An envelope-based pushover analysis procedure is presented that assumes that the seismic demand for each response parameter is controlled by a predominant system failure mode that may vary according to the ground motion. To be able to simulate the most important system failure modes, several pushover analysesneed to be performed, as in a modal pushover analysis procedure, whereas the total seismic demand is determined by enveloping the results associated with each pushover analysis. The demand for the most common system failure mode resulting from the "first-mode" pushover analysis is obtained by response history analysis for the equivalent "modal-based" SDOF model, whereasdemand for other failure modes is based on the "failure-based" SDOF models. This makes the envelope-based pushover analysis procedure equivalent to the N2 method provided that it involves only "first-mode" pushover analysisand response history analysis of the corresponding "modal-based" SDOF model. It is shown that the accuracy of the approximate 16th, 50th and 84th percentile response expressed in terms of IDA curves does not decrease with the height of the building or with the intensity of ground motion. This is because the estimates of the roof displacement and the maximum storey drift due to individual ground motions were predicted with a sufficient degree of accuracy for almost all the ground motions from the analysed sets.
COBISS.SI-ID: 6305121
A closed-form solution of the risk equation incorporating intensity bounds is derived and analysed. The new equation, compared to the well-known risk equation developed in the 1990s, includes a correction factor, which has a value less than one if the effect of the intensity bounds is significant. The lower bound of ground-motion intensity represents a minimum ground-motion intensity, which causes a designated limit state, whereas the upper bound of ground-motion intensity is, in general, related to the physics of earthquakes, the tectonic regime, and the geology of the terrain in the region from the epicentre to the site of the building. In the paper typical values of the minimum collapse intensity and of the fragility parameters of code-conforming frames are discussed. An approximate procedure for assessing the upper bound of ground-motion intensity on the basis of ground-motion prediction models is also proposed. Finally, the procedure for seismic risk assessment is demonstrated by assessing the collapse risk for a 4-storey and a 15-storey building. It is shown that the collapse risk assessed on the basis of peak ground acceleration can be significantly affected by the lower bound of the collapse intensity, whereas the impact of the upper bound of the ground-motion intensity on the collapse risk can be more pronounced when the assessment of the collapse risk is based on the spectral acceleration at the first vibration period.
COBISS.SI-ID: 6723937
The closed-form solution for assessing the proportion of the mean annual frequency of limit-state exceedance as a function of integration limits is introduced, in order to study whether or not the mean annual frequency of limit-state exceedance is overestimated if the lower and(or)upper integration limit of the risk equation are(is) not selected in a physically consistent manner. Simple formulas for assessing the threshold value of the lower and upper integration limits are also derived. These formulas can be used to quickly assess the significant range of ground motion intensity that affects the mean annual frequency of limit-state exceedance. It is shown that the threshold values of the integration limits depend on the median intensity causing a limit-state, the corresponding dispersion and the slope of the hazard curve in the log domain. For several reinforced concrete buildings located in a region with moderate seismicity, it is demonstrated that the mean annual frequency of collapse can be significantly overestimated when assessed by integrating the risk equation over the entire range of ground motion intensity.
COBISS.SI-ID: 6420833
The concept of intensity-based assessment for risk-based decision-making is introduced. It is realized by means of the so-called 3R method (response analysis, record selection and risk-based decision-making), which can be used to check the adequacy of design of a new building or of the strengthening of an existing building by performing conventional pushover analysis and dynamic analysis for only a few ground motions, which are termed characteristic ground motions. Because the objective of the method is not a precise assessment of the seismic risk, a simple decision model for risk acceptability can be introduced. The engineer can decide that the reliability of a no-collapse requirement is sufficient when collapse is observed in the case of less than half of, for example, seven characteristic ground motions. From the theoretical point of view, it is shown that the accuracy of the method is acceptable if the non-linear response history analyses are performed at a low percentile of limit-state intensity, which is also proven by means of several examples of multi-storey reinforced concrete frame buildings. The 3R method represents a compromise between the exclusive use of either pushover analysis or dynamic analysis and can be easily introduced into building codes provided that its applicability is further investigated (e.g. asymmetric structures and other performance objectives) and that the procedure for the selection of characteristic ground motions is automated and readily available to engineers (www.smartengineering.si)
COBISS.SI-ID: 7229793
Risk-based seismic design, as introduced in this paper, involves the use of different types of analysis in order to satisfy a risk-based performance objective with a reasonable utilization rate and sufficient reliability. Differentiation of the reliability of design can be achieved by defining different design algorithms depending on the importance of a structure. In general, the proposed design is iterative, where the adjustment of a structure during iterations is the most challenging task. Rather than using automated design algorithms, an attempt has been made to introduce three simple guidelines for adjusting reinforced concrete frames in order to increase their strength and deformation capacity. It is shown that an engineer can design a reinforced concrete frame in a few iterations, for example, by adjusting the structure on the basis of pushover analysis and checking the final design by means of nonlinear dynamic analysis. A possible variant of the risk-based design algorithm for the collapse safety of reinforced concrete frame buildings is proposed, and its application is demonstrated by means of an example of an eight-storey reinforced concrete building. Four iterations were required in order to achieve the risk based performance objective with a reasonable utilization rate.
COBISS.SI-ID: 7401313