Torsional Stiffness Research Articles

Three-dimensional elastic properties of open-cell porous structures: Analytic and finite element modelling

The current paper introduces a three-dimensional micromechanical model of open-cell cellular solid materials and presents the homogenization of the model to an orthotropic continuum. An orthotropic microstructural beam model was created and tested under pure stretch and pure angular distortion to identify the dominant deformation modes by mapping the contributions of normal-, bending- and torsional stiffness to the total strain energy. In the case of unidirectional tension, the deformation mode was dependent primarily on the proportion of normal- and bending stiffnesses, except for the cases with similarly small bending- and torsional stiffness values, where the contribution of torsion was significant. In the case of the pure angular distortion, the key deformation mode was defined by the ratio of bending- and torsional stiffness values, except for the case of large normal- and torsional stiffness values, which resulted in normal-deformation-driven behaviour.The homogenization of the micromodel was conducted by creating an equivalent spring model, by means of which the equivalent elastic modulus values for the main directions of orthotropy have been derived as functions of the geometric and elastic properties of the beams. With the aid of the equivalent spring models, the relative density dependence of Young’s modulus and shear modulus have been examined. The typical second-degree relationship was found to become inaccurate in the range of lower porosity. In the case of increasing relative density values, the exponent of the elastic modulus function decreased while the exponent of the shear modulus increased.

Experimental assessment of the eigenstress state in two-ply yarns and its effect on tensile properties

Propaedeutical to a better understanding of the mechanics of cables, with potential applications in material science and biology, tensile tests were performed on two-ply yarns made of rubber rods, manufactured by transforming the twist on two adjacent straight rods into tortuosity for the resulting double-helix shape. Modeling of the yarn as a pair of Kirchhoff rods in reciprocal contact, fails to provide results in agreement with experiments, especially when the helix slope angle α tends to π/4, representing the geometric limit for material interpenetration. This discrepancy could not be justified by considering the viscosity of the rods, their cross-sectional distortion, or cohesive/frictional contact. Our contribution starts from the experimental observation that the rods are in an eigenstress state already in the reference balanced configuration. This is characterized by a high twist, dictated by the ratio between torsional and bending rod stiffness, which increases as α decreases, growing unboundedly as α→π/4. Experiments confirm that twisting can significantly increase the tensile stiffness of straight rubber rods, in agreement with non-linear elasticity theory. Tensile tests on the yarns can be reproduced excellently only if the twist-induced stiffening is considered.

GRILLAGE ANALYSIS OF CELLULAR PLATE STRUCTURESOF VARYING DEPTH WITH INCL

A static analysis of cellular plate structures of linearly varying depth is presented by using thesimplified grillage method. The cellular plate structure in this study consists of top and bottomflange plates (non-parallel) separated by longitudinal webs having varying depth. A variationalformulation of thin-walled beam element with linearly varying depth has been carried out for thederivation of the stiffness matrix of the grillage members for various warping restraint effects. Theeffect of warping restraint in stiffness is included by two methods, firstly; the implicit method(through the torsional constant) and secondly; by the explicit method (as independent warpingdegree of freedom). Two differer,t approaches are used to derive the torsional stiffness matrix,namely:by the assumed displacement field and by the differential equation of equilibrium. Theeffect of secondary shear stresses from the warping restraint is also considercd.The varying cross section properties of the eguivalent grillage members are derived from theproperties of the actual cellular plate structure.Several numerical examples and applications are presented . The results are compared with thoseobtained from the flat plate / shell elements of MSCA.{ASTRAN program. Acceptable agreement isobtained.

