Effective Shear Stiffness Research Articles

Salvaged lumber for structural mass timber panels: manufacturing and testing

Portland, OR, was the first US city to implement a deconstruction ordinance in 2016. Although salvaged lumber can have a high demand, the market for small-sized lumber from deconstructed dwellings is near saturation. New applications for this material are required for market development, industry diversification, and increasing deconstruction practices. Mass timber products such as cross-laminated timber (CLT) could be a new market for this material, but presently there is minimal information qualifying the performance of mass timber panels made with salvaged lumber. Three, full-sized 3-ply experimental layups, with varying amounts of salvaged/recycled wood content, were manufactured and tested to characterize panel properties. Manufacturing processes and testing methods followed ANSI/APA PRG 320-2018; Standard for Performance Rated Cross-Laminated Timber. Each panel layup had three replicates for nine panels in total. Panels measured 1.1 m by 2.3 m by 3 plys, and test results were used to calculate the effective flatwise bending moment resistance ((FbS)eff), effective flatwise bending stiffness ((EI)eff) effective shear stiffness in flatwise bending ((GA)eff), flatwise shear resistance (Vs), percent wood failure (WF%), and percent delamination (Delamination %). Results were compared with E3 grade 3-ply CLT panels made in the United States and indicated that salvaged lumber could be used as feedstock for mass timber panels in core layers or all layers. All panel layups passed benchmarks for (FbS)eff and (EI)eff benchmarks with values greater than PRG320. Panels having salvaged lumber in core layer also met Vs benchmarks. Furthermore, all panels passed examination for WF% but struggled to meet delamination requirements. Possibilities exist for better performance if panels were made in a commercial setting. This research shows salvaged lumber has promise for manufacturing structural CLT, but more research and a larger samples size is needed to verify findings.

Fragility-based analysis of the influence of effective stiffness of reinforced concrete members in shear wall buildings

When modeling RC shear wall buildings for seismic analysis there is little consensus in the literature on the appropriate value of the wall effective shear stiffness (GAeff) and the slab effective bending stiffness (EIeff). A probabilistic analysis based on fragility curves is a robust technique to assess the influence of these parameters on the expected seismic performance, but such studies are scarce because they require computationally expensive analysis such as Incremental Dynamic Analysis (IDA). In this paper, fragility curves are developed following the recently introduced SPO2FRAG procedure, a simplified methodology that does not require IDA but the computationally more affordable incremental static (pushover) analysis. The fragility curves provided by SPO2FRAG are used to evaluate the influence of the values of GAeff and EIeff on the analytical seismic response of full 3D nonlinear models of two actual (and representative) residential wall buildings of 17 and 26 stories located in Santiago (Chile). The accuracy of SPO2FRAG is also evaluated through comparisons with empirical fragilities.

On stability of stratified elastic geosystems in a gravity field

Stability of stratified elastic geosystems in a gravity field is studied analytically with regard for the shear stiffness of geomaterial. A sufficient condition for stability of a geomass clamped at the lateral boundaries, is obtained: for any ratios of dimensions of the geomass it is sufficient for stability that the rate of density increase with depth (in the loaded equilibrium state) exceed a certain positive value which depends on shear stiffness so that the greater the stiffness, the less the value, and vice versa (the stabilizing effect of shear stiffness). At zero shear stiffness the value mentioned is maximal and characterizes the necessary and sufficient condition for stability of a bulk-elastic geomass. Geophysical consequences of obtained stability condition are analyzed.

Effective Rheology Across the Fragmentation Transition for Sea Ice and Ice Shelves

AbstractSea ice and ice shelves can be described by a viscoelastic rheology that is approximately linear elastic and brittle at high strain rates and viscously shear thinning at low strain rates. Brittle ice easily fractures under compressive shear and forms shear bands as the material undergoes a transition to a fragmented, granular state. This transition plays a central role in the mechanical behavior at large scales of sea ice in the Arctic Ocean or Antarctic ice shelves. Here we demonstrate that the fragmentation transition is characterized by an essentially discontinuous drop of three to five orders of magnitude in effective viscosity and stress relaxation time. Beyond the fragmentation transition, grinding in shear zones further reduces both effective viscosity and shear stiffness, but with an essentially constant relaxation time of ∼10 s. These results are relevant for ice rheology implementation in large‐scale climate‐related models of sea ice and thin ice shelves.

