Inelastic Range Research Articles

Control of Structural Seismic Damage in Prefabricated Reinforced Concrete Frames through Hybrid-Selfcentering Connections

Current seismic design philosophy of industrial structures in Chile aims at the protection of life and continuity of operation in the industry. The compliance with these requirements allows controlling structural damage based on resistance criteria, without detecting the failure mode or specifying its location in the event of a major seismic event. In this paper, we discuss the application of an innovative technique for controlling the structural damage in prefabricated reinforced concrete frames, which are founded on granular soils. This technique is applied in the construction of the Forest and Paper Pulp Plant Concepción. This is done by incorporating hybrid post-tensioned joints in precast columns of the project, and this approach aims to control energy dissipation in the union and maintain the initial stiffness of the system. Using a nonlinear dynamic analysis with 2D Ruaumoko software, potential performance in traditional design versus innovative design is compared. The analysis is performed for various Chilean representative seismic records and different types of soils. The results indicate that the structure with the traditional design could suffer displacement in the roof of the order of 40 cm, moving heavily into the inelastic range, with residual deformations and concentrating the damage generation of plastic hinges at the ends of the columns and some beams not designed for ductility. In contrast, the use of self-centering hybrid joints causes the structure to recover its original position, without the presence of remnant deformations.

Seismic response of combined piled raft foundation using advanced liquefaction model

The design of earthquake resistant structures founded on combined piled raft foundation (CPRF) mainly depends on raft-pile-soil interaction (RPSI). This interaction become more complex for these heavy structures, if founded on the liquefiable soil. The CPRF is considered to be useful foundation in practice to support such heavy structure; in which both raft and pile increase the bearing capacity of the soil. Where raft reduces the liquefaction induced settlement and piles help to transfer the load of the structure to the non-liquefiable soil layer. The aim of this paper is to carry out the 3D nonlinear finite difference analysis of CPRF considering the RPSI. A recently developed constitutive model i.e. CycLiq for the liquefaction modelling of the soil is utilized to represent the behaviour of sand in inelastic range which consider the cyclic behaviour and large post-liquefaction shear deformation of sand. The validation of the model is carried out with the centrifuge data. The effect of CPRF over the raft and pile group is carried out for harmonic excitation with varying frequency and earthquake motion with varying PGA. The study provides important observations and insights that were not previously evident. The findings emphasize the need to consider frequency effects, geometrical nonlinearity, and material nonlinearity in the design of NPP structures. Additionally, the study introduces the application of the CycLiq liquefaction model and the development of a user-defined material for FLAC3D. Further, the outcome shows the useful conclusion on the importance of CPRF foundation over the conventional foundation i.e. raft and pile group in the liquefiable soil. It is found that excitation frequency, ground motion PGA, porosity of sand and pile spacing of CPRF have great effects on the response.

Fibre-Based Nonlinear Viscous Damping Model Defined for Dynamic Analysis Using Distributed Plasticity Elements

ABSTRACT This paper presents a new nonlinear viscous damping model implemented in the fibre where a constitutive rule is defined between the strain rates and the damping stresses. This model is developed for nonlinear dynamic analyses using distributed plasticity frame elements with fibre cross-sections. The model is proportional to the initial stiffness of the fibre material, but the maximum damping stress is limited to avoid local and global high damping forces and prevent them from decaying or taking negative values when the structure is in the inelastic range. The manuscript details the formulation used to find the fibre strain rates, the damping forces at each level of the structure and its implementation using the Newmark method. The predictions of the model are compared with the real response of a reinforced concrete structure tested on a seismic table under high demands. Additionally, a numerical case study addressing the inelastic response of a steel structure and sensitivity analyses are presented.

