Torsional Shear Stress Research Articles

Deformation characteristics of medium-dense sand-clay mixtures under a principal stress rotation

A moving wheel load induces a principal stress rotation (PSR) in pavement foundation geomaterials including subgrade/subbase soils. Simulating such a stress condition is not possible with stress path tests conducted with conventional cyclic triaxial (CT) equipment. More complex stress paths such as a heart-shaped stress path are required to determine the deformation characteristics of these under a PSR. A heart-shaped stress path can be simulated on a soil specimen in cyclic hollow cylinder (CHC) tests via user-defined waveforms for its stress components (axial stress, and torsional shear stress). In this study, a series of CT and CHC tests were performed to analyze the impact of a PSR on strain behaviors of medium-dense sand-clay mixtures. The specimens contained 0%, 5%, 10%, and 20% clay by weight and were prepared at an initial relative density of 50%. All specimens were anisotropically consolidated under K0≈0.5. It was determined that all CT specimens underestimated the strain performances (both axial strain and shear strain) of the sand-clay mixtures. On the other hand, a heart-shaped stress path was simulated successfully in CHC tests and thus, all specimens yielded more accurate strain results. At low clay content (≤10%), the impact of a PSR on strain performances of the sand-clay mixtures was observed to be less (axial strain (εz) < 0.12%, and shear strain (γzθ) < 0.8% after number of load cycles (N) = 5000) due to the low stress ratios (CVSR = 0.15 and η = 1/3). On the other hand, despite the low stress ratios, a PSR caused a rapid increase in axial strain and shear strain (εz = 5%, and γzθ > 0.8%) of the specimen containing 20% clay, which resulted in the failure of the specimen at N = 478. Results of this study clearly indicated that the effect of a PSR should be taken into consideration while evaluating the strain characteristics of the sand-clay mixtures that contain clay particularly at high contents (≥20%) under traffic loads.

Structural response of concrete segmental linings in transverse interaction with the TBM. Part 2: Non-axisymmetric conditions

In the second part of this paper, the behaviour of the last assembled ring when loaded simultaneously by the tail seal pressures and the jack forces is investigated in detail for eccentric scenarios of tail seal passage such as those encountered in the Crossrail’s Thames tunnel (CTT). In these non-axisymmetric scenarios, the sealing pressures grow linearly with depth and the ram pad restraints against the tunnel uplift are unevenly distributed over the ring circumference. The parametric study targeted the effect of uneven pad boundaries, tunnel unsupported length, Lu, and lining features on the numerical outputs of selected ten-ring finite element (FE) models. The numerical outputs of interest were ring deformations, internal forces, segment interactions and stress concentrations within the segment bodies. It was found that ring distortions can develop within Lu. The distortion mode is determined by the ram pad boundary. The ring deformations increase with the advance of the sealing pressures and decay with distance from the TBM pads. For a given pad boundary, Lu governs the magnitude of distortion, which, in the cases studied, raised up to 0.30% the tunnel diameter D by the end of the first advance. The tangential component of the jacks’ downward reaction can induce hoop tension at the ring front. The radial reaction forces result in significant hoop and torsional moments, differential radial rotations at transitional longitudinal joints and longitudinal moments in constrained segments. The total angularities of longitudinal joints can exceed recommended tolerances. The lower joints are at a higher risk of developing permanent angularities. Gasket offsets in joints undergoing differential radial rotations are sensitive to Lu. Temporary spear bolts can trim extreme offsets, e.g. 12 mm, down to moderate values. The transverse action of the pads increases the magnitude of peak tensile stresses in constrained segments: hoop spalling stresses at pad interspaces plus radial bursting stresses and ‘longitudinal’ spalling stresses near the rear corner of the longitudinal joints. Torsional shear stresses combined with hoop tension can cause excessive extrados surface tension near the front of constrained segments. Shear failure was identified in convex-convex transitional joints with considerable joint imperfections.