On Stability of Stratified Elastic Geosystems in a Gravity Field

Stability of stratified elastic geosystems in a gravity field is studied analytically with regard for the shear stiffness of geomaterial. A sufficient condition for stability of a geomass clamped at the lateral boundaries, is obtained: for any ratios of dimensions of the geomass it is sufficient for stability that the rate of density increase with depth (in the loaded equilibrium state) exceed a certain positive value which depends on shear stiffness so that the greater the stiffness, the less the value, and vice versa (the stabilizing effect of shear stiffness). At zero shear stiffness the value mentioned is maximal and characterizes the necessary and sufficient condition for stability of a bulk-elastic geomass. Geophysical consequences of obtained stability condition are analyzed.

Steel modules of composite plate shear walls: Behavior, stability, and design

Abstract Concrete-filled composite plate shear walls (CPSW) consist of a concrete (infill) wall sandwiched between two steel plates that are connected to each other using ties and anchored to the concrete infill using these embedded ties or shear connectors. Steel modules consisting of plates, ties and shear connectors are prefabricated in the shop, transported to the field, and assembled first. The erected modules serve as falsework for construction activities and stay-in-place formwork for concrete casting. This is a primary advantage and appeal of this system. However, there is a lack of knowledge regarding the structural behavior of empty steel modules (before and during concrete casting). This paper presents the results of analytical, numerical, and experimental investigations conducted to evaluate: (i) the structural behavior of empty steel modules under their own self-weight, (ii) the stability and axial load capacity of steel modules for construction loads and activities, and (iii) the effects of concrete casting (hydrostatic pressure) in terms of the deflections and stresses induced in the steel plates. The results indicate that the effective shear stiffness of the empty modules governs their structural behavior as well as their stability. The effective shear stiffness can be estimated using the finite element method (verified using test results), or conservatively using mechanics-based equations presented in this paper. The effective shear stiffness is governed by plate slenderness, defined by the tie spacing and plate thickness, and the relative flexural rigidity of the steel plates and the connecting ties. These parameters can be designed to limit the flexibility and the critical buckling stress of the empty modules. The paper also provides equations for calculating the out-of-plane displacement and stresses induced in the steel plates by the concrete casting hydostatic pressure.

