Determination of the critical angle of seismic incidence in standardised procedures for the seismic safety assessment of 3D RC buildings

This study proposes an analytical expression for the straightforward determination ofthe angle of seismic incidence that leads to the maximum structural demand ofreinforced concrete buildings when subjected to Lateral Force Analysis. The demandparameter under consideration is the maximum total displacement of single storey andisotropic multi-storey buildings, while the maximum interstorey drift may also beemployed. The proposed expression is defined based on the geometrical andmechanical characteristics of the structure. The characteristics of the seismic loadingrepresented by the elastic response spectrum are also integrated into the formulationof the expression

Proposals to account for the angle of seismic incidence when applying the PEER-PBEE methodology

The paper discusses the overall effect of the angle of seismic incidence during the seismic safety assessment of reinforced concrete buildings employing state-of-the-art methods of analysis, and provides proposals on how to account for this effect. Particularly, the Performance Based Earthquake Engineering (PBEE) methodology developed by the Pacific Earthquake Engineering Research (PEER) Centre is applied to six reinforced concrete buildings and the effect of the angle of seismic incidence is evaluated in all relevant stages of the procedure. The PEER-PBEE methodology provides a general framework for the probabilistic assessment of the seismic performance of individual buildings, it comprises four stages of analyses, and yields results that are of interest both for practitioner engineers and stakeholders. The angle of seismic incidence is involved in the second stage of the framework, which includes the structural analysis of the building, and primarily affects the resulting engineering demand parameters. Subsequently, the propagation of the effect of the angle of seismic incidence is also examined in the following two stages of the framework, which involve the damage and the loss analysis of the building. Different metrics of building performance are analysed in each stage of the framework, including two engineering demand parameters (in the structural analysis stage), the probability of collapse (in the damage analysis stage) and the expected annual loss of the building (in the loss analysis stage). Proposals to account for the angle of seismic incidence are provided based both on results obtained for each individual stage of the framework, as well as on the overall assessment procedure

Medium Earth Orbit dynamical survey and its use in passive debris removal

The Medium Earth Orbit (MEO) region hosts satellites for navigation, communication, and geodetic/space environmental science, among which are the Global Navigation Satellites Systems (GNSS). Safe and efficient removal of debris from MEO is problematic due to the high cost for maneuvers needed to directly reach the Earth (reentry orbits) and the relatively crowded GNSS neighborhood (graveyard orbits). Recent studies have highlighted the complicated secular dynamics in the MEO region, but also the possibility of exploiting these dynamics, for designing removal strategies. In this paper, we present our numerical exploration of the long-term dynamics in MEO, performed with the purpose of unveiling the set of reentry and graveyard solutions that could be reached with maneuvers of reasonable DV cost. We simulated the dynamics over 120-200 years for an extended grid of millions of fictitious MEO satellites that covered all inclinations from 0 to 90deg, using non-averaged equations of motion and a suitable dynamical model that accounted for the principal geopotential terms, 3rd-body perturbations and solar radiation pressure (SRP). We found a sizeable set of usable solutions with reentry times that exceed ~40years, mainly around three specific inclination values: 46deg, 56deg, and 68deg; a result compatible with our understanding of MEO secular dynamics. For DV <= 300 m/s (i.e., achieved if you start from a typical GNSS orbit and target a disposal orbit with e<0.3), reentry times from GNSS altitudes exceed ~70 years, while low-cost (DV ~= 5-35 m/s) graveyard orbits, stable for at lest 200 years, are found for eccentricities up to e~0.018. This investigation was carried out in the framework of the EC-funded "ReDSHIFT" project.Comment: 39 pages, 23 figure

Does the angle of seismic incidence affect inelastic seismic demand? A probabilistic point of view

Probabilistic analysis allows taking into account uncertainties that deterministic approaches usually don't permit. In this context, the uncertainty of the angle of seismic incidence is addressed and its effect on the seismic demand of buildings is examined in a probabilistic framework. Buildings comprising different configurations in-plan and in-elevation are subjected to nonlinear time history analysis with forty bi-directional ground motions. The ground motions are applied along twelve angles of incidence, which are sampled from a uniform distribution, and are further re-sampled into groups of different sizes. The seismic demand distributions of samples derived from different ground motion group sizes applied along different number of angles of incidence are compared to the demand distribution of the reference case considered to be the true demand distribution. The results show that considering more than one angle of seismic incidence always improves the result. The effect of the angle seems to be dependent on the size of the ground motion group and, from a probabilistic point of view, considering more than five angles of incidence has no significant effect on the seismic demand

The effect of the angle of seismic incidence when defining a statistical model for structural demand

Probabilistic analyses often require making assumptions concerning the statistical distribution of the variables involved. In this context, the statistical distribution of two demand parameters is examined herein when threedimensional analysis of RC buildings is performed considering multiple angles of seismic incidence. Six buildings are subjected to multi-stripe analysis with bi-directional ground motion groups of various sizes applied along one to twelve angles of incidence and datasets of demand parameters are collected. Seven statistical models are then fitted to the datasets and their performance is examined based on quantile-quantile plots and the corresponding coefficient of determination. The results show that using more than one angle of seismic incidence doesn't affect the type of demand distribution, unless highly inelastic structural response is achieved. The generalized extreme distribution exhibits a marginally higher fitting performance when compared to that of the lognormal distribution. However, due to the larger variability of the coefficient of determination of the generalized extreme value distribution when small ground motion groups are used, the lognormal distribution is preferred to fit the demand data even when multiple angles of seismic incidence are used

Seismic demand variability of RC buildings accounting for the number of ground motions and the angle of seismic incidence

According to Eurocode 8, nonlinear time history analyses can be performed using a group of 7 ground motions, applied using only one angle of incidence (ASI). Under these conditions, the mean value of the response under consideration can be used to represent seismic demand. Since it is known that, the smaller the group of ground motions, the larger the variability of the seismic demand, the variability of selected demand parameters is studied considering the effect of the number of bi-directional ground motions and the number of ASIs. Groups of ground motions of size 7 to 35 are involved in this analysis, all applied along 1 to 12 ASIs. Two demand parameters are examined and their variability is analysed in terms of acceptable risk, where risk corresponds to the probability of having a demand parameter outside preselected acceptable margins, which are defined with respect to a reference demand value. The results indicate that different demand parameters are influenced differently by the ground motion group size and the number of ASIs. Finally, it is demonstrated that an optimum combination of number of ground motions and ASIs can be selected depending on the acceptable margin that is selected

Analysing the critical orientation of seismic loading in 3D buildings: preliminary results for constant lateral forces

The angle of seismic excitation has been proven to be an important factor when analysing the 3D behaviour of buildings. However, modern earthquake-related standards only cover partially the effects of this factor and practicable results of relevant studies are still limited. The proposed paper focuses on the determination of the critical angle of incidence based on the building's structural characteristics. An analytical expression is developed to define the critical angle for the case of single storey buildings and a special category of multi storey buildings under constant lateral forces assuming linear elastic behaviour of the structures