Analysis of torsional vibration characteristics for wind turbine drivetrain under external excitation

This work studies the torsional vibration characteristics analysis of the wind turbine drivetrain with the variation of internal parameter and external excitation. The electromechanically coupled torsional vibration model for wind turbine drivetrain is first established by taking into account the torsional vibration angle of the PMSG. Then, frequency response analysis of main parametric resonance is illustrated by multiple scale method, and the influences of the system parameters involving power factor angle, number of pole pairs, torsional stiffness, and wind speed excitation on the torsional vibration characteristics of wind turbine drivetrain are investigated. Moreover, the critical condition for homoclinic chaos in terms of the system parameters is derived by means of Melnikov’s method. The function relationship and the boundary curve of chaos threshold are obtained. Meanwhile, the effects of excitation amplitude and damping factor on the system transition to chaos are studied in detail. The analytical predictions including phase portrait, bifurcation diagram and Lyapunov exponent are investigated. The research results can offer a theoretical basis for further the parameter design and control of wind turbine drivetrain.

Computational biomechanical analysis of Ti-6Al-4V porous bone plates for lower limb fractures

The current study investigates the biomechanical performance of porous bone plates augmented with three different cellular lattice structures, e.g., body-centered cube (BCC), simple cube (SC), and the superposition of simple and body-centered cube (SC-BCC) structures. The SC-BCC cellular structures, exhibiting improved torsional, compression, and bending stiffness, were strategically integrated into the bone plates. Configurations ranging from one to three rows, with porosity ranging from 30% to 90%. Increasing the number of rows and porosity maximized the interfragmentary movement at the fracture site. Specifically, SC-BCC configurations with one, two and three rows at 90% porosity demonstrated callus volume improvements of 31.33%, 42%, and 43.2%, respectively, compared with the lowest callus volume observed with SC-BCC at one row and 30% porosity. Regardless of the improved volume, callus stiffness was highest at 30% and 90% porosity levels across all cases, indicating more mature tissue formation in calluses and better physiological load support. High stresses located at 90% porosity, followed by 50% porosity, discouraged their mechanical performance. Therefore, employing 30% porosity configurations with appropriate vertical rows for desired movement is recommended for optimal biomechanical performance. However, 90% porosity may be suitable in scenarios involving minimal forces and restricted patient movement.

Compliant variable negative to zero to positive stiffness twisting elements

Compliant mechanisms have the potential to be utilized in numerous applications where the use of conventional mechanisms is unfeasible. These mechanisms have inherent stiffness in their range of motion as they gain their mobility from elastic deformations of elements. In most systems, however, complete control over the elasticity is desired. Therefore, compliant mechanisms with variable, including zero, stiffness can have a great advantage. We present a novel concept based on the prestressing of open thin-walled multi-symmetric beams. It is demonstrated that by changing the prestress on the center-axis of these beams, a range of variable torsional stiffness can be achieved. For beams with a large warping constant, the stiffness changes from positive to zero and negative as the prestress increases, while for beams with a near-zero warping constant, the range of neutrally stable twisting motion increases. A planar equivalent is shown in this work to elucidate the notion, and numerical and experimental analyses are performed to validate the prestress-related behavior.

Influence of Torsional Stiffness in Badminton Footwear on Lower Limb Biomechanics.

Torsional stiffness of athletic footwear plays a crucial role in preventing injury and improving sports performance. Yet, there is a lack of research focused on the biomechanical effect of torsional stiffness in badminton shoes. This study aimed to comprehensively investigate the influence of three different levels of torsional stiffness in badminton shoes on biomechanical characteristics, sports performance, and injury risk in badminton players. Fifteen male players, aged 22.8 ± 1.96 years, participated in the study, performing badminton-specific tasks, including forehand clear stroke [left foot (FCL) and right foot (FCR)], 45-degree sidestep cutting (45C), and consecutive vertical jumps (CVJ). The tasks were conducted wearing badminton shoes of torsional stiffness measured with Shore D hardness 50, 60, and 70 (referred to as 50D, 60D, and 70D, respectively). The primary biomechanical parameters included ankle, knee, and MTP joint kinematics, ankle and knee joint moments, peak ground reaction forces, joint range of motion (ROM), and stance time. A one-way repeated measures ANOVA was employed for normally distributed data and Friedman tests for non-normally distributed data. The 70D shoe exhibited the highest ankle dorsiflexion and lowest ankle inversion peak angles during 45C task. The 60D shoe showed significantly lower knee abduction angle and coronal motions compared to the 50D and 70D shoes. Increased torsional stiffness reduced stance time in the FCR task. No significant differences were observed in anterior-posterior and medial-lateral ground reaction forces (GRF). However, the 70D shoe demonstrated higher vertical GRF than the 50D shoe while performing the FCR task, particularly during 70% - 75% of stance. Findings from this study revealed the significant role of torsional stiffness in reducing injury risk and optimizing performance during badminton tasks, indicating that shoes with an intermediate level of stiffness (60D) could provide a beneficial balance between flexibility and stability. These findings may provide practical references in guiding future badminton shoe research and development. Further research is necessary to explore the long-term effects of altering stiffness, considering factors such as athletic levels and foot morphology, to understand of the influence of torsional stiffness on motion biomechanics and injury prevalence in badminton-specific tasks.