Lumped system model for elastic steel-concrete beams with partial interaction

PurposeThe purpose of this paper is to introduce a numerical model to investigate static response of elastic steel-concrete beams. The numerical model is based on the lumped system with the combination of the transfer matrix and the analog beam methods (ABM). The beams are composed of an upper concrete slab and a lower steel beam, connected at the interface by shear transmitting studs. This type of beam is widely used in constructions especially for highway bridges. The static field and point transfer matrices for the element of the elastic composite beam are derived. The present model is verified and is applied to study the static response of elastic composite beams with intermediate conditions. The intermediate condition is considered as an elastic support with various values of stiffness. The elastic support can be considered rigid when the stiffness has very high values. The influence effect of shear stiffness between the upper slab and lower beam, and the end shear restraint on the static behavior of the composite beams is studied. In addition, the change in the stiffness of the elastic support is also highlighted.Design/methodology/approachThe objective of this study is to introduce a numerical model based on lumped system to calculate the static performance of elastic composite bridge beams having intermediate elastic support by combining the ABM with the transfer matrix method (TMM). The developed model is applicable for studying static and dynamic responses of steel-concrete elastic composite beams with different end conditions taking into account the effect of partial shear interactions. The validity of the lumped mass model is checked by comparing its results with a distributed model and good agreements are achieved (Ellakany and Tablia, 2010).FindingsA model based on the lumped system of the elastic composite steel-concrete bridge beam with intermediate elastic support under static load is presented. The model takes into consideration the effect of the end shear restraint together with the interaction between the upper slab and the lower beam. Combining the analogical beam method with the TMM and analyzing the behavior of the elastic composite beam in terms of shear studs and stiffness, the following outcomes can be drawn: end shear restraint and stiffness of the shear layer are the two main factors affecting the response of elastic composite beams in terms of both the deflection and the moments. Using end shear restraint reduces the deflection extensively by about 40 percent compared to if it is not used assuming that: there is no interaction between the upper slab and the lower beam and the beam is acting as simply supported. As long as the shear layer stiffness increases or interaction exists, the deflection decreases. This reduced rate in deflection is smaller in case of existence of end shear restraint. The effect of the end shear restraint is more prevailing on reducing the deflections in case of partial interactions. However, its effect completely diminishes in case of complete interaction. Presence of the end shear restraint and shear layer stiffness produces almost the same variations in the components of the bending moments of the composite beam. Finally, for a complete interaction, comparing the case of using end shear restraint or the case without it, the differences in the values of the deflections and moments are almost negligible.Research limitations/implicationsThe following assumptions related to the theory of ABM: shear studs connecting both sub-beams are modeled as a thin shear layer, each sub-beam has the same vertical displacement and the shear deformation in the sub-beams is neglected.Practical implicationsThe developed model can be effectively used for a quick estimation of the dynamic responses of elastic composite beams in real life rather than utilizing complicated numerical models.Social implicationsThe applications of this model can be further extended for studying the behavior of complex bridge beams that will guarantee the safety of the public in a quick view.Originality/valuePrevious models combined the TMM with the ABM for studying the static and free-vibration behaviors of elastic composite beams assuming that the field element is subjected to a distributed load. To study the dynamic response of elastic composite beams subjected to different moving loads using transfer matrix ABM, it was essential to use a massless field element and concentrate the own weight of the beam at the point element. This model is considered a first step for studying the impact factors of elastic composite beams subjected to moving loads.

Effect of diagonal cracks on shear stiffness of pre-stressed concrete beam

PurposeDuring service period, due to the overload or other non-load factors, diagonal cracks of the pre-stressed concrete beam are seriously affecting the safety of the bridge structure. The purpose of this paper is to quickly realize the shear bearing capacity and shear stiffness through maximum width of the diagonal cracks and make correct judgments.Design/methodology/approachThrough the shear failure test of four test beams, collecting data of diagonal cracks and shear stiffness loss value. According to the deformation curve of the shear stiffness, and combined with the calculation formula of the maximum width of diagonal cracks, the formula for calculating the effective shear stiffness based on the maximum width of diagonal cracks is deduced, then the results are verified by test data. Data regression method is used to establish the effective shear stiffness loss ratio calculation formula, the maximum width of diagonal cracks used as a variable factor, and the accuracy of this formula is verified by comparing the shear failure test results of pre-stressed hollow plates.FindingsWith the increase in width of the diagonal crack, the loss rate of shear stiffness of the concrete beams is initially fast and then becomes slow. The calculation formulae for shear stiffness based on the maximum width of the diagonal cracks were deduced, and the feasibility and accuracy of the formulae were verified by analysis and calculation of shear test data.Originality/valueA method for quickly determine the shear stiffness loss of structures by using maximum width of the diagonal cracks is established, and using this method, engineers can quickly determine effective shear stiffness loss ratio, without complex calculations. So this method not only ensures the safety of human life, but also saves money.