Compressive Behaviors of Steel Braces with Different Sectional Shapes

AbstractSteel braces are an essential structural element to resist lateral seismic forces and widely utilized in various types of buildings. The primary source of load carrying capacity in steel braced frames is through buckling and yielding of diagonal braces. Hysteretic behaviors of steel braces exhibit unsymmetric properties in tension and compression. Especially, they show significant strength degradation when loaded into the inelastic range in compression. Therefore, the governing failure modes of steel braces shall be global buckling in compression and this phenomenon shall occur prior to brittle limit states such as net section rupture or local buckling of elements. Except for effects of material properties, most of influential parameters is strongly related to the configuration and sectional shape of steel braces. Of them, the objective of this study is to investigate effects of sectional shapes on compressive behaviors of steel braces. Especially, this study focuses on the variation in the plastic hinge rotation and residual deformation of steel braces with representative sectional shapes which are typically applied on the construction field.

Probabilistic-based discrete model for the seismic fragility assessment of masonry structures

Classical Finite-Element and Discrete-Element strategies are expensive to carry when analysing masonry structures in the inelastic range, under a seismic excitation, and considering uncertainty. Their application to the seismic fragility assessment of masonry structures through non-linear time-history analysis becomes thus a challenge. The paper addresses such difficulty by presenting an alternative probabilistic-based numerical strategy. The strategy couples a discrete macro-element model at a structural-scale with a homogenization model at a meso-scale. A probabilistic nature is guaranteed through a forward propagation of uncertainty through loading, material, mechanical, and geometrical parameters. An incremental dynamic analysis is adopted, in which several assumptions decrease the required computational time-costs. A random mechanical response of masonry is provided by numerical homogenization, using Latin hypercube sampling with a non-identity correlation matrix, and only a reduced number of representative random samples are transferred to the macro-scale. The approach was applied to the seismic fragility assessment of an English-bond masonry mock-up. Its effectiveness was demonstrated, and its computational attractiveness highlighted. Results may foster its use within the seismic fragility assessment of larger structures, and the opportunity to better analyze the effect of material and geometric-based uncertainties in the stochastic dynamic response of masonry structures.

The role of soil in structure response of a building damaged by the 26 December 2018 earthquake in Italy

Local soil conditions can significantly modify the seismic motion expected on the soil surface. In most cases, the indications concerning the influence of the underlying soil provided by the in-force European and Italian Building Codes underestimate the real seismic amplification effects. For this reason, numerical analyses of the local seismic response (LSR) have been encouraged to estimate the soil filtering effects. These analyses are generally performed in free-field conditions, ignoring the presence of superstructures and, therefore, the effects of dynamic soil-structure interaction (DSSI). Moreover, many studies on DSSI are characterised by a sophisticated modelling of the structure and an approximate modelling of the soil (using springs and dashpots at the foundation level); while others are characterised by a sophisticated modelling of the soil and an approximate modelling of the structure (considered as a simple linear elastic structure or a single degree of freedom system). This paper presents a set of finite element method (FEM) analyses on a fully-coupled soil-structure system for a reinforced concrete building located in Fleri (Catania, Italy). The building, designed for gravity loads only, was severely damaged during the 26 December 2018 earthquake. The soil was modelled considering an equivalent visco-elastic behaviour, while the structure was modelled assuming both the visco-elastic and visco-inelastic behaviours. The comparison made between the results of the FEM analyses and the observed damage is valuable. • Soil filtering phenomena are a key aspect for structure seismic response. • FEM modelling of the soil cannot ignore the dynamic properties of the bedrock. • Modelling of the structures should be performed in the inelastic range. • Earthquake damage is not necessarily a "physical" process for vulnerable buildings. • FEM analyses of DSSI must be encouraged for all buildings.

