Initial Eccentricity Research Articles

Post-fire behaviour and capacity of high strength concrete-filled high strength steel tube (HCFHST) stub columns under combined compression and bending

The post-fire behaviour and capacity of high strength concrete-filled high strength steel tube (HCFHST) stub columns under combined compression and bending have been investigated through testing and numerical modelling and reported in this paper. Eccentric compression tests were conducted on eight square HCFHST stub column specimens after exposure to the ISO-834 standard fire for 15 min, 30 min, 45 min and 80 min and two reference specimens at ambient temperature. The test results, including the load–deformation response at each load stage as well as the confinement effect, the ductility index, the evolution of the neutral axis, the effect of heating duration and the effect of initial loading eccentricity, were discussed. Numerical simulations were then carried out, where thermal and mechanical finite element models were developed and validated against the test results and afterwards used to perform parametric studies to generate further numerical data over a wide range of cross-section dimensions and loading combinations. Given that there are no established design codes for composite structures after exposure to fire, the relevant ambient temperature design rules were evaluated, using post-fire material properties, for their applicability to post-fire HCFHST stub columns under combined compression and bending, based on the test and numerical data. The evaluation results revealed that the European code, American specification and Australian/New Zealand standard result in relatively accurate and consistent post-fire residual resistance predictions.

Slenderness Ratio Effect on the Eccentric Compression Performance of Chamfered Laminated Bamboo Lumber Columns

Eccentric compression tests on 15 chamfered laminated bamboo lumber (LBL) columns with a height ranging from 600 to 3000 mm were conducted in order to study the eccentric mechanical performance. The failure of all specimens was caused by the crack of bamboo fiber in the tensile region. When the ultimate strength was reached, except specimens with a height of 600 mm, all other specimens could bear large deformation, showing good ductility. The lateral displacements of the specimens under eccentric compression were approximately parabolic in the direction of column height. The ultimate bending moment of LBL columns with different slenderness ratios under compression with the same initial eccentricity was a fixed value. The relationship between ultimate capacity, axial displacement, lateral displacement, and slenderness ratio was analyzed based on test results. It was found that the plane section assumption could be used to express the stress and strain distribution of chamfered LBL columns under eccentric compression. A method for calculating the ultimate bearing capacity was proposed using a constitutive model based on the Ramberg-Osgood relation and the empirical formula for calculating the ultimate capacity was given on the basis of the former research as well as the test results in this paper.

Studying light flavour hadrons produced in the collision of different nuclei at the LHC

The study of identified particle production as a function of event multiplicity is a key tool for understanding the similarities and differences among different colliding systems. Now for the first time, we can investigate how particle production is affected by the collision geometry in heavy-ion collisions at the LHC. In these proceedings, we report newly obtained ALICE results on charged and identified particle production in Pb–Pb and Xe–Xe collision at √SNN = 5.02 and √SNN = 5.44 TeV, respectively, as a function of transverse momentum (pT) and collision centrality. Particle spectra and ratios are compared between two different colliding systems at similar charged-particle multiplicity densities (〈dNch/dη〉), and different initial eccentricities. We find that in central collisions, spectral shapes of different particles are driven by their masses. The pT-integrated particle yield ratios follow the same trends with 〈dNch=dη〉 as previously observed in other systems, further suggesting that at the LHC energies, event hadrochemistry is dominantly driven by the charged-particle multiplicity density and not the collision system, geometry or center-of-mass energy.

Fatigue crack paths in eccentric circumferentially cracked round bar (CCRB) subjected to tensile cyclic loading

In this paper, a numerical modelling was developed to study (on the basis of the Paris law) the fatigue propagation paths of eccentric external cracks in circumferentially-cracked round bars (CCRB) subjected to axial displacement. Results demonstrate how the eccentricity (in relation to the wire axis) of the circular resistant ligament increases with the fatigue crack growth. This phenomenon is favoured by the increment of the initial ligament eccentricity (for an initial ligament diameter) and the increase of the Paris exponent m of the material.

