Effective Shear Stiffness Research Articles

Generic and simplified approaches for the structural analysis of precast concrete sandwich panels

This paper presents a comparison between three numerical models developed for the structural analysis of composite precast concrete sandwich panels under lateral loading. The first model is based on a full finite element analysis where “slip” between the layers is obtained from the elastic deformability of the various components. The second model is based on a simplified finite element analysis where the effect of the shear connectors is smeared and modeled through an effective shear stiffness of the insulation layer. The third approach provides closed-form expressions for evaluating the deflection and is based on the classical sandwich beam theory where the shear connectors are considered through the effective stiffness of the insulation, similar to the second model. The structural response obtained from the three models was compared for various panel configurations and good correlation was obtained. A reasonable agreement with test results from the literature was also demonstrated. Therefore, both the simplified finite element model and the classical sandwich beam theory (closed-form solution) are recommended for the elastic structural analysis and for estimating the degree of composite action at the serviceability limit state of precast concrete sandwich panels.

Thickness-dependent selection of adhesive joints

ABSTRACT The fracture resistance of adhesive joints depends on the bondline thickness, especially in the toughest systems. While increasing the adhesive thickness to operate at peak fracture toughness is anticipated to be attractive, it leads to a mass increase and to a decrease of the effective shear stiffness and strength, calling for a trade-off. Here, we follow a rational materials selection approach for mechanical design to address different sets of objectives and constraints representative of different classes of applications. The approach is applied to select the best conventional adhesive based on a novel database. Mechanical analysis with two different degrees of complexity is considered. The elementary level only accounts for the influence of thickness on toughness, while more advanced models introduce the dependence of shear strength on thickness as well as the stiffness mismatch with the adherends. The best adhesive choice strongly depends on the objectives, constraints, and loading configuration. However, the ranking is not drastically affected by the adherends’ stiffness. Gaps found for stiff/strong and tough adhesives motivate the development of architected joints. Inserting stop holes improves damage tolerance and density but reduces the shear strength and stiffness, requiring an optimum design.

Experimental and theoretical study on seismic behavior of non-seismically designed shear walls with moderate shear span-to-length ratios

This study aims to examine the seismic performance of non-seismically designed shear wall with moderate shear span-to-length ratios (SLR) under relatively high axial loads. Four wall specimens with varying parameters, such as shear-to-flexure strength ratio, SLR, and axial load ratio (ALR) are fabricated and tested under cyclic loads. The experimental results, encompassing crack patterns, failure modes, hysteretic behavior, stiffness degradation, energy dissipation, and reinforcing bars strains, are presented and discussed. Digital Image Correlation (DIC) technology is employed for a comprehensive analysis of the crack patterns and deformation components of the tested specimens. The effective stiffness, including both effective flexural and shear stiffness is obtained through a deformation components analysis. These values are compared to the recommended values provided in FEMA 356 and ASCE 41–17. Moreover, the generalized force-deformation relationships in ASCE 41–17 are evaluated using the experimental results. Subsequently, a novel theoretical model for determining the force-deformation relationship of shear walls, incorporating stiffness degradation and flexural-shear interaction, is proposed and validated with test results. The results demonstrate that the proposed model effectively predicts the relationship between force and displacement.

Numerical simulation on the influence of delamination on the critical buckling load of CLT panels

This work aims to evaluate the critical buckling load of panels made of cross-laminated timber, considering finite element simulations and different analytical methods of calculating the effective bending and shear stiffness. In addition, the effect of openings, pre-cracks, and adhesive strength on the critical buckling load is analyzed. Results indicate that the approach with thin external faces is both simpler and more effective. When estimating the bending and shear stiffness, the methods that show the least difference are the γ-method and the shear analogy method, with the first of them being more conservative. The corrected Timoshenko method tends to overestimate the critical load. Moreover, using cohesive zone models embedded in finite element simulations, the critical load is reduced by an average of 10% due to the stiffness of the adhesive. Furthermore, when panels have adhesive-free edges, the critical load can be reduced by more than 50%.

