SHEAR BEAM MODEL FOR INTERFACE FAILURE UNDER ANTIPLANE SHEAR(Ⅱ)—INSTABILITY

Based on the (Ⅰ) of the present work, the behavior of shear beam model at crack initiation stage and at instable propagation stage was studied. The prime results include: 1) discriminant equation which clarifies the mode of instability, snap_back or snap_through, was established; 2) analytical solution was given out for the double shear beam and the load_displacement diagram for monotonic loading was presented for a full process; and 3) the problem of the energy release induced by instability was discussed.

SHEAR BEAM MODEL FOR INTERFACE FAILURE UNDER ANTIPLANE SHEAR(Ⅰ)—FUNDAMENTAL BEHAVIOR

The propagation of interlayer cracks and the resulting failure of the interface is a typical mode occurring in rock engineering and masonry structure. On the basis of the theory of elasto^plasticity and fracture mechanics, the shear beam model for the solution of interface failure was presented. The concept of `cohesive crack' was adopted to describe the constitutive behavior of the cohesive interfacial layer. Related fundamental equations such as equilibrium equation, constitutive equations were presented. The behavior of a double shear beam bonded through cohesive layer was analytically calculated. The stable propagation of interface crack and process zone was investigated.

Theory of Flexural Shear, Bending and Torsion for a Thin-Walled Beam of Open Section

Aspects of the general Vlasov theory are examined separately as applied to a thin-walled channel section cantilever beam under free-end end loading. In particular, the flexural bending and shear that arise under transverse shear and axial torsional loading are each considered theoretically. These analyses involve the location of the shear centre at which transverse shear forces when applied do not produce torsion. This centre, when taken to be coincident with the centre of twist implies an equivalent reciprocal behaviour. That is, an axial torsion applied concentric with the shear centre will twist but not bend the beam. The respective bending and shear stress conversions are derived for each action applied to three aluminium alloy extruded channel sections mounted as cantilevers with a horizontal principal axis of symmetry. Bending and shear are considered more generally for other thin-walled sections when the transverse loading axes at the shear centre are not parallel to the section = s centroidal axes of principal second moments of area. The fixing at one end of the cantilever modifies the St Venant free angular twist and the free warping displacement. It is shown from the Wagner-Kappus torsion theory how the end constrained warping generates an axial stress distribution that varies with the length and across the cross-section for an axial torsion applied to the shear centre. It should be mentioned here for wider applications and validation of the Vlasov theory that attendant papers are to consider in detail bending and torsional loadings applied to other axes through each of the centroid and the web centre. Therein, both bending and twisting arise from transverse shear and axial torsion applied to each position being displaced from the shear centre. Here, the influence of the axis position upon the net axial and shear stress distributions is to be established. That is, the net axial stress from axial torsional loading is identified with the sum of axial stress due to bending and axial stress arising from constrained warping displacements at the fixing. The net shear stress distribution overlays the distributions from axial torsion and that from flexural shear under transverse loading. Both arise when transverse forces are displaced from the shear centre.

Short beam shear properties and failure modes of the wood-based X-type lattice sandwich structure

A wood-based X-type lattice sandwich structure was manufactured by insertion-glue method.The birch was used as core,and Oriented Strand Board was used as panel of the sandwich structure.The short beam shear properties and the failure modes of the wood-based X-type lattice sandwich structure with different core direction(vertical and parallel),unit specification(120 mm×60 mm and 60 mm×60 mm),core size(50 mm and 60 mm),and drilling depth(9 mm and 12 mm)were investigated by a short beam shear test and the establishment of a theoretical model to study the equivalent shear modulus and deflection response of the X-type lattice sandwich structure.Results from the short beam shear test and the theoretical model showed that the failure modes of the wood-based X-type lattice sandwich structure were mainly the wrinkling and crushing of the panels under three-point bending load.The experimental values of deflection response of various type specimens were higher than the theoretical values of them.For the core direction of parallel,the smaller the unit specification is,the shorter the core size is,and the deeper the drilling depth is,the greater the short beam shear properties of the wood-based X-type lattice sandwich structure is.