The Test Study on Tension-torsion Coupling Effect of ACSR in Overhead Transmission Lines

In order to analyze the relationship between the tensile and torsional characteristics of the Aluminum Conductor Steel Reinforced (ACSR), test research on the coupling effect of tension and torsion in conductors was carried out. A conductor tension-torsion coupling test device was designed, and selected the JL/G1A-630/45-45/7 ACSR as sample which is commonly used in ultra-high voltage AC engineering. The relationship between conductor tension, torque, and tensile strain, torsional strain was measured. And obtain the stiffness coefficients of conductor tension, torsion, and tension-torsion coupling. The testing results show that the tension and torque of the conductor gradually change from non-linear to linear under the action of tension or torsion deformation; The torsional stiffness Kφφ and tension-torsion coupling stiffness Kεφ when the conductor is turned to the right are greater than the corresponding stiffness when it is turned to the left.

Influence of altered torsional stiffness through sole modification of air pressure shoes on lower extremity biomechanical behaviour during side-step cutting maneuvers.

Directional changes in cutting maneuvers are critical in sports, where shoe torsional stiffness (STS) is an important factor. Shoes are designed based on different constructions and movement patterns. Hence, it is unclear how adjustable spacers into the sole constructions of air pressure chambers (APC) affect the STS in side-step cutting. Therefore, this study investigated the effects of altered STS through adjustable sole spacers on ground reaction force (GRF) and ankle and knee joint moments in side-step cutting. Seventeen healthy recreational athletes performed side-step cutting with experimental conditions including (i) barefoot (BF), (ii) unaltered shoes (UAS): soles consisting of APC, and (iii) altered shoes (AS): modified UAS by inserting elastomeric spacers into cavities formed by APC. Mechanical and biomechanical variables were measured. Significant differences were revealed across shoe conditions for impact peak (p = 0.009) and impulse (p = 0.018) in vertical GRF, time to achieve peak braking (p = 0.004), and peak propulsion (p = 0.025) for anterior-posterior GRF in ANOVA test. No significant differences were observed in GRF peaks and impulses between UAS and AS except for a trend of differences in impact peak (p = 0.087) for vertical GRF. At the ankle and knee joint, peak ankle power absorption (p = 0.019), peak knee internal rotation moment (p = 0.042), peak knee extension moment (p = 0.001), peak knee flexion moment (0.000), peak knee power absorption (p = 0.047) showed significant difference across three shoe conditions. However, no significant differences between the UAS and AS were noticed for peak joint moments and power. Altered shoe torsional stiffness did not significantly affect the peak forces and peak ankle and knee joint moments or powers; hence sole adjustment did not influence the cutting performance. This study might be insightful in sports footwear design, and adjusting shoe torsional stiffness by sole modification might be advantageous for athletes playing sports with cutting maneuvers to reduce the risk of injuries by controlling the twisting force at the ankle that frequently happens during cutting maneuvers.

Low-profile prosthetic foot stiffness category and size, and shoes affect axial and torsional stiffness and hysteresis.

