Inelastic Distributions Research Articles

Seismic design procedures for concentrically braced frames

This paper deals with the main behavioural issues involved in the seismic design of typical forms of concentrically braced frames. The response of bracing members under monotonic and cyclic axial loading is first considered, and the key parameters affecting the performance are highlighted. This is followed by an assessment of the different design approaches employed for the treatment of brace buckling, and the influence of the underlying assumptions on various aspects of frame response. The provisions of international codes of practice are examined within the discussions, with emphasis on the recommendations of Eurocode 8. Selected results from static and dynamic non-linear analysis on idealised frame configurations are presented in order to illustrate salient response criteria, particularly those related to ductility demand and inelastic distribution. The primary sources of inconsistency existing in code provisions are demonstrated, and their implications on the seismic performance of concentrically braced frames are addressed. It is shown that several code modifications are required in order to alleviate causes of undesirable performance and to facilitate a rational implementation of capacity design concepts.

Predicting inelastic rovibrational state distributions from an energy constrained angular momentum mechanism

We present a quantitative version of the velocity–angular momentum plots of Besley et al. that we have used extensively to represent the key processes at work in collisional transfer mechanisms. Rotational state distributions are obtained by incorporating probability distributions of the relevant variables, and the Monte Carlo (MC) trajectory technique is used to sample these distributions. The method is illustrated with the case of weakly quasi-resonant vibration rotation transfer in A( 1Σ u +) Li 2+ Ne collisions. The results show excellent agreement with published experimental data, indicating the apparent dominance of the factors governing angular momentum (AM) conversion in shaping rovibrational distributions.

Inelasticity distribution of hadron-Pb collisions in the energy region exceeding1014eV from mountain cosmic ray experiments

The inelasticity distribution of hadron-lead collisions in the energy region exceeding ${10}^{14}$ eV is estimated on the basis of 66 events, induced by cosmic ray hadrons and detected at high mountain altitudes at Pamir (4300 m, 595 ${\mathrm{g}/\mathrm{c}\mathrm{m}}^{2}).$ The distribution of the best fitting is approximated as $g(K)dK=[\ensuremath{\alpha}(1\ensuremath{-}{K)}^{{m}_{1}\ensuremath{-}1}+\ensuremath{\beta}{K}^{{m}_{2}\ensuremath{-}1}]dK,$ where ${m}_{1}=0.5,$ ${m}_{2}=1.125,$ $\ensuremath{\alpha}=0.26,$ $\ensuremath{\beta}=0.55,$ giving $〈K〉=0.60.$ The errors of the parameters are discussed in the text. The distribution is compared with those which are based on theoretical models.

Inelasticity distribution of hadron-Pb collisions in 10 14 eV (revised)

Inelasticity distribution of hadron-Pb collisions in 10 14 eV (revised)

Numerical Simulation of Residual Stresses Caused by Quenching Process in Aluminium Gas Cylinders

Residual stresses introduced during quenching process in aluminium gas cylinders contribute to the development of cracks. This may result in leakage or fracture of the cylinders. Finite element studies were conducted to evaluate the effect of the quenching process on through thickness inelastic strain and residual stress distributions in the neck area of the gas cylinder. The numerical modeling and experimental studies confirmed that high level of tensile residual stresses exists at the internal surface of the neck of the aluminium gas cylinders which is susceptible to cracking.

Inelasticity Distributions in High-Energyp-Nucleus Collisions

Inelasticity distributions in high-energy p-nucleus collisions are computed in the framework of the interacting gluon model, with the impact-parameter fluctuation included. A proper account of the peripheral events by this fluctuation has shown to be vital for the overall agreement with several reported data. The energy dependence is found to be weak. [S0031-9007(97)02894-9] Inelasticity, i.e., the fraction of the incident energy E0 which is transformed into produced particles, is one of the basic quantities in high-energy hadronic and nuclear collisions. It is crucial in cosmic-ray data analysis where the primary mass composition, which is an important piece of information about the Universe, is deduced by using cascade models of the development of the mass composition with appropriate inelasticity distributions [1] and cross sections as the inputs. So, it is natural that since early times the study of the inelasticity has received special attention by both experimentalists and theoreticians. More recently, it has also aroused interest in connection with the production of a quark-gluon plasma

Inelasticity of hadron-lead collisions, estimated by thick lead emulsion chambers at the Pamirs

The inelasticity distribution of hadron-lead collisions in the energy region exceeding 1014 eV is estimated by 74 events of hadron interactions, observed by thick lead chambers at the Pamirs. The distribution is approximated as g(K)dK = 3.0 K2.0 dK (with 〈K〉 = 0.75) as a minimum estimate. The distribution is consistent with that by the simulation made under the assumptions of UA5 algorithm for hadron collisions and of geometrical model for intra-nuclear cascade. It is inferred that the average value of the inelasticity of hadron-nucleon collision is smaller than 0.5 in the energy region exceeding 1014 eV.