Experimental research on shear carrying capacity of H-steel concrete composite beam with small shear span ratio

In order to investigate shear carrying capacity of H-steel concrete beam with small shear span ratio,shear test on 5 H-steel concrete composite beams with small span ratio (from 0.7 to 1.1) are reported,including test design,test scheme,test method,failure characteristics and test results. Influences of shear span ratio,web of H steel and concrete on shear carrying capacity of this kind of beam are investigated. The main components comprising shear bearing capacity are analyzed. The results show that with the shear span ratio increasing,the contribution of web of H steel and concrete on shear carrying capacity decrease. Based on test data,the calculation formula of shear carrying capacity for this beam is established by curve fitting.

Closed-form solution for shear lag effects of steel-concrete composite box beams considering shear deformation and slip

Based on the consideration of longitudinal warp caused by shear lag effects on concrete slabs and bottom plates of steel beams,shear deformation of steel beams and interface slip between steel beams and concrete slabs,the governing differential equations and boundary conditions of the steel-concrete composite box beams under lateral loading were derived using energy-variational method.The closed-form solutions for stress,deflection and slip of box beams under lateral loading were obtained,and the comparison of the analytical results and the experimental results for steel-concrete composite box beams under concentrated loading or uniform loading verifies the closed-form solution.The investigation of the parameters of load effects on composite box beams shows that:1) Slip stiffness has considerable impact on mid-span deflection and end slip when it is comparatively small;the mid-span deflection and end slip decrease significantly with the increase of slip stiffness,but when the slip stiffness reaches a certain value,its impact on mid-span deflection and end slip decreases to be negligible.2) The shear deformation has certain influence on mid-span deflection,and the larger the load is,the greater the influence is.3) The impact of shear deformation on end slip can be neglected.4) The strain of bottom plate of steel beam decreases with the increase of slip stiffness,while the shear lag effect becomes more significant.

A new higher-order shear deformation theory and refined beam element of composite laminates

A new higher-order shear deformation theory based on global-local superposition technique is developed. The theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. The global displacement components are of the Reddy theory and local components are of the internal first to third-order terms in each layer. A two-node beam element based on this theory is proposed. The solutions are compared with 3D-elasticity solutions. Numerical results show that present beam element has higher computational efficiency and higher accuracy.

AN ANALYSIS oF THE SHEAR FAILURE OF RIGID-LINEAR HARDENING BEAMS UNDER IMPULSIVE LOADING

A theoretical rigid-plastic analysis for the dynamic shear failure of beams under impulsive loading is presented when using a travelling plastic shear hinge model which tabes into account material strain hardening. The maximum dynamic shear strain and shear strain-rate can be predicted in addition to the permanent transverse deflections and other parameters. The conditions for the three modes of shear failure, i.e., excess deflection failure, excess shear strain failure and adiabatic shear failure are analyzed. The special case of an infinitesimally small plastic zone is discussed and compared with Nonaka's solution for a rigid, perfectly plastic material. The results can also be generalized to examine the dynamic response of fibre-reinforced beams.

A fiber-section model based Timoshenko beam element using shear-bending interdependent shape function

A fiber-section model based Timoshenko beam element is proposed in this study that is founded on the nonlinear analysis of frame elements considering axial, flexural, and shear deformations. This model is achieved using a shear-bending interdependent formulation （SBIF）. The shape function of the element is derived from the exact solution of the homogeneous form of the equilibrium equation for the Timoshenko deformation hypothesis.The proposed element is free from shear-locking. The sectional fiber model is constituted with a multi-axial plasticity material model, which is used to simulate the coupled shear-axial nonlinear behavior of each fiber. By imposing deformation compatibility conditions among the fibers, the sectional and elemental resisting forces are calculated. Since the SBIF shape functions are interactive with the shear-corrector factor for different shapes of sections, an iterative procedure is introduced in the nonlinear state determination of the proposed Timoshenko element. In addition, the proposed model tackles the geometric nonlinear problem by adopting a corotational coordinate transformation approach. The derivation procedure of the corotational algorithm of the SBIF Timoshenko element for nonlinear geometrical analysis is presented. Numerical examples confirm that the SBIF Timoshenko element with a fiber-section model has the same accuracy and robustness as the flexibility-based formulation. Finally, the SBIF Timoshenko element is extended and demonstratedin a three-dimensional numerical example.