Passive-elastic prosthetic feet are manufactured with numerical stiffness categories and prescribed based on the user's body mass and activity level, but mechanical properties, such as stiffness values and hysteresis are not typically reported. Since the mechanical properties of passive-elastic prosthetic feet and footwear can affect walking biomechanics of people with transtibial or transfemoral amputation, characterizing these properties can provide objective metrics for comparison and aid prosthetic foot prescription and design. We characterized axial and torsional stiffness values, and hysteresis of 33 categories and sizes of a commercially available passive-elastic prosthetic foot model [Össur low-profile (LP) Vari-flex] with and without a shoe. We assumed a greater numerical stiffness category would result in greater axial and torsional stiffness values but would not affect hysteresis. We hypothesized that a greater prosthetic foot length would not affect axial stiffness values or hysteresis but would result in greater torsional stiffness values. We also hypothesized that including a shoe would result in decreased axial and torsional stiffness values and greater hysteresis. Prosthetic stiffness was better described by curvilinear than linear equations such that stiffness values increased with greater loads. In general, a greater numerical stiffness category resulted in increased heel, midfoot, and forefoot axial stiffness values, increased plantarflexion and dorsiflexion torsional stiffness values, and decreased heel, midfoot, and forefoot hysteresis. Moreover, for a given category, a longer prosthetic foot size resulted in decreased heel, midfoot, and forefoot axial stiffness values, increased plantarflexion and dorsiflexion torsional stiffness values, and decreased heel and midfoot hysteresis. In addition, adding a shoe to the prosthetic foot resulted in decreased heel and midfoot axial stiffness values, decreased plantarflexion torsional stiffness values, and increased heel, midfoot, and forefoot hysteresis. Our results suggest that manufacturers should adjust the design of each category to ensure the mechanical properties are consistent across different sizes and highlight the need for prosthetists and researchers to consider the effects of shoes in combination with prostheses. Our results can be used to objectively compare the LP Vari-flex prosthetic foot to other prosthetic feet to inform their prescription, design, and use for people with a transtibial or transfemoral amputation.

Dynamic behavior of pin-free beam with torsional spring and hub at pinned end

This paper described the free vibration of a Euler-Bernoulli beam and discovered the first five dimensionless natural frequencies and mode shapes of motion for the pin-free beam model with a helical spring and rotating mass on the pinned side of the beam. The effect of changing the dimensionless torsional stiffness ratios was investigated, as was the effect of changing the dimensionless rotational inertia torque ratios Concerning the vibration properties of the beam. The mathematical equations that regulate the pin-free beam model were constructed using the exact analytical solution, establishing the Admissible Function and the natural frequency equation for the basic pin-free beam system. The approximate Rayleigh-Ritz approach was then used to determine the first five dimensionless natural frequencies, as well as the movement pattern for the pin-free beam model with a helical spring and a rotating mass on the side of the hinge. The results demonstrated that modifying the beam's natural frequencies is dependent on the ratios of the additional torsional spring parameters as well as the ratios rotational moment of inertia. The threshold system frequencies increase when the spring parameters are the major factor, and decrease when the inertia moment parameters are the main factor. Both play a role in influencing natural frequency to varied degrees. Unifying the final distribution of parameters might lead to optimizing the impact of parameters on the natural frequencies of the system.