The Ice Coverage of Earth-like Planets Orbiting FGK Stars

Abstract The photometric and spectroscopic signatures of habitable planets orbiting FGK stars may be modulated by surface ice coverage. To estimate its frequency and locations, we simulated the climates of hypothetical planets with a 1D energy balance model and assumed that the planets possess properties similar to modern Earth (mass, geography, atmosphere). We first simulated planets with fixed rotational axes and circular orbits, finding that the vast majority (≳ 90%) of planets with habitable surfaces are free of ice. For planets with partial ice coverage, the parameter space for ice caps (interannual ice located at the poles) is about as large as that for “ice belts” (interannual ice located at the equator), but belts only persist on land. We then performed simulations that mimicked perturbations from other planets by forcing sinusoidal orbital and rotational oscillations over a range of frequencies and amplitudes. We assume initially ice-free surfaces and set the initial eccentricity distribution to mirror known exoplanets, while the initial obliquity distribution matches planet formation predictions, i.e., favoring 90°. For these dynamic cases, we find again that ∼90% of habitable planets are free of surface ice for a range of assumptions for ice’s albedo. Planets orbiting F dwarfs are three times as likely to have ice caps than belts, but for planets orbiting K and G dwarfs ice belts are twice as likely as caps. In some cases, a planet’s surface ice can cycle between the equatorial and polar regions. Future direct imaging surveys of habitable planets may be able to test these predictions.

Experimental Investigation and Design of Hollow Section, Centrifugal Concrete-Filled GFRP Tube Columns

The compressive response of hollow section, centrifugal concrete-filled GFRP tube (HS-CFGT) members is examined experimentally and reported analytically in this paper. A total of 17 specimens separated into two groups were tested; the specimens in each group were of four different lengths and included thirteen straight columns and four tapered columns. The details of the test rigs, procedures as well as key test observations composed of ultimate-moment capacities, load-displacement curves, and failure modes were truthfully reported. The test results were analyzed to evaluate the influence of initial eccentricity on the structural performance. Therefore, the aim of this paper is: (1) to propose a proper coefficient, φe, reflecting the effect of initial eccentricity based on the Chinese design code; and (2) to determine a new confinement coefficient, kcc = 1.10, for centrifugal concrete confined by GFRP tubes. Comparisons of the present design codes and specifications of confined concrete members with test results on 17 full-scale tube columns are also presented. Accordingly, new design equations, whose predictions generally agree well with the test results, are recommended to estimate the compressive capacity of the proposed HS-CFGT columns.

Residual eccentricity of inspiralling orbits at the gravitational-wave detection threshold: Accurate estimates using post-Newtonian theory

We use equations of motion containing gravitational radiation-reaction terms through 4.5 post-Newtonian order to calculate the late-time eccentricities of inspiraling binary systems of non-spinning compact bodies as they cross the detection threshold of ground-based gravitational-wave interferometers. The initial eccentricities can be as large as 0.999. We find that the final eccentricities are systematically smaller than those predicted by the leading quadrupole approximation, by as much as 30 percent for a 300 solar mass binary crossing the LIGO/Virgo detection threshold at 10 Hz, or eight percent smaller for a 60 solar mass binary. We find an analytic formula for the late-time eccentricity that accurately accounts for the higher-order post-Newtonian effects, generalizing a formula derived by Peters and Mathews in the 1960s. We also find that the final eccentricities are independent of the ratio of the masses of the two compact bodies to better than two percent.

Dynamical orbital evolution scenarios of the wide-orbit eccentric planet HR 5183b

