Compressible Strips Research Articles

THE INFLUENCE OF CONCRETE COMPRESSION ZONE ON THE SHEAR RESISTANCE OF REINFORCED CONCRETE BEAMS

The paper analyzes the effect of the compressed zone of concrete on the shear resistance of reinforced concrete flexible beams. The calculation models are considered, by which the contribution of the compressed zone of concrete to the total value of the shear resistance is further determined. The features of each model are described, and schemes and dependencies for calculating the transverse force in the compressed zone of concrete are presented. The experimental database of specimens is presented and the analysis by the considered calculation models is carried out. Varying parameters in the database are marked and the analysis by the obtained calculated values of transverse force in the compressed concrete strip by models is performed. The contribution of the transverse force in the compressed zone to the quantitative contribution to the shear resistance is indicated and appropriate conclusions are drawn on the models presented and the parameters considered.

Стержневые модели среза сжатых бетонных полос консольных опор ригелей многоэтажных каркасов

Rod models for assessing the strength of compressed concrete strips under the action of a cut of short cantilevers of crossbars between the supporting and “conditional” cargo platforms are proposed based on modeling their physical work. The basis for improving the calculation method is a single principle for constructing rod models of compressed concrete strips of short elements – there is the method of copying the trajectories of force cracks and fracture patterns. The improvement of the calculation method was carried out on the basis of the development of the above-considered method for determining the strength of concrete strips under the action of compression along an inclined strip and the action of a cut between the faces of the cargo and support platforms inside the compressed strip. In the process of improving practical recommendations for the calculation, the patterns of modification of rod models under the action of compression and shear were used, depending on the change in the main factors. All proposals for the calculation are brought to the level of practical application and are substantiated by experiment.

DESIGN MODELS OF THE BEARING CAPACITY OF THE SUPPORT SECTIONS OF BASALT-CONCRETE BEAM STRUCTURES

Abstract. In the past decade, structures with non-metallic composite reinforcement (FRP) find more and more widespread use in construction practice, especially in buildings and structures for special purposes. Due to its high strength, resistance to chemical and physical corrosion, dielectric and diamagnetic properties, low weight and low thermal conductivity, FRP is increasingly replacing steel reinforcement. However, the wider use of concrete structures with FRP is constrained by insufficient knowledge of the features of their work, insufficient regulatory support and little experience in operating these facilities. Practice has shown the promise and economic feasibility of using FRP in road, hydraulic engineering, transport construction, in the construction of bridge spans, treatment facilities, chemical and food industry facilities, and foundations in an aggressive soil environment. At the same time, the prospects for using basalt-plastic reinforcement (BFRP) are primarily due to the low cost of the main raw material, basalt fibers, due to the presence of significant reserves of basalt in the world. The basic principles of calculation of bending structures reinforced with FRP, in all foreign standards, as well as in the domestic Manual, are the same as for elements with steel reinforcement. The design models of the bearing capacity of the bearing sections of concrete beams reinforced with BFRP are considered. The bearing capacity of inclined sections of elements with large and medium shear spans should be determined by an inclined crack using variable coefficients , taking into account the real length of a dangerous inclined crack , a significant reduction in tensile stresses in transverse reinforcement to . The bearing capacity of the support sections with small shear spans must be determined as for short cantilevers along an inclined compressed strip between the concentrated force and the support using a variable coefficient . This approach provides satisfactory convergence between the calculated and experimental values of the bearing capacity of inclined sections (coefficient of variation BFRP.

A Limit Equilibrium Model of Tabular Mine Pillar Failure

An improved understanding of pillar strength and pillar failure mechanisms is required to optimize tabular mine layout designs. The paper describes the application of a limit equilibrium model for pillar failure analysis. It is shown that the model is capable of reproducing a hardening or softening response for uniformly compressed strip or square pillars. The stress–strain behavior depends on three non-dimensional parameters Q, M and β. Q represents the ratio of the limit failed uniaxial strength to the intact material strength, M is the ratio of the failed limit strength envelope slope to the intact strength envelope slope and β is proportional to the pillar width to height ratio. The model is implemented in a displacement discontinuity solution scheme using unstructured triangular elements to allow irregular plan-view pillar shapes and mining step increments to be represented. The seam-parallel confining stress distribution in the fracture zone is determined using a fast marching solution algorithm. A case study of an experimental pillar extraction site in a platinum mine is presented to illustrate the capability of the model to simulate the evolution of pillar failure as pillar extraction proceeds. Good qualitative agreement to observed failure trends are obtained but the detailed calibration of the model parameters remains a challenge. Further work is required to enhance the representation of pillar edge spalling processes.