STODOLA-VIANELLO ITERATION METHOD FOR FREE TORSIONAL VIBRATION ANALYSIS OF MONOSYMMETRIC BOX-BEAM BRIDGES

Box-beam bridges are used in large spans and wider decks due to their high strength and greater torsional and flexural stiffness. They are usually prone to vibration due to moving vehicular traffic. Their eigenfrequency analysis is a crucial aspect of their design in order to ensure that the natural frequency is not close to the excitation frequency to avert resonance failures. The free torsional vibration equation is a fourth order partial differential equation (PDE) with variable parameters. For prismatic cross-sections, homogeneous and isotropic materials the governing PDE have constant parameters. This paper explores the Stodola-Vianello iteration method (SVIM) for solving the PDE for isotropic, homogeneous prismatic box-beams. Harmonic response is assumed, decoupling the PDE to two equations, one in terms of time and the second an ordinary differential equation (ODE) in terms of space coordinates. The Stodola-Vianello method is used by the method of four successive integrations to express the ODE as an algebraic iteration problem with four constants of integration. The four boundary conditions are used to solve for the four constants of integration, thus making the problem determinate. Application of the boundary conditions results in the full determination of the iteration equations. For simply supported boundaries studied in the work, a trigonometric buckling shape function that satisfies all the boundary conditions is employed in the SVIM formula to obtain the next bucking modal shape function. The requirement for convergence is then used to establish the characteristic buckling equation from which the eigenvalues are obtained. The solution to the characteristic buckling equation gave the exact mathematical expression for the natural torsional frequency at the nth vibration mode. The frequencies are determined for the first eight vibration modes and compared with previously obtained values. It was found that the natural frequencies are identical with previously found values of the exact natural frequencies. The natural frequency obtained is exact because it satisfies the PDE and the boundary conditions at all points in the domain.

Torsional actuation and vari-stiffness characteristics of SMA/basalt hybrid braided composite tubes

Shape memory alloy hybrid composite (SMAHC) tubes have the potential to actively control the torsional stiffness of structures. In this work, shape memory alloy (SMA) wires orthogonally braided with basalt fiber were heated by electricity to generate the torsional torque of the SMAHC tube, and then the torsional stiffness of the tube was measured. The macroscopic finite element model of the SMAHC tube was established to assist in the analysis of the torsional stiffness variation before and after heating. According to the experimental results, the actuating torsional ability was affected by the phase transformation recovery force of SMA. The active control of torsional stiffness depends on the change of SMA modulus, the magnitude and direction of SMA wires’ recovery force, and the thermodynamic properties of matrix at different temperatures. Then an evaluation model for the torsional stiffness control effect was proposed. These research results can be used for the adaptive control of the stiffness and vibration characteristics of rotating composite structures, and provide a novel and effective method for the control of structural torsional characteristics with lightweight effects.

Analysing the Effect of Chassis Torsional Flexibility on the Rollover Threshold of a Multi-Purpose Agricultural Vehicle

Multi-purpose agricultural tractors are vehicles that are usually involved in different operations, including road maintenance in small villages and cultivation of small agricultural plots, particularly in mountainous areas. These vehicles typically feature narrow tracks to enhance manoeuvrability, making rollover stability a critical consideration in operational settings. This characteristic arises from the interplay between the suspension and vehicle chassis. This paper introduces a numerical multi-body model designed to replicate the dynamics of a multi-purpose tractor with a torsional chassis. Model parameters were derived through experimental measurements conducted on an actual vehicle. Static measurements were performed to assess tire and suspension stiffness while tilting tests were performed to establish the static rollover limit of the vehicle. Dynamic tests conducted on a four-post test rig characterised the vehicle’s dynamics. The validated model was utilised to explore the vehicle’s stability by reproducing the static rollover tests and simulating the vehicle’s performance under working conditions on a banked road. The vehicle rollover stability was studied by performing a sensitivity analysis that considered both chassis torsional stiffness and suspension stiffness under different loading conditions. The results indicate a trade-off between frame and suspension stiffnesses that enhances overall vehicle stability.

Comparative experimental study of the biomechanical properties of retrograde tibial nailing and distal tibia plate in distal tibia fracture.