ABSTRACT The recently discovered giant exoplanet HR5183b exists on a wide, highly eccentric orbit (a = 18 au, e = 0.84). Its host star possesses a common proper-motion companion which is likely on a bound orbit. In this paper, we explore scenarios for the excitation of the eccentricity of the planet in binary systems such as this, considering planet–planet scattering, Lidov–Kozai cycles from the binary acting on a single-planet system, or Lidov–Kozai cycles acting on a two-planet system that also undergoes scattering. Planet–planet scattering, in the absence of a binary companion, has a $2.8{-}7.2{{\ \rm per\ cent}}$ probability of pumping eccentricities to the observed values in our simulations, depending on the relative masses of the two planets. Lidov–Kozai cycles from the binary acting on an initially circular orbit can excite eccentricities to the observed value but require very specific orbital configurations for the binary and overall there is a low probability of catching the orbit at the high observed high eccentricity ($0.6{{\ \rm per\ cent}}$). The best case is provided by planet–planet scattering in the presence of a binary companion: here, the scattering provides the surviving planet with an initial eccentricity boost that is subsequently further increased by Kozai cycles from the binary. We find a success rate of $14.5{{\ \rm per\ cent}}$ for currently observing e ≥ 0.84 in this set-up. The single-planet plus binary and two-planet plus binary cases are potentially distinguishable if the mutual inclination of the binary and the planet can be measured, as the latter permits a broader range of mutual inclinations. The combination of scattering and Lidov–Kozai forcing may also be at work in other wide-orbit eccentric giant planets, which have a high rate of stellar binary companions.

Experimental study on the behavior of eccentrically compressed reinforced concrete columns strengthened with CFRP composite sheets

Strengthening of reinforced concrete (RC) columns is needed when the actual load-carrying capacity of the columns does not reach the required level due to either structural deterioration or increasing acting loads. This experimental study aims to evaluate the strengthening effect on the eccentrically-compressed RC columns using Carbon fiber reinforced polymer (CFRP) sheets, that confine around the column cross-section. Three RC column specimens with the same geometrical dimensions, reinforcement detailing, and concrete compressive strength were cast and tested in the current experimental investigation. One RC column without being strengthened is referred as the control specimen whereas two other RC columns were partially strengthened by CFRP sheets. All three RC columns were axially loaded with the same initial eccentricity e0 of 80 mm. Based on the test results such as the ultimate load-carrying capacity, the load-rotation relationship, and load-curvature at the middle of column height, the effectiveness of the strengthening technique is discussed.

Modeling of Cross-Laminated Timber (CLT) panels loaded with combined out-of-plane bending and compression

Rolling shear is one of the major concerns that significantly impact the performance of CLT walls if they are subjected to combined out-of-plane bending and compression loads. Because the effects of rolling shear and out-of-plane bending are coupled to each other, prediction of the load-carrying capacity of CLT wall is always a challenge for the design of CLT structures. Current design codes employ an Ayrton-Perry type interaction equation as the failure criterion to check the safety of a CLT panel loaded with combined bending and compression. Nevertheless, there is no model available to predict their load-carrying capacity. The presented work aims at developing an analytical model to predict the load-carrying capacity of CLT wall loaded with combined out-of-plane bending and compression. In total 12 five-layer CLT panels loaded with different initial load eccentricities were tested to investigate the failure modes. Observed during the test were two ultimate failure modes, i.e., compression crush on the concave side and tension rupture in convex side. Based on these failure modes and deeming the test member as a beam-column, an analytical model which takes rolling shear effects into account to predict the load-carry capacity of CLT compression-bending members was developed. An explicit formula based on compression failure mode was proposed. The model is capable of determining the distribution of rolling shear stress along longitudinal direction, rolling shear-induced axial force and moments in CLT beam-columns. By calculating the load-carrying capacities of the specimens tested in this study as well as the additional three- and seven-layer specimens tested by another studies, it was found that the compression failure mode-based formula can provide good agreements with the test results.

Local buckling of S960 ultra-high strength steel welded I-sections subjected to combined compression and major-axis bending

This paper presents an in-depth experimental and numerical investigation into the local buckling behaviour of S960 ultra-high strength steel welded I-sections under combined compression and bending moment about the major principal axis. Two I-sections (I-120 × 120 × 6 and I-150 × 75 × 6) were considered in the experimental investigation, and for each I-section, five eccentrically loaded stub column tests were conducted under different initial loading eccentricities. The experimental results were then adopted in a numerical investigation for validating finite element models, by means of which parametric studies were conducted to generate additional numerical data over a wide range of cross-section dimensions and initial loading eccentricities (i.e. loading combinations). The obtained experimental and numerical results were used to evaluate the applicability of the relevant design interaction curves, as set out in the European code, American specification and Australian standard, to S960 ultra-high strength steel welded I-sections under major-axis combined loading. The evaluation results revealed that (i) the European code results in safe but slightly conservative failure load predictions, (ii) both the American specification and Australian standard lead to relatively accurate failure load predictions and (iii) all the three design codes offer a good level of design consistency.

