Moment Ratio Research Articles

Experiment and analysis on walnut (Juglans regia L.) shedding force based on low-frequency vibration response

Walnut (Juglans regia L.) is a highly valuable crop and is widely used as a food, medicine, and industrial product. Studying walnut detachment force is an important prerequisite for bed harvesting through low-frequency shaking. In this study, the stalk–branch and stalk–fruit kinetic models were analyzed under different vibration modes by establishing a local vibration model. A platform was built to conduct tests of static separation force separately for different modes. The inertial force and static separation force of the vibration response were analyzed by combining each vibration parameter with the local fruit–stalk–branch vibration model, and the separation ratios were derived under different vibration parameters. In the vibration response with a frequency of 10 Hz and amplitude of 80 mm, the maximum separation ratios of inertial tensions at connection points between the branch and stalk, stalk and tail fruit, and stalk and side fruit were 0, 25.5%, and 26.3%, respectively; the maximum separation ratios of the inertial bending moment were 86.4%, 96%, and 83%, respectively; and the detachment difficulty coefficient of the motion mode generating inertial bending moments was much lower than that of the mode generating inertial tensions. The relationship between the separation force and biological characteristics was analyzed, and field vibration tests were conducted to verify the separation force tests. The results of the study can guide development and adjustment of vibration parameters of a vibrating device for harvesting and help further study of the effect of excitation mode on fruit shedding.

Seismic vulnerability of shield tunnels in interbedded soil deposits: Case study of submarine tunnel in Shantou Bay

This paper presents a numerical approach for deriving seismic fragility curves for a submarine shield tunnel subjected to transverse ground shaking in interbedded soil deposits. To simulate the nonlinear behavior of soils, PM4Sand and HS-small constitutive models were adopted. In contrast, the closed-form elastic design method or elastic–plastic design method was used for modeling the shield tunnel lining considering the effect of joints on the seismic performance of structures. Fully coupled numerical analyses provided a satisfactory interpretation of the seismic responses of soil–structure systems considering the effects of groundwater level and soil–tunnel interaction. Subsequently, free-field peak ground acceleration was selected as the intensity measure. The ratio of maximum bending moment to capacity bending moment or permanent joint rotation of the tunnel lining was selected as the damage measure, combined with incremental dynamic analysis, a series of fragility curves were generated. In this study, one-dimensional equivalent-linear earthquake site response analysis was implemented to validate the nonlinear dynamic analysis under weak earthquakes. However, the analysis overestimates the amplitude periodic vibrations in interbedded soil deposits under strong earthquakes. Additionally, numerical results show that the examined tunnel is prone to slight or moderate damage under ground shaking, and its joints are more vulnerable to damage than its segments. The fragility curves constructed were compared with existing fragility curves, highlighting the significant effects of local soil profiles, groundwater conditions, soil–tunnel interaction, and segmental joints on the seismic vulnerability of shield tunnels in a submarine environment. The developed fragility functions contribute to the prediction of seismic damage to submarine shield tunnels of similar characteristics, enabling the rapid and efficient response of structures to disasters in ocean engineering.

BUCKLING STRENGTH OF COLUMNS IN LOW-RISE MULTI-SPAN FRAMES EVALUATED BY THE STABILITY INDEX

The objective of this study was to investigate the validity of the effective length factors for low-rise multi-span frames obtained by the stability index (SI) method, and SI is defined by the ratio of PΔ moment to story moment. The SI method calculates the buckling load based on the condition that the story with the maximum stability index is the first to lose its stiffness compared with the other stories at the time of buckling. The analytical parameters used in the present study were the stiffness ratios of beams and columns. The effective length factors obtained by the SI method were compared with the exact effective length factors provided by the buckling slope-deflection method. The story displacement Δ of the PΔ moments was calculated by the application of horizontal forces at the top of the column of each story. This paper outlines a valid process to evaluate the effective length factors using the SI method and demonstrates the impact of the horizontal force distribution and Pδ moments on the accuracy of the SI method in low-rise, multi-span frames.