Electron dynamics in planar radio frequency magnetron plasmas: II. Heating and energization mechanisms studied via a 2d3v particle-in-cell/Monte Carlo code

The present work investigates electron transport and heating mechanisms using an (r, z) particle-in-cell simulation of a typical rf-driven axisymmetric magnetron discharge with a conducting target. Due to a strong geometric asymmetry and a blocking capacitor, the discharge features a large negative self-bias conducive to sputtering applications. Employing decomposition of the electron transport parallel and perpendicular to the magnetic field lines, it is shown that for the considered magnetic field topology the electron current flows through different channels in the (r, z) plane: a ‘transverse’ one, which involves current flow through the electrons’ magnetic confinement region (EMCR) above the racetrack, and two ‘longitudinal’ ones, where electrons’ guiding centers move along the magnetic field lines. Electrons gain energy from the electric field along these channels following various mechanisms, which are rather distinct from those sustaining dc-powered magnetrons. The longitudinal power absorption involves mirror-effect heating (MEH), nonlinear electron resonance heating, magnetized bounce heating (MBH), and the heating by the ambipolar field at the sheath-presheath interface. The MEH and MBH represent two new mechanisms missing from the previous literature. The MEH is caused by a reversed electric field needed to overcome the mirror force generated in a nonuniform magnetic field to ensure sufficient flux of electrons to the powered electrode, and the MBH is related to a possibility for an electron to undergo multiple reflections from the expanding sheath in the longitudinal channels connected by the arc-like magnetic field. The electron heating in the transverse channel is caused mostly by the essentially collisionless Hall heating in the EMCR above the racetrack, generating a strong azimuthal drift velocity. The latter mechanism results in an efficient electron energization, i.e. energy transfer from the electric field to electrons in the inelastic range. Since the main electron population energized by this mechanism remains confined within the discharge for a long time, its contribution to the ionization processes is dominant.

Electron dynamics in planar radio frequency magnetron plasmas: I. The mechanism of Hall heating and the µ-mode

The electron dynamics and the mechanisms of power absorption in radio-frequency (RF) driven, magnetically enhanced capacitively coupled plasmas at low pressure are investigated. The device in focus is a geometrically asymmetric cylindrical magnetron with a radially nonuniform magnetic field in axial direction and an electric field in radial direction. The dynamics is studied analytically using the cold plasma model and a single-particle formalism, and numerically with the inhouse energy and charge conserving particle-in-cell/Monte Carlo collisions code ECCOPIC1S-M. It is found that the dynamics differs significantly from that of an unmagnetized reference discharge. In the magnetized region in front of the powered electrode, an enhanced electric field arises during sheath expansion and a reversed electric field during sheath collapse. Both fields are needed to ensure discharge sustaining electron transport against the confining effect of the magnetic field. The corresponding azimuthal -drift can accelerate electrons into the inelastic energy range which gives rise to a new mechanism of RF power dissipation. It is related to the Hall current and is different in nature from Ohmic heating, as which it has been classified in previous literature. The new heating is expected to be dominant in many magnetized capacitively coupled discharges. It is proposed to term it the ‘µ-mode’ to separate it from other heating modes.

Influence of Post-Elastic Range Bidirectional Interaction for Various Angles of Incidence of Ground Motions on One-Story Asymmetric Structures

ABSTRACT The effect of the angle of incidence of ground motion on an asymmetric structure is recognized to be significant. However, the previous studies considered only shear wall-type elements for analyses with in-plane stiffness. These models did not capture the bidirectional structural response exhibited by column-type elements, especially in the inelastic range. A detailed investigation has been undertaken to evaluate the effect of angle of incidence on asymmetric structures considering bidirectional interaction arising in the post-yield behaviour of such lateral load-resisting elements. The study shows that bidirectional interaction is a critical design consideration for asymmetric structures.

Assessment of Torsional Amplification of Drift Demand in a Building Employing Site-Specific Response Spectra and Accelerograms