Inelastic models of lithospheric stress-I. Theory and application to outer-rise plate deformation

SUMMARY Outer-rise stress distributions determined in the manner that mechanical engineers evaluate inelastic stress distributions within conventional materials are contrasted with those predicted using simple elastic-plate models that are frequently encountered in studies of outer-rise seismicity. This comparison indicates that the latter are inherently inappropriate for studies of intraplate earthquakes, which are a direct manifestation of lithospheric inelasticity. We demonstrate that the common practice of truncating elastically superimposed stress profiles so that they are not permitted to exceed laboratory-based estimates of lithospheric yield strength will result in an accurate characterization of lithospheric stress only under relatively restrictive circumstances. In contrast to elastic-plate models, which predict that lithospheric stress distributions depend exclusively upon the current load, inelastic plate models predict that stress distributions are also significantly influenced by the plate-loading history, and, in many cases, this influence is the dominant factor in determining the style of potential seismicity (e.g. thrust versus normal faulting). Numerous ‘intuitive’ interpretations of outer-rise earthquakes have been founded upon the implicit assumption that a unique relationship exists between a specified combination of plate curvature and in-plane force, and the resulting lithospheric stress distribution. We demonstrate that the profound influence of deformation history often invalidates such interpretations. Finally, we examine the reliability of ‘yield envelope’ representations of lithospheric strength that are constructed on the basis of empirically determined frictional sliding relationships and silicate plastic-flow laws. Although representations of this nature underestimate the strength of some major interplate faults, such as the San Andreas, they appear to represent a reliable characterization of the strength of intraplate oceanic lithosphere.

Shakedown Tests of One-Third–CALE Composite Bridge

This paper presents shakedown and plastic collapse test results for a one-third–scale bridge system. The bridge was a three-span, four-girder composite bridge comprising compact and noncompact sections. Experimental results are compared to analytical results from an inelastic grillage analysis. Inelastic force distribution in the longitudinal and transverse directions was examined along with inelastic deformations, reactions, and moments. The results show that bridge systems have a significant ability to redistribute force effects. However, the behavior of bridge systems is very complex and involves many characteristics that are difficult to incorporate into current modeling techniques. This paper discusses current research targeted to advance bridge engineering practice in the area of inelastic design and evaluation techniques.

Inelasticity distribution and relationship between e+e- and pp hadron-production mechanisms.

The inelasticity distribution is used to relate the hadron-production data in [ital e][sup +][ital e[minus]] annihilation to the corresponding data in [ital pp] collisions. If [ital e][sup +][ital e[minus]] annihilation data are used as input, the hadron multiplicity distributions [ital P][sub [ital n]]([ital s]), the average multiplicities [l angle][ital n][prime]([ital s])[r angle], the normalized moments [ital C][sub [ital q]][sup [prime]]([ital s]), the energy dependence of the average transverse momentum [l angle][ital p][sub [ital t]]([ital s])[r angle], the height of the central plateau [ital h]([ital s]), and the strength of the forward-backward multiplicity correlations [ital b]([ital s]) are qualitatively reproduced over the range of energies from those reached at the CERN ISR to [radical][ital s] =900, 1800, and 10[sup 4] GeV in [ital pp] collisions. The discrepancies observed between predicted and experimental values of [ital C][sub [ital q]][sup [prime]]([ital s]), [ital q][ge]4, and [ital h]([ital s])[sub [ital p][ital p]] are indicated and commented upon. Other possible tests of the [ital e][sup +][ital e[minus]-][ital pp] universality are briefly mentioned.

Inclusive inelastic scattering of heavy ions in the independent particle model

The authors consider the inclusive inelastic scattering of heavy ions using the Glauber model and the independent particle approximation. Inclusive inelastic distributions for projectile excitation of the target and total inelastic scattering, where all projectile and target excited states are summed, are discussed using closure. The total inelastic distribution when integrated is shown to be equivalent to the absorption cross section found from applying the optical theorem to the elastic scattering amplitude in the coherent approximation. Calculations are presented for several heavy-ion pairs using realistic nuclear densities in a large mass number approximation.

A molecular beam study of the O 2[sbnd]Pt(111) interaction

We have performed scattering experiments for O 2 on Pt(111) for translational energies up to 1.7 eV (1.09 eV normal energy). The scattered O 2 flux from the surface is measured as function of arrival time and outgoing angle. The experimental results reveal pronounced lobular scattering. The final energy shows for most experimental conditions a maximum near the specular direction. At higher incident energy, however, no such maximum is observed and the final energy is increasing monotonically with final angle. These results suggest a transition from scattering at a “flat” vibrating surface for low energies to scattering from a corrugated surface for the higher energies. The angular width at low incoming energy is comparable to that for Ar scattering, and is quite low compared with O 2 scattering from Ag(111) where a broadening of the angular spectrum towards the surface normal is observed. For Pt(111) we see a much reduced broadening despite the fact that the binding energies of the physisorption, chemisorption and dissociation states are similar for both systems. The broadening in the case of both Ag(111) and Pt(111) at higher normal energies can be ascribed to the influence of the chemisorption precursor in the interaction potential. In the case of Pt(111), however, the direct inelastic distributions are additionally modified by the significant probability of dissociation.