Press-braked stainless steel channel sections under major-axis combined loading: Tests, simulations and design

This paper reports an experimental and numerical investigation into the cross-section behaviour and resistances of press-braked stainless steel channel sections under combined compression and major-axis bending moment. A testing programme was firstly conducted, including initial local geometric imperfection measurements and major-axis eccentric compression tests on ten press-braked stainless steel channel section stub column specimens. Following the testing programme, a numerical modelling programme was performed, where finite element models were developed and validated against the test results and then adopted to perform parametric studies to generate further numerical data over a wide range of cross-section dimensions and initial loading eccentricities. Based on the obtained test and numerical data, the existing design interaction curves, as given in the European code, American specification and Australian/New Zealand standard, were assessed and shown to result in conservative cross-section resistance predictions for press-braked stainless steel channel sections under major-axis combined loading. The conservatism of the codified design interaction curves stems from the conservative end points (i.e. cross-section resistances under pure compression and pure bending), which are determined without considering the effect of material strain hardening, and the inefficient linear shape, which ignores the effect of stress redistribution. Improved design interaction curves were proposed through the adoption of (i) more accurate end points, which are calculated with a rational exploitation of material strain hardening by continuous strength method and (ii) more efficient nonlinear shape, which allows for the stress redistribution. The proposed design interaction curves were shown to result in substantially more accurate resistance predictions for press-braked stainless steel channel sections under major-axis combined loading than their codified counterparts. The reliability of the proposed design interaction curves was confirmed by means of statistical analyses.

Simplified design procedures for the structural analysis of reinforced concrete columns in fire

Simple analytical procedures are described to predict the structural behavior (axial displacements and failure) of reinforced concrete (RC) columns exposed to fire. The analyses assume a concentric load (no initial eccentricity) or an equivalent axial load to take into account first and second order effects. The main objective is to provide reliable and straightforward tools for a preliminary assessment of the structural integrity of RC columns. The procedures compute the total displacements and the failure (time and type) of RC columns with different concrete strengths (normal to ultra-high performance), shapes, fire incidences, load levels and initial eccentricities. The results of 24 experimental tests from different authors are predicted and compared with the analytical solution. The displacements are estimated by the introduction of EN 1992-1-2 (2004) stress–strain curves and a simplified bilinear constitutive law that takes into account the Load Induced Thermal Strain (LITS) as a reciprocal to the modulus of elasticity. In general, a good agreement with the experimental time vs. displacement curves was obtained. Failure is predicted with the adoption of the nominal stiffness method (EN 1992-1-2, 2004) to take into account the second order effects. Sectional analyses (axial-bending equilibrium) and simplified analytical procedures assuming an equivalent axial load replacing the axial-bending force (force equilibrium) are carried out. The results of both analyses were very close, indicating the reliability of the simplified procedure. The prediction of the fire resistance time demonstrated a good approximation, on the safe side, with the experimental data. The results are compared with the EN 1992-1-2 (2004) prescriptive formula.

Weight optimization of stainless‐steel built‐up structural elements

AbstractThis paper describes the use of stainless‐steel as a structural material, discusses current structural design considerations, reviews recent research work, and highlights important findings and developments.Over the past 25 years, structural design codes for stainless‐steel have been introduced or substantially altered or are still being modified, while at the same time there is a growing interest in the use of stainless‐steel in construction. Realistic modeling of structural elements of stainless‐steel plays an important role in the analysis and design of steel framed structures. Structural element modeling and optimization using stainless‐steel, in case a built‐up column, can contribute to existing research on stainless‐steel. The object under consideration is a stainless‐steel built‐up column, which is classified as atypical structural elements. The purpose of this optimization problem is to perform the minimization of the weight of the selected built‐up column, when the height of the column and the load acting on it are known. The built‐up column is considered with two different types of cross‐sectional chords: at first with circular (CHS) cross‐sectional chords and then with elliptical (EHS) cross‐sectional chords.A genetic algorithm based optimum design is presented for such a built‐up column. The design algorithm obtains a built‐up column with the least weight by selecting appropriate sections from standard set of duplex stainless‐steel hollow elliptical cross‐sections. The optimization model accounts for the strength and stability constraints. The built‐up column is under action of compressive axial force, bending moment and combination compressive axial force and bending moment. The parameters under consideration include the height and width of the outer cross‐section of the column's chords, the ratio of the outer cross‐sectional dimensions to the thickness and the initial eccentricity of the load. The computation results showed that the chosen optimization model and genetic algorithm allow efficiently obtaining the column of minimum weight, where the variables are column chord cross‐section and diagonals cross‐section. The design algorithm used to solve the problem is described in detail in this work.Until today, there is known that the lack of information prevented the recommended methodology from being properly established. Because of this, the obtained results confirmed that these types of structural elements of the steel in question are needed to develop a more efficient design of stainless‐steel structures in the design method and thus contribute to its wider use in construction.

