Pure Torsion Research Articles

Steel fibers for replacing minimum reinforcement in beams under torsion

This paper concerns an investigation on six large-scale Steel Fiber Reinforced Concrete (SFRC) beams tested in pure torsion. All beams had longitudinal rebars to facilitate the well-known space truss resisting mechanism. However, in order to promote economic use of the material, the transverse reinforcement (i.e. stirrups/links) was varied in the six large scale beams. The latter contained either no stirrups, or the minimum amount of transverse reinforcement (according to Eurocode 2), or hooked-end steel fibers (25 or 50 kg/m3). Material characterization were also carried out to determine the performance parameters of SFRC. The results of this study show that SFRC with a post-cracking performance class greater than 2c (according to Model Code 2010) is able to completely substitute the minimum reinforcement required for resisting torsion. In fact, the addition of steel fibers contributes to significantly increase the maximum resisting torque and maximum twist when compared to the same specimen without fibers. Moreover, SFRC provides a rather high post-cracking stiffness and a steadier development of the cracking process as compared to classical RC elements. This phenomenon improves beam behavior at serviceability limit state. The experimental results are critically discussed and compared to available analytical models as well as with other tests available into the literature.

Robot-aided fN\u2219m torque sensing within an ultrawide dynamic range

In situ scanning electron microscope (SEM) characterization have enabled the stretching, compression, and bending of micro/nanomaterials and have greatly expanded our understanding of small-scale phenomena. However, as one of the fundamental approaches for material analytics, torsion tests at a small scale remain a major challenge due to the lack of an ultrahigh precise torque sensor and the delicate sample assembly strategy. Herein, we present a microelectromechanical resonant torque sensor with an ultrahigh resolution of up to 4.78 fN∙m within an ultrawide dynamic range of 123 dB. Moreover, we propose a nanorobotic system to realize the precise assembly of microscale specimens with nanoscale positioning accuracy and to conduct repeatable in situ pure torsion tests for the first time. As a demonstration, we characterized the mechanical properties of Si microbeams through torsion tests and found that these microbeams were five-fold stronger than their bulk counterparts. The proposed torsion characterization system pushes the limit of mechanical torsion tests, overcomes the deficiencies in current in situ characterization techniques, and expands our knowledge regarding the behavior of micro/nanomaterials at various loads, which is expected to have significant implications for the eventual development and implementation of materials science.

Theoretical study on the nonlinear performance of single-box multi-cell composite box-girder with corrugated steel webs under pure torsion

Composite box-girders with corrugated steel webs (CBGCSWs) have become attractive structures in bridge engineering. However, wide single-box multi-cell CBGCSWs (SBMC-CBGCSWs) under heavy eccentric load may suffer sudden failures, because of the sharp decrease in torsional stiffness induced by the thin corrugated steel webs (CSWs). Thus, the accurate prediction of their entire torsional performance becomes necessary to avoid failure or damage. In this study, a theoretical model based on rotating-angle theory is proposed for SBMC-CBGCSW with prestressing under torsion. This model primarily incorporates the influence of prestressing on concrete element and proposes new average stress-strain relationships for prestressed concrete strut. Furthermore, a rational shear strain relationship between inner and outside CSWs is employed to better calculate the torsional contribution of inner CSWs. The proposed model is validated by experimental and numerical results taken from the companion paper, and the comparison between this proposed model and other models proves its superiority in predicting cracking and ultimate stages of SBMC-CBGCSW with prestressing. In addition, it is found that neglecting the initial state of concrete element caused by prestressing will result in underestimation of cracking and ultimate torques, and meanwhile the shear strain relationship between inner and outside CSWs adopted in this model can predict the torsional behavior of inner CSWs more accurately and reasonably.

