Shear Springs Research Articles

Multi-spring Edge-to-Edge Contact Model for Discontinuous Deformation Analysis and Its Application to the Tensile Failure Behavior of Rock Joints

Edge-to-edge is the most common form of contact in a two-dimensional joint block system. Discontinuous deformation analysis (DDA) is a powerful tool for handling block systems and treats an edge-to-edge contact as two vertex-to-edge contacts with a couple of normal and shear springs at the extremes of the contact segment. However, this method is unsuitable for evaluating the tensile failure of a joint under asymmetrical tension conditions, even though it can simplify the contact type and increase computational efficiency. This is mainly because the distributed forces at an edge-to-edge contact are simplified as two couples of concentrated forces. To solve this problem, this paper proposes incorporating a multi-spring edge-to-edge contact model with DDA. In the model, several contact pairs with normal and shear springs on an edge-to-edge contact are set to simulate the distributed forces. Several benchmark tests were performed to demonstrate the discrepancy between the original and improved DDAs. The results revealed that the latter more accurately models the stress distribution across the edge-to-edge contact, providing a more reasonable acceleration required to topple a series of blocks resting on an inclined stepped base.

Dynamic analysis of vibrating flip-flow screens equipped with support and shear rubber springs

Vibrating flip-flow screens provide an effective means of screening highly viscous or fine materials, and the dynamic characteristics of the main and the floating screen frames are largely responsible for a flip-flow screen’s screen performance and its processing capacity. An accurate dynamic model of the rubber shear springs used within the frame of the screen is critical for its dynamic analysis – to understand deficiencies and improve its performance. In this paper, the Sjöberg model is used to predict the frequency-and amplitude-dependent behaviour of the rubber shear springs. A friction model represents the amplitude dependency of the rubber shear springs. The fractional derivative model is used to describe its frequency dependency with its elasticity being represented by a linear spring. This model is further validated by cyclic tests of the rubber shear springs. Furthermore, dynamic response of the VFFS have been analysed using the Sjöberg model and the Kelvin-Voigt model, respectively. Experimental results indicate that dynamic response of VFFS can be better predict using the Sjöberg model than Kelvin-Voigt model in time region as well as in the frequency domain.

Efficient modeling of flexural and shear behaviors in reinforced concrete beams and columns subjected to low-velocity impact loading

Detailed finite element (FE) models with 3-D solid elements are typically used to simulate impact behaviors of reinforced concrete (RC) beams and columns. However, the method usually requires a substantial amount of time and effort to model concrete and reinforcement and conduct nonlinear contact-impact analyses. Also, the accuracy of the method cannot be guaranteed due to the limitations in concrete material models implemented in general-purpose FE codes. In this paper, an efficient modeling method is proposed to capture both flexural and shear behaviors of RC beams and columns under low-velocity impact loading. A macroelement-based contact model was developed in the proposed method to capture interaction behaviors between impacting objects and RC members. In the contact model, a compression-only spring with an initial gap behavior was used to account for the stiffness and the kinematic response of an impacting object, and a combination of an elastic spring and a viscous damper in parallel was employed to simulate the contact stiffness and damping. By properly approximating the strain-rate effects, traditional fiber-section elements were demonstrated to be capable of predicting impact-induced flexural failures for RC members. On this basis, a general approach for both flexural- and shear-critical RC columns under impact loading was presented with the inclusion of additional shear springs in the fiber-section elements. Nearly fifty impact tests on RC beams and columns reported in the literature were employed to validate the proposed modeling method. Comparisons between the experimental and numerical results indicate that failure modes of the impacted members can be identified explicitly by the use of the proposed modeling method. Also, reasonable agreements were achieved for the impact forces and the impact-induced responses obtained from the impact tests and the analyses. The proposed method can be readily implemented without coding in any FE software as long as traditional fiber-section elements, and discrete macroelements are available. This feature would offer an advantage for the applications of the proposed method such as when assessing the structural response and vulnerability of a bridge structure subjected to vessel and vehicle collisions.

Considering Shear Behavior of Beam-Column Connections to Assess the Seismic Performance of RC Frames Subjected to Freeze-Thaw Cycles

ABSTRACT Freeze-thaw of concrete is significantly responsible for serious damage to RC buildings, which may result in premature failure with little warning. Therefore, it is necessary to consider the effects of freeze-thaw environment when assessing seismic performance for RC structures. In this study, pseudo-static experiments of interior beam-column joints were conducted in terms of different axial compression ratios and the number of freeze-thaw cycles (FTC). Based on the experimental results, the effects of freeze-thaw were mathematically modeled using a reduced envelope and a parameter of cyclic deterioration for the joint shear–strain relationships. The constitutive parameters of joint panels were defined by transforming the shear–strain relation into the moment–rotation relation of a shear spring. Finally, a numerical model of a beam-column joint was proposed in order to predict its shear behavior after being subjected to FTC. The numerical model was well validated by the experimental results of two RC beam-column joint test series. As an application to RC structures, model calculations were applied to five-story and three-bay RC frames of 0 and 30 years, respectively.

Study of shear behavior of grouted vertical joints between precast concrete wall panels under direct shear loading

A precast wall‐type building is constructed by stacking wall panels and slabs. This paper presents a study of the in‐plane shear behavior of vertical grouted joints between precast panels. Thirteen jointed wall panel specimens were tested under direct shear. Based on the results, analytical expressions were developed to predict the shear load versus slip behavior. These can be used in computational models of precast wall type buildings, through modeling of shear springs between the panels. To demonstrate the application, a numerical analysis of an isolated jointed shear wall was performed. The wall was modeled for three cases, (a) monolithic wall, (b) two walls with a gap and (c) two walls with shear links. Based on non‐linear pushover analysis, it was demonstrated that the modeling of jointed walls using shear links reduces the conservatism inherent in a model neglecting the shear transfer across the joint.

Nonlinear Analytical Model of Unreinforced Masonry Wall using Fiber and Shear Spring Elements

Nonlinear Analytical Model of Unreinforced Masonry Wall using Fiber and Shear Spring Elements

On parameters affecting the racking stiffness of timber-glass walls

An extensive parametric numerical study was performed after completed experimental campaign of timber-glass hybrid walls (TGW and TGWE). 36 timber-glass models (TG) with different outer dimensions were built and analysed with a goal to capture the basic response of mechanically tested timber-glass walls and to determine the racking stiffness of the calculated numerical models. Timber frame was modelled using linear beam elements with hinges in all four corners, an IGU was modelled as a multilayer shell and finally a layer of adhesive was modelled with linear and nonlinear springs, which were distributed circumferentially around the edge of IGU and connected onto a timber frame. Normal and shear stiffness coefficients for linear-elastic springs were calculated, while for nonlinear springs a special series of mechanical tests on polyurethane (PU) adhesive was performed since a lack of data available in addition to the desired amount of information needed for the numerical analysis. Uniaxial tension, compression and shear tests were made to obtain the results in form of the load-displacement curve, which presented a direct input for nonlinear normal and shear springs of the mathematical model. For each compression and tension mechanical test three specimens were prepared and tested up to rupture, while a double-lap shear test was conducted using two specimens giving two results each. PU adhesive specimens of the first series had dimensions of 50 mm $$\times $$ 50 mm and thickness of 5.0 mm. Mechanical tests were repeated for two additional thicknesses of PU adhesive, namely 7.0 mm and 9.0 mm. After completed experimental investigation on PU adhesive joint, together 108 numerical models with different external dimensions were analysed in commercial code SAP2000. Having the correct information about the stiffness of the single TG shear wall one can calculate the stiffness of the entire timber-glass building built with such walls.