Wing twisting by elastic instability: A purely passive approach

The design of morphing structures requires attaining concurrently light-weight, load-carrying and shape adaptable systems that minimize complexity, actuation requirements and part count. Exploiting the external loads to produce local stiffness variations induced by elastic instabilities offers the potential to activate shape deformations purely passively. Following this approach, we present the structural response study of wings capable of attaining compliant buckling-induced twisting deformations. The structure is designed such that a specific level of aerodynamic load triggers the elastic instability in a shear web part of the wing box. The buckling-induced variation in effective shear stiffness, resulting from the development of a stable, reversible diagonal tension field, leads to a twisting deformation. The structural behaviour is characterized by two drastically different mechanical responses, delimited by the onset of elastic instability. The influence of the buckling component design on the attainable change in spanwise angle of attack is investigated for the specific case of a finite composite wing structure under aerodynamic loads. The type of composite material, its thickness, and the fibre orientation are the considered design parameters. The buckling-induced variation in twist angle, and the corresponding aerodynamic pressure redistribution on the wing, is exploited for achieving load alleviation, reducing the global lift coefficient and decreasing the wing root bending moment.

Determination and modeling of bending properties for continuous fiber reinforced C/C-SiC sandwich structure with grid core

The sandwich structures based on continuous fiber reinforced grid cores and skin panels have been developed via Liquid Silicon Infiltration (LSI) and in situ joining methods. Because of its excellent specific stiffness and temperature resistance, these lightweight structures have a sound potential for various application areas such as aerospace and construction industries. In this study, the characterization of the mechanical performance of grid core structures for continuous fiber reinforced C/C-SiC sandwich composites under four-point-bending load is presented. The effective bending and shear stiffness and the deflection at mid-span of the sandwich structure are determined and compared through experimental, analytical and FE-simulation (Finite Element simulation) approaches. The comparison showed good correlation. The analytical and FE-simulation approaches have been further used to study the parameter effects and the influence of the different grid core structures on the bending properties respectively. The proposed different approaches are suitable to determine and simulate the mechanical properties of C/C-SiC sandwich structures and are versatile tools for further product development.

A new biaxial tensile shear test method to measure shear behaviour of coated fabrics for architectural use

Shear properties of coated fabrics is poorly understood and the effects of shear stiffness on the behaviour of tensile fabric structures are usually ignored in the current design practice. The paper presents a new test method for the investigation of architectural coated fabric shear properties. The method relies on the biaxial pretension of cruciform specimens, where warp and weft yarns are oriented 45° with respect to the loading directions. Loading protocol is used to generate consecutive shear stress wave with specific biaxial tensile stress aligned with the yarns. An advanced biaxial tensile test system has been developed to implement biaxial loading by either displacement or force control strategy. Biaxial tensile shear tests of PVDF-coated polyester materials have been carried out to validate the new method. The implications of shear deformation, and material’s viscosity and plasticity from the experimental results are addressed. The determination of shear stiffness is described and a comparison of results derived from different methods has been made. The advantages of the new biaxial tensile shear test method and some experimental findings are concluded.

Numerical Evaluation of Settlement trough Width Parameter

Construction of tunnel results in ground movements with a settlement trough which is well described by a Gaussian distribution curve. For near surface settlements, it was established that the trough width i is an approximately linear function of the tunnel depth zo in relation to a trough width parameter K and broadly independent of tunnel construction method and tunnel diameter (except for very shallow tunnels where the cover to diameter ratio is less than one). The choice of an appropriate value of K may require some judgement, since it depends on whether the ground is primarily cohesive or frictional. Published literatures recommended that for practical purposes K could be taken as 0.5 for tunnels in clays and 0.25 for tunnels in sands and gravels. This paper discusses the evaluation of trough width parameter which has not been studied much for typical soil types encountered in the Klang Valley of Malaysia (e.g. Kenny Hill formation weathered materials, granitic soil, alluvium, etc.) of which are commonly in cohesive-frictional nature. The main objective of study is to investigate, using numerical method, the arbitrary relationship of the trough width parameter for different soil types in terms of its effective shear strength parameters and stiffness parameter. A parametric study was carried out to identify parameter(s) which have a significant influence on the settlement trough width and simple equation is presented subsequently for estimating appropriate K values for empirical calculation. This study has excluded two-layered system of different geology where, for example, a tunnel in Kenny Hill formation is overlain by significant thickness of alluvium deposits. Preliminary findings based on numerical analysis showed some promising results. Effort to continually build up the field database to further refine the deduced relationship for the surface settlement trough width parameter is in progress over the course of construction for Klang Valley MRT tunnels.