Щодо розрахунку релаксації напружень в тонкостінних циліндричних оболонках із лінійно-в'язкопружних матеріалів

The problems of stress relaxation analysis in thin-walled cylindrical shells made of linear viscoelastic materials under uniaxial and biaxial loading have been solved. The analysis is based on a there-dimensional model of viscoelasticity starting from the hypothesis of the deviators proportionality. The viscoelastic properties of a material are given with relationships that establish the dependence between stress and strain intensities as well as between the mean stress and volumetric strain by the Bolzmann-Volterra type equation. The kernels of relaxation intensity and volumetric relaxation are given with the Rabotnov exponential-fractional functions. The parameters of relaxation kernels are determined from creep test result using the relationships between creep kernels under the complex stress state and creep kernels under the one- dimensional stress state. The problems of the analysis of normal and tangential stresses relaxation in thin-walled cylindrical shells made of high density polyethylene “ПЭВП” under uniaxial tension, pure torsion and combined tension with torsion loading have been solved and experimentally approved.

Nonlinear Dynamic Characteristics of Automotive Gear Transmission System Based on Pure Torsion Model

With the rapid development of automobile industry, the performance requirements of gear transmission system are higher and higher. In order to improve the quality and reliability of gear transmission products, reduce the manufacturing cost of the whole vehicle and ensure the high-speed operation of the engine, it is necessary to carry out reasonable design, calculation and selection. In this paper, the gear transmission system is taken as the research object, the pure torsional vibration theory is studied, and the simulation analysis is carried out by MATLAB. The simulation results show that the automotive gear transmission based on the pure torsion model performs very well in the dynamic meshing force and the error is very small. This shows that the model can reduce the degree of gear wear.

On the Influence of Mean Shear Stress on Multiaxial High Cycle Fatigue of Metallic Materials

A study has been made of the influence of a superimposed mean shear stress on the capability of some multiaxial high cycle fatigue criteria to predicting fatigue behavior of 42CrMo4 and 34Cr4 alloy steels. Five selected critical plane-based criteria, namely Matake (M), Susmel & Lazzarin (S&L), Findley (F), Carpinteri & Spagnoli (C&S) and Liu & Mahadevan (L&M), were applied to a number of published experimental fatigue resistance limit tests, involving synchronous sinusoidal in-phase and out-of-phase bending and torsion. Applying to the same loading conditions a mesoscopic scale-based criterion proposed by Papadopoulos (P), one could verify that predictive capability of such an approach is almost invariably superior to those associated with the M, S&L, F, C&S and L&M models. As the Papadopoulos criterion is independent of mean shear stress, it seems appropriate to conclude that the inclusion of such a stress as loading parameter in the critical plane-based models does, in fact, exert a negative influence on their predictive capability. Finally, it is worth mentioning that, except for the Matake, S&L and L&M criteria, the other critical plane-based criteria exhibit a dependence of the fatigue resistance in pure torsion with respect to a superimposed mean shear stress, in disagreement with well-established experimental observations.

Development of a lattice model for predicting nonlinear torsional behavior of RC beams

Seismic design criteria based on performance of structures have recently been adopted by practicing engineers in response to destructive earthquakes. A simple but efficient structural-analysis tool capable of predicting both strength and ductility is needed to analyze reinforced concrete (RC) structures subjected to such events. Hence, a three-dimensional lattice model is developed in this study to analyze torsions in high-strength RC beams. Optimization techniques for determining optimal variables in each lattice model are introduced. Pure torsion tests of RC beams were performed to use to propose a threedimensional lattice model. The experimental test results of pure torsion on RC beam specimens were used to compare with numerical results obtained using the proposed model. Then, the proposed model was also compared to 3D solid model in commercial finite element analysis program, ABAQUS. Correlation studies between the numerical and experimental results confirm that the proposed model is well capable of representing salient features of the experimental results. Furthermore, the proposed model provides better predicted displacement corresponding to peak load. than the result from ABAQUS.

Coupled bending and torsional beam vibrations excited by a moving load

AbstractFor a simply supported Bernoulli‐Euler beam under a moving load with constant velocity the bending and torsion vibrations are analysed. An analytical solution of the decoupled partial differential equations is derived based on the eigenmode expansion considering the boundary and initial conditions. For the pure bending and the pure torsion the analysis is performed and the beam vibrations are calculated. For various longitudinal speeds the results are plotted. The coupled bending and torsion deformations are computed using a modal transformation. The modal decoupling yields two separated ordinary differential equations in time which are computed using the derived closed form solutions. The solutions of the coupled equations are plotted and discussed. A comparison with a numerical calculation of a finite element model which shows good agreement.

