Dynamic response analysis of solitary flexible rocking bodies: modeling and behavior under pulse‐like ground excitation

Results obtained for rigid structures suggest that rocking can be used as seismic response modification strategy. However, actual structures are not rigid: structural elements where rocking is expected to occur are often slender and flexible. Modeling of the rocking motion and impact of flexible bodies is a challenging task. A non‐linear elastic viscously damped zero‐length spring rocking model, directly usable in conventional finite element software, is presented in this paper. The flexible rocking body is modeled using a conventional beam‐column element with distributed masses. This model is verified by comparing its pulse excitation response to the corresponding analytical solution and validated by overturning analysis of rocking blocks subjected to a recorded ground motion excitation. The rigid rocking block model provides a good approximation of the seismic response of solitary flexible columns designed to uplift when excited by pulse‐like ground motions. Guidance for development of rocking column models in ordinary finite element software is provided. Copyright © 2014 John Wiley & Sons, Ltd.     

Evaluation of the influence of vertical irregularities on the seismic performance of a nine‐storey steel frame

A methodology based on incremental dynamic analysis (IDA) is presented for the evaluation of structures with vertical irregularities. Four types of storey‐irregularities are considered: stiffness, strength, combined stiffness and strength, and mass irregularities. Using the well‐known nine‐storey LA9 steel frame as a base, the objective is to quantify the effect of irregularities, both for individual and for combinations of stories, on its response. In this context a rational methodology for comparing the seismic performance of different structural configurations is proposed by means of IDA. This entails performing non‐linear time history analyses for a suite of ground motion records scaled to several intensity levels and suitably interpolating the results to calculate capacities for a number of limit‐states, from elasticity to final global instability. By expressing all limit‐state capacities with a common intensity measure, the reference and each modified structure can be naturally compared without needing to have the same period or yield base shear. Using the bootstrap method to construct appropriate confidence intervals, it becomes possible to isolate the effect of irregularities from the record‐to‐record variability. Thus, the proposed methodology enables a full‐range performance evaluation using a highly accurate analysis method that pinpoints the effect of any source of irregularity for each limit‐state. Copyright © 2006 John Wiley & Sons, Ltd.     

Distribution of Matter in the Solar System

A new formula for the distribution of matter in the solar system is derived by assuming that the planets were formed from trapped particles of a cosmic dust disk attached to the Sun. Contrary to Boltzmann's distribution which predicts thermal collapse of this cloud on the Sun, it is found that if the primeval particles move on circular orbits according to Kepler's law, then their velocities obey a 2-D global Maxwellian and their distribution in space is given by p ₀ (r)=(α r ²)\exp(-α r) (Km^-1); α = 888.73 × 10⁶ Km. The form ofp ₀ (r) agrees with the observed mass distribution of the planets and explains their present large angular momentum. PACS numbers: 96.35.Cp, 96.35.Fs This revised version was published online in July 2006 with corrections to the Cover Date.     

Rainfall thresholds for flood triggering. The case of Marathonas in Greece

Basins across Mediterranean coast are often subject to rapid inundation phenomena caused by intense rainfall events. In this flash flooding regime, common practices for risk mitigation involve hydraulic modeling, geomorphic, and hydrologic analysis. However, apart from examining the intrinsic characteristics of a basin, realistic flood hazard assessment requires good understanding of the role of climatic forcing. In this work, peak rainfall intensities, total storm accumulation, average intensity, and antecedent moisture conditions of the 52 most important storms in record, during the period from 1993 to 2008, in northeast Attica, in Greece, are examined to investigate whether there is a correlation between specific rainfall conditions and flood triggering in the area. For this purpose, precipitation data from a network of five rain gauges installed across the study area were collected and analyzed. Storms totals, average intensity, antecedent moisture conditions, and peak intensities variations were calculated and compared with local flooding history. Results showed that among these rainfall measures, only peak storm intensity presents a significant correlation with flood triggering, and a rainfall threshold above which flooding becomes highly probable can be defined.     

A systematic hailpad calibration procedure for operational hail suppression in Greece

Summary Hailpads are used to provide quantitative hailfall measurements in several hail experiments and hail suppression operations around the world. The dented hailpads record the time-integrated size distribution and concentration of hailfall. In the five-year Greek National Hail Suppression Program (GNHSP) hailpad data have been used to estimate the global (impact) energy of hailswaths for the evaluation of the GNHSP.In this paper a systematic hailpad calibration procedure is developed applicable to operational programs. To meet this objective a calibration experiment has been conducted consisting of several tests to: consider differences between pad types; to examine the effects of ultra violet-light on hailpads for varying periods of time; to investigate the effect of painting and inking of the hailpad surfaces; to consider the effect of analyst's variability, loose hailpad stands, and bouneing; and to develop calibration eqqations. The concluded results seem to justify the design and performance of the hailpad calibration procedure.With 9 Figures     

Incremental dynamic analysis for estimating seismic performance sensitivity and uncertainty

Incremental dynamic analysis (IDA) is presented as a powerful tool to evaluate the variability in the seismic demand and capacity of non‐deterministic structural models, building upon existing methodologies of Monte Carlo simulation and approximate moment‐estimation. A nine‐story steel moment‐resisting frame is used as a testbed, employing parameterized moment‐rotation relationships with non‐deterministic quadrilinear backbones for the beam plastic‐hinges. The uncertain properties of the backbones include the yield moment, the post‐yield hardening ratio, the end‐of‐hardening rotation, the slope of the descending branch, the residual moment capacity and the ultimate rotation reached. IDA is employed to accurately assess the seismic performance of the model for any combination of the parameters by performing multiple nonlinear timehistory analyses for a suite of ground motion records. Sensitivity analyses on both the IDA and the static pushover level reveal the yield moment and the two rotational‐ductility parameters to be the most influential for the frame behavior. To propagate the parametric uncertainty to the actual seismic performance we employ (a) Monte Carlo simulation with latin hypercube sampling, (b) point‐estimate and (c) first‐order second‐moment techniques, thus offering competing methods that represent different compromises between speed and accuracy. The final results provide firm ground for challenging current assumptions in seismic guidelines on using a median‐parameter model to estimate the median seismic performance and employing the well‐known square‐root‐sum‐of‐squares rule to combine aleatory randomness and epistemic uncertainty. Copyright © 2009 John Wiley & Sons, Ltd.     

Robustness of simplified analysis methods for rocking structures on compliant soil

Recognizing the beneficial effect of nonlinear soil–foundation response has led to a novel design concept, termed ‘rocking isolation’. The analysis and design of such rocking structures require nonlinear dynamic time history analyses. Analyzing the entire soil–foundation–structure system is computationally demanding, impeding the application of rocking isolation in practice. Therefore, there is an urgent need to develop efficient simplified analysis methods. This paper assesses the robustness of two simplified analysis methods, using (i) a nonlinear and (ii) a bilinear rocking stiffness combined with linear viscous damping. The robustness of the simplified methods is assessed by (i) one-to-one comparison with a benchmark finite element (FE) analysis using a selection of ground motions and (ii) statistical comparison of probability distributions of response quantities, which characterize the time history response of rocking systems. A bridge pier (assumed rigid) supported on a square foundation, lying on a stiff clay stratum, is used as an illustrative example. Nonlinear dynamic FE time history analysis serves as a benchmark. Both methods yield reasonably accurate predictions of the maximum rotation θ_max. Their stochastic comparison with respect to the empirical cumulative distribution function of θ_max reveals that the nonlinear and the bilinear methods are not biased. Thus, both can be used to estimate probabilities of exceeding a certain threshold value of θ. Developed in this paper, the bilinear method is much easier to calibrate than the nonlinear, offering similar performance.     

Rolling and rocking of rigid uplifting structures

Allowing structures to uplift modifies their seismic response; uplifting works as a mechanical fuse and limits the forces transmitted to the superstructure. However, engineers are generally reluctant to construct an unanchored structure because the system could overturn due to lacking redundancy. Using a safety factor for the design of a flat rocking foundation, ie, designing it wider, goes against the main idea of this seismic modification method as the force demand for the structure increases. We propose to extend the flat base of a rocking block with curved extensions to better protect the block from overturning, yet not prevent its uplifting. After investigating the seismic response of such rocking blocks, we extend the study to investigate the seismic response of rolling and rocking frames comprising columns with curved base extensions. The equations of motion are derived, time history analyses are performed, and rocking spectra are constructed. We draw two important conclusions: (a) the response of a class of rocking oscillators with curved base extensions is equivalent to the response of a flat-base rocking oscillators of the same slenderness, yet larger size; (b) the rotation demand on two negative stiffness rocking and rolling oscillators with the same uplifting acceleration and the same size is roughly the same as long as the rocking oscillators are not close to overturning. The above findings can serve as a basis for the rational seismic design of structures supported on rocking columns with curved bases, a system that has been used since the 1960s.