Searching for a 0(980)-meson parton distribution function

In this paper, we calculate the scalar a 0(980)-meson leading-twist wave function by using the light-cone harmonic oscillator model (LCHO), where the model parameters are determined by fitting the ξ-moments of its light-cone distribution amplitudes. Then, the a 0(980)-meson leading-twist light-cone distribution amplitudes with three different scales ζ = (1.0, 2.0, 5.2)GeV are given. After constructing the relationship between the a 0(980)-meson leading-twist parton distribution functions/valence quark distribution function and its LCHO wave function, we exhibit the and with different scales. Furthermore, we also calculate the Mellin moments of the a 0(980)-meson’s valence quark distribution function with n = (1, 2, 3), i.e. , and . Finally, the scale evolution for the ratio of the Mellin moments are presented.

Seismic performance of bolted T-stub Beam-to-Box column connection

Using internal continuity plates in box columns due to accessibility problems and complicated detailing of connection was perceived as fraught with shortcomings and limitations. To overcome this deficiency, the effectiveness of external continuity plates in conjugation with T-stub connectors in I-beam to box-column connections under cyclic action is investigated in this study. Three damage control strategies based on the fuse action of T-stubs (T-F), strengthening the connections (T-S), and using reduced beam section (RBS) connections (T-R) are pursued and are compared to a corresponding end-plate connection (E). Nonlinear finite element analyses are conducted using the ABAQUS/STANDARD software on the connections under the qualification cyclic loading conditions to elucidate all the main seismic behavioral aspects, including the strength, initial stiffness, energy dissipation, ductility, von-Mises stress, and equivalent plastic strain distributions of models. First, the accuracy of numerical models is validated by a series of available experimental results. Then, a parametric study is performed on the effects of the moment ratio of the beam to column, the number of continuity plates, stiffeners embedded on the beam, and using high strength materials on the seismic performance of the connections. From the results, it is found that the T-S model was the most efficient among the different connections studied, supplying the stiffness, strength, energy absorption, and ductility increases by 2%, 21%, −17%, and 22%, respectively with respect to the E model, satisfying the requirements of AISC Seismic Provisions for SMF. Increasing the beam-to-column moment ratio and the number of continuity plates, had limited effects by less than 10% on the seismic performance of the connections. In the absence of continuity plates, the connections exhibited worse inelastic seismic performance with decreases in stiffness, strength, and energy dissipation up to 67%, 44%, and 74%, respectively. The T-F connection gained a 13% strength increase and satisfied the AISC requirements when high-strength T-stubs are used. Based on the numerical observations, design strength and rotational stiffness of the proposed connections on the component-based joint design strategies, are finally outlined.

Cross-sectional and bidirectional connection design methods for volumetric steel modules

Modular steel constructions (MSCs) are becoming increasingly popular because of their advantages such as rapid construction speed, less demand for on-site labor, quick demolition, and recycling after demolition. An architecturally pleasing all bolted joint called modular bidirectional load-bearing and energy-dissipating joint (MBJ) with innovative modular bidirectional load-bearing and energy-dissipating connectors (MBC) was proposed in this study to achieve vertical and horizontal connection of adjacent modules simultaneously. Design methods that involve cross-sectional design of modules, as well as bidirectional connection design among modules were proposed to establish a relationship between the design of modules and MSCs by “equal initial stiffness” principles of MBJs and traditional bidirectional joints (TBJ). The initial stiffness of MBJs is based on a deep analysis of the force transfer mechanism and deformation characteristics of MBJ panel zones. The FEM of the MBJs was set according to the verified modeling approach, in contrast to the experimental results. Finite element models were set to verify the proposed design method, and theoretical studies were conducted. Our findings show that the ratio of the total cross-sectional moment of inertia of adjacent columns to that of the traditional column ranged from 0.600 to 1.228, the “equal initial stiffness” of MBJs to that of TBJs can be achieved, and the lateral strength of MBJs is consistently greater than that of the corresponding TSJs. In addition, the proposed design method can easily achieve standardization of modules because the ratio of the total cross-sectional moment of inertia of the MBC, ceiling beam, and floor beam to that of traditional beams is in a large range. The maximum error of the initial stiffness of the MBJs between the FEM results and theoretical values was 13.89 %, which meets the engineering accuracy requirements. The research results provide a theoretical basis for the design of MSCs for seismic regions.