Nonlinear Finite Element Analysis of Reinforced and Plain Concrete Haunched Beams Under Torsion

Abstract The present paper is focused on analysis of reinforced and plain concrete haunched beam under torsion based on non-linear finite element analysis NLFEA approach. Ten cantilever beams (five of them are steel reinforced and the rest are not reinforced) were modelled by using ANSYS software with different haunched angles to achieve the purpose of the present study. The verification was done for two prismatic beams under torsion, and two reinforced concrete haunched beams (RCHBs) under static shear load to ensure the correctness of modelling. The verification work illustrated a good agreement between the NLFEA results by using ANSYS and previous experimental work results. No specific details in torsional design for RCHB in many codes, and no/very less works have done regarding analysis or design of RCHB under torsion. The main purpose of the present work is checking the capability of using ACI-318 code in analysis and design of concrete haunched beam for torsion. The presented paper confirms the validation of using ACI-318-2019 in analysis and design of RCHB and plain concrete haunched beam PCHB as well, where the FEA results by using ANSYS were at accuracy not less than 92 % with the ACI-318-2019 results for all specimens. The torsional mechanism failure and shear stresses distribution of RCHB are discussed in the present paper.

Study on the helicoidal flow through cylindrical annuli with prescribed shear stresses

In this article, we presented an analysis of the helical flow, for evaluating the incompressible Maxwell fluid indwelling between the two circular regions created by infinitely long concentric circular cylinders. Time-depended longitudinal and torsional shear stresses are implemented around the periphery of the inner circular cylinder to set the fluid in motion, while keeping the outer one inert. Exact analytic solution of the mathematical model in form of partial differential equations(PDE) is obained by performing the integral transform. We also retrieved the analogous solution of fluid, encompassing same properties as of Newtonian fluid in form of our general solutions. To end up with, we presented different graphs, showing the sway of appropriate parameters affecting the shear stresses and velocity components. In addition, we also presented graphs for comparison of Newtonian and Maxwell fluids. To end up with, the significance of appropriate parameters on the components of shear stresses and velocities, as well as motion for Newtonian and Maxwell fluids are analyzed and discussed via graphs.

Mechanical properties of curved composite box girders with corrugated steel webs

Several methods derived for use on traditional concrete curved box girders (CBGs) are used in design practice. However, these typically consider only one elastic modulus and one shear modulus, and consequently cannot be applied directly to CBGs with corrugated steel webs (CSWs) due to the large shear deformations and small longitudinal stiffness of CSWs, while these shear deformations are small and usually ignored for common concrete webs. In this paper, firstly, the flexure-torsion governing differential equations considering the shear deformations and the accordion effect of CSWs, and the distortion governing differential equation considering the accordion effect of CSWs are derived for CBGs with CSWs. A practical method which can solve the deflections, torsional angles, distortional angles, stresses and internal forces of simple and continuous CBGs with intermediate diaphragms is proposed. Secondly, the results of a series of tests performed on three CBGs with CSWs, published test results, as well as finite element analysis results and theoretical results of straight box girders (SBGs) with CSWs are used to verify the correctness of the analytical method. The agreement between analytical, experimental and numerical results is good. Finally, a parametric analysis is conducted and the results show that: (a) the influence of shear deformations of CSWs on the deflections of CBGs with CSWs increases with increasing curvature radius R. For SBGs with CSWs, the deflections may increase by 30% when considering shear deformations. For CBGs with CSWs, the deflection increase ranges between 8% and 30% for concentrated loads depending on the curvature radius. (b) the distortional shear stress, which is small and typically neglected for CBGs with concrete webs, may be as big as, or larger than the flexural shear stress, and must be considered. The restrained torsional shear stress, which is also small and typically neglected for CBGs with concrete webs, can reach 9% of the flexural shear stress, and also must be considered.