Objective: A biomechanical comparative analysis was conducted to evaluate the retrograde tibial nailing (RTN) and distal tibia plate techniques for the treatment of distal tibia fractures. Methods: Fourteen fresh adult tibia specimens were selected, consisting of seven males and seven females aged 34-55years. The specimens were randomly divided into two groups (Group A and Group B) using a numerical table method, with seven specimens in each group. Group A underwent internal fixation of distal tibial fractures using RTN, while Group B received internal fixation using a plate. The axial compression properties of the specimens were tested in the neutral positions under pressures of 100, 200, 300, 400, and 500N. Additionally, the torsional resistance of the two groups was assessed by subjecting the specimens to torques of 1.0, 2.0, 3.0, 4.0, and 5.0Nm. Results: At pressures of 400 and 500N, the axial compression displacement in Group A (1.11 ± 0.06, 1.24 ± 0.05) mm was significantly smaller than that in Group B (1.21 ± 0.08, 1.37 ± 0.11) mm (p = 0.023, 0.019). Moreover, at a pressure of 500N, the axial compression stiffness in Group A (389.24 ± 17.79) N/mm was significantly higher than that of the control group (362.37 ± 14.44) N/mm (p = 0.010). When subjected to torques of 4 and 5Nm, the torsion angle in Group A (2.97° ± 0.23°, 3.41° ± 0.17°) was significantly smaller compared to Group B (3.31° ± 0.28°, 3.76° ± 0.20°) (p = 0.035, 0.004). Furthermore, at a torque of 5Nm, the torsional stiffness in Group A (1.48 ± 0.07) Nm/° was significantly higher than that in Group B (1.36 ± 0.06) N·m/° (p = 0.003). Conclusion: The results obtained from the study demonstrate that the biomechanical performance of RTN outperforms that of the distal tibial plate, providing valuable biomechanical data to support the clinical implementation of RTN.

A comparative study on the deformation behavior and mechanical properties of new lower extremity arterial stents

Background and ObjectiveThe lower extremity movement involves a complex and large amplitude extremity movement process, and arterial stents implanted in the lower extremity are prone to complex mechanical deformation behavior. Hence, the lower extremity arterial stent is required to have favorable comprehensive mechanical properties. MethodsIn this study, a new lower extremity arterial stent (New) was proposed, and its deformation behavior and mechanical properties were analyzed by numerical simulations under different deformation modes, such as radial compression, axial compression/tension, bending, and torsion. Stents with different diameters were modeled to compare the effect of diameter size on their biomechanical properties. Additionally, a comparative analysis was conducted between this new stent and seven commercially available stents. ResultsThe results demonstrated that the stent diameter exerted a significant effect on its deformation behavior and mechanical properties. Specifically, with the increase of the stent diameter, the radial expansion rate, radial shrinkage rate, radial support stiffness, axial compression stiffness, and axial tensile stiffness tended to decrease, and the expansion inhomogeneity, stenosis rate, bending stiffness, and torsional stiffness tended to increase. In contrast, the stent diameter exerted a small effect on the stent axial shortening rate and ellipticity. The new lower extremity arterial stent was validated to outperform other stents in terms of most performance indicators. Especially, the radial expansion rate and ellipticity of the New stent were better than those of all commercially available stents. Moreover, the New stent presented favorable mechanical properties and flexibility under the premise of ensuring the support performance. ConclusionsBased on these findings, this lower extremity arterial stent may play a better therapeutic effect in clinical application. Furthermore, these analysis results may provide reference for the clinical application and selection of the stent.

Design of a torsional stiffener for a cable-driven hyper-redundant robot composed of gear transmission joints

AbstractThis work describes the advancement in developing a cable-driven gear transmission joint designed as a basic element for a long-reach hyper-redundant robot. Hyper-redundancy allows the robot to perform auxiliary tasks such as obstacle avoidance and joint limits satisfaction. This feature makes hyper-redundant robots particularly useful for performing tasks in confined and hazardous environments and areas that are not reachable by a human operator. The long-reach feature of the robot requires a detailed study of the overall structure and its components. The joint must be capable of transmitting forces and movements over a long distance without losing the precision and accuracy of the end-effector, so it is designed to optimise the robot’s performance in terms of stiffness, structural resistance, and functional characteristics. In light of the above considerations, the main focus of this work is to improve the structural performance of the entire robotic system. Consequently, since the most critical component of the robot in terms of torsional deformation is the gear transmission joint, this paper aims to design a torsional stiffener element to reduce its deformation and, thus, an increase of torsional stiffness of the overall robotic system. Tube-shaped and rectangular-shaped stiffener elements, which can fit the joint design satisfying its geometrical constraints, are proposed. A computer-aided engineering approach is implemented to improve the precision of positioning of the end-effector by adding stiffener elements in the joint. Two sensitivity analyses, varying the geometry of the proposed stiffener elements, are performed to evaluate their performance in terms of added mass and displacement reduction.

