticity, the yield stress, the tensile strength, and the ultimate strain of the reinforcement, respectively [44,66,73]
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