Modulation of the magnetization and Gilbert damping in Heusler-alloy Co3–xFexAl thin films

The saturated magnetization (mtot) and the Gilbert damping constant (α) are the two key factors that determine the critical current density of the magnetization reversal in the spin-transfer-torque magnetic memory devices. Here, this study demonstrates the efficient modulation of these two parameters by tunning the composition of the Heusler Co3–xFexAl thin films, utilizing the x-ray magnetic circular dichroism technique and ferromagnetic resonance measurements. With the increase in Fe concentration, the mtot shows a downward trend mainly resulting from the decrease in Fe local magnetic moment instead of Co. On the other hand, the ultralow α decreases from 0.004 to 0.0012. This has been attributed to the reduction in the spin–orbit coupling, which is corroborated by the decrease in the orbit-to-spin moment ratio. Our findings add a building block for the Heusler compounds with tunable Gilbert damping and appropriate magnetization and show great potential in spintronic applications.

The influence of residual plural scattering after deconvolution in electron magnetic chiral dichroism

This work investigated the existence and influence of residual plural scattering in electron magnetic chiral dichroism (EMCD) spectra. A series of low-loss, conventional core-loss, and q-resolved core-loss spectra at Fe-L2,3 edges were detected from areas of different thicknesses in a plane-view sample of Fe/MgO (001) thin film. It reveals by comparison that there remains noticeable plural scattering in q-resolved spectra acquired at two particular chiral positions after deconvolution, and the residual scattering is more significant in thicker areas than thinner ones. Accordingly, the orbital-to-spin moment ratio extracted from EMCD spectra, which is the difference between the two q-resolved spectra after deconvolution, would be in principle increased with increasing sample thickness. The randomly fluctuated moment ratios displayed in our experiments are greatly attributed to a slight and irregular variation of local diffraction conditions due to the bending effect and imperfect epitaxy in detected areas. We suggest EMCD spectra should be acquired from sufficiently thin samples to minimize the plural scattering effect in originally detected spectra before any deconvolution. In addition, great care should be taken for slight misorientation and imperfect epitaxy when performing EMCD investigation on epitaxial thin films using a nano beam.

Minimum longitudinal reinforcement in rectangular and flanged reinforced concrete walls

The amount of longitudinal steel in reinforced concrete walls is a key point in the damage distribution along the wall, although it is usually associated mainly with the prevention of temperature and shrinkage problems. A recent earthquake in New Zealand pointed out its relevance after the observation of a localized failure mode found in walls due to insufficient longitudinal steel reinforcement. Low amounts of longitudinal steel reinforcement prevent the correct distribution of the damage and can even lead to an early fracture of the reinforcement. The following study analyzes walls with different sections, such as T, L, and C-shaped walls, among others, subjected to pushover analysis, where the amount of longitudinal boundary reinforcement is varied, using values close to the minimum provided by ACI 318-19 code. The main parameter under analysis was the strain at the boundaries, revealing different behavior depending on the amount of boundary steel. When using steel amounts less than the minimum provided by the code, a greater growth for the tensile strain is observed, which in turn localizes the damage in a few zones along the wall height at low drift levels. This is overcome when using the recommended minimum steel amount. In addition, regarding the strength-to-cracking moment ratio (Mn/Mcr), although related to the growth of tensile strains, there is no specific value that can be recommended for all wall cross-sections.

Particle-size polydispersity analysis based on the unified exponential/power-law approach to small-angle scattering

Controlling particle dispersity is of huge importance for practical applications in nanoscience and technology. The analysis of small-angle scattering of X-rays and neutrons for strongly polydisperse particulate systems is considered from the point of view of describing the type of size distribution function without applying classical regularization approaches. This article presents the development of a method for determining the polydispersity parameters of nanoobjects, based on the analysis of the ratio of various moments of the size distribution function, which are proportional to different invariants of the scattering curve. The use of the unified exponential/power-law approximation to describe small-angle scattering data makes it possible to determine the type of distribution, the average size and the spread. The possibilities of the method were tested for several hydrosols of metallic nanoparticles.