Normal and High-Strength R/C Deep Beams under Pure Torsion and Codes Evaluation.(Dept.C)

Fourteen reinforced concrete deep beams were tested under pure torsion in order to evaluate the torsion design provisions of ACI 318-02 Building Code, the Egyptian code (ECCS-2001), the New Zealand code (NZS 3101-95), and the Eurocode 2 (EC-2) when applied to High Strength Concrete (HSC) deep beams. The results of these tests have been used to compare the torsional behavior of reinforced deep beams constructed from Normal-Strength Concrete (NSC with characteristic cube compressive strength fcu of about 35 MPa) and HSC (with fcu of about 81 MPa). The main parameters examined in this study were the design compressive strength, the provided transverse reinforcement ratio, the quantity of longitudinal and skin reinforcement and the size of the tested beams in the form of the tested span to total height ratio (L/h=1.0, 2.0 and 3.0). The results showed that the reserve in the torsional strength of the HSC deep beams aster cracking is considerably less than that of the similar NSC deep beams. The cracking torsional strength of the tested NSC deep beans is about 38-54% of the measured ultimate torsional strength, while the same ratio for the similar HSC deep beams is about 57-77% of the measured ultimate strength. The design torsional strength equations of the four international codes considered in this study were safe and conservative when applied to NSC and HSC deep beams. The predictions of the ultimate torsional strength of the deep beams according to the method of ACI 318-02 and using a value of the angle between the concrete struts and the longitudinal axis of the beam θ equal to 45 deg may give a conservative results less than that calculated using this angle between 30 and 60 deg.

Torsional Strengthening of Low-Strength RC Beams with Post-Tensioned Metal Straps: An Experimental Investigation

This article investigates the behaviour of low-strength reinforced concrete beams under pure torsion with and without strengthening. Four beams were cast and tested in torsion: i) a control beam without vertical reinforcement, ii) two beams with internal stirrups designed for shear and torsion demands using different stirrup spacing (50 and 100 mm), and iii) a beam having steel stirrups with a spacing of 100 mm strengthened using high ductile post-tensioned metal straps (PTMS). The main objective of the PTMS strengthening solution was to investigate the enhancement of torsional strength confined along the beam. The failure modes, torsional capacities, rotation, and strengthening performance in torsion are discussed in in this study. The experimental results indicate that the PTMS improved the cracking torque capacity by up to 15 % compared to the control beam. Moreover, the PTMS also increased the ultimate torque by up to 19 % compared to the unstrengthened beam. Current code equations to predict the torsional capacity of RC beams are also compared with the experimental results. It is found that the predictions obtained by current ACI equation gives a good agreement and yield in general conservative values compared to the experimental ones.

Torsional strength of RC members using a plasticity-based variable-angle space truss model accounting for non-uniform longitudinal reinforcement

The torsional strength of reinforced concrete (RC) members is typically calculated through the thin-walled tube, space truss analogy. The governing equations are simple equilibrium conditions satisfied by closed stirrups, longitudinal reinforcement and spiral concrete diagonals at a variable angle. In building codes, like EC2 and ACI 318, the contribution of longitudinal reinforcement is averaged among the walls, considering the total amount of longitudinal re-bars of the overall cross section. However, longitudinal re-bars may be non-uniformly distributed along the walls. This is particular evident in beams with large aspect ratios and re-bars mainly located at the corners, or in beams with unsymmetrical bending-type longitudinal reinforcement arrangement. This paper presents a plasticity-based variable-angle space truss model accounting for non-uniform distribution of longitudinal reinforcement along the walls. The model, which is based on equilibrium conditions and the lower-bound theorem of plasticity, is first elaborated for a polygonal cross-section with an arbitrary number of walls incorporating arbitrary longitudinal reinforcement ratios and corresponding variable-angle concrete strut inclinations, and then particularized to the more common case of rectangular section with two representative longitudinal reinforcement ratios and two corresponding variable-angle strut inclinations. For practical design purposes, the results of this model are illustrated through normalized torsional strength curves in terms of non-dimensional reinforcement indexes. The model is validated by comparison with more than 200 experimental results of RC members under pure torsion collected from the literature, and very good agreement is found. The predictions of the model are also compared with those of some codes of practice and better results are obtained especially for beams with markedly non-uniform longitudinal reinforcement arrangement.