Cyclic Response of Loose Anisotropically Consolidated Calcareous Sand under Progressive Wave–Induced Elliptical Stress Paths

Observations of the performance of coastal and marine structures in weather events that produce standing and/or progressive waves have pointed to liquefaction of the seabed as a contributing cause of damage. The cyclic response of marine sediments under wave loading can serve to improve the understanding of seabed liquefaction triggering and its consequences. This paper presents the results of an experimental study of the cyclic behavior of loose isotropically and anisotropically consolidated calcareous sand under elliptical stress paths representing progressive waves. Various ratios, λ, of the axial stress difference and torsional shear stress amplitudes were investigated in a hollow-cylinder torsional shear apparatus. The results indicate that the failure mode of isotropically and anisotropically consolidated (IC and AC, respectively) specimens are cyclic mobility and residual deformation failure, respectively. The difference in the observed failure mode appears to be related to particle shape and is independent of λ. However, the cyclic resistance of the calcareous sand is strongly influenced by λ and increases with decreasing consolidation stress ratio, Kc. The cyclic resistance of IC specimens is relatively independent of the orientation of elliptical stress paths, whereas the AC specimens exhibited a marked dependence. The terminal peak excess pore pressure ratio, ru,t, and shear work required for cyclic failure, Wf, are independent of λ; however, ru,t and Wf increases with increasing and decreasing Kc, respectively. Moreover, the relationship between the normalized peak excess pore pressure ratio and normalized shear work is related to the type of soil, but is independent of λ and Kc.

Influence of spatially varying material properties on the bimoment normal and shear stresses by warping torsion of FGM beams

In this contribution, which is an extension of author’s research [1,2], an influence of the in two and three directions varying material properties on non-uniform torsion of the Functionally Graded Material (FGM) thin-walled beams is originally investigated. Based on the semi-analytical solution of the fourth order differential equation for non-uniform torsion, the local finite element equations of the twisted FGM beam are presented, considering the non-uniform torsion with effect of warping and secondary deformations due to the angle of twist. The warping part of the first derivative of the twist angle caused by the bimoment is considered as an additional degree of freedom at the beam nodes. The Multi-Layers Method (MLM) [3], and the Reference Beam Method (RBM) [4] are extended for homogenization of the spatially varying material properties and relevant stiffnesses in the real beam onto effective longitudinally varying ones in the homogenized beam for the load case of non-uniform torsion.The focus of the numerical investigation, with consideration of the warping and Deformation Effect due to the Secondary Torsional Moment (STMDE), is on elastostatic analysis of straight FGM beams with rectangular hollow cross-sections. The influence of the variation of the material properties with respect to two or three directions on the angle of twist and the bimoment normal and torsional shear stresses is investigated. The obtained results are compared with the ones calculated by a very fine mesh of standard solid finite elements. This FGM warping non-uniform torsion beam finite element can be used not only in torsional analysis of general thin-walled beams but also in the design of FGM sensors and actuators in mechatronics.

Cyclic resistance of saturated silt under wave-induced non-proportional loading

The significance and complexity of cyclic behavior of saturated silt under non-proportional loading are still of great concern in practice, due to the highly inherent anisotropy of soil fabric. This paper presents an experimental investigation conducted in an automated hollow cylinder apparatus into the undrained anisotropy and cyclic resistance of a saturated marine silt under wave-induced non-proportional loading, which is replicated by simultaneous changeover in magnitudes and directions of the principal stress. Special attention is paid to the influence of cyclic shear mode and stress path, characterized by the cyclic stress ratio (CSR) and the ratio (δ) of the amplitude of deviatoric stress components (i.e. deviator stress and torsional shear stress), on the pore pressure response and deformation characteristics. The cyclic stress path is not a negligible factor for the cyclic resistance of saturated silt in the non-proportional loading, but had significant impact. The CSR can not properly characterize the resistance of silt to cyclic shearing, involving continuous rotation of the principal stress. This observation is considered to be directly associated with the soil fabric anisotropy. Remarkably, for all loading patterns investigated, the pore pressure ratio ru is uniquely correlated with the generalized shear strain γg, rather than to the CSR. Consequently, a closed-form expression is proposed to relate γg and ru, which can be used to predict the onset of failure as well as the pore pressure at a specific strain. By using the equivalent cyclic stress ratio (ESR) to characterize the cyclic undrained resistance of saturated marine silt (in terms of the number of cycles required to failure, NL), a virtually unique correlation between ESR and NL can be established for all the non-proportional loading investigated.