Relationships between stiffness of material, lamellas and CLT elements with respect to out of plane bending and rolling shear

The use of cross laminated timber (CLT) for construction has increased greatly in recent years and the large volumes of wood used for CLT means that it is important to optimize the use of the material. This requires relevant grading of lamellas and knowledge of relationships between lamella and CLT properties. In the present study, the relationship between dynamic axial modulus of elasticity (MoE) of lamellas and the quasi-static out of plane bending stiffness of CLT is investigated. By means of four-point bending test, it is shown that the effective quasi-static MoE of lamellas in CLT is only 2–6% lower than the average axial dynamic MoE of the individual lamellas. With this knowledge, producers of CLT can easily predict and control the important out of plane bending stiffness of the produced CLT. Moreover, it is shown that effective rolling shear stiffness of layers in CLT can be accurately determined by means of digital image correlation performed in connection to four-point bending of CLT, even for long test spans. For layers of lamellas of Scots pine of size 40 × 190 mm2 the average apparent or effective rolling shear modulus was determined to be 159 MPa. The average rolling shear modulus of the same material was determined to be 56 MPa.

Stiffness tailoring in sinusoidal lattice structures through passive topology morphing using contact connections

Structures with adaptive stiffness characteristics present an opportunity to meet competing design requirements, thus achieving greater efficiency by the reconfiguration of their topology. Here, the potential of using changes in the topology of planar lattice structures is explored to achieve this desired adaptivity and observe that lattice structures with rectangle-like unit-cells may undergo elastic buckling or bending of cell walls when subject to longitudinal compression. Under sufficient load intensity, cell walls can deform and contact neighbouring cells. This self-contact is harnessed to change the topology of the structure to that of a kagome-like lattice, thereby establishing new load paths, thus enabling enhancement, in a tailored manner, of the effective compressive and shear stiffness of the lattice. Whilst this phenomenon is independent of characteristic length scale, we focus on macroscopic behaviour (lattices of scale ≈ 200 mm). Experimentally observed responses of 3D-printed lattices correlate excellently with finite element analysis and analytical stiffness predictions for pre- and post-contact topologies. The role of key geometric and stiffness parameters in critical regions of the design space is explored through a parametric study. The non-linear responses demonstrated by this topology morphing lattice structure may offer designers a new route to tailor elastic characteristics.

Nonlinear frequency behavior of cracked functionally graded porous beams resting on elastic foundation using Reddy shear deformation theory

This paper presents the nonlinear frequency behavior of cracked functionally graded porous beams subjected to various boundary conditions using Reddy shear deformation theory and Green’s tensor together with the Von Karman geometric nonlinearity. The material properties of the beam vary exponentially in thickness direction. A generalized differential quadrature method (GDQM) in conjunction with a direct numerical iteration method is developed to solve the system of equations derived by means of Hamilton’s principle. Demonstrating the convergence of this method, the verification is performed by using extracted results from a previous study based on the Euler and Timoshenko beam theory. The results for extensive studies are provided to understand the influences of the different gradient indexes, vibration amplitude ratios, porosity indexes, shear and elastic foundation parameters, and boundary conditions on the nonlinear frequency behavior. The location of crack plays the significant role on the nonlinear frequency ratios. The frequency ratios hit the minimum when the crack is located in mid-span of the beam. In this regard, the effect of shear stiffness of foundation is much more than that of Winkler one in the increasing mid-span value of nonlinear frequency ratio. It is also shown that the crack location results in decline of frequency ratios in the mid-span of beam specially for the cracks located closer to surface, the deeper ones lead to get nonlinear frequency ratios rise much more due to the fact that the deeper the crack is, the weaker the crack section becomes. The results of this paper and the effects of these parameters can be used in the optimal design of functionally graded beams and in crack prediction, detection, and monitoring techniques.

Bending performance of a sandwich beam with sheet metal pyramidal core

Metallic sandwich structures with pyramidal cellular cores have proven to be highly effective in the industry of advanced lightweight materials thanks to their high strength-to-weight ratios. This paper presents the investigation of the bending performance of a sandwich structure based on a novel pyramidal cellular core. The effective bending and shear stiffness are investigated using numerical and experimental approaches. Furthermore, the finite element model created for the four-point bending scenario is in good agreement with the experimental one and can be subsequently used for further product development. This represents a cost-efficient method used for structural optimisation and may lead to improved mechanical properties and higher lightweight capabilities. The study includes a comparison to other existing periodic core topologies which shows that the investigated pyramidal structure has high potential to be used for the construction of sandwich panel assemblies.

