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Purpose Neutral zone (NZ) parameters in spinal biomechanics studies are sensitive to spinal instability, disc degeneration, and repair. Multiple methods in the literature quantify NZ, yet no consensus exists on applicability and comparability of methods. This study compares five different NZ quantification methods using two different load‐deflection profiles. Methods Rat caudal and lumbar motion segments were tested in axial rotation to generate load‐deflection curves with profiles exhibiting prominent distinction between elastic and NZ regions (ie, triphasic) and profiles that did not (ie, viscoelastic). NZ was quantified using five methods: trilinear, double sigmoid (DS), zero load, stiffness threshold (ST), and extrapolated elastic zone. Absolute agreement and consistency of NZ parameters were assessed using intraclass correlation (ICC), Bland‐Altman analyses, and analysis of variance. Results For triphasic profiles, NZ magnitude exhibited high consistency (methods correlate but differ in absolute values), and only some methods exhibited agreement. For viscoelastic profiles, NZ magnitude showed limited consistency and no absolute agreement. NZ stiffness had high agreement and consistency across most methods and profiles. For triphasic profiles, the linear NZ regions for all methods were not well‐described by a linear fit yet for viscoelastic profiles all methods characterized a linear NZ region. Conclusion This NZ comparison study showed surprisingly limited agreement and consistency among NZ parameters with approximately 5% to 100% difference depending on the method and load‐deflection profile. Nevertheless, the DS and ST methods appeared to be most comparable. We conclude that most NZ quantification methods cannot be applied interchangeably, highlighting a need to clearly state NZ calculation methods. Future studies are required to identify which methods are most sensitive to disc degeneration and repair in order to identify a “best” method. The neutral zone (NZ) is a clinically relevant metric of spinal motion segment laxity, but measuring it is difficult due to the viscoelastic nature of the intervertebral disc. Various NZ quantification methods are currently used in the field, yet the degree of agreeability and interchangeability between methods remains unknown. Our findings indicate that methods rarely agree in measurement and should therefore not be considered interchangeable, highlighting the need to clearly describe the underlying methodology in order to contextualize NZ results.

This research examines the effect of incorporating hybrid fibres and rubber aggregates on the flexural behaviour of reinforced concrete beams. Rubber shreds, prepared from waste conveyor belts and coated with sand to enhance bonding, were used as partial replacements for coarse aggregates at levels of 2.5%, 5%, and 7.5%. Additionally, glass fibre and polypropylene fibres were introduced into the concrete mix at dosages of 0.3% at different combinations, including PP 70% + Glass 30%, PP 60% + Glass 40%, PP 50% + Glass 50%, PP 40% + Glass 60%, and PP 30% + Glass 70%. A total of eighteen reinforced concrete beams were cast for this investigation, each with dimensions of 250 mm × 150 mm × 3000 mm. The beams were subjected to four-point bending tests over a clear span of 2800 mm to evaluate their flexural response. Values such as first crack load, deflection at first crack, yield load, deflection at yield, ultimate load, and deflection at ultimate were recorded. Load–deflection curves were plotted for all beam types. The results revealed that beams incorporating both sand-coated rubber shreds and hybrid fibres generally exhibited improved flexural performance compared to conventional concrete beams and those containing only rubber aggregates. Specifically, the beam containing 7.5% sand coated rubber and hybrid fibres (40% polypropylene + 60%glass fibres) showed notable improvement, with the first crack load increasing by 29.77%, deflection at first crack load by 21.47%, yield load by 52.86%, deflection at yield load by 28.73%, ultimate load by 14.32% and deflection at load by 53.84 relative to the control specimens.