Study of the relation between torsional shear stress and transverse torsion angle of cable

The relation between torsional shear stress and transverse rotational angle of earphone cable was investigated due to hypothecated to play an important role in the cable entanglement. The cable was hung with a circular plate and attached to force sensor on top. The experiment was carried out by rotating the plate stepwise at 90 degrees each for 80 times reaching 7200 degrees in total. Experimental results exhibit the fluctuation of longitudinal force with period almost exactly equals to a complete circle of transverse rotational displacement. It is also found that average longitudinal force tends to increase with counter clockwise rotation while decreasing in clockwise direction. We then conclude that the relationship between torsional shear stress and transverse torsion of the cable can be described by trigonometric function with linear changing of average amplitude.

MHD Flows of Second Grade Fluid Through the Moving Porous Cylindrical Domain

The flows of Magnetohydrodynamics(MHD) second grade fluid between two infinite porous coaxial circular cylinders are studied. At time t=0^+, the inner cylinder begins to rotate around its axis and to slide along the same axis due to torsional and longitudinal time dependent shear stresses and the outer cylinder is also rotate around its axis and to slide along the same axis with acceleration. The exact solutions obtained with the help of discrete Laplace and finite Hankel transform, satisfy all imposed initial and boundary conditions. The solution presented in convolution product of Laplace transform . The corresponding solutions for second grade and Newtonian fluids are also obtained as limiting cases with and without MHD effect. Finally, the influence of pertinent parameters on the velocity components and shear stresses, as well as a comparison among, second grade and Newtonian fluids with and without MHDÂ is also analyzed by graphical illustrations.

Finite element analysis of different internal fixation methods for the treatment of Pauwels type III femoral neck fracture

ObjectiveTo compare the bifomechanical advantages and disadvantages of different internal fixation methods for the treatment of Pauwels type III femoral neck fractures. Methods4 internal fixations were developed to treat Pauwels type III femoral neck fracture finite element models: a: the “F” shaped cannulated screw model, b: the traditional cannulated screw model, c: the “F” shaped cannulated screw coupled with medial plate model, d: the traditional cannulated screw coupled with medial plate. Under the same conditions, the 4 internal fixations and femur of von Mises stress and displacement distribution were studied. ResultsThe most significant displacement of all models occurred at the femoral head. The maximum displacement of the femoral heads included: a: 1.53 mm, b: 1.73 mm, c: 1.18 mm and d: 1.34 mm. The von Mises peak stresses of the femoral calcar area in different models were: a: 115.2 MPa, b: 143.5 MPa, c: 107.8 MPa and d: 120.5 MPa. The peak stresses of the four internal fixation models included: a: 318.0 MPa, b: 360.9 MPa, c: 468.8 MPa and d: 771.5 MPa. ConclusionThe “F” shaped cannulated screw technique is capable of eliminating the torsional stress and shear stress while maintaining the axial compressive stress at the fracture end. Besides, the medial support plate can effectively resist the shearing force of the Pauwels III femoral neck fracture and create an excellent mechanical environment for fracture healing. Thus, for the Pauwels III femoral neck fracture, the use of “F” shaped cannulated screws combined with medial plate internal fixation are recommended.

FEM Simulation of Electric Car Chassis Design with Torsional Bar Technology

A design of electrical vehicle chasis is presented, specifically a FEM simulation is employed to simulate the different kind of load and reaction on vehicle frame. The main goal in this research is to develop an electric car with torsion bar, where the frame will have a self-suspension system. The frame design will be made as original equipment. This research will focus on how an electric car chassis withstand certain load with a defined boundary condition, where the analysis is conducted using Finite element Method using ANSYS software. The main analysis is the Von-Misses Stress, the safety factor, bending, torsion shear stress and vibration.

