The evaluation of structural collapse capacity is an integral part of the estimation of collapse risk in performance based earthquake engineering. Several methods and procedures have been proposed in the past to quantify collapse capacity. However, there is no clear consensus on which method is most appropriate. Recently physics-based collapse criteria have been proposed, but their effectiveness is yet to be compared with codes of practice. In order to ensure safety and consistency, different code/standard based recommendations enforce the use of thresholds predominantly in terms of the engineering demand parameter (EDP) for the performance level of collapse prevention. These thresholds serve as limit-state criteria to evaluate the collapse capacity of a structure. This paper compares several performance measures that are derived using different criteria to understand their impact on the final collapse risk estimates. Four different criteria are studied, two of which are based on standards, and the other two are physics-based, which use energy formulations. Three different ASCE 7-16 code conforming RC buildings are designed and analysed. The effects of modelling uncertainties and of the ground motion spectral shape have been considered to impart more confidence in the results. The collapse risk estimates are interpreted in terms of different collapse performance measures. The estimates derived from all the four criteria are compared. It was found that the collapse risk is significantly affected by the choice of the criterion. For the same collapse risk, the physics-based criteria allow higher ultimate deformation at collapse. On the other hand, the code/standard based criteria tend to be conservative as they censor the deformation response of the structure using upper bound thresholds. It was also found that the physics-based criteria could underestimate the collapse risk, yet they can still be employed to produce more economical designs.

In performance-based earthquake engineering design, quantification of the collapse capacity of a structure is of paramount requirement for the development of collapse fragility models. Different methods for predicting collapse provide varying estimates. Consequently, performance design is highly sensitive to the method employed to quantify the collapse capacity. Recently, new energy-based methods have emerged as alternatives to the conventionally used criterion with the aim of objectively quantifying structural collapse. Although these new energy-based criteria are much more robust than the conventional ones, they inherently rely on the occurrence of large deformations. This makes them lagging indicators of collapse resulting in un-conservative results. Moreover, they mainly focus on describing P–Δ instability governed collapse mechanisms, which typically occur in ductile structures. As an improvement, this study presents a new power balance-based numerical collapse criterion that tracks the rate at which energy is supplied and dissipated in the structure. It acts as a leading indicator and successfully predicts seismic collapse in framed structures under both gravity load and sidesway collapse mechanisms. This is illustrated using a wide range of validated collapse simulations. It is found that the probability of collapse predicted using the power criterion falls between that derived from the IM/DM (intensity measure/damage measure) based rules and the energy-based criterion.

The development of collapse fragility curves is an essential requirement for the assessment of the collapse risk of structures. These fragility curves depend on the structural collapse capacity that is evaluated in terms of either the intensity measure (IM) or the damage measure (DM); such as the engineering demand parameter (EDP). In turn, collapse capacity estimates are sensitive to the method employed for their assessment. Conventionally, the IM and DM rules are employed in conjunction with incremental dynamic analyses (IDA) to quantify the collapse capacity of a structure. However, this approach has been criticised for being subjective in nature, since it depends on the structural response approaching predetermined threshold values. Therefore, it does not relate to the actual dynamic instability. Although the selection of these thresholds stems from the results of experimental investigations and equivalent numerical models and serve as an indirect check for dynamic instability, the present study seeks to provide a mathematical basis for defining collapse criteria. A dynamical system approach is used to formulate a mathematical criterion for defining P-Delta instability induced seismic collapse in single-degree-of-freedom (SDOF) structures. The non-linear SDOF structure is considered as a non-autonomous, non-smooth system, and is studied as an ensemble of different sub-systems. Collapse is defined as the point when the dominant system eigenmode of the structure changes from stable to unstable, and remains unstable as the structure collapses. This approach can be applied to first mode governed multi-degree-of-freedom (MDOF) structures when studied as an equivalent SDOF structure. It is found that the dynamical systems approach results in higher deformations at collapse when compared to the conventional IM/DM rule based approach, suggesting the conservatism involved in the latter. However, it results in lower deformations at collapse when compared to the energy criterion, which relies on the occurrence of large deformations to predict collapse. Furthermore, the derived fragility curves show that the proposed approach yields lower probabilities of collapse when compared to the conventional method. Therefore, the proposed method can be used an alternative method for the performance design of structures.

Construction in earthquake prone areas is an expensive task, as the structural design warrants high material consumption. This is partly due to the fact that the seismic design philosophy is based on the concept of stability through energy dissipation. The energy dissipation is conventionally achieved by controlled plastifi-cation and hysteresis of the structural elements that require high quantities of reinforcements and sophisticated detailing, in both steel and concrete structures. Further, due to inherent uncertainty in the occurrence and the characteristics of earthquakes and also in the current simulation models, a conservative design is essential that can provide a sufficient margin of safety against failure. In the last two decades, however, there is a push towards developing performance designs. This new evolved philosophy of seismic design aims to quantify the uncertainties and the unknown aspects of the design to reduce the margins of safety, while sustaining equally high reliability. As a result, this leads to designs with low requirements of material consumption, thereby making them economic. Consequently, the complexity in the design process increases in almost every aspect, right from quantification of uncertainty by performing Monte-Carlo simulations to developing high-fidelity models that can incorporate all forms of non-linearity in the design. Moreover, to reduce the margins of safety, it becomes imperative to accurately estimate the point of failure or structural collapse capacity. However, currently under the Performance Based Earthquake Engineering (PBEE) framework, the collapse capacity is not evaluated corresponding the the actual dynamic instability in the structural system. Instead, it is estimated corresponding to subjective threshold values of engineering demand parameters, such as lateral deformation. Therefore, in the current paper, a novel-approach is presented that uses dynamical system theory for evaluat-ing dynamic instability in a structure that can be used to accurately estimate its collapse capacity. A P-Delta instability is the dynamic instability that occurs when gravity loads magnify the force demand due to the ge-ometry of the deformed structure, leading to high overturning moments on the base. This is widely studied under mainstream structural analysis. For simplicity, a single-degree-of-freedom (SDOF) system is studied. Therefore, the current work is targeted towards the structures that can be idealised as an SDOF system. The dynamic instability leading to “structural collapse” is defined when the real part of the dominant eigenvalue of the oscillator system becomes positive and remains positive until large deformations occurs. The current study uses harmonic excitations for evaluating dynamic instability and therefore acts as a precursor to a larger study aimed at evaluating mathematical instability in structures under the effects of seismic ground motions.