Attenuation and dispersion characteristic of Rayleigh waves in a compressed viscoelastic strip: a comparative study

The present study develops the dispersion and attenuation characteristics of Rayleigh wave regulations through a pre-stressed Voigt type viscoelastic strip of finite thickness. The displacement expressions of Rayleigh wave in the strip are introduced. The complex frequency equation of the wave motion is thus obtained. We have studied the effects of initial stress, attenuation coefficients and dissipation factor on the phase and damped velocities simultaneously.

Engineering method for assessing the strength of reinforced concrete beams

A calculation method is proposed that combines two existing methods for calculating the strength of reinforced concrete beams. The author of the article considers the possibility of presenting the work of a reinforced concrete beam in the form of an arch with a curvilinear shape with a puff, which is a statically definable system. The operation of a reinforced concrete beam with a relative span of a slice from 1 to 3 is modeled as an arched system with a horizontal stretched reinforcing belt and a compressed concrete strip of curvilinear shape. The purpose of the tightening in a beam with an average relative cut span is to cancel the bending moment inherent in a simple beam. Thus, this model (arch with tightening) most fully reflects the work of reinforced concrete beams with an average relative cut span compared to the model adopted in regulatory documents.

Quantum Hall effect in narrow graphene ribbons

The edge states in the integer quantum Hall effect are known to be significantly affected by electrostatic interactions leading to the formation of compressible and incompressible strips at the boundaries of Hall bars. We show here, in a combined experimental and theoretical analysis, that this does not hold for the quantum Hall effect in narrow graphene ribbons. In our graphene Hall bar, which is only 60 nm wide, we observe the quantum Hall effect up to Landau level index k=2 and show within a zero free-parameter model that the spatial extent of the compressible and incompressible strips is of a similar magnitude as the magnetic length. We conclude that in narrow graphene ribbons the single-particle picture is a more appropriate description of the quantum Hall effect and that electrostatic effects are of minor importance.

Spin polarization andg-factor enhancement in graphene nanoribbons in a magnetic field

We provide a systematic quantitative description of spin polarization in armchair and zigzag graphene nanoribbons in a perpendicular magnetic field. We first address spinless electrons within the Hartree approximation studying the evolution of the magnetoband structure and formation of the compressible strips. We discuss the potential profile and the density distribution near the edges and the difference and similarities between armchair and zigzag edges. Accounting for the Zeeman interaction and describing the spin effects via the Hubbard term we study the spin-resolved subband structure and relate the spin polarization of the system at hand to the formation of the compressible strips for the case of spinless electrons. At high magnetic field the calculated effective g-factor varies around a value of <g*>~2.25 for armchair nanoribbons and <g*>~3 for zigzag nanoribbons. An important finding is that in zigzag nanoribbons the zero-energy mode remains pinned to the Fermi-energy and becomes fully spin-polarized for all magnetic fields, which, in turn, leads to a strong spin polarization of the electron density near the zigzag edge.

Acoustic magnetoplasmons in a two-dimensional electron system with a smooth edge

Acoustic edge magnetoplasmon (AEMP) modes are detected in a wide range of magnetic fields by the resonant microwave absorption technique. It is established that in the case of a smooth edge of a two-dimensional electron system, the resonant signal is strongly enhanced with the AEMP excitation, whereas in the case of an abrupt edge, these modes are strongly damped. One fundamental mode and three AEMP modes are observed, and it is shown that the number of AEMP modes is directly related to the filling factor value. As a result, a sequence of abrupt terminations of AEMP modes is observed at the integer filling factors, in accordance with the number of edge compressible strips available in the electron system. Also the dependence of the relative AEMP amplitude versus the filling factor is addressed.

Scanning capacitance imaging of compressible and incompressible quantum Hall effect edge strips

We use dynamic scanning capacitance microscopy to image compressible and incompressible strips at the edge of a Hall bar in a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime. This method gives access to the complex local conductance, Gts, between a sharp metallic tip scanned across the sample surface and ground, comprising the complex sample conductance. Near integer filling factors we observe a bright stripe along the sample edge in the imaginary part of Gts. The simultaneously recorded real part exhibits a sharp peak at the boundary between the sample interior and the stripe observed in the imaginary part. The features are periodic in the inverse magnetic field and consistent with compressible and incompressible strips forming at the sample edge. For currents larger than the critical current of the QHE break-down the stripes vanish sharply and a homogeneous signal is recovered, similar to zero magnetic field. Our experiments directly illustrate the formation and a variety of properties of the conceptually important QHE edge states at the physical edge of a 2DEG.