On the Effect of Shear Stiffness and Compressibility on the Stability of Heavy Stratified Geomasses

On the Effect of Shear Stiffness and Compressibility on the Stability of Heavy Stratified Geomasses

On stability and instability of stratified elastic solids in a gravity field

Stability and instability of the equilibrium of stratified elastic solids in a uniform gravity field are studied by means of analysis of the second variation of total (elastic and gravitational) potential energy of the solid. By stratification is meant a continuous dependence of density and incremental elastic moduli of the material on vertical coordinate. The unperturbed stress state is supposed to be hydrostatic, whereas the incremental shear stiffnesses for perturbing deformations are nonzero. Obtained analytically both the necessary condition and the sufficient condition for stability demonstrate stabilizing effect of shear stiffness. For shear stiffnesses approaching zero, each of the conditions converts into obtained earlier by the authors the necessary and sufficient stability condition for stratified compressible fluids (having zero shear stiffness).The sufficient condition for stability for given stratifications of density and bulk modulus, and arbitrary dimensions of the domain, occupied by the solid, yields semi-infinite range of values of shear stiffnesses ensuring stability of the solid for conditions under which the corresponding stratified compressible fluid would be unstable.The sufficient condition for instability (negation of the necessary condition for stability) yields such a nonzero value of shear stiffness, that for shear stiffnesses below it the solid is surely unstable. This value (the lower bound for the exact critical value) depends on horizontal dimensions of the domain occupied by the solid, and on thickness of the layer where the stability condition for corresponding stratified fluid would be violated.Possible applications of obtained theoretical results are discussed.

Simplified shear force-chord rotation relationship for concrete-filled steel plate composite coupling beams

Concrete-filled steel plate (CFSP) composite coupling beam is a new type of coupling beam with large deformation and energy dissipation capacity. Given the need for shear force-chord rotation envelope curve of the coupling beam in the general modeling and analysis of coupled CFSP composite shear wall structures, this paper presents an envelope curve for CFSP composite coupling beams based on the results of nonlinear finite element analysis. A comparison between the results of finite element analysis (FEA) and the existing experimental data demonstrates the ability of the numerical model to accurately predict the shear force-chord rotation hysteresis curve and the local response of CFSP composite coupling beams. To gather sufficient data for plotting the envelope curve, multiple numerical models with different values assigned to the span/depth ratio, web plate thickness, flange plate thickness, and compressive strength of the concrete are analyzed under cyclic lateral loading. The analysis results are used to derive some equations for calculating the effective flexural and shear stiffness of the coupling beam based on the stiffness of steel plates and concrete infill, with a reduction coefficient applied to the stiffness contribution of the concrete. Some suggestions are provided for calculating the maximum and yield strengths of the coupling beam, based on the minimum strength corresponding to shear failure and flexural capacity. Finally, the analysis results are used to provide a trilinear model for the shear force-chord rotation hysteresis envelope of CFSP composite coupling beams.

Experimental and numerical analysis of 3D printed suture joints under shearing load

The shear resistance of bio-inspired suture joints with different waviness is explored through an integrated experimental and numerical approach. Polymeric single lap shear specimens with different waviness are designed and fabricated via multi-material additive manufacturing. Quasi-static mechanical experiments are performed to quantify the effective shear stiffness and strength of the joints. SEM images show that the 3D printed suture joints fail under combined adhesive and cohesive failure mechanisms. To evaluate the effects of printing direction on the mechanical behaviors of suture joints, both tensile and single lap shear specimens are designed and printed in two orthogonal directions: parallel to the interface (H direction) and perpendicular to the interface (V direction). An inverse method was used to obtained the effective material properties of the interfacial layer printed in both directions. Nonlinear Finite Element models with cohesive interaction and mixed mode damage initiation and evolution are developed.

Structural performance of hybrid Poplar-Beech cross-laminated-timber (CLT)

The purpose of this research was to investigate the structural out-of-plane bending performance of three-layer hybrid cross-laminated-timber manufactured from outer layers of fast-growing Poplar (Populus alba) and a cross-layer of Iranian Beech species (Fagus orientalism) using polyurethane as a binder. The bending performance of the hybrid CLT was determined in both major and minor axis orientations in diverse span-to-thickness ratios by experimental and theoretical methods. It was compared to that of Poplar CLT reported in our previous research. The experimental and theoretical methods indicated that the bending performances comprising maximum shear force (Vmax), maximum bending moment (Mmax), apparent modulus of elasticity (MOEapp), modulus of rupture (MOR), shear strength (τmax), effective bending stiffness (EIeff), and effective shear stiffness (GAeff) of hybrid Poplar-Beech CLT in all span-to-thickness ratios at both major and orientations were greater than those of Poplar CLT. Moreover, in both orientations, the results of bending and shear stress distributions of the specimens showed that the hybrid Poplar-Beech CLT had greater load-carrying capacity than Poplar CLT. However, in both orientations, the failure modes of hybrid CLT were similar to those of Poplar CLT. The experimental dominant failure modes in the major axis orientation of CLTs were rolling shear and delamination, while tensile failure and crack were mainly observed in the minor axis orientation. In summary, in comparison with Poplar CLT, both experimental and theoretical results revealed that hybrid Poplar-Beech CLT had more tremendous potential for structural bending performance in the construction and building sector.