CALCULATION MODEL OF A MULTI-STOREY REINFORCED CONCRETE FRAME WITH COMPLEXLY STRESSED BEAMS UNDER ACCIDENTAL IMPACT

A computational model is presented for determining deformations in complexly stressed beams of a structurally non-linear reinforced concrete frame in a transcendental state caused by a special emergency action in the form of a sudden removal of one of the structural elements. The determination of the stress-strain state after the formation of spatial cracks in the reinforced concrete elements of the frame was carried out using the calculated spatial section. At the same time, dynamic additional loads in the design section of the reinforced concrete frame element from a special impact are determined on an energy basis using the “bending moment-curvature” and “torque-angle of rotation” diagrams. The considered calculation algorithm includes the determination of forces in compressed concrete, longitudinal and transverse reinforcement for primary and secondary design schemes and verification of special limit state criteria. The results of a numerical analysis of the effect of cracking, the ratio of torque and bending moment on the stress state in transverse and longitudinal reinforcement and on the dissipative properties of a frame structural system are presented

Symmetry resolved entanglement of excited states in quantum field theory. Part III. Bosonic and fermionic negativity

In two recent works, we studied the symmetry resolved Rényi entropies of quasi-particle excited states in quantum field theory. We found that the entropies display many model-independent features which we discussed and analytically characterised. In this paper we extend this line of investigation by providing analytical and numerical evidence that a similar universal behavior arises for the symmetry resolved negativity. In particular, we compute the ratio of charged moments of the partially transposed reduced density matrix as an expectation value of twist operators. These are “fused” versions of the more traditionally used branch point twist fields and were introduced in a previous work. The use of twist operators allows us to perform the computation in an arbitrary number of spacial dimensions. We show that, in the large-volume limit, only the commutation relations between the twist operators and local fields matter, and computations reduce to a purely combinatorial problem. We address some specific issues regarding fermionic excitations, whose treatment requires the notion of partial time-reversal transformation, and we discuss the differences and analogies with their bosonic counterpart. We find that although the operation of partial transposition requires a redefinition for fermionic theories, the ratio of the negativity moments between an excited state and the ground state is universal and identical for fermions and bosons as well as for a large variety of very different states, ranging from simple qubit states to the excited states of free quantum field theories. Our predictions are tested numerically on a 1D Fermi chain.

Morphology, flow structure, and sediment transport in the Paraná and Piquiri Rivers confluence, Brazil

Confluences are places of complex interaction of flow and sediments coming from different channels. Studies at large confluences have advanced the understanding of these environments on a larger scale. This study is carried out at the confluence formed by the Paraná and Piquiri rivers in the state of Paraná - Brazil. It characterizes the morphology, flow structure and sediment dispersion for these two channels. The methodology consists of: interpoling bathymetric data; analyze the ADCP data – Acoustic Doppler Current Profiler and quantify the suspended and bottom sediments. ADCP data was processed in VMT software and generated the following information: flow direction, sediments load (bed and suspended) and also used to calculate the moment ratio (Mr), discharge ratio (Qr), flow power (Ω), and specific flow power (ꞷ) in both channels. The results reveal the variation of channel depth, and specific morphological areas for the confluence with a sediment accumulation zone, submerged lateal bar and excavation area. The flow dynamics shows an increase in velocity in the Paraná River downstream of the confluence, and a decrease in the flow velocity of the Piquiri River as it approaches the junction. The confluence has flow stagnation zone, acceleration and shear layer. The concentration of suspended sediment is higher in the Piquiri River, on the other hand the Paraná River presents thicker fractions of bed material.

High resolution FTIR spectrum of CH2D37Cl: ν4 and ν8 fundamental bands

The high-resolution Fourier transform infrared spectrum of CH2D37Cl has been analyzed in the region of the ν4 and ν8 bands from 1170 to 1370 cm−1. The upper states of these fundamentals, separated by 0.6 cm−1, interact with each other by a-type as well as b-type Coriolis resonance, and a strong asymmetric distribution of the intensity of the rotational structure in each band is observed. The spectral analysis resulted in the assignment of 2774 and 1611 rovibrational transitions for ν4 and ν8 bands, respectively, which have been simultaneously fitted using Watson's A-reduction Hamiltonian in the Ir representation and the relevant perturbation operators. A set of spectroscopic constants for the two fundamentals as well as seven coupling terms have been determined. From spectral simulations, the dipole moment ratio |Δµa/Δµb| of ν4 has been determined to be 1.3 ± 0.1 while the intensity ratio between ν4 and ν8 has been estimated to be 5.0 ± 1.0.

Seismic Behavior Analysis of Recycled Aggregate Concrete-Filled Square Steel Tube Frames.