Approximate expression of the Prandtl membrane analogy in linear elastic pure torsion of open thin-walled cross sections and regular polygons

This paper presents a new general methodology to obtain an approximate analytical expression of the Saint-Venant's torsion. The shear stress in each of the principal Cartesian directions is obtained by the derivation of the stress function, whose analytical expression is obtained from the Prandtl analogy. The proposed methodology uses two variables quadratic piecewise functions to define the Prandtl membrane. This document shows that the approximate procedure is especially suitable for steel shapes, giving values very close to those obtained with more precise methods. The main advantage of the presented methodology is its simplicity, which makes it useful for both pedagogic and practical applications. Several examples are developed.

Characterization of Pure Face-Shear Strain in Piezoelectric α-Tellurium Dioxide (α-TeO2)

Paratellurite, also known as α-tellurium dioxide, is a ceramic that is primarily employed for its interesting optical properties. However, this material’s crystal structure belongs to the 422 symmetry class that allows a unique piezoelectric behavior to manifest itself: deformation in pure face-shear. This means that crystal symmetry necessitates the piezoelectric tensor to have only a single non-zero coefficient, d123 = d14: such unique behavior has the potential to enable novel gyroscopic sensors and high-precision torsional microelectromechanical systems (MEMS) actuators, as pure face-shear can be used to induce pure torsion. Although α-TeO2 is one of the few known materials belonging to this symmetry class, considerable uncertainty in its single piezoelectric coefficient exists, with the few reported literature values ranging from 6.13 to 14.58 pC/N; this large uncertainty results from the difficulty in using conventional piezoelectric characterization techniques on paratellurite, limiting measurements to indirect methods. The novel applications that would be enabled by the adoption of this extraordinary material are frustrated by this lack of confidence in the literature. We therefore leverage, for the first time, a first-principles analytical physical model with electrochemical impedance spectroscopy (EIS) to determine, directly, the lone piezoelectric coefficient d123 = d14 = 7.92 pC/N.

Experimental Investigation of the Seismic Performance of Rectangular Reinforced Concrete Columns Subjected to Combined Flexure-torsion Cyclic Loading

ABSTRACT This paper investigates the seismic behavior of the rectangular-reinforced concrete columns subjected to pure flexure, pure torsion, and combined flexural-torsional loadings using 4 quarter-scaled experimental specimens. During flexural-torsional loading, the axial rotation to the relative displacement ratios were considered to be 2 and 4. The ultimate displacement capacity and the flexural moment capacities of the specimens under combined flexural-torsional loadings were found to be decreased compared to the pure-flexural case for different rotation over drift ratios. An equation expressing the interaction curve between the flexural and torsional moment strength capacity of rectangular-reinforced concrete sections is proposed.

Screening of Process Factors for Silicon Torsional Bar by Static Pure Torsion Destructive Test

Screening of Process Factors for Silicon Torsional Bar by Static Pure Torsion Destructive Test

Gradient recrystallization to improve strength and ductility of medium-entropy alloy

Gradient recrystallized CrCoNi medium-entropy alloy (MEA) was processed by vacuum arc melting, pure torsion and subsequent annealing. MEAs with different gradient recrystallizations (GRs) were produced by controlling the annealing time and the cooling type. Uniaxial tensile tests show that the gradient recrystallized MEA annealed at 1073 K for 2.5 min exhibits high yield strength and good ductility. Compared with the homogeneous coarse-grain MEA, the yield strength in the gradient recrystallized MEA is increased from 245 MPa to 930 MPa while a considerable elongation of ∼27% is obtained. Even for higher-strength gradient recrystallized MEA annealed at 1073 K for 2 min, the yield strength is above 1 GPa and the elongation still maintains ∼17%. Microstructural characterizations and theoretical analysis were employed to explain the mechanism for the excellent mechanical properties in the gradient recrystallized MEA. The forest dislocations and nanotwins resulting from pure torsion strengthen the gradient recrystallized MEA. The gradient recrystallization and nanotwins resulting from heat treatment provide extra strain hardening capability, which contribute to the improvement of ductility.