Displacement and Stress Function-based Linear and Quadratic Triangular Elements for Saint-Venant Torsional Problems

Torsional problems commonly arise in frame structural members subjected to unsym­metrical loading. Saint-Venant proposed a semi inverse method to develop the exact theory of torsional bars of general cross sections. However, the solution to the problem using an analytical method for a complicated cross section is cumbersome. This paper presents the adoption of the Saint-Venant theory to develop a simple finite element program based on the displacement and stress function approaches using the standard linear and quadratic triangular elements. The displacement based approach is capable of evaluating torsional rigidity and shear stress distribution of homogeneous and nonhomogeneous; isotropic, orthotropic, and anisotropic materials; in singly and multiply-connected sections. On the other hand, applications of the stress function approach are limited to the case of singly-connected isotropic sections only, due to the complexity on the boundary conditions. The results show that both approaches converge to exact solutions with high degree of accuracy.

Torsional Shear Stress Minimization Techniques and Implications on Electromagnetic Performance of Flux-Modulated Double Rotors

Magnetic-geared machines are based on the flux-modulation principle and typically constructed with a flux-modulated double rotor (FMDR). The modulator experiences high torsional stresses when designed for high torque transmission. As a result, the FMDR has high probability of failure if not designed appropriately. In this paper, the FMDR design options are investigated with mechanical and electromagnetic finite element (FE) modeling. The addition of filler material in between the poles of the modulator pole-pieces is found to reduce the shear stresses by $61.7\%$ to $87.2\%$ at the cost of $2.6\%$ to $3.2\%$ lower pull-out torque. Possible shear stress reduction with the design of bridged modulators is investigated. Increase in pole number is shown to increase localized stress levels in bridged modulators. Electromagnetic simulations show that for a given FMDR specification, the highest pull-out torque is at an optimal pole number. The tradeoff between FMDR weight, losses, and shear stress are discussed. A scaled-size prototype FMDR with a bridged modulator is constructed. The FMDR is tested and is shown to achieve comparable results with the FE simulations. At field intensity levels above 600 kA/m in the periphery, the FMDR achieves reduced pull-out torque $28.7\%$ lower in comparison with three-dimensional simulations. The losses at different load levels of the FMDR are also compared with experimental and FE simulation result and are shown to confirm the FE simulation results.

Mechanical properties improvement and fire hazard reduction of expandable graphite microencapsulated in rigid polyurethane foams

Nowadays, reducing the fire hazard and improving the mechanical strength of rigid polyurethane foams (RPUFs) at the same time are important research direction in the fields of safety materials. Expandable graphite (EG) is an effective flame retardant for RPUF, but would destroy the compatibility of the matrix. In this article, EG is capsuled by melamine cyanurate (MCA) and then microencapsulated expandable graphite (MCEG) is obtained, which is added into RPUF. The mechanical properties of composites were evaluated by compressive strength test, torsion strength test and shear stress test. The fire characteristics including smoke and heat production of RPUF composites were studied using cone calorimeter test. And the thermal decomposition and flammable properties were further evaluated using thermogravimetric analysis and limiting oxygen index. The results show that the mechanical properties of RPUF containing MCEG are similar with RPUF and better than RPUF containing EG. Furthermore, MCA cover would impede expanding of EG, which weakens the protective and insulation effects of expanding layer. Therefore, the composites containing MCEG decompose faster and produce more smoke than the composites containing EG. However, MCA and EG have the synergistic enhancing effect on the flame retardant property of composite. POLYM. COMPOS., 40:E1006–E1014, 2019. © 2018 Society of Plastics Engineers

Undrained behaviour of intact soft clay under cyclic paths that match vehicle loading conditions

Vehicle traffic loading appears to contribute significantly to long-term settlement beneath highways, airport runways, and metro lines in China. Wheel loading imposes cycles in both the magnitude and direction of the principal stresses acting on the soils beneath pavement or rail-track structures. Conventional cyclic triaxial (CT) testing, which is not capable of imposing such stress paths, may underestimate how heavy traffic loading affects any underlying soft clay layers. A hollow cylinder apparatus (HCA) can simulate such traffic loading stress paths more accurately, including rotation of the principal stress directions. This paper presents a systematic experimental study of cyclic HCA (CHCA) tests on K0-consolidated saturated soft clay involving cyclic variations in both vertical and torsional shear stresses, along with a parallel programme of CT tests, considering the undrained response of saturated samples of intact soft clay. It is shown that when applied above certain critical cyclic stress ratios, principal stress rotation accelerates excess pore-water pressure and permanent strain development. Corresponding changes are also seen in the resilient modulus and damping ratio trends. The discrepancies between the behaviour of CHCA and equivalent CT tests grow as the cyclic stress ratios increase.