Comparison of Test Methodologies for Computing Bending and Shear Stiffness of Cross-Laminated Timber

Abstract Current testing methods for evaluating the out-of-plane bending and shear stiffness terms of cross-laminated timber (CLT) materials use a relatively long span panel. When new CLT layups and composites are proposed, especially when manufactured from pilot-scale facilities, the length requirement may be a barrier for material property evaluation. The purpose of this paper was to compare current bending and shear stiffness test methods of CLT with alternative forms, including a simultaneous calculation method and the five-point bending test, which uses a shorter beam than current testing methods. Both experimental evaluation and finite element modeling of the mechanical properties were used to compare the proposed test methods. In general, numerical and experimental results demonstrated that effective bending stiffness (EIeff) values of CLT panels evaluated by different test methods were similar (maximum 12.7 % difference). Effective bending and shear stiffness values from the finite element method (FEM) agreed with experimental results. FEM demonstrated that both the simultaneous solution and the five-point bending test can be used as alternative test methods for evaluation of the bending and shear stiffness for CLTs. However, the effective shear stiffness values of CLTs from current industry standards were at least 450 % less than both the experimental evaluation and FEM prediction.

Three-dimensional model for nonlinear analysis of slender flanged reinforced concrete walls

A new, three-dimensional, four-node, macroscopic model element for nonlinear analysis of reinforced concrete walls is developed and implemented in the structural analysis software OpenSees. The two-dimensional, beam-column formulation of the Multiple-Vertical-Line-Element Model (MVLEM) is extended by implementing the geometrical transformation of the element degrees of freedom that convert the model element from a two-node to a four-node element, and by incorporating linear-elastic element out-of-plane behavior. The three-dimensional analytical model developed, namely the MVLEM-3D, is validated based on load-deformation responses and vertical strains obtained from tests on one T-shaped wall specimen tested under uniaxial cyclic loading and four U-shaped wall specimens tested under complex multidirectional loading protocols. In addition, results of sensitivity studies on model geometric discretization and selection of an effective shear stiffness are presented. The model exhibits a high level of numerical stability and computational efficiency for all specimens investigated. Comparisons of experimental and analytical results demonstrate that the proposed MVLEM-3D captures, with good accuracy, the cyclic load-displacement behavior of non-planar walls in loading directions that are parallel to the principal axes of the cross-section. However, the analysis results overestimate the wall lateral strength in diagonal (relative to the principal axes) loading directions by 20–50%. This discrepancy is associated with the inability of the plane-sections hypothesis implemented in the model to capture the experimentally-observed nonlinear strain distributions developing along the wall cross-section due to shear lag effect. Despite this issue, the proposed model is shown to be a powerful tool for practical applications, as nonlinear response history analysis is becoming more common in engineering practice.

Depth-Dependent Seabed Properties: Geoacoustic Assessment

Offshore geoengineering requires reliable sediment parameters for analysis and design. This study proposes a robust framework for effective stress-dependent geotechnical and geoacoustic properties for seabed analysis based on geophysical models, new experimental data, and extensive data sets compiled from published studies that cover a wide range of marine sediments and depths. First, effective stress-dependent porosity versus depth profiles are computed using compaction models that are valid for a wide stress range. Then, P- and S-wave velocity data are analyzed in the context of effective stress-controlled density, shear stiffness, and bulk modulus within a Hertzian-Biot-Gassmann framework. Finally, this study selects six distinct “reference sediments” that range from clean sands to high-plasticity clays and assigns self-consistent compaction and shear stiffness properties using well-known correlations reported in the literature in terms of specific surface, plasticity, and grain characteristics. Results show that robust physical models for compaction and stiffness adequately predict depth-dependent geotechnical and geoacoustic properties according to sediment type. The asymptotic void ratio at low effective stress eL determines the sediment density ρo at the sediment–water boundary. New experimental studies show that the characteristic asymptotic sediment density ρo at very low effective stress σz′→0 controls the high-frequency acoustic reflection used for bathymetric imaging. The proposed analysis of geoacoustic data can be used to obtain first-order estimates of seafloor sediment properties and to produce sediment-type seafloor maps.