This paper aims at giving structural designers guidance on how to transform seismic demand on a building structure from two-dimensional (2D) to three-dimensional (3D) in an expedient manner, taking into account amplification of the torsional actions. This paper is to be read in conjunction with either paper #3 or #4. Torsional amplification of the drift demand in a building is of major concern in the structural design for countering seismic actions on the building. Code-based seismic design procedures based on elastic analyses may understate torsional actions in a plan of asymmetric building. This is because the inability of elastic analyses to capture the abrupt increase in the torsional action as the limit of yield of the supporting structural walls is surpassed. Nonlinear dynamic analysis can provide accurate assessment of torsional actions in a building which has been excited to respond in the inelastic range. However, a 3D whole building analysis of a multi-storey building can be costly and challenging, and hence not suited to day-to-day structural design. To simplify the analysis and reduce the scale of the computation, closed-form expressions are introduced in this paper for estimation of the Δ3D/Δ2D drift demand ratio for elastic conditions when buildings are subjected to moderate-intensity ground shaking. The drift demand of the 3D model can be estimated as a product of the 2D drift demand and the Δ3D/Δ2D drift demand ratio. In dealing with higher-intensity ground shaking causing yielding to occur, a macroscopic modelling methodology may be employed. The estimated Δ3D/Δ2D drift demand ratio of an equivalent single-storey building is combined with separate analysis for determination of the 2D drift demand. The deflection profile of the multi-storey prototype taking into account 3D effects, including torsional actions, is hence obtained. The accuracy of the presented methodologies has been verified by case studies in which drift estimates generated by the proposed calculation procedure were compared against results from whole building analyses, employing a well-established computer software.

Effect of out-of-plane displacements on the in-plane capacity of lightly precompressed rocking unreinforced masonry piers

Unreinforced masonry (URM) buildings subject to bidirectional seismic excitation are under the effects of simultaneous in-plane and out-of-plane actions. Seismic assessment carried out without considering the combined effects due to these actions could result in non-conservative capacity estimates and inadequate strengthening requirements. Bidirectional effects are not explicitly considered in the seismic assessment of existing URM buildings, owing to the limitations in existing protocols and analytical models and the simplicity achieved in performing the assessment. The current work attempts to quantify the effect of out-of-plane displacements on the in-plane capacity of masonry walls undergoing a flexural rocking mechanism of failure, thereby improving the existing understanding of bidirectional interaction in masonry structures. Response of lightly precompressed masonry piers with different aspect ratios in the presence of out-of-plane displacements, were studied experimentally and replicated using numerical and analytical studies. Results indicate that the interaction problem in URM structures should not be considered only from a force capacity reduction perspective. The force capacity reduction predicted using the interaction equations employing an exceedance of net tensile stress-based approach shall be applicable only for the flexural cracking strength and not the ultimate flexural capacity. The in-plane flexural cracking capacity reduces in proportion to the applied out-of-plane displacements when the applied out-of-plane displacements are in the elastic range. In the inelastic range of out-of-plane displacements, the ultimate flexural capacity corresponding to toe-crushing and also the initial stiffness of the pier was observed to decrease due to the reduction in net area available for compression. Also, even small range of out-of-displacements could result in inelasticity in a URM pier leading to a reduced toe-crushing capacity. Hence, it may not be conservative to define the in-plane restoring shear as the failure capacity for rocking URM piers under bidirectional loading. Accordingly, modifications are proposed for the response of masonry walls undergoing rocking mechanism.

Nonlinear time history seismic analysis of inelastic 3D frame buildings in a reduced modal space

This research investigates the formulation of a reduced modal space for the nonlinear dynamic seismic analysis of elasto-plastic 3D frame buildings. Starting from a full finite element model, the modal shapes of the reduced model for the kinematics are selected as the relevant linear elastic modes of the generalized stiffness/mass linear eigenvalue problem in terms of participation factor plus collapse mechanisms associated to appropriate static lateral loads. The internal forces are evaluated on the full model to guaranty an accurate description of the constitutive laws. The equations of motion are then projected in the modal space for the step-by-step solution by a Newmark average acceleration scheme. The advantage is that the Newton iteration of the implicit method are carried out by inverting only the reduced tangent matrix. The proposed reduction method is tested for a reinforced concrete building varying frequency content, direction and amplitude of the ground motion. Accuracy and robustness are demonstrated employing a few tens of modes, including elastic modes and plastic collapse mechanisms. The need for plastic modes for describing the structural dynamics in case of seismic actions leading to significant plastic excursions is highlighted, together with the limits of simplified approaches, as the pushover analysis, based on the hypothesis of shape conservation in the inelastic range regardless of the building regularity.