Theoretical investigation of local electron temperature in quantum Hall systems

In this work we solve thermo-hydrodynamical equations considering a two dimensional electron system in the integer quantum Hall regime, to calculate the spatial distribution of the local electron temperature. We start from the self-consistently calculated electrostatic and electrochemical potentials in equilibrium. Next, by imposing an external current, we investigate the variations of the electron temperature in the linear-response regime. Here a local relation between the electron density and conductivity tensor elements is assumed. Following the Ohm's law we obtain local current densities and by implementing the results of the thermo-hydrodynamical theory, calculate the local electron temperature. We observe that the local electron temperature strongly depends on the formation of compressible and incompressible strips.

Interacting electrons in graphene nanoribbons in the lowest Landau level

We study the effect of electron-electron interaction and spin on electronic and transport properties of gated graphene nanoribbons (GNRs) in a perpendicular magnetic field in the regime of the lowest Landau level (LL). The electron-electron interaction is taken into account using the Hartree and Hubbard approximations, and the conductance of GNRs is calculated on the basis of the recursive Greens function technique within the Landauer formalism. We demonstrate that, in comparison to the one-electron picture, electron-electron interaction leads to the drastic changes in the dispersion relation and structure of propagating states in the regime of the lowest LL showing a formation of the compressible strip and opening of additional conductive channels in the middle of the ribbon. We show that the latter are very sensitive to disorder and get scattered even if the concentration of disorder is moderate. In contrast, the edge states transport is very robust and can not be suppressed even in the presence of a strong spin-flipping.

MAPPING OF QUANTUM-HALL EDGE CHANNELS BY A DILUTION-REFRIGERATOR BASED NEAR-FIELD SCANNING OPTICAL MICROSCOPE

A real-space mapping of photovoltage near the edge of the Hall-bar of a GaAs/AlGaAs single heterojunction has been obtained using a dilution-refrigerator-based near-field scanning optical microscope in magnetic fields. The optical probe-sample surface distance dependence of photovoltage is investigated. We obtain photovoltage profile in the vicinity of the edge, which reflects the local chemical potential of the two-dimensional electron gas determined by the distribution of the compressible and incompressible strips.

Generic suppression of conductance quantization of interacting electrons in graphene nanoribbons in a perpendicular magnetic field

The effects of electron interaction on the magnetoconductance of graphene nanoribbons (GNRs) are studied within the Hartree approximation. We find that a perpendicular magnetic field leads to a suppression instead of an expected improvement of the quantization. This suppression is traced back to interaction-induced modifications of the band structure leading to the formation of compressible strips in the middle of GNRs. It is also shown that the hard wall confinement combined with electron interaction generates overlaps between forward and backward propagating states, which may significantly enhance backscattering in realistic GNRs. The relation to available experiments is discussed.

Edge-channel interference controlled by Landau level filling

We study the visibility of Aharonov-Bohm interference in an electronic Mach-Zehnder interferometer in the integer quantum Hall regime. The visibility is controlled by the filling factor $\ensuremath{\nu}$ and is observed only between $\ensuremath{\nu}\ensuremath{\approx}2.0$ and 1.0, with an unexpected maximum near $\ensuremath{\nu}=1.5$. Three energy scales extracted from the temperature and voltage dependences of the visibility change in a very similar way with the filling factor, indicating that the different aspects of the interference depend sensitively on the local structure of the compressible and incompressible strips forming the quantum Hall edge channels.

Quantum wires in magnetic field: a comparative study of the Hartree–Fock and the spindensity functional approaches

We present a detailed comparison of the self-consistent calculations based on theHartree–Fock and the spin density functional theory for a split-gate quantum wire inthe IQH regime. We demonstrate that both approaches provide qualitatively(and, in most cases, quantitatively) similar results for the spin-resolved electrondensity, spin polarization, spatial spin separation at the edges and the effectiveg factor. Both approaches produce the same values of the magnetic fields corresponding tothe successive subband depopulation and qualitatively similar evolution of themagnetosubbands. Quantitatively, however, the HF and the DFT subbands are different(even though the corresponding total electron densities are practically the same). Incontrast to the HF approach, the DFT calculations predict much larger spatial spinseparation near the wire edge for the low magnetic fields (when the compressible strips forspinless electrons are not formed yet). In the opposite limit of the large fields, theHartree–Fock and the DFT approaches give very similar values for the spatial spinseparation.