Shear deformable finite beam elements for composite box beams

The shear deformable thin-walled composite beams with closed cross-sections have been developed for coupled flexural, torsional, and buckling analyses. A theoretical model applicable to the thin-walled laminated composite box beams is presented by taking into account all the structural couplings coming from the material anisotropy and the shear deformation effects. The current composite beam includes the transverse shear and the restrained warping induced shear deformation by using the first-order shear deformation beam theory. Seven governing equations are derived for the coupled axial-flexural-torsional-shearing buckling based on the principle of minimum total potential energy. Based on the present analytical model, three different types of finite composite beam elements, namely, linear, quadratic and cubic elements are developed to analyze the flexural, torsional, and buckling problems. In order to demonstrate the accuracy and superiority of the beam theory and the finite beam elements developed by this study,numerical solutions are presented and compared with the results obtained by other researchers and the detailed threedimensional analysis results using the shell elements of ABAQUS. Especially, the influences of the modulus ratio and the simplified assumptions in stress-strain relations on the deflection, twisting angle, and critical buckling loads of composite box beams are investigated.

Ultrasonic beam focusing characteristics of shear-vertical waves for contact-type linear phased array in solid

We investigate the beam focusing technology of shear-vertical(SV) waves for a contact-type linear phased array to overcome the shortcomings of conventional wedge transducer arrays. The numerical simulation reveals the transient excitation and propagation characteristics of SV waves. It is found that the element size plays an important role in determining the transient radiation directivity of SV waves. The transient beam focusing characteristics of SV waves for various array parameters are deeply studied. It is particularly interesting to see that smaller element width will provide the focused beam of SV waves with higher quality, while larger element width may result in erratic fluctuation of focusing energy around the focal point. There exists a specific range of inter-element spacing for optimum focusing performance. Moreover, good beam focusing performance of SV waves can be achieved only at high steering angles.

Dynamic stability analysis of porous functionally graded beams under hygro-thermal loading using nonlocal strain gradient integral model

We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.

Analysis and seismic tests of composite shear walls with CFST columns and steel plate deep beams

A composite shear wall concept based on concrete filled steel tube （CFST） columns and steel plate （SP） deep beams is proposed and examined in this study. The new wall is composed of three different energy dissipation elements： CFST columns; SP deep beams; and reinforced concrete （RC） strips. The RC strips are intended to allow the core structural elements - the CFST columns and SP deep beams - to work as a single structure to consume energy. Six specimens of different configurations were tested under cyclic loading. The resulting data are analyzed herein. In addition, numerical simulations of the stress and damage processes for each specimen were carried out, and simulations were completed for a range of location and span-height ratio variations for the SP beams. The simulations show good agreement with the test results. The core structure exhibits a ductile yielding mechanism characteristic of strong column-weak beam structures, hysteretic curves are plump and the composite shear wall exhibits several seismic defense lines. The deformation of the shear wall specimens with encased CFST column and SP deep beam design appears to be closer to that of entire shear walls. Establishing optimal design parameters for the configuration of SP deep beams is pivotal to the best seismic behavior of the wall. The new composite shear wall is therefore suitable for use in the seismic design of building structures.

Experimental Research on Shear Behavior of Reinforced Concrete Composite Beams Under Uniformly Distributed Load

An experimental program was carried out to study the shear behavior of the reinforced concrete composite beam (RCCB) subjected to two-phase uniformly distributed load. A total of 12 reinforