Shear Stiffness Ratio Research Articles

Vibration isolation of infinitely periodic pile barriers for anti-plane shear waves: An exact series solution

The application of periodic pile barriers for isolating ambient vibrations has emerged as a significant research topic, which is essentially the problem of wave scattering by periodically distributed structures. This study presents an analytical series solution for anti-plane shear (SH) wave scattering by infinitely periodic pile barriers using the wave function expansion method, incorporating the wave field characteristics of infinitely periodic distributed scatterers subjected to plane waves. From the perspective of periodic theory, the wave fields around each scatterer are completely identical, differing only by a phase shift (frequency domain) or a time difference (time domain). As a result, as long as the boundary condition of one scatterer is satisfied, boundary conditions of the remaining scatterers can be satisfied simultaneously. This novel approach allows the selection of an arbitrary single pile as a reference in the infinitely periodic model to be solved, yielding accurate results without truncation errors and significantly reducing computational and storage requirements. A FORTRAN code is developed to achieve numerical evaluation of the theoretical formulation, followed by verification of the solution's accuracy using two degenerate examples. Numerical examples are conducted, focusing on the influence of pile stiffness, pile spacing, and pile type on the vibration isolation. The results demonstrate that decreasing the spacing between piles can effectively increase the bandgap width and reduce the displacement response. The screening effectiveness of solid piles is better than that of hollow pipe piles and filled pipe piles. In vibration mitigation design for engineering projects, the larger the shear stiffness ratio of the pile-soil is not always better, an economical and reasonable pile stiffness should be selected.

Efficient Machine Learning Model for Predicting the Stiffness of Circular Footings on Clay Overlying Sand

Assessing the stiffness of circular foundations is the key to evaluating their deformation; thus, it is important for foundation design. The current determination methods for the stiffness coefficient are either time-consuming or inaccurate. In this paper, a novel stiffness prediction model has been proposed, using the decision tree (DT) algorithm optimized by particle size optimization (PSO). The condition of the embedded foundation, the embedded depth (ZD/2R), the thickness of the clay layer beneath the foundation base (T/2R), and the ratio of shear stiffness between clay and sand (Gsand/Gclay) were used as input variables, while the elastic stiffness coefficients (Kc, Kh, Km, and Kv) were used as output variables. The optimum DT model has undergone comprehensive validation, and independent model verification using extra simulations. The results illustrate that PSO could promote further increases in the capability of DT modeling in predicting stiffness coefficients. The optimum DT model achieved a good level of performance on stiffness coefficient modeling. (The R for the training set was greater than 0.98 for all of the stiffness coefficients.) The variable importance analysis showed that the T/2R was the most significant variable for all stiffness coefficients, followed by Gsand/Gclay. The optimum DT model achieved good predictive performance upon independent verification, with the R being 0.97, 0.99, 0.99, and 0.95 for Kv, Kh, Km, and Kc, respectively. The proposed reliable and efficient DT-PSO model for stiffness coefficients in layered soil could further promote the safe and efficient utilization of circular foundations.

Analytical dispersion curves and bandgap boundaries for quadrilateral lattices

The two-dimensional quadrilateral lattice structures are the most common periodic structures in industrial engineering application. This paper investigates the Bragg bandgap mechanism of classical quadrilateral periodic lattice structures. The explicit expressions of dispersion relations are obtained analytically and those with the eigenmodes corresponding to the same dispersion relation solution are connected to form the band structure. Unlike the existing works, it is the first to connect dispersion curves with the same eigenmodes, which explains the bandgap formation and transmission loss more reasonably. Four kinds of two-dimensional quadrilateral lattice structures are investigated to discuss the effects of shear force and mid-masses. The analytic expressions of bandgap boundaries are obtained and the influence of parameters including the mass ratio, tensile stiffness ratio and shear stiffness ratio on the bandgap boundaries is discussed.

Proposing Cubic-Grid System as a New Structural System for Tall Buildings

Background: Changes in the skyline of cities all over the world show that tall buildings are an interesting solution to accommodating growth more sustainably in today’s urban areas. Stability against lateral loading is the main issue for designing high-rise buildings. Diagrid systems or grid structures are one of these stable systems. For a long time, the only structural pattern used in this system was the triangular modulus (diagrid). Methods: In the present study, a new pattern for grid structures was introduced, and its performance was compared with the two previous common patterns (triangular and hexagonal). The new pattern is called the Isometric Cube grid, thanks to its particular shape. The design process was performed based on a simple stiffness criterion presented in the previous research. In order to calculate the stiffness of the structure for the new pattern, two types of existing structural nodes were distinguished, and the results were combined to determine the stiffness of the unit forming the entire grid. Results and Conclusion: From the results of analysis, it was found that the optimal angles of diagonal elements were in the range of 50-65 degrees. Although the behavior of the new pattern in terms of shear stiffness was between the two previous patterns (and closer to the hexagonal pattern), the shear stiffness ratio increased from 30° to 65° for cube pattern, while for hexagrid, it decreased over the same range of angles.

Bandgap and wave propagation of spring–mass–truss elastic metamaterial with a scissor-like structure

Inspired by the inertial amplification mechanism and bandgap characteristic of periodic structures, a type of scissor-like elastic metamaterial is studied for low-frequency vibration attenuation in this paper. Firstly, the 1DOF (degree of freedom) scissor-like chain consisting of masses, trusses, and springs is investigated. The formation of inertial amplification is illustrated, that is, input horizontal movements are converted into larger vertical movements of vertex masses by a scissor-like structure. The resonance and anti-resonance phenomena in transmission curves are explained. Especially, the optimal configuration for low-frequency attenuation is obtained by analytical expressions of the dispersion relation. Then, a 2DOF spring–mass–truss chain is considered to open a bandgap below the vibration attenuation range of the 1DOF chain. The relative movement of masses at different frequencies is explored to understand the bandgap generation. The influence of parameters including the mass ratio, tensile stiffness ratio, shear stiffness ratio, and angle on bandgap boundaries is discussed. Finally, the spatial propagation of a wavelet packet is presented to illustrate the efficiency of the proposed structure in terms of minimizing a broadband excitation transmission. The transmitted component of a wavelet packet through three units of the proposed structure is only 3.8%, which is 22.8% of that through the classic 1D local resonance metamaterial.

Theoretical and practical models for shear strength of corroded reinforced concrete columns

In order to predict the shear strength of corroded reinforced concrete column (CRCC) accurately and efficiently, both theoretical and practical models for shear strength of the CRCC were established through theoretical derivation and experimental validation. The deterioration mechanism for shear strength of the CRCC due to the steel reinforcement corrosion was explored first based on the shear mechanism analysis of the truss-arch model. Then a theoretical model for shear strength of the CRCC was developed by taking into account the influences of steel reinforcement corrosion on the effective yield strength of transverse reinforcement, the effective cross-sectional area of both corroded transverse and longitudinal reinforcements as well as the effective concrete shear area. Meanwhile, three practical models to evaluate the shear strength of the CRCC were proposed based on 54 sets of experimental data by determining the approximate values of three important parameters, including the contribution coefficient of shear strength for concrete, the ratio of shear stiffness between the truss model and the arch model, as well as the tangent value of the critical crack angle. Finally, the accuracy and applicability of both theoretical and practical models for shear strength of the CRCC were validated by comparing with five existing empirical shear strength models.

Effect of Segmental Joint on Internal Forces in Tunnel Lining under Seismic Loading by Numerical Method

Although segmental tunnel linings are often used for seismic areas, the influence of segment joints on the segmental lining behavior under seismic loading has not been thoroughly considered in the literature. This paper presents the results of a numerical study investigating the effects of the rotational, axial, and radial joint stiffness of the longitudinal joints on the structural forces in segmental tunnel lining under seismic loading. A 3D finite element method is adapted to establish elaborate numerical models of the segments. The validity of the numerical model was tested by comparing the results obtained with the well-known analytical methods presented by Wang and Penzien. The results demonstrate that by increasing the rotational stiffness of the segmental joint, the bending moment increases. When the rotational stiffness ratio is less than 0.5, the positive and negative bending moment variations are more. The numerical modeling results show the variations in the bending moment and the difference between the positive and negative bending moment values increased by increasing the acceleration of seismic loading. Moreover, it is significant for the values. By increasing the rotational stiffness ratio of the segmental joint, the axial force ratio decreases. By increasing the axial and shear stiffness ratio of segmental joint, the variations in the bending moment and axial force in segmental lining is not significant and is ignorable in designing segmental lining.

On the linear elastic responses of the 2D bonded discrete element model

SummaryThe bonded discrete element model (DEM) is a numerical tool that is becoming widely used when studying fracturing, fragmentation, and failure of solids in various disciplines. However, its abilities to solve elastic problems are usually overlooked. In this work, the main features of the 2D bonded DEM which influence Poisson's ratio and Young's modulus, and accuracy when solving elastic boundary value problems, are investigated. Outputs of numerical simulations using the 2D bonded DEM, the finite element method, a hyper elasticity analysis, and the distinct lattice spring model (DLSM) are compared in the investigation. It is shown that a shear interaction (local) factor and a geometric (global) factor are two essential elements for the 2D bonded DEM to reproduce a full range of Poisson's ratios. It is also found that the 2D bonded DEM might be unable to reproduce the correct displacements for elastic boundary value problems when the represented Poisson's ratio is close to 0.5 or the long‐range interaction is considered. In addition, an analytical relationship between the shear stiffness ratio and the Poisson's ratio, derived from a hyper elasticity analysis and applicable to discontinuum‐based models, provides good agreement with outputs from the 2D bonded DEM and DLSM. Finally, it is shown that the selection of elastic parameters used the 2D bonded DEM has a significant effect on fracturing and fragment patterns of solids.

Various Occurrence Mechanisms of Large Acceleration over 20 m/s2 and Its Suitability in Design Use

Three amplification mechanisms of large accelerations over 20m/s2 are related to various non-liner behaviors and explained by using the non-stationary Fourier spectra. The frequencies of dominant components are compared with the natural frequencies with the ratios (1:3:5:7) of a shear-spring model of the underground soil. Thus, one of the amplification mechanisms is supposed to result from the natural modes in the underground soil. Furthermore the similarity of pulse waves between MYG012 (EW) and AKTH04 (EW) is pointed out in the non-stationary Fourier spectra and the double-integrated displacement profiles. The pulse waves are identified by the Ricker wavelet. This amplification mechanism is supposed to be caused by the collision between the observation house and the side soil. The modulation of dominant component is also detected in the high frequency range. The shear strain of AKTH04 is calculated using the relative displacement profiles between the surface and the borehole. The peak shear strain is fitted to the G-γ relation and the deterioration ratio of shear stiffness is evaluated. The third amplification mechanism is related to the change of depth of isolated surface soil. The depth of the isolated surface soil is evaluated from the deterioration area shallower than 20m. It is pointed out finally that the seismic records at the ground surface are unsuitable for the database of seismic design wave.

Assessment of shear stiffness ratio of cohesionless soils using neural modeling

Properly estimating strain-dependent shear stiffness of soils is necessary for accurate analysis of soil-structure interaction and seismic ground response problems during earthquake motions. In this research, an artificial neural network (ANN) model was developed for shear stiffness ratio of cohesionless soils. The input variables in this model are shear strain amplitude (γ), effective confining pressure (σ′ 0 ), mean grain size (D 50 ), and relative density (D r ) and output is shear stiffness ratio (G/G max ). A large experimental database was compiled from available published laboratory cyclic tests. Validation of model was carried out with using centrifuge tests results. Subsequently, sensitivity analysis and model accuracy was conducted. Finally, proposed model has been compared with other researcher’s relationships. The results clearly demonstrate the good performance and capability of the proposed ANN-based model.

Analysis of Ground Motion Amplification during Soil Liquefaction via Nonstationary Fourier Spectra

ABSTRACTIn this study, the transient properties of dominant frequencies and their components during soil liquefaction were evaluated by the nonstationary Fourier spectra of the records at Kawagishi-cho during the Niigata-ken Chuetsu-oki earthquake in 1964, at Port Island during the Hyogoken-Nanbu earthquake in 1995, and at K-NET CHB024 during the 2011 off the Pacific Coast of Tohoku earthquake. The deterioration ratio of soil shear stiffness was calculated from the ratio of dominant frequencies at the beginning and the ending of the liquefaction process. The displacement profile was calculated through numerical integration of the acceleration record, and the shear strain was calculated from the relative underground displacement of Port Island from 0 to 83 m from ground level (GL-0m to GL-83m) to GL-83m. The deterioration ratio of shear stiffness was also evaluated by fitting the maximum shear strain to the G-γ relation, and the deterioration ratio was evaluated by the nonstationary spectrum was confirmed ...

Underground Excavation Behaviour of the Queenston Formation: Tunnel Back Analysis for Application to Shaft Damage Dimension Prediction

The Niagara Tunnel Project (NTP) is a 10.1 km long water-diversion tunnel in Niagara Falls, Ontario, which was excavated by a 7.2 m radius tunnel boring machine. Approximately half the tunnel length was excavated through the Queenston Formation, which locally is a shale to mudstone. Typical overbreak depths ranged between 2 and 4 m with a maximum of 6 m observed. Three modelling approaches were used to back analyse the brittle failure process at the NTP: damage initiation and spalling limit, laminated anisotropy modelling, and ubiquitous joint approaches. Analyses were conducted for three tunnel chainages: 3 + 000, 3 + 250, and 3 + 500 m because the overbreak depth increased from 2 to 4 m. All approaches produced similar geometries to those measured. The laminated anisotropy modelling approach was able to produced chord closures closest to those measured, using a joint normal to shear stiffness ratio between 1 and 2. This understanding was applied to a shaft excavation model in the Queenston Formation at the proposed Deep Geological Repository (DGR) site for low and intermediate level nuclear waste storage in Canada. The maximum damage depth was 1.9 m; with an average of 1.0 m. Important differences are discussed between the tunnel and shaft orientation with respect to bedding. The models show that the observed normalized depth of failure at the NTP would over-predict the depth of damage expected in the Queenston Formation at the DGR.

Thermal Post-Buckling of Heated Cross-Ply Laminated Composite Beams

Abstract: On the basis of Reddy’s higher order shear deformation plate theory and the von Kármán’s geometry nonlinear theory, governing equations for nonlinear thermal buckling and post-buckling of cross-ply laminated composite beam subjected to a temperature rise are derived, in which the stretching-bending coupling terms produced by the non-homogenous distribution of the material properties are included. By using the shooting method to solve the corresponding nonlinear boundary value problem, numerical solutions for thermal post-buckling of cross-ply shear deformation laminated composite beam with its both ends immovably simply supported under uniform temperature rise are obtained. As an example, equilibrium paths and configurations for laminated composite beam paved in term of 0/90/0 are presented and characteristic curves of the nonlinear deformation changing with the thermal load were plotted. The effects of the geometric and physical parameters on the deformation of the beam are also examined. The theoretical analysis and numerical results show that different thermal expansion coefficient ratio, elastic moduli ratio, shear stiffness ratio will influence of the non-dimension critical buckling temperature.

Geometrically Nonlinear Analysis of Cross-Ply Laminated Composite Beams Subjected to Uniform Temperature Rise

Abstract: On the basis of Reddy’s higher order shear deformation plate theory and the von Kármán’s geometry nonlinear theory, governing equations for nonlinear thermal buckling and post-buckling of cross-ply laminated composite beam subjected to a temperature rise are derived, in which the stretching-bending coupling terms produced by the non-homogenous distribution of the material properties are included. By using the shooting method to solve the corresponding nonlinear boundary value problem, numerical solutions for thermal post-buckling of cross-ply shear deformation laminated composite beam with its both ends immovably simply supported under uniform temperature rise are obtained. As an example, equilibrium paths and configurations for laminated composite beam paved in term of 0/90/0 are presented and characteristic curves of the nonlinear deformation changing with the thermal load were plotted. The effects of the geometric and physical parameters on the deformation of the beam are also examined. The theoretical analysis and numerical results show that different thermal expansion coefficient ratio, elastic moduli ratio, shear stiffness ratio will influence of the non-dimension critical buckling temperature.

Buckling behavior of blade-, angle-, T-, and hat-stiffened FRP panels subjected to in-plane shear

This article presents parametric studies on simply supported laminated composite stiffened panels subjected to in-plane shear loading. A number of models were analyzed using ANSYS and a database is prepared for blade-, angle-, T-, and hat-stiffened laminated composite panels. Studies are carried out by changing the type of stiffeners, the panel orthotropy ratio, smeared extensional stiffness ratio of stiffener to that of the plate, and extensional stiffness to shear stiffness ratio of the plate. The difference in buckling behavior of different types of stiffened panels is presented. Based on key parameters influencing the buckling behavior, guidelines for better stiffener proportioning are developed, which will be helpful to the designers.