Improved numerical analysis for ultimate behavior of elastomeric seismic isolation bearings

SummaryElastomeric isolation bearings consist of multiple rubber layers with their top and bottom surfaces bonded to steel plates to restrict compressive deformation. Deformation constraints result in a variation of elastic modulus over the cross section of the rubber layers. In this paper, we describe a normalized compression modulus distribution on a circular rubber pad. The compressive and bending moduli of the rubber pad can be reproduced by applying the distribution to a series of axial springs. We also present a mechanical model for predicting the behavior of elastomeric seismic isolation bearings subject to large shear deformation and high compressive load. The mechanical model consists of a series of multiple shear springs at midheight and a series of axial springs at the top and bottom interfaces of the bearing. Simulation analyses of bearing tests were conducted to validate the proposed model. The analyses demonstrated that a model for circular lead‐rubber bearings can successfully capture the influence of the axial load magnitude on the bearing shear behavior. The new model can simulate much more realistic behavior than prior models based on a uniform modulus assumption.

Elastic Foundation Constants for Sandwich Composites

Elastic foundation models are often used in fracture mechanics applied to face/core debonds in sandwich composites or in face wrinkling studies. The elastic constants to be used in these models are the most important element in these formulations. This paper presents closed-form solutions for the determination of these constants based on 1) the extended high-order sandwich panel theory and 2) the elasticity theory. The extended high-order sandwich panel theory results in a system of seven algebraic equations, which can be directly solved for the seven real constants that enter into the formulas (all calculations are in real variables). The elasticity solution results in a system of 12 linear algebraic equations, which can be directly solved for the twelve complex constants that enter into the formulas, and it also involves the direct solution of three characteristic equations (for the 2 faces and the core). In the elasticity approach, the calculations are done in complex variables. Direct formulas are derived for both the normal and the shear spring constants. The definition of the elastic foundation constants and possible misconceptions surrounding them are discussed. New simple formulas are also suggested, which are variations of “crude” formulas existing in the literature.

Torsional Response Induced by Lateral Displacement and Inertial Force

Eccentric distribution of stiffness, damping, and mass of a structure, and spatially non-uniform ground motion input to a long or large base mat of a structure are well-known causes of torsional response. We have discovered that the torque generated by horizontal displacement and perpendicular inertial force, which we call the Q- effect, can be a cause of torsional response. We formulated the equation of motion of a single finite-size mass-linear elastic shear and torsion spring model and clarified the resonance condition of the torsional response to sinusoidal ground acceleration. Time-history response analysis verified that the torsional response forms beat and the maximum torsional response of the simulation result agrees with that theoretically predicted. Further time-history response analysis conducted of white noise ground acceleration showed that even one-directional white noise ground acceleration can induce torsional response in a linear elastic system without any structural eccentricity.

A simplified analytical model for U-shaped steel dampers considering horizontal bidirectional deformation

Hysteresis steel dampers are widely used in earthquake-resistant structures, where some of them are anisotropic and capable of sustaining earthquake-induced bidirectional deformation. In this paper, a simplified analytical model is proposed for simulating the hysteretic behavior of U-shaped steel dampers with horizontal bidirectional deformation. The proposed model is composed of a series of shear springs with different nonlinear characteristics in a radial configuration, and the Menegotto–Pinto hysteresis model is employed to represent the hysteretic characteristics of the springs. The mechanical and shape-related parameters of the hysteresis model are set according to the multi-directional deformation characteristics of steel dampers. With the aim of validating the effectiveness and applicability of the analytical model, a U-shaped steel damper was used as an example. The pseudo-static hysteretic characteristics of the steel damping element were analyzed and the elasto-plastic seismic response of a curved bridge featuring a steel hysteresis device was investigated. The results showed that the proposed model is sufficiently accurate to simulate the hysteretic behavior of U-shaped steel dampers, and thus provides a practical method to assess U-shaped steel dampers through seismic response analysis.

Buckling of a piezoelectric nanobeam with interfacial imperfection and van der Waals force: Is nonlocal effect really always dominant?