Theoretical and Experimental Study of Effective Shear Stiffness of Reinforced ECC Columns

Engineered cementitious composites (ECC) possesses characteristics that make it suitable in the zones of high shear and ductility demand of structural elements; however, there is a lack of an adequate model to predict its shear stiffness. A theoretical model for the effective shear stiffness of reinforced ECC (RECC) columns is proposed on the basis of the truss-arch model, with the consideration of the unique property of ECC material. A total of six column specimens subjected to cyclic reverse loading are conducted, and the main test variables include the shear span-to-depth ratio, the transverse reinforcement ratio and the axial load ratio. Results show that the shear contribution to the total deflection in the diagonally cracked RECC beam is significant, and the proposed theoretical model can predict the shear deformation with reasonable accuracy.

Nonlinear seismic modeling of reinforced concrete cores including torsion

Reinforced concrete (RC) cores are used in many residential multi-story buildings as the primary seismic force resisting system (SFRS). Due to architectural limitations, these buildings are often torsionally flexible. To assess the effect of torsion on the nonlinear seismic response of RC cores, a wide-column model (WCM) with fiber elements is used. The nonlinear warping and the nonlinear biaxial (P-Mx-My) cyclic behaviors of the WCM are validated against experimental results and exhibit excellent agreement. According to modal and linear time history analyses, the model can adequately capture the dynamic characteristics and seismic response of core structures, including torsion. The WCM is then extended to the nonlinear range to perform three-dimensional (3D) time history analyses of a typical RC building structure located in Eastern North America (ENA) that is subjected to high-frequency ground motions. Three different building configurations with increasing torsional flexibility (B=1.7, B=2.1 and B=2.5, according to the current National Building Code of Canada) are studied to investigate the effect of torsion on the seismic behavior. The nonlinear envelopes of key response parameters are similar to the design envelopes obtained from the linear response spectrum analysis of a shell elements model (B=1.7) with proper inelastic force modification factors. Aside from the story torque, the shear and moment demands remain relatively constant, regardless of the torsional flexibility value. The effective shear stiffness must be carefully selected in the WCM to avoid large questionable rotations.

Shear stiffness prediction of Reissner–Mindlin plates with periodic microstructures

ABSTRACTIn this article, an intuitionistic interpretation of the new numerical implementation of asymptotic homogenization for effective bending stiffness of in-plane periodic plate structures is presented. Based on this interpretation, a two-step method of effective shear stiffness prediction for their Reissner–Mindlin model is developed. An equivalent displacement field of linear curvature is applied to a unit cell in the first step; in the second step, a new unit cell problem is constructed and solved, and the effective shear stiffness is obtained through energy equivalence. This method can be easily implemented in commercial software and several examples are given to demonstrate its validity.

Shear Deformations of RC Beams under Service Loads

AbstractShear deformations of reinforced concrete (RC) beams are not negligible after shear cracking. However, unlike the well-established procedure for calculating bending deformations of cracked beams, the calculation of shear deformations is still ignored in codes of practice due to a lack of practical models. This study aims to develop a practical approach for estimating instantaneous shear deformations of RC beams under service loads. Based on the truss analogy, an explicit equation for evaluating the yield shear stiffness of fully diagonally cracked beams is derived. It is discovered that the shear retention factor (ratio of the yield shear stiffness to the initial elastic shear stiffness) is approximately the cubic root of the shear-reinforcement ratio. An analytical approach for evaluating the degradation of effective shear stiffness and the development of shear deformation is proposed. Two restrained I-beams with thin webs are tested. This test and shear-deformation tests available in the literat...

