SUMMARY
This paper investigates the planar rocking response of an array of free-standing columns capped with a freely supported rigid beam in an effort to explain the appreciable seismic stability of ancient free-standing columns that support heavy epistyles together with the even heavier frieze atop. Following a variational formulation, the paper concludes to the remarkable result that the dynamic rocking response of an array of free-standing columns capped with a rigid beam is identical to the rocking response of a single free-standing column with the same slenderness yet with larger size, that is a more stable configuration. Most importantly, the study shows that the heavier the freely supported cap beam is (epistyles with frieze atop), the more stable is the rocking frame regardless of the rise of the center of gravity of the cap beam, concluding that top-heavy rocking frames are more stable than when they are top light. This ‘counter intuitive’ finding renders rocking isolation a most attractive alternative for the seismic protection of bridges with tall piers, whereas its potential implementation shall remove several of the concerns associated with the seismic connections of prefabricated bridges. Copyright © 2012 John Wiley & Sons, Ltd.

Planar rocking response and stability analysis of an array of free-standing columns capped with a freely supported rigid beam

Numerous existing structures exhibit rocking behavior during earthquakes, and there is a continuing need to retrofit these structures to prevent collapse. In addition, while rocking behavior is typically prevented instead of utilized, an increasing number of structures are being designed or retrofitted to allow rocking motion as a means of seismic isolation. This paper investigates the use of viscous damping to limit the rocking motion by characterizing the fundamental behavior of damped rocking structures through analytical modeling. A single rocking block analytical model is used to determine the viscous damping characteristics, which exploit the beneficial aspects of the rocking motion, while dissipating energy and preventing overturning collapse. To clarify the benefits of damping, overturning envelopes for pulse-type ground accelerations are presented and compared with the pertinent envelopes of the free rocking block. A semianalytical solution to the linearized equations of motion enables ra...

Overturning of Retrofitted Rocking Structures under Pulse-Type Excitations

Summary
A new finite element model to analyze the seismic response of deformable rocking bodies and rocking structures is presented. The model comprises a set of beam elements to represent the rocking body and zero-length fiber cross-section elements at the ends of the rocking body to represent the rocking surfaces. The energy dissipation during rocking motion is modeled using a Hilber–Hughes–Taylor numerically dissipative time step integration scheme. The model is verified through correct prediction of the horizontal and vertical displacements of a rigid rocking block and validated against the analytical Housner model solution for the rocking response of rigid bodies subjected to ground motion excitation. The proposed model is augmented by a dissipative model of the ground under the rocking surface to facilitate modeling of the rocking response of deformable bodies and structures. The augmented model is used to compute the overturning and uplift rocking response spectra for a deformable rocking frame structure to symmetric and anti-symmetric Ricker pulse ground motion excitation. It is found that the deformability of the columns of a rocking frame does not jeopardize its stability under Ricker pulse ground motion excitation. In fact, there are cases where a deformable rocking frame is more stable than its rigid counterpart. Copyright © 2016 John Wiley & Sons, Ltd.

A finite element model for seismic response analysis of deformable rocking frames

Summary
This paper extends previously developed models to account for the influence of the column and the foundation masses on the behavior of top-heavy deformable elastic cantilever columns rocking on a rigid support surface. Several models for energy dissipation at impact are examined and compared. A novel Vertical Velocity Energy Loss model is introduced. Rocking uplift and overturning spectra for the deformable elastic cantilever model excited by sinusoidal ground motions are constructed. The effects of non-dimensional model parameter variations on the rocking spectra and the overturning stability of the model are presented. It is shown that the remarkable overturning stability of dynamically excited large cantilever columns is not jeopardized by their deformability. Copyright © 2015 John Wiley & Sons, Ltd.

An analytical model of a deformable cantilever structure rocking on a rigid surface: development and verification

Summary
An argument of engineers and researchers against the use of rocking as a seismic response modification technique is that the rocking motion of a structure is chaotic and the existing models are incapable of predicting it well. This argument is supported by the documented inability of rocking models to predict the motion of a specimen excited by a single ground motion. A statistical comparison of the experimental and the numerical responses of a rigid rocking oscillator not to a specific ground motion, but to ensembles of ground motions that have the same statistical properties, is presented. It is shown that the simple analytical model proposed by Housner in 1963 is capable of predicting the statistics of seismic response of a rigid rocking oscillator.