Thin plates subjected to transverse load and undergoing large deflections have been widely studied and published in the literature. However, there is still a lack of information and understanding about the membrane stresses created under large deflections and their associated Airy stress function, as displayed in the well-known von Kármán equations set. The present study aims at providing explicit expressions for the membrane stresses, the deflections, and the Airy stress function for a general square plate area vertically uniformly loaded to reach large deflection state. This was obtained by using the results of a high-fidelity finite element analysis applied on a lateral loaded simply supported thin square plate, which are then casted to yield approximate Fourier series expressions for the membrane stresses, deflections, and the Airy stress function. The stress map figures provide a good understanding of the critical points on the plate, while the explicit mathematical expressions enabled the calculation of deflections and stresses for the entire plate area. Among other interesting findings, the presence of relatively high tensile and compressive membrane stresses existing near the plate edges was revealed, which might lead to potential failure hazards. The derivatives of the deflections and the Airy stress function enabled the validation of the large deflections von Kármán equations set for the investigated case, and it turned out that the generated expressions for the stresses and the lateral deflection based on a high-fidelity finite element model satisfy the second equation with a good accuracy, while the first one remains to further be investigated. Moreover, using the generated explicit equations, the load influence on the deflections and stresses was also analyzed to yield general novel expressions for the medium and very large deflections states. To generalize the investigated case, the stresses and the deflections were non-dimensionalized so they can be used for any material and plate dimensions.

Large deflection of rectangular plates under transverse pressure is described by Föppl–von Kármán equations, which have only approximated solutions. One of these methods is the separation into a small deflection plate and a thin membrane described by a simple third order polynomial expression. The present study presents an analysis to obtain analytical expressions for its coefficients by using the plate’s elastic properties and dimensions. To validate the non-linear relationship between the pressure and the lateral displacement of the multiwall plate, a vacuum chamber loading test is used to measure the plate’s response, with a large number of plates and length–width combinations. In addition, to further validate the analytical expressions, several finite element analyses (FEA) were performed. It has been found that the polynomial expression fairly describes the measured and calculated deflections. This method allows the prediction of plate deflections under pressure as soon as the elastic properties and the dimensions are known.

Key messageLarger differences of maximum load among families were found in mature wood compared to juvenile wood, suggesting the possibility of improving mature wood with higher resistance to rupture and maintaining characteristics of material in Larix kaempferi (Lamb.) Carr. by selecting specific mating parents.ContextBecause the wood from L. kaempferi trees is used for construction lumber, wood properties and bending properties should be focused on as targeted traits of tree breeding programs.AimsWe clarified the radial variation of inheritance for wood properties and bending properties and classified the features of bending properties among families in L. kaempferi.MethodsAnnual ring width, latewood percentage, air-dry density, microfibril angle, modulus of elasticity, modulus of rupture, and bending work at five radial positions were investigated for 15 full-sib families of 36-year-old L. kaempferi grown in two progeny test sites in Japan.ResultsHigher heritability at almost all radial positions was found in air-dry density. Phenotypic and genetic correlations between air-dry density and bending properties showed relatively higher values at almost all radial positions. Load-deflection curves in 15 families could be divided into three groups in juvenile and mature wood. Variation among groups for load-deflection curves in mature wood was relatively larger than that in juvenile wood.ConclusionAir-dry density can be used as a criterion to select trees with superior bending properties. Mature wood in L. kaempferi could be effectively improved by selecting individuals.

Wood properties (annual ring width, tracheid length, microfibril angle [MFA], basic density, and air-dry density) and mechanical properties (modulus of elasticity [MOE], modulus of rupture [MOR], bending work, and compressive strength) in 34-year-old Chamaecyparis obtusa trees of six half-sib families were measured from pith to bark to clarify radial variations in inheritance of these traits and the relationships between wood properties and mechanical properties. In addition, within-tree and among-family differences in the load–deflection curves were discussed. Radial variations of all wood properties were fitted to linear or nonlinear mixed-effects models with random effects of families. The MFA was correlated with MOE in all radial positions, whereas air-dry density correlated with all mechanical properties in mature wood. Radial variations in broad-sense heritability differed between wood properties. A relatively higher broad-sense heritability was recognized in almost all wood properties for mature wood. Based on the results, it was concluded that mechanical properties in mature wood can be effectively improved using MFA and air-dry density as criteria. In addition, the types of load–deflection curve in mature wood differed from those in juvenile wood, suggesting that not only elastic properties, but also plastic properties in C. obtusa are affected by genetic controls, especially in mature wood.