Shear stiffness of headed studs on structural behaviors of steel-concrete composite girders

Steel-concrete composite structures have been extensively used in building, bridges, and other civil engineering infrastructure. Shear stud connectors between steel and concrete are essential in composite members to guarantee the effectiveness of their behavior in terms of strength and deformability. This study focuses on investigating the shear stiffness of headed studs embedded in several types of concrete with wide range of compressive strength, and their effects on the elastic behavior of steel-concrete composite girders were evaluated. Firstly, totally 206 monotonic push-out tests from the literature were reviewed to investigate the shear stiffness of headed studs embedded in various types of concrete (NC, HPC, UHPC etc.). Shear stiffness of studs is defined as the secant stiffness of the load-slip curve at 0.5Vu, and a formulation for predicting defined shear stiffness in elastic state was proposed, indicating that the stud diameter and the elastic modulus of steel and concrete are the main factors. And the shear stiffness predicted by the new formula agree well with test results for studs with a diameter ranging from 10 to 30 mm in the concrete with compressive strength ranging from 22.0 to 200.0MPa. Then, the effects of shear stiffness on the elastic behaviors of composite girders with different sizes and under different loading conditions were analyzed, the equations for calculating the stress and deformation of simply supported composite girders considering the influence of connection

Bending and shear properties of cross-laminated timber panels made of poplar (Populus alba)

With the expansion of cross-laminated timber (CLT) material throughout the global construction community, an effort is being made to explore the use of regionally produced CLT materials from Iran, including the testing of fast-grown, hand-planted poplar (Populus alba). This paper investigated the out-of-plane bending properties of CLT panels manufactured using poplar at various span-to-depth ratios (SDR). Mechanical properties of poplar CLTs investigated included the modulus of rupture, apparent modulus of elasticity, effective bending stiffness, effective shear stiffness, and maximum shear stress in both the major and minor directions. Experimental test results were compared with both the shear analogy model and finite element method (FEM) results to examine the use of predictive modeling. Bending properties were predicted using the shear analogy method and FEM compared well with experimental results, with the FEM able to predict the distribution of bending and shear stress across the beam thickness. Modulus of rupture and apparent modulus of elasticity increased with increasing SDR in both the major and minor strength directions. In the major strength direction, the effective modulus of elasticity and maximum shear strength values predicted by the shear analogy method were in good agreement with experimental results. As noted in previous studies, the effective shear stiffness predicted by the shear analogy method in the major strength direction was 510% less than that of experimental results.

Effective bending and shear stiffness of cross-laminated timber by modal testing: Method development and application

Cross-laminated timber (CLT) is gaining popularity worldwide with the development of tall wood buildings. A non-destructive testing (NDT) technique employing modal testing for the measurement of natural frequencies and a genetic algorithm for minimizing the difference between calculated and measured natural frequencies has been proposed for the inverse determination of in-plane and out-of-plane elastic constants of orthotropic Mindlin plates. Based on the exact solution of free transverse vibration of orthotropic Mindlin plates under a pair of opposite edges simply supported and the other pair free (SFSF), the effective bending and shear stiffness of two three-layer and one five-layer symmetric CLT panels were inversely determined. Moreover, the results showed that the inclusion of five sensitive vibration modes was more efficient than having more modes for the inverse determination. This study demonstrated the efficiency and potential of the non-destructive method in measuring the effective bending and shear stiffness of mass timber panels.

A simple closed-form solution for kinematic responses of retaining wall incorporating the effects of shear stiffness of soils

The seismic behavior of retaining wall is governed by the kinematic soil-retaining wall interaction, which has been described by various methods such as elastic continuum model and Scott model. Due to their over-complexity in the expression or low accuracy, practical applications of such methods are limited. Thus, inherited the simplicity of the Scott model, a concise analytical solution, involving the effect of the shear stiffness of soils, based on the Pasternak model is presented in this technical note to evaluate the kinematic soil-retaining wall interaction. In addition, both the soil spring factor k and shear stiffness factor γ in the proposed model have been demarcated. As compared with the existing literature, a good prediction is achieved in the present model. Besides, the physical mechanisms underlying kinematic soil-wall interaction are detailed elaborated by carrying out a group of parametric studies regarding the effects of kinematic soil-retaining wall interaction. The results emphasize that the soil shear stiffness significantly influence the kinematic behaviors of retaining wall so that it is a critical element in the seismic design of retaining wall.