Seismic design and parametric study of steel modular frames with distributed seismic resistance

Structures in modular buildings typically have some unique characteristics as compared with conventional structures, e.g., discrete connection of modules through inter-module connections, discontinuous floor diaphragms. The behavior of steel modular structures under earthquake excitations has not been fully understood, and no seismic design method specifically tailored for modular building structures is available. Moreover, although various inter-module connections with different rotational connectivity have been proposed, their suitability for seismic application is questionable. In this paper, the distributed seismic design method, which makes use of the lateral resistance inherent in all modules, was proposed for modular buildings with steel frames. A numerical parametric study was conducted on a 9-story prototype building. The effect of three parameters, i.e., the rotational stiffness of inter-module connections, the seismic design force level, and the height-wise distribution of the design base shear, were studied. The results show that the rotational stiffness of inter-module connections has limited impact on the elastic lateral stiffness and the fundamental period of modular steel frames. However, in the inelastic range, the increase in the rotational stiffness will lead to less plastic drift concentration and better collapse prevention performance. Increasing the seismic design force may not result in enhanced collapse prevention performance, as it is also dependent on the height-wise distribution of the design base shear and if significant higher-mode response is involved in the total response of the structure.

Axial behavior of basalt FRP-confined reinforced concrete columns with square sections of different corner radii

Axial compressive tests were conducted on fourteen BFRP-confined square reinforced concrete (RC) columns, involving variations of the corner radius and FRP layers. The test results demonstrate thatthe Basalt-FRP confinement leads to strength improvement, such as 109% gain at a corner radius ratio of 0.6, and also improves the ductility of the RC column. The stress–strain response has a bilinear type, and the difference in confinement level is mainly reflected in the inelastic range. Furthermore, the observation of the distribution of hoop strain values shows that the confinement pressure uniformity increases with thecornerradius. Finally, a prediction equation for the strain efficiency factor is proposed to improve the accuracy of existing square section strength models. A modified strength model of Wu and Zhou shows good agreement with the experimental results.

Yielding and buckling behavior of aluminium and steel shear panels with different slenderness ratios

The present study investigates the effects of material mechanical properties and plate slenderness ratios on the nonlinear and cyclic behavior characteristics of metal shear panels (including carbon steel (CS), low yield point steel (LYP160) and aluminium (AL)), using the finite element method. The plates are first qualitatively and quantitatively classified into the five groups of very slender, slender, moderate, stocky and very stocky, regarding their slenderness ratios. Very slender plates have negligible buckling capacity and thus, they buckle at the initial stages of loading. Slender plates buckle in the elastic range of behavior. Moderate plates buckle in the inelastic range of stresses before material yielding occurs in the plates. Stocky plates buckle in the plastic (post-yield) range of stresses. The behavior of very stocky plates is only dominated by yielding phenomenon and they do not buckle during loading. Based on the statistical analysis of results, new relationships for estimation of inelastic and plastic buckling loads are also proposed. The cyclic analysis results show that the energy dissipation capability of very stocky/stocky/moderate plates is solely dependent on the material yield stress and elastic modulus of elasticity, whereas for the slender plates, the effectiveness of material yield stress in the energy dissipation of plates is decreased and the role of the material elastic modulus of elasticity becomes more important. In the case of very slender shear plates, the energy dissipation capability seems to be dependent on the initial and secondary modulus of material only.