In this study, the seismic behavior of a recycled aggregate concrete-filled square steel tube (S-RACFST) frame under different design conditions was investigated. Based on previous studies, a finite element model for the seismic behavior of the S-RACFST frame was developed. Moreover, the axial compression ratio, beam-column line stiffness ratio, and yield bending moment ratio of the beam-column were regarded as the variation parameters. It was through these parameters that the seismic behavior of eight S-RACFST frame finite element specimens was discussed. The seismic behavior indexes, such as the hysteretic curve, ductility coefficient, energy dissipation coefficient, and stiffness degradation were obtained-which, in turn, revealed the influence law and the degree of the design parameters regarding seismic behavior. Moreover, the sensitivity of the various parameters with respect to the seismic behavior of the S-RACFST frame was evaluated via grey correlation analysis. The results show that the hysteretic curves of the specimens were fusiform and full with respect to the different parameters. Firstly, with the axial compression ratio increasing from 0.2 to 0.4, the ductility coefficient increased by 28.5%. In addition, the equivalent viscous damping coefficient of the specimen with the axial compression ratio of 0.4 was 17.9% higher than that of the specimen with the axial compression ratio of 0.2, which was 11.5% as well as that with an axial compression ratio of 0.3. Second, when the line stiffness ratio rises from 0.31 to 0.41, the specimens' bearing capacity and displacement ductility coefficient both get better. However, the displacement ductility coefficient gradually decreases when the line stiffness ratio is greater than 0.41. As a result, an optimal line stiffness ratio (0.41) thus exhibits good energy dissipation capacity. Thirdly, with the increase in the yield bending moment ratio from 0.10 to 0.31, the bearing capacity of the specimens improves. In addition, the positive and negative peak loads increased by 16.4% and 22.8%, respectively. Moreover, the ductility coefficients were all close to three, thus demonstrating good seismic behavior. The stiffness curve of the specimen with a large yield bending moment ratio with respect to the beam-column, is higher than those that possess a small beam-column yield moment ratio. In addition, the yield bending moment ratio of the beam-column possesses a significant influence on the seismic behavior of the S-RACFST frame. Furthermore, the yield bending moment ratio of the beam-column should be considered first in order to ensure the seismic behavior of the S-RACFST frame.

On the low-frequency acoustic center.

Acousticians typically consider the acoustic center of a source to be the point from which sound waves appear to diverge spherically. Many applications require the center's accurate determination, but its deeper significance and means of assessment have often remained ambiguous. This work revisits the acoustic center and shows how a low-frequency sound radiator with omnidirectional far-field directivity has a center defined by its dipole-to-monopole moment ratio. This definition yields conclusive results for several theoretical sources and highlights the limitations of characterizing the acoustic center only in terms of an equivalent point source.

Interlimb Asymmetry in Knee Extension Moment During Double-Leg Squatting Is Associated With Persistent Quadriceps Weakness After ACL Reconstruction

Background: Although double-leg squatting is less dynamic and places less demand on the quadriceps compared with landing tasks, the relationship between double-leg squatting biomechanics and persistent quadriceps weakness after anterior cruciate ligament reconstruction (ACLR) is unknown. Purpose: To clarify the relationships between asymmetries in quadriceps strength and lower limb biomechanics during double-leg squatting >1 year after ACLR. Study Design: Controlled laboratory study. Methods: A total of 26 participants (5.5 ± 3.8 years after ACLR) were enrolled. The limb symmetry index (LSI) of isokinetic quadriceps strength was used to divide participants into the high-quadriceps (HQ) group (LSI ≥90%; n = 18) and the low-quadriceps (LQ) group (LSI <90%; n = 8). The knee, hip, and ankle extension moment (relative to body weight and support moment [sum of knee, hip, and ankle moments]) and vertical ground-reaction force during double-leg squatting were analyzed using 3-dimensional motion analysis. The association of quadriceps strength and biomechanical variables was tested using 2-way analysis of variance and univariate regression analysis. Results: A significant group-by-limb interaction was found for the peak knee extension moment and the ratios of knee and hip extension moment to support moment ( P < .001, P = .015 and P < .001, respectively). The LQ group showed a significantly smaller peak knee extension moment and knee to support moment ratio but a larger hip to support moment ratio in the involved limb than in the uninvolved limb (95% CIs: knee extension moment, −0.273 to −0.088 N·m/kg; knee to support moment ratio, −10.7% to −2.2%; hip to support moment ratio, 3.2% to 8.5%). No interlimb difference was found for the HQ group. The LSI of quadriceps strength was significantly associated with the LSI of peak knee extension moment ( R 2 = 0.183), knee to support moment ratio ( R 2 = 0.256), and hip to support moment ratio ( R 2 = 0.233). The mean maximum isokinetic quadriceps strength and peak knee extension moment during squatting on the involved limb of the LQ group were 2.40 ± 0.39 and 0.90 ± 0.16 N·m/kg, respectively. Conclusion: Asymmetrical biomechanics during double-leg squatting was associated with persistent quadriceps weakness after ACLR. The LQ group had reduced knee extensor moment on the involved side during squatting despite loading at approximately half the maximum strength. Clinical Relevance: Quadriceps strengthening exercises, together with interventions to improve neuromuscular control, may reduce asymmetrical biomechanics during double-leg squatting.