With the development of NEMSs (nano-electro-mechanical systems), the size-dependent behavior has been an active topic. The scale parameter seems an essential factor dominating mechanical behavior at nanoscale. However, is it always dominant? This is a question deserving careful investigation. For this reason, the buckling of a bi-layered PE (piezoelectric) nanobeam is analyzed. The main purpose is to reveal and compare the effects of the nonlocal scale, imperfect interface, interlaminar van der Waals force and loading ratio. The imperfect interface is modeled by normal and shear springs, and the van der Waals force is represented by the Hamaker formula. Based on the principle of virtual work, the analytical solution of the critical buckling loading is derived by using the trigonometric shear deformation theory. After the verification in some degenerated cases, parametric studies are conducted. It is indicated that if the nonlocal parameter varies in the typical range [0, 4 nm^2], it only has quite limited effect on the buckling behavior, as compared with the other three factors. In this case, although the buckling relies on the nonlocal scale, it is far more dependent on the conventional non-nanoscale factors. The conclusions can provide references for optimal design of NEMSs.

Shear spring model proposed for seismic evaluation of a timber framed masonry infilled wall

Masonry infilled timber frames (TFM) are widely used for residential houses in many countries in the world. Last two decades’ seismic events showed that this typology is resilient for earthquakes, and even though it exhibits damages, it rarely collapses. For developing countries, TFM is a valid solution for life protection of the inhabitants.Interaction between timber and masonry is difficult to assess and although numerical models simulate roughly the seismic behavior of TFM, they need expensive resources (time and software) to reach acceptable accuracy level. For this reason, this study proposes a simplified seismic evaluation method for timber framed masonry walls, based on a shear spring model calibrated with experimental result. The resulting envelope curve simulates satisfactorily the initial stiffness and maximum strength.

Analysis of Brick Masonry Wall using Applied Element Method

The Applied Element Method (AEM) is a versatile tool for structural analysis. Analysis is done by discretising the structure as in the case of Finite Element Method (FEM). In AEM, elements are connected by a set of normal and shear springs instead of nodes. AEM is extensively used for the analysis of brittle materials. Brick masonry wall can be effectively analyzed in the frame of AEM. The composite nature of masonry wall can be easily modelled using springs. The brick springs and mortar springs are assumed to be connected in series. The brick masonry wall is analyzed and failure load is determined for different loading cases. The results were used to find the best aspect ratio of brick to strengthen brick masonry wall.

Effect of dowel joints on dynamic behavior of train–discrete floating slab track system

Dowel joints are installed at the end of floating slabs and can effectively reduce the discontinuity of deformation between adjacent floating slabs. The shear spring model had been proposed for mod...

Geometrically nonlinear inelastic analysis of steel–concrete composite beams with partial interaction using a higher-order beam theory

A comprehensive finite element model based on a higher-order beam theory (HBT) is developed for an accurate prediction of the response of steel–concrete composite beams with partial shear interaction. The formulation of the proposed one dimensional finite element model incorporated nonlinearities due to large deformations of the beam as well as inelastic material behaviour of its constituent components. The higher-order beam model is achieved by taking a third order variation of the longitudinal displacement over the beam depth for the steel and concrete layers separately. The deformable shear studs used for connecting the concrete slab with the steel girder are modelled as distributed shear springs along the interface between these two material layers. The Green–Lagrange strain vector is used to capture the effect of geometric nonlinearity due to large deflections. The von Mises plasticity theory with an isotropic hardening rule and a damage mechanics model are incorporated within the proposed finite element model for simulating the inelastic response of the beam materials. The nonlinear governing equations are solved by an incremental-iterative technique following the Newton–Raphson method. A dissipation based arc-length method is employed to capture the post peak response of these beams successfully. The capability of the proposed model is assessed through its validation and verification using existing experimental results and numerical results produced by detailed finite element modelling of these beams.