Torsional statics of two-dimensionally functionally graded microtubes

ABSTRACTA size-dependent governing equation is derived to investigate the torsional static behaviors of two-dimensionally functionally graded microtubes based on the modified couple stress theory. The shear modulus is assumed to vary along the tube’s length direction according to an exponential distribute function, and varies along the tube’s radius direction according to a power-law function. A generalized differential quadrature method is developed to determine the rotational angle and shear stresses. Some illustrative examples are given to investigate the effects of applied torques, the length scale parameter and various material compositions on the torsional angle and shear stresses.

Effect of drained static shear on cyclic deformation behavior of K0-consolidated sand

The K0-consolidated soil elements beneath structures like quay walls, bridge abutments, cut and cover tunnels and similar structures may be subjected to static shear involving the rotation of the principal stress prior to cyclic loading, which results in the presence of initial shear stress. A hollow cylindrical apparatus was employed and a series of drained cyclic tests was conducted to examine the effects of the initial shear stress induced by drained static shear prior to the application of cyclic loading. Both the initial vertical stress and the initial torsional shear stress were considered in the drained cyclic deformation behavior. The experimental observations indicate that the initial vertical stress accelerates the accumulation of vertical permanent strain during the first 100 cycles only when the initial vertical stress exceeds the value corresponding to the K0-consolidated stress state. The average growth rate of strain increases due to the presence of the initial torsional shear stress. A Critical Static Shear Line (CSSL), initiating from the K0-consolidated stress state in the (σz−σθ)−2σzθ plane, divides the volume change responses into contraction and dilation in subsequent cyclic loading. To account for the combined effects of the initial vertical stress and the initial torsional shear stress on the deformation behavior, a modified model is proposed to predict the vertical permanent strain.

Slight asymmetry in the winding angles of reinforcing collagen can cause large shear stresses in arteries and even induce buckling

Many models of the mechanical response of arteries assume a reinforcement with two families of helically wound fibres of collagen of opposite pitch. Motivated by experimental observations, the consequences for the internal pressurisation of arteries of a slight asymmetry in the winding angles is investigated here. It is shown that a torsional shear stress is generated as a result of this flaw, with some common models of the mechanical response of arteries exhibiting significant shear stresses. If the shear stress is significant, then the corresponding model would not seem to be robust, given that an infinitesimal change in a model parameter results in a large change in system response, although it is also shown that there is a ‘magic-angle’ for fibre winding that eliminates torsional shear stress for many of the commonly used models. Finite Element simulations are used to further illustrate the main consequences of fibre asymmetry for some of the more common models of arterial response. If the fibre asymmetry is localised in a region, then simulations show that there is the possibility of significant bending of the artery centred in this region at physiological blood pressure.

Effects of starch concentration on calcium-enhanced black bullhead catfish protein gels.

Calcium‐enhanced protein recovered from black bullhead catfish was used to develop gels containing increasing amounts of potato starch (0–20 g/kg protein paste) and the effects of starch on functional, textural, and color properties were tested. Energy required to unfold protein groups was greater with the addition of 5 g starch/kg protein paste. Gels containing starch were harder, chewier, and less springy (p < .05) than gels without starch. For most measurements, regression analysis showed that increasing the starch concentration beyond 5 g/kg did not contribute to further significant textural changes. Torsional shear stress and strain along with Kramer shear force increased as the concentration of starch increased (R 2 = .79, .79, and .53, respectively). The addition of ≥10 g starch/kg protein paste resulted in darker gels and gels got darker as more starch was added (R 2 = .71). Results showed no benefit to increasing starch concentration in gels beyond 5 g starch/kg protein paste.