Water hydration of polyethylene glycol dimethyl ether.

In this work, GHz and THz complex dielectric spectra of a polyethylene glycol dimethyl ether (2000 g/mol) aqueous solution were studied. The reorientation relaxation of water in this kind of macro-amphiphilic molecule solution can be well described by three Debye models, including under-coordinated water, bulk-like water [water molecules in a tetrahedral hydrogen bond network (bulk water) and bulk water molecules affected by hydrophobic groups], and slow hydrating water (water molecules donating hydrogen bonds to hydrophilic ether groups). The reorientation relaxation timescales of bulk-like water and slow hydration water both show increases with concentration from 9.8 to 26.7ps and from 46.9 to 100.1ps, respectively. By estimating the ratios of the dipole moment of slow hydration water to the dipole moment of bulk-like water, we calculated the experimental Kirkwood factors of bulk-like and slow hydrating water. The experimental Kirkwood factor of bulk-like water increased from 3.17 to 3.44 with concentrations, while the experimental Kirkwood factor of slow hydrating water roughly remained constant at 4.13 from concentrations of 15%-60%. The estimated water molecule numbers of three water components around monomers also confirm our sorting for water components.

Distribution of moments of Hurwitz class numbers in arithmetic progressions and holomorphic projection

In this paper, we study moments of Hurwitz class numbers associated to imaginary quadratic orders restricted into fixed arithmetic progressions. In particular, we fix t t in an arithmetic progression t ≡ m ( mod M ) t\equiv m\ \, \left ( \operatorname {mod} \, M \right ) and consider the ratio of the 2 k 2k -th moment to the zeroeth moment for H ( 4 n − t 2 ) H(4n-t^2) as one varies n n . The special case n = p r n=p^r yields as a consequence asymptotic formulas for moments of the trace t ≡ m ( mod M ) t\equiv m\ \, \left ( \operatorname {mod} \, M \right ) of Frobenius on elliptic curves over finite fields with p r p^r elements.

PROBLEMS OF COMPUTER STRUCTURAL ANALYSIS AND REINFORCEMENT CALCULATION TECHNIQUES OF REINFORCED CONCRETE RIBBED SLABS

This paper proposes an overview of computer structural analysis and reinforcement calculation techniques of reinforced concrete ribbed slabs that are used in Ukraine. It considers the fundamental hypotheses and assumptions of these techniques and analyzes the possibility of implementation of the building codes’ requirements into automated calculations. Numerical experiments confirm the existence of a relationship between the normal stress distribution pattern in the rib’s cross section and the width of the slab zone, which participates in the rib’s bending. We conclude the need to develop a generalizing methodology of FEM structural analysis for such structures, which could be implemented in modern FEM-analysis packages implementing building information modelling technology (BIM).Design forces in the elements of monolithic ribbed floors are determined taking into account plastic deformations. This approach is based on the assumption of the formation with increasing load in statically indeterminate systems of plastic hinges, each of which leads to a decrease in the static indeterminacy of the system by one degree. The appearance of plastic hinges leads to a redistribution of bending moments, which is calculated using a static or kinematic method. In the general case, the sum of the span moment and half of the support moments for the span of a single-span beam is always equal to the span moment in a similar single-span beam. That is, the ratio of support and span moments does not affect the bearing capacity of the statically indeterminate system as a whole, but only determines the order of formation of plastic hinges.