To investigate the biomechanical properties of Camellia oleifera branches under two loading speeds within a specific diameter range, three-point bending tests were conducted using a universal material–testing machine. The tests were performed at loading speeds of 10 mm/min and 20 mm/min on branches with diameters ranging from 5 mm to 40 mm. This study aims to provide insights into the design of a manipulator gripper used in a vibrating harvester for Camellia oleifera fruit. Four main varieties of Camellia oleifera were tested to determine their elastic modulus. The nonlinear least squares method, based on the hyperbolic tangent function, was employed to fit the bending load–deflection curves of the branches. This process constructed multi-parameter transcendental equations involving elastic modulus, diameter, and loading speed. Results indicated that the branches of four Camellia oleifera varieties exhibited significant differences in their biomechanical properties, with their modulus of elasticity ranging from 459.01 MPa to 983.33 MPa. This suggests variability in the bending performance among different varieties. For instance, Huaxin branches demonstrated the highest rigidity, while Huashuo branches were softer in general. For the proposed empirical fitting equations, when the fitting parameter k is 168 ± 20 and the parameter c is 3.102 ± 0.421, the bending load–deflection relationship of the branches can be predicted more accurately. This study provides a theoretical basis for enhancing the efficiency of mechanized vibratory picking of Camellia oleifera and optimising the design of the gripper.

Bridge displacement is an important part of safety evaluations. Currently, bridge displacement monitoring uses only a few measurement points, making it difficult to evaluate safety. To address this problem, we propose a multi-point displacement synchronous monitoring method. The structural surface has abundant natural texture features, so we use the feature points of the structural surface as the displacement measurement points and propose a feature point displacement calculation method. Furthermore, we conduct experiments on a beam in the laboratory and obtain the beam’s multi-point displacement monitoring results. The monitoring results show that the displacement of some feature points is mismatched. We propose the use of the structural deflection curve to eliminate the feature point displacement mismatches. This method uses the maximum rotation angle of the deflection curve to eliminate displacement mismatches. The results indicate that it is effective to eliminate displacement mismatches in simple structures, such as simply supported beams. Finally, we obtain the test beam’s multi-point displacement synchronous monitoring results. Compared with the 3D laser scanning measurement method, the maximum error of the monitoring results is 8.70%. Research shows that the main reason for the monitoring error is image noise, and the noise interference problem due to its application in practical bridges requires further investigation. Compared with traditional displacement monitoring, this method has significant economic, efficiency, and data integrity advantages. The method has application prospects for multi-point displacement monitoring of simple structures, such as simply supported beams.

Glass fiber reinforced cement (GRC) incorporating foam has good thermal insulation. Micro pores not only lowered the strength of the cement matrix but also changed the friction between the fiber and the matrix. It has an influence on modulus of rupture (MOR) and fracture energy of GRC. In this work, the effect of the glass fiber and foam contents of GRC on the MOR and fracture energy were evaluated using four-point flexural tests. The results show that glass fiber content has little influence on MOR of GRC. However, the MOR decreased significantly with increasing foam content. The empirical formula summarized by experiments can well characterize the relationship between the MOR and density of foamed GRC. The content of glass fiber and foam has a significant influence on the fracture energy of GRC. The fracture energy of foamed GRC decreased with the decrease of dry bulk density, and the decrease was fast and then slow.

Alkali-activated concrete (AAC) has recently gained a lot of potential to become one of the most recommended sustainable replacements for Ordinary Portland cement concrete (OPCC). In the present investigation, an attempt has been made to study the static and fatigue flexural behavior of AAC compared to that of OPCC by using numerical modeling FEA software, ABAQUS. The nonlinear behavior of the stress-strain curve of the concrete has been studied using the concrete damage plasticity (CDP) model. A 2D notched beam was modelled using plane stress condition and three-point bending tests were performed under monotonic loading to obtain the static behavior of concrete. The result obtained has been utilized to fix the loading range for cyclic loads in fatigue analysis and at different loading frequencies. The load-CMOD curves and load-deflection curves were obtained for both static and fatigue loading, and the number of cycles to failure during fatigue. From the results, it has been observed that the Ordinary Portland cement concrete specimens sustain more load than that of Alkali-activated concrete under monotonic loading. However, AAC has shown more resistance to fatigue than that of the OPCC and the frequency of loading significantly influences the fatigue performance.