Magnetoconductance of interacting electrons in quantum wires: Spin density functional theory study

We present a systematic quantitative description of the magnetoconductance of split-gate quantum wires focusing on formation and evolution of the odd spin-resolved conductance plateaus. We start from the case of spinless electrons where the calculated magnetoconductance in the Hartree approximation shows the plateaus quantized in units of 2e 2 /h separated by transition regions, whose width grows as the magnetic field is increased. We show that the transition regions are related to the formation of the compressible strips in the middle of the wire occupied by electrons belonging to the highest spin-degenerate subband. Accounting for the exchange and correlation interactions within the spin density functional theory DFT leads to the lifting of the spin degeneracy and formation of the spin-resolved plateaus at odd values of e 2 /h. The most striking feature of the magnetoconductance is that the width of the odd conductance steps in the spin DFT calculations is equal to the width of the transition intervals between the conductance steps in the Hartree calculations. A detailed analysis of the evolution of the Hartree and the spin DFT subband structure provides an explanation of this finding. Our calculations also reveal the effect of the collapse of the odd conductance plateaus for lower fields. We attribute this effect to the reduced screening efficiency in the confined wire geometry when the width of the compressible strip in the center becomes much smaller than the extent of the wave function. A detailed comparison to the experimental data demonstrates that the spin DFT calculations reproduce not only qualitatively but also quantitatively all the features observed in the experiment. This includes the dependence of the width of the odd and even plateaus on the magnetic field as well as the estimation of the subband index corresponding to the last resolved odd plateau in the magnetoconductance.

Hall Potential Profiles in Quantum Hall Samples Measured by a Low-Temperature Scanning Force Microscope

Our measurements of the Hall potential distribution in GaAs/AlGaAs quantum Hall samples using a scanning force microscope at a temperature of 1.4 K are reviewed. The results emphasize the important role of compressible and incompressible strips, running along the edges of the two-dimensional electron system (2DES), for the quantum Hall effect. At the interface line between the 2DES and its alloyed metal contact with good ohmic behavior, a partial depletion of the electron concentration in the 2DES in front of contact is identified, causing for certain magnetic field regimes an incompressible strip lying in parallel to the interface line and therefore isolating the compressible 2DES bulk from the 2DES edge with the contact.

Quenching of compressible edge states around antidots

We provide a systematic quantitative description of the edge state structure around a quantum antidot in the integer quantum Hall regime. The calculations for spinless electrons within the Hartree approximation reveal that the widely used Chklovskii et al. electrostatic description [Phys. Rev. B 46, 4026 (1992)] greatly overestimates the widths of the compressible strips; the difference between these approaches diminishes as the size of the antidot increases. By including spin effects within density functional theory in the local spin-density approximation, we demonstrate that the exchange interaction can suppress the formation of compressible strips and lead to a spatial separation between the spin-up and spin-down states. As the magnetic field increases, the outermost compressible strip related to spin-down states starts to form. However, in striking contrast to quantum wires, the innermost compressible strip (due to spin-up states) never develops for antidots.

Magnetosubband and edge state structure in cleaved-edge overgrown quantum wires in the integer quantum Hall regime

We provide a systematic quantitative description of the structure of edge states and magnetosubband evolution in hard wall quantum wires in the integer quantum Hall regime. Our calculations are based on the self-consistent Green's function technique where the electron- and spin interactions are included within the density functional theory in the local spin density approximation. We analyze the evolution of the magnetosubband structure as magnetic field varies and show that it exhibits different features as compared to the case of a smooth confinement. In particularly, in the hard-wall wire a deep and narrow triangular potential well (of the width of magnetic length $l_B$) is formed in the vicinity of the wire boundary. The wave functions are strongly localized in this well which leads to the increase of the electron density near the edges. Because of the presence of this well, the subbands start to depopulate from the central region of the wire and remain pinned in the well region until they are eventually pushed up by increasing magnetic field. We also demonstrate that the spin polarization of electron density as a function of magnetic field shows a pronounced double-loop pattern that can be related to the successive depopulation of the magnetosubbands. In contrast to the case of a smooth confinement, in hard-wall wires the compressible strips do not form in the vicinity of wire boundaries and spatial spin separation between spin-up and spin-down states near edges is absent.