Is rocking motion predictable

SUMMARY
This paper examines the rocking response and stability of rigid blocks standing free on an isolated base supported: (a) on linear viscoelastic bearings, (b) on single concave and (c) on double concave spherical sliding bearings. The investigation concludes that seismic isolation is beneficial to improve the stability only of small blocks. This happens because while seismic isolation increase the ‘static’ value of the minimum overturning acceleration, this value remains nearly constant as we move to larger blocks or higher frequency pulses; therefore, seismic isolation removes appreciably from the dynamics of rocking blocks the beneficial property of increasing stability as their size increases or as the excitation pulse period decreases. This remarkable result suggests that free- standing ancient classical columns exhibit superior stability as they are built (standing free on a rigid foundation) rather than if they were seismically isolated even with isolation system with long isolation periods. The study further confirms this finding by examining the seismic response of the columns from the peristyle of two ancient Greek temples when subjected to historic records. Copyright © 2011 John Wiley & Sons, Ltd.

Analysis of the rocking response of rigid blocks standing free on a seismically isolated base

This chapter summarizes the restoration–preservation of two large marble statues – those of Athena and Apollo – which decorate for the last 130 years the forefront of the main building of the Academy of Athens. Each statue rests atop a 13.65-m tall multi-drum marble column. Our study initially focuses on the restoration of the marble surfaces of the statues and their bases due to atmospheric pollution which has increased significantly during the last 20 years. Subsequently, the chapter presents the fundamental elements of the seismic response analysis and protection of the statue-multi-drum column system.

Restoration–Preservation in an Urban Environment and Seismic Stability of the Statues of Athena and Apollo Along the Forefront of the Academy of Athens

Third generation advanced high strength steels exhibit outstanding mechanical properties in tandem with the goals of higher productivity, zero carbon footprint and in service structural integrity. Study of paraequilibrium phase transformation through electron microscopy techniques, is vital to transfer modern physical metallurgy principles into upcoming production technologies and further downgauging in engineering applications [1]. Ongoing microscopical research on automotive steels with multiphase microstructure, containing retained austenite, shows that tailored thermal cycles combined with novel chemical compositions could exhibit the desired micro and nano constituents to yield enhanced mechanical properties [2]. An experimental thermal simulation was carried out on a cold-rolled and annealed low C, Mn, Al and high Si TRIP steel. Starting with ferrite-perlite microstructure, austenitisation took place at 900 o C for 120s soaking time, followed by isothermal quenching, employing critical cooling rate of 30-50 o C/s, on a molten metal bath at temperature ranging between 250 o C - 450 o C for 300s followed by water quenching at ambient. Standard metallographic preparation techniques and ion milling was employed, before examination of the microstructure via Scanning and Transmission electron microscopy. Bright field TEM imaging, electron diffraction and EDS spot microanalysis, employing parallel or convergent beam modes, took place on a TEM Jeol 2100HR unit operating at 200kV. The purpose of this experimental study is to perform a detailed microscopical characterization of metastable retained austenite, assess and quantify attained volume fractions, spatial distribution, crystallographic

TEM Characterization of Retained Austenite Stabilization on TRIP Steel

Haynes 282 (H282) is a newly developed wrought, γ  -strengthened Ni-based superalloy, suitable for the fabrication of hot section components in aircraft and land-based gas turbines, satisfying the demand for higher operating temperatures and pressures, thus resulting in improved efficiency and environmental performance. H282’s superior mechanical properties and thermal stability are established, due to its unique chemical composition permitting a standard full heat treatment (SFHT) to be applied. SFHT consists of a solution treatment (ST) at 1140°C for 2h, followed by water quenching and then a two-step precipitation treatment [1]. ST step is carefully designed, to take place above the secondary carbides’ and γ  solvus temperature (997°C), achieving significant γ matrix hardening through solid-solution strengthening. In ST of precipitation-strengthened Ni superalloys, apart from temperature and holding time, cooling rate (CR) is also of critical importance, tailoring the size, morphology, distribution, and volume fraction of γ  phase, which is principally precipitated during the second ageing step of SFHT, at 788°C. This study assesses the effect of three different CRs from ST, namely water quenching (WQ), air cooling (AC), and furnace cooling (FC), on the microstructure evolution and attained hardness of H282. The nominal chemical composition (wt.

Nikolaos Makris

Papers

Analysis of the rocking response of rigid blocks standing free on a seismically isolated base

Restoration–Preservation in an Urban Environment and Seismic Stability of the Statues of Athena and Apollo Along the Forefront of the Academy of Athens

TEM Characterization of Retained Austenite Stabilization on TRIP Steel

Effect of the Cooling Rate on the Microstructure Evolution of Haynes® 282® Ni-based Superalloy Subjected to γ′ Super-Solvus Heat Treatment