Modelling and Optimal Design of Thick-Walled Composite Pipes under In-Service Conditions

The current study is focused on the stress-strain analysis of multi-layered thick-walled fibre reinforced composite pipes under torsional load. Three-dimensional elasticity solution has been obtained and Finite Element Method model has been developed to predict the stress-strain distribution and compute the Tsai-Hill failure coefficients. The models have been validated by comparing with the results available in the literature. As a numerical example the composite pipe subjected to pure torsion load has been considered. The effects of the torque magnitude and layers’ thickness for specific pipe lay-ups have been investigated, and the appropriate engineering conclusions and design suggestions have been reported.

Intrinsic size dependent plasticity in BCC micro-pillars under uniaxial tension and pure torsion

The mechanical behavior of submicron body-centered cubic (BCC) micro-pillars is investigated by three-dimensional dislocation dynamics (DD) simulations to better understand the governing mechanisms for size dependent plasticity under uniaxial tension and pure torsion. A formula is developed to compute the incremental plastic twist due to dislocation motion in DD simulations. The DD simulations show that different dislocation microstructures are created depending on the loading conditions, which leads to different size dependent mechanical behavior. While in tension plasticity is mainly governed by the kinetics of dislocation motion controlled partly by the surface dislocation sources, plastic flow in torsion is controlled by dislocation pile-ups associated with strain gradients. The simulation results also reveal a Bauschinger effect and plastic recovery under cyclic twist, which have been observed in recent experiments.

Behavior of Strengthened RC Beams with CFRP Sheets under Combined Bending and Torsion

The experimental investigations were carried out to study the behavior of reinforced concrete beams strengthened by CFRP sheets under different loading conditions (pure bending, combined bending and torsion and pure torsion). The experimental work included testing twenty RC beams of the rectangular cross-section of dimensions of 160×240 mm and of 2600 mm length with an area of the ordinary reinforcement being kept constant for all beams. Two parameters were taken into consideration (Twisting to bending moment ratio (T/M) and CFRP strengthening pattern). The tested beams are divided into five groups. Each group consists of four beams; the first beam is without CFRP strengthening, the other three are strengthened with CFRP sheets of different arrangements (U-stirrups, U-stirrups and longitudinal CFRP sheets in the bottom and Full U- stirrups wrapping). Each beam is loaded to a different loading conditions (pure bending, T/M = 0.5, T/M = 1.0, T/M = 2.0 and pure torsion). The CFRP sheets were attached externally to the beam. Test results were analyzed based on the influence of CFRP on the ultimate load, vertical mid-span deflection and failure modes. In the experimental work, it was found that all strengthening patterns of CFRP sheets exhibited a significant increase in ultimate strength. This increase reached up to 78.9% for tested beams, when the beam strengthened in the form of full U- stirrups wrapping pattern for T/M = 0.5. In this study, it is observed that the use of external CFRP sheets attached to the tension sides of beams (U-stirrups and longitudinal CFRP in the bottom) could enhance the ultimate load capacity by 32.7% over the capacity of the unstrengthen control beam for T/M = 1.0.

A novel semi-analytical method for notch stress and fatigue strength analysis of tube-flange welded joints

This paper presents a semi-analytic method to rapidly estimate the notch stress and fatigue strength for tube-flange welded joints. Considering the stress singularity effect at the weld toe, the parameters related to geometry and opening angle are simplified as singular intensity factors. The equivalent singular intensity factors can be fitted by the stress distribution rather than the peak stress at the corner. On this basis, the modified notch stress formulas for tube-flange welded joint (TFWJ) under pure bending or torsion load were fitted and verified. Meanwhile, the simple relationships between singular intensity factor, notch stress intensity factor, strain energy density and peak stress were further deduced, separately. The comparison results show that the fatigue assessment parameters calculated by the traditional approaches and the proposed method are in good agreement. Finally, four groups of fatigue data of TFWJs were summarized to verify the simplified assessment formulas.