A new modal lateral load pattern for improving pushover analysis to estimate nonlinear responses of structures

ABSTRACT Pushover analysis is a nonlinear procedure that is widely used as the primary tool for the nonlinear analysis of structures. In the conventional pushover method, the fundamental mode of the structure is selected as the dominant response mode of the multi degree of freedom (MDOF) system while neglecting the influence of higher modes. It has been proved that for many structures, higher vibration mode effects should be considered to boost the outcomes of the pushover analysis. In this study, a new Modal Load Pattern (MLP) is developed to improve pushover analysis procedure in estimating nonlinear responses of structures. For this purpose, MLP is defined by the directed algebraic combination of the weighted vibration mode-shape vectors of the structure. The weights of modes are determined using an optimisation algorithm such that the difference between the nonlinear responses of the structure under MLP and1 those of nonlinear time-history analysis is reduced to the minimum possible value. Comparing the outcomes of MLP with some well-known lateral load distributions shows that the proposed method increases the accuracy of responses resulting from pushover analysis. It is illustrated that against elastic behaviour, in the inelastic range of structural behaviour, it is likely that higher modes have a significant effect on the optimal lateral load distribution.

Effects of the excited states on electron kinetics and power absorption and dissipation in inductively coupled Ar plasmas

The effects of the excited states on electron kinetics as well as plasma power absorption and dissipation are numerically studied in radio frequency low-pressure inductively coupled Ar plasmas. The model used in this work is based on the coupling of the kinetic module, the electromagnetic field module, and the global model module. The existence of excited states caused by the electron-impact excitations of the ground state of Ar decreases the electron temperature due to the significant depletion of the electron energy probability function in the inelastic energy range. The reduction in electron temperature decreases the power dissipation of an electron per unit volume and, therefore, increases the electron density for the fixed total power. The profile and maximum variations of the absorption power density indicate that the increased electron density suppresses the power deposition deeper into the plasma with inclusion of the electron-impact excitations of the ground state to excited states of Ar. However, the collision processes involving the excited states as reactants hardly affect the electron kinetics and electromagnetic field properties due to far lower densities of the excited states than that of the ground state of Ar.

The transfer function method reveals how age‐structured populations respond to environmental fluctuations with serious implications for fisheries management

AbstractFluctuations in wild fish populations result from interaction between population dynamics and environmental forcing. Age‐structured populations can magnify or dampen particular frequencies of these fluctuations, depending on life cycle and species traits. The transfer function (TF) gives a detailed analytical description of these phenomena. In this study, we derive a generalized form of TF to investigate the fluctuations of fish populations in response to species traits and environmental noise characteristics. We found that for semelparous species, fluctuations in fish stocks log‐size are directly proportional to the recruitment elasticity and inversely proportional to the age of maturity, and for iteroparous species, fluctuations in fish stocks log‐size are inversely proportional to the adult lifespan. In addition to the already known effect of cohort resonance (increased sensitivity to environmental fluctuations on cohort timescales in the elastic range of recruitment elasticity), we find a stock resonance effect (increased sensitivity to environmental fluctuations on double cohort timescales in the inelastic range of recruitment elasticity). These results were then applied to fisheries management. The relationship between fishing mortality and species‐specific variability of fish stocks was formalized. In accordance with this analysis, precautionary levels for different catches were estimated.

Parametric analysis of mast guys within the elastic and inelastic range

Parametric analysis of mast guys within the elastic and inelastic range

Thermal Fatigue Life Prediction of BGA Solder Joint Incorporating Microstructural Coarsening Effect due to Thermal Diffusion.

A creep constitutive equation incorporating the effect of microstructure coarsening was introduced into the Finite Element Method analysis using a user subroutine to predict thermal fatigue life of solder joint. Dispersed particles in the microstructure grew due to thermal diffusion with increasing fatigue cycles, which resulted in the inelastic strain range and the inelastic strain energy density range increased. This increase in the inelastic strain range reduced the fatigue life by approximately 77% compared to the case where no microstructure coarsening effect was incorporated. Thus, it is necessary to incorporate the microstructure coarsening effect in the fatigue analysis of solders. Thermal fatigue life was found to be significantly affected by the microstructure coarsening effect. Thus, it is necessary to incorporate the microstructure coarsening effect in the fatigue analysis of solders.