Torsional vibration behavior of a restrained non-circular nanowire in an elastic matrix

This study introduces an approach to analyze torsional vibration in non-circular nanowires within magnetic fields, considering various boundary conditions on an elastic foundation. Analytical formulas for natural angular frequencies are obtained using nonlocal strain gradient theory. The analysis covers three non-circular cross-sections, incorporating the warping effect. Elastic springs at the wire ends simulate support conditions, restricting rotation around the wire’s axis. The torsion function around the axis is represented by a Fourier series, discretized at the spring points and linked using the Stokes’ transform alongside the boundary values. This leads to an eigenvalue problem that includes higher-order material size parameters (strain gradient, nonlocal), spring parameters, and the warping function. The study’s novelty lies in effectively solving torsional vibration for non-circular sections, addressing warping function, elastic medium, and size effects under both deformable and non-deformable boundary conditions. The presented solution is capable of determining vibration frequencies for both rigid and deformable boundary conditions. This is accomplished by specifying the torsional spring stiffness values, thereby obviating the necessity for additional recalculations. In order to verify the obtained results and compare them with the existing literature, nanowires with free and clamped boundary conditions are solved numerically by changing the spring parameters in the eigenvalue problem. In the formulation of natural angular frequency; length scale parameters, warping, magnetic field, elastic medium effects are included. In addition, since the support conditions are modeled with elastic springs, the resulting formulas are quite general and can be used to solve different types of torsional vibration problems.

Compressive behavior of novel cold-formed steel built-up closed L-shaped section columns

This paper proposes a novel type of cold-formed steel (CFS) built-up closed L-shaped section column (CSBC-L). The CSBC-L is a part of the novel special built-up column prefabricated modularized mid-rise CFS structural system (SPMM-CFS), and it can be used to compose the corner-column modulus. The CSBC-L can install sheathing walls in two crossed directions without any other connecting components, and it exhibits large torsional stiffness and inertia moment. This paper conducted experimental investigations on the compressive behavior of CSBC-L with different configurations. Totally 18 test specimens with different plate thicknesses, web heights and screw spacings were designed and tested. The results show that the ultimate strength of CSBC-L can be effectively improved with increasing the web height and plate thickness. Finite element (FE) models were developed for the test specimens, and the failure modes as well as the nonlinear load‒displacement curves were simulated and validated. Finally, the effective width method (EWM) and direct strength method (DSM) are used to predict the ultimate strength of the CSBC-L specimens in AISI S100-16 and EN 1993-1-3. It is found that the DSM is more accurate to predict the axial compressive ultimate strength, and most of the errors are less than 10%.

Study on the mechanism of belt cord angle contribution to tire cornering power

In this study, tests on the cornering and self-aligning stiffness of tires with various belt cord angles were conducted. Subsequently, a new cornering power model was developed to analyze the mechanism of the belt cord angle’s influence. It was observed that the cornering stiffness is influenced by the combined effect of the length of contact patch and the lateral stiffness of the belt, both of which are affected by the belt cord angle. Specifically, an increase in the belt cord angle leads to a longer contact patch, which results in an increase in the cornering stiffness. Additionally, an increase in the belt cord angle causes a decrease in the lateral stiffness of the belt. Consequently, the lateral flexibility of the carcass increases, leading to a decrease in cornering stiffness. Furthermore, the influence of the lateral flexibility of the carcass becomes more prominent with an increase in the load. As a result, under heavy loads, the cornering stiffness decreases with an increasing belt cord angle. It was also observed that the influence of the belt cord angle on self-aligning stiffness is mainly achieved through the impact on contact length, with self-aligning stiffness increasing as contact length increases. The torsional stiffness of the carcass, influenced by variations in the belt cord angle, does not significantly impact the self-aligning stiffness of the tire. These findings provide valuable insights into tire mechanics and offer guidance for the design and development of tires with enhanced cornering performance.