Experimental and analytical investigation of arched steel haunches under cyclic loading

In this study, the cyclic performance of innovative less-invasive haunches, as fuse elements, called Arched Steel Haunches (ASHs) for seismic retrofitting of reinforced concrete frames was investigated. The axes of these haunches are like circle arcs, which are more geometrically compatible with architecture than straight haunches. Two physical models were proposed to identify the ASHs’ behavioral curves. To evaluate the models’ accuracy, a series of cyclic tests were conducted on eight ASH specimens in two groups with various axial eccentricities equal to 0.1 and 0.2 of the nominal haunch length. Seven specimens with double cross-sections and various connectors, and later as a single cross-section, were fabricated and then subjected to cyclic loading.The experimental results showed that ASHs as ever subjected to the buckling phase at a larger deformation, more desirable cyclic performance would be achieved in compression and even tension. Furthermore, the specimens without overall buckling potential as a fuse, by reaching their fully plastic strength, exhibited a more symmetrical hysteretic behavior and could upgrade the energy dissipation and maximum equivalent damping ratio about 3 and 2 times, respectively. Different behaviors in tensile and compressive ultimate strength and plastic stiffness were more considerable when the initial axial eccentricity was decreased. It should be noted that the results of this pilot study will be used for further research on the experimental behavior of RC beam-column joints.

Extended phase-space symplectic-like integrators for coherent post-Newtonian Euler-Lagrange equations

Coherent or exact equations of motion for a post-Newtonian Lagrangian formalism are the Euler-Lagrange equations without any terms truncated. They naturally conserve energy {and} angular momentum. Doubling the phase-space variables of positions and momenta in the coherent equations, we establish extended phase-space symplectic-like integrators with the midpoint permutations. The velocities should be solved iteratively from the algebraic equations of the momenta defined by the Lagrangian during the course of numerical integrations. It is shown numerically that a fourth-order extended phase-space symplectic-like method exhibits good long-term stable error behavior in energy {and} angular momentum, as a fourth-order implicit symplectic method with a symmetric composition of three second-order implicit midpoint rules or a fourth-order Gauss-Runge-Kutta implicit symplectic scheme does. For given time step and integration time, the former method is superior to the latter integrators in computational efficiency. {The extended phase-space method is used to study the effects of the parameters and initial conditions on the orbital dynamics of the coherent Euler-Lagrange equations for a post-Newtonian circular restricted three-body problem. It is also applied to trace the effects of the initial spin angles, initial separation and initial orbital eccentricity on the dynamics of the coherent post-Newtonian Euler-Lagrange equations of spinning compact binaries.

Common envelope evolution of eccentric binaries

ABSTRACT Common envelope evolution (CEE) is believed to be an important stage in the evolution of binary/multiple stellar systems. Following this stage, the CE is thought to be ejected, leaving behind a compact binary (or a merger product). Although extensively studied, the CEE process is still little understood, and although most binaries have non-negligible eccentricity, the effect of initial eccentricity on the CEE has been little explored. Moreover, most studies assume a complete circularization of the orbit by the CE onset, while observationally such eccentricities are detected in many post-CE binaries. Here we use smoothed particle hydro-dynamical simulations to study the evolution of initially eccentric (0 ≤ e ≤ 0.95) CE-systems. We find that initially eccentric binaries only partially circularize. In addition, higher initial eccentricity leads to a higher eccentricity following the end of the inspiral phase, with eccentricities as high as 0.18 in the most eccentric cases, and even higher if the initial pericentre of the orbit is located inside the star (e.g. following a kick into an eccentric orbit, rather than a smooth transition). CEE of more eccentric binaries leads to enhanced dynamical mass-loss of the CE compared with more circular binaries, and depends on the initial closest approach of the binary. We show that our results and the observed eccentricities of post-CE binaries suggest that the typical assumptions of circular orbits following CEE might potentially be revised. We expect post-CE eccentricities to affect the delay time distributions of various transients such as supernovae, gamma-ray bursts, and gravitational-wave sources by up to tens of per cents.

An analytic solution to the Kozai–Lidov evolution equations

ABSTRACT A test particle in a non-coplanar orbit about a member of a binary system can undergo Kozai–Lidov oscillations in which tilt and eccentricity are exchanged. An initially circular highly inclined particle orbit can reach high eccentricity. We consider the non-linear secular evolution equations previously obtained in the quadrupole approximation. For the important case that the initial eccentricity of the particle orbit is zero, we derive an analytic solution for the particle orbital elements as a function of time that is exact within the quadrupole approximation. The solution involves only simple trigonometric and hyperbolic functions. It simplifies in the case that the initial particle orbit is close to being perpendicular to the binary orbital plane. The solution also provides an accurate description of particle orbits with non-zero but sufficiently small initial eccentricity. It is accurate over a range of initial eccentricity that broadens at higher initial inclinations. In the case of an initial inclination of π/3, an error of 1 per cent at maximum eccentricity occurs for initial eccentricities of about 0.1.

PT dependence of the correlation between initial spatial anisotropy and final momentum anisotropies in relativistic heavy ion collisions

The particle momentum anisotropy (vn) produced in relativistic nuclear collisions is considered to be a response of the initial geometry or the spatial anisotropy ϵn of the system formed in these collisions. The linear correlation between ϵn and vn quantifies the efficiency at which the initial spatial eccentricity is converted to final momentum anisotropy in heavy ion collisions. We study the transverse momentum and collision centrality dependence of this correlation for charged particles using a hydrodynamical model framework at LHC. The (ϵn−vn) correlation is found to be stronger for central collisions and also for n=2 compared to that for n=3 as expected. However, the transverse momentum (pT) dependent correlation coefficient shows interesting features which strongly depends on the mass as well as pT of the emitted particle. The correlation strength is found to be larger for lighter particles in the lower pT region. We see that the relative fluctuation in anisotropic flow depends strongly on the value of η/s specially in the region pT<1 GeV unlike the correlation coefficient which does not show significant dependence on η/s.

Production of pions, kaons, (anti-)protons and phi mesons in Xe\u2013Xe collisions at sqrt{s_{mathrm{NN}}}\xa0=\xa05.44 TeV

The first measurement of the production of pions, kaons, (anti-)protons and phi mesons at midrapidity in Xe–Xe collisions at sqrt{s_{mathrm{NN}}} = 5.44~text {TeV} is presented. Transverse momentum (p_{mathrm{T}}) spectra and p_{mathrm{T}}-integrated yields are extracted in several centrality intervals bridging from p–Pb to mid-central Pb–Pb collisions in terms of final-state multiplicity. The study of Xe–Xe and Pb–Pb collisions allows systems at similar charged-particle multiplicities but with different initial geometrical eccentricities to be investigated. A detailed comparison of the spectral shapes in the two systems reveals an opposite behaviour for radial and elliptic flow. In particular, this study shows that the radial flow does not depend on the colliding system when compared at similar charged-particle multiplicity. In terms of hadron chemistry, the previously observed smooth evolution of particle ratios with multiplicity from small to large collision systems is also found to hold in Xe–Xe. In addition, our results confirm that two remarkable features of particle production at LHC energies are also valid in the collision of medium-sized nuclei: the lower proton-to-pion ratio with respect to the thermal model expectations and the increase of the phi -to-pion ratio with increasing final-state multiplicity.