Flexural creep response of pultruded GFRP deck panels: Proposal for obtaining full-section viscoelastic moduli and creep coefficients

Abstract Glass fiber reinforced polymer (GFRP) pultruded flexural members are generally analyzed for serviceability limit states using shear-deformable beam theories, considering their short-term full-section moduli. However, regarding long-term design, for which the effect of viscoelasticity must be taken into account, the time-dependency of those full-section properties were not yet properly defined, namely for multicellular panels used in bridge decks. To address this issue, this paper describes an experimental study about the flexural creep response of full-scale multicellular GFRP pultruded deck panels subjected to uniformly distributed loads for about 5 months under normal laboratory environmental conditions. The creep behaviour of the panels was first successfully modelled using Findley's power law, confirming the ability of this empirical approach to simulate the viscoelastic response of multicellular deck panels. Next, an experimental methodology involving the measurement of creep deflections in panels with different spans and applying the Timoshenko beam theory in the time domain was proposed in order to characterize simultaneously the full-section flexural and shear moduli over time. The results obtained, including design formulae for the time-dependent creep coefficients for shear and bending, indicate that the creepocity due to shear is much higher, with reductions after 50-years in the effective flexural and shear stiffness of 22% and 43%, respectively. Finally, a comparison is made between these creep coefficients and those suggested in the most relevant design guidelines.

On the effect of shear stiffness on the plane deformation of linear second gradient pantographic sheets

Recently it has been proposed the study of a new class of bidimensional metamaterials, [33, 34] which have been called extensible pantographic sheets. Such bidimensional continua are the generalization of the continua introduced in [68, 69, 80] as they take simultaneously into account the elastic energy in the extensional deformation and geodesic bending of constituting fibers. In the present paper we consider in the deformation energy a term accounting for the effect of shear deformation. The phenomena which we highlight can be of relevance to model the mechanical behavior of composite fiber reinforcements and of some lattices of beams constrained by internal pivots. We compare the effect of different linear or cubic shear stiffnesses i) on the deformation of pairs of pantographic sheets suitably interconnected and ii) on the deformation of pantographic sheets deformed under the action of forces concentrated on points.

Shear stiffness of neo-Hookean materials with spherical voids

In this paper, the shear stiffness of neo-Hookean materials with spherical voids is investigated using a numerical homogenization approach. Three-dimensional representative volume element (RVE) models with non-overlapping identical randomly distributed spherical voids are generated to simulate the mechanical responses of the porous neo-Hookean materials. Pure shear deformations are simulated using the finite element method (FEM) and the numerical results show a clear linear relation between the nominal shear stress and the nominal shear strain. The effective shear stiffness of the porous neo-Hookean materials can then be computed by fitting the numerical data. It is further verified by more FEM simulations that the effective shear stiffness can be extended to predict the mechanical responses of the porous neo-Hookean materials subjected to any general isochoric deformations. It is also shown that the effective shear stiffness of the porous neo-Hookean materials can be well predicted as a function of the volume fraction of the voids using the classical three phase model originally proposed for linear elastic composites. Finally, RVE models with spherical voids of various sizes are created to study the effect of the size distribution of voids and the FEM results illustrate that it has negligible effect on the effective shear stiffness.

Practical Nonlinear Modeling of Reinforced Concrete Structural Walls

AbstractCurrent engineering practice typically relies on the use of fiber-based modeling approaches with uncoupled axial-bending (P-M) and shear (V) responses to simulate nonlinear behavior of reinforced concrete (RC) structural walls. However, more sophisticated numerical models are available that incorporate coupled P-M-V behavior. The effect of using uncoupled and coupled modeling approaches and the influence of various modeling assumptions, particularly modeling parameters related to wall shear behavior, on computed global and local building responses are reported. A five-story archetype RC wall-frame building designed according to current U.S. code provisions is used for the assessment. The results indicate that modeling parameters associated with wall shear behavior have a significant effect on computed responses for uncoupled models; use of commonly recommended effective shear stiffness of 0.2EcAw to account for effects of concrete cracking provides a reasonable estimate of roof displacement respon...