Determination of the anisotropic shear stiffness of an unsaturated decomposed soil

The shear modulus at very small strains (0·001% or less), G0, is one of the most important parameters for predicting ground movements and dynamic responses of many engineering earth structures. With advances in the use of bender elements for soil testing, anisotropic shear moduli G0(ij)can now be evaluated by measuring the velocities of shear waves propagating in a soil specimen in different planes and polarisations. This leads to the determination of the stiffness anisotropy at very small strains. While almost all previous studies of anisotropic soil stiffness have been conducted with saturated soils, experimental results from unsaturated soils have rarely been reported in the literature. A new computer-controlled triaxial apparatus equipped with three pairs of bender elements was developed to measure shear wave velocities and hence to investigate the degree of stiffness anisotropy of recompacted completely decomposed tuff (CDT) under both saturated and unsaturated conditions. The axis-translation technique was applied to control matric suction. New state-dependent equations describing aniso-tropic moduli of unsaturated soil were derived and verified by experimental results. Based on the derived equations and measurements, it was possible to identify that there was an inherent shear stiffness anisotropy of about 1·03–1·04, due to sample preparation by moist tamping, for isotropic net mean stress varying from 110 to 400 kPa. When suction was increased from 0 kPa to the air-entry value of 50 kPa, suction-induced anisotropy in terms of the shear stiffness ratio, G0(hh)/G0(hv), ranged from about 1·06 to 1·09 for isotropic net mean stress varying from 110 to 500 kPa. No further significant increase in suction-induced stiffness anisotropy was observed at suctions higher than the air-entry value.

Effect of beam stiffness–column reinforcement on creep and shrinkage behaviour of R.C frames

AbstractVertical deflections and load transfer among columns of R.C frames depend on the percentage of reinforcement in columns and stiffness of beams. No systematic studies are available in the literature on the effect of these parameters. Such systematic studies are reported in this paper. The beam stiffness is expressed in terms of a non‐dimensional parameter, designated as stiffness factor, which is the ratio of shear stiffness of beams to axial stiffness of columns. It is shown that depending on stiffness factor and column reinforcement, a column may receive the load from the adjacent columns or transfer the load to the adjacent columns, or may receive the load from one of the adjacent columns and at the same time transfer the load to the other adjacent column. Further, the effect of the creep and shrinkage on column axial forces can be of design significance in the lower and middle portions of buildings. The effect becomes greater with the increase in stiffness factor and difference in percentage reinforcement of the adjacent columns. Copyright © 2007 John Wiley & Sons, Ltd.

Buckling of laminated composite stiffened panels subjected to in-plane shear: A parametric study

The presence of in-plane loading may cause buckling of stiffened panels. An accurate knowledge of critical buckling load and mode shapes are essential for reliable and lightweight structural design. This paper presents some parametric studies on simply supported laminated composite blade-stiffened panels subjected to in-plane shear loading. A total of 450 models were analyzed using ANSYS 7.1 and a database is prepared for different plate and stiffener combinations. Studies are carried out by changing the panel orthotropy ratio, stiffener depth, pitch length (number of stiffeners), smeared extensional stiffness ratio of stiffener to that of the plate and extensional stiffness to shear stiffness ratio of the plate. Based on the studies, few important parameters influencing the buckling behaviour are identified and guidelines for better stiffener proportioning are developed, which will be helpful for the designer.

Crack face sliding effect on stiffness of laminates with ply cracks

The rate of stiffness reduction in damaged laminates with increasing transverse crack density in plies depends on two micromechanical parameters: normalized crack face opening displacement (COD) and crack face sliding displacement (CSD). A FE-based parametric study shows that the only properties that affect the CSD are the thickness ratio and the in-plane shear stiffness ratio of the damaged and neighboring undamaged layers. The dependence is described by a power function with respect to the above mentioned properties. This relationship and the previously obtained power law for COD [Lundmark P, Varna J. Constitutive relationships for damaged laminate in in-plane loading. Int J Dam Mech 2005:14(3):235–59] are used in the damaged laminate constitutive relationships [Lundmark P, Varna J. Constitutive relationships for damaged laminate in in-plane loading. Int J Dam Mech 2005:14(3):235–59], which are closed form exact expressions for general symmetric laminates in in-plane loading.The model is validated analyzing reduction in shear modulus of [Sn,90m]s laminates and comparing with direct FE-calculations. The results are excellent in case of cracks in one layer only. For laminates with two orthogonal systems of cracks, the power law underestimates the CSD. To account for interaction between both systems of cracks, which is of importance for crack face sliding, the power law is modified using the effective shear modulus of the cracked neighboring layer.