Double controller of wind induced bending oscillations in telecom towers

Wind induced large bending oscillation amplitudes in tall and slender telecommunication steel towers may lead to precocious fatigue cracks and consequent risk of collapse of these structures, many of them installed in rural areas alongside highways and in highly populated urban areas. Varying stress amplitudes at hot spots may be attenuated by means of passive control mechanical devices installed in the tower. This paper gives an account of both mathematical-numerical model and the technique applied to design and evaluate the performance of a double controller installed in existing towers which is composed by a nonlinear pendulum and a novel type of passive controller described herein as a planar motion disk mounted on shear springs. Results of experimental measurements carried out on two slender tubular steel towers under wind action demonstrate the efficiency of the double controllers in attenuating the towers bending oscillation amplitudes and consequent stress amplitudes extending the towers fatigue life.

A review of lattice type model in fracture mechanics: theory, applications, and perspectives

The lattice model is a discrete model that is typically used to simulate the fracture process of brittle materials. This review summarizes the main achievements during the development history of the state-of-the-art lattice model during the past 80 years from the theory and application viewpoints. It is found that the classical lattice spring model (LSM) can only simulate a fixed Poisson’s ratio. This problem has been partially or fully solved in developed versions of novel lattice models by using (1) extra nodal DOFs, (2) extra shear springs, (3) extra nonlocal energy parameters, and (4) higher dimensional normal springs. The lattice model has already been successively applied in simulations of fracture processes of different materials and under different loads. However, the applications in fracture analyses of metals, dynamic load-induced fracture, and real large-scale structures, are not sufficient. Innovative areas of future research in reference to the use of the lattice model in engineering practice include constitutive relations, failure criteria, anisotropic material modeling and efficient computing techniques to expand its use and range of applications.

Fragility analysis of the nave macro-element of the Cathedral of Santiago, Chile

This paper presents the fragility analysis of a typical nave macro-element of the Metropolitan Cathedral of Santiago, Chile. The analysis is carried out by using the rigid body spring model approach, in which rigid elements are connected to each other by means of axial and shear springs. The 2D model generated is initially verified by comparing modes with a 3D finite element model previously calibrated in DIANA software. The methodology used in this study is based on a set of eleven real seismic records corresponding to four major earthquakes that have affected Santiago city. Nonlinear incremental dynamic analyses together with a damage index based on stiffness degradation, which considers the relation between shear at the base and deformation of the macro-element, are used to generate the fragility curves. As a result of this study, the probability of exceedance for different damage states has been obtained based on a possible peak ground acceleration of the site. In particular, the results of the study demonstrate that the proposed damage index satisfactorily describes the damage suffered by some of the nave transverse sections of the Cathedral after the 2010 Maule earthquake (PGA 2.11 m/s2—Santiago Centro station).

APPLICATION OF AEM IN PROGRESSIVE COLLAPSE DYNAMICS ANALYSIS OF R.C. STRUCTURES

The Finite Element Method (FEM) and the other numerical strategies are viably actualized in linear and non-linear analysis of structures. Recently, a new displacement based on Applied Element Method (AEM) has been developed. It is applicable for static and dynamic for both linear and non-linear analysis of framed and continuum structures. In AEM, the structural member is partitioned into virtual elements connected through normal and shear springs representing stresses and strains of certain portion of structure. FEM assumes the material as continuous and can indicate highly stressed region of structure, however it is difficult to model separation of element unless crack location is known. The main advantage of AEM is that it can track the structural collapse behavior going through all phases of the application of loads.In the current research, the application of AEM is illustrated through a non-linear dynamic analysis. Progressive collapse simulation is conducted using Extreme Loading for Structures software (ELS), which follows the AEM. The experimental and analytical works carried by Park et al. [17 and 28] for 1/5 scaled 3 and 5 stories reinforced concrete structures are used for verification. Good matching between the experimental and numerical results has been obtained using ELS. Therefore, it can be confirmed that ELS is capable in simulating the structures’ behavior up to collapse.Furthermore, a study has been made to investigate the effect of considering the floor slabs on progressive collapse. The results show that considering slab in progressive collapse analysis of multistory buildings is important as neglecting the slabs’ contribution leads to incorrect simulation and uneconomic design.