The threshold anomaly in inelastic scattering

New measurements of the elastic scattering of 16O by 208Ph and inelastic scattering to the 208Pb(3 − 1) state have been made at 70, 74, 78, 82 and 94 MeV. These, together with existing data, have been analyzed using a conventional collective model and DWBA formalism. The real and imaginary parts of the transition potential determined in the surface region exhibit a rapid energy variation in the threshold region reminiscent of the threshold anomaly observed in the elastic potential. At several energies above threshold, inelastic distributions could not be adequately reproduced within the confines of the model. These results cast doubt on the adequacy of the collective model to describe this inelastic excitation process in regions of a threshold anomaly.

A QCD-inspired model for exclusive vector meson production in deep inelastic scattering

Most of the features of the exclusive γ ∗ p→ϱ 0 p signal can be reproduced by a simple model which extends perturbative QCD to small momentum transfers in a natural way while linking pomeron behaviour with the gluon condensate. The data, however, seem to exhibit features characteristic of inelastic distributions, even after subtraction of a possible inelastic background.

Interacting gluon model for hadron-nucleus and nucleus-nucleus collisions in the central rapidity region.

The interacting gluon model developed to describe the inelasticity distribution in hadron-nucleon collisions has been generalized and applied to hadron-nucleus and nucleus-nucleus interactions. Leading particle spectra and energy distributions in hadron-nucleus and nucleus-nucleus collisions are calculated.

Energy fraction of the central region in the Chou-Yang model.

For the energy fraction of the central region in the Chou-Yang model we investigate dependencies on the total center-of-mass energy, multiplicity of charged particles, partition temperature, and average transverse momentum. Upper and lower bounds are obtained for the energy fraction. It is shown that the energy fraction approaches zero in the high-energy limit if the partition temperature is given by the empirical formula obtained through the analysis of experimental data of the pseudorapidity distribution via the Chou-Yang model. We examine the connection with the inelasticity distribution in hadron-hadron collision derived by Fowler and collaborators.

Formulation of the plastic source method for plane inelastic problems Part 2: Numerical implementation for elastoplastic problems

In Part 1 of this paper, Green's function representation for the residual stress, arising from any plane inelastic strain distribution under no applied load, has been given. In Part 2 (i.e., the current paper) we focus our attention to the plastic strain arising in plane elastoplastic problems subject to applied loads. A numerical procedure, based on the Green's function approach, to determine the unknown plastic strain distribution under the applied load is established. The numerical result for an elastoplastic steady crack growth problem demonstrates, overwhelmingly, the advantage of the proposed method over the finite element method approach for the same problem.

High energy limit of the energy fraction of the central region in the Chou-Yang model

The high energy behavior of the energy fraction of the central region in the Chou-Yang model is investigated. Bounds are obtained for the energy fraction. If the partition temperature is given by the empirical formula obtained via the analysis of experimental data for the pseudorapidity distribution, the energy fraction vanishes in the high energy limit. The connection between this result and the inelasticity distribution of Fowler et al. is discussed.

Systems of colliding bodies in a gravitational field: Impact velocity, inelasticity and sizes distributions

We study numerically the dynamical evolution of a system of colliding bodies. Collisions are inelastic and the coefficient of rebound is a function of the impat velocity. Various functions are used. The system can reach an equilibrium state characterized by a finite thickness independently on the sense of variation of the functions. Within the frame of various distributions of the body sizes we observe a segregation rather than equipartition of the kinetic energy of random motions.

Small angle, quasielastic and inelastic neutron scattering from 0.85 AgPO 3−0.15 PbI 2 glass

A small angle neutron scattering (SANS) experiment and a quasielastic neutron scattering (QENS) experiment were performed on the fast ionic conductor 0.85 AgPO 3−0.15PbI 2, which is a vitreous electrolyte. The SANS data show that the scattering obeys Guinier's law for Q<7 × 10 −2 Å; dispersed heterogeneities are present in the glass with a mean radius of gyration of 20 Å. The QENS spectra show a quasielastic broadening of the elastic peak and a long tail up to 40 meV which is due to an inelastic distribution. The mechanism of the conductivity is a translational diffusion with a coefficient of self-diffusion of the mobile silver ions D=3.7 × 10 −6 exp(−8.778/ RT) (activation energy being in J-mol −1). The value of the activation energy is very close to that of α-AgI and 0.5AgPO 3−0.5AgI. The value of the proportion of purely elastic scattering: 0.925 indicates that the observed quasielastic scattering is due to silver ions which can be coordinated with the iodide ions. The two peaks observed in the inelastic frequency distribution function can be related to vibrations of the AgPO 3 host glass and of AgI 4 structural units respectively. These three last results and the SANS result seem to confirm our hypothesis on the structure of this glass: small “clusters” of AgI with tetrahedral coordination are dispersed in the AgPO 3 host glass. In order to build these clusters, an exchange between Ag + and Pb 2+ is proposed. These hypotheses assume that ionic conduction in the glass is almost entirely within the cluster phase and that the ionic conductivity of the host glass varies with the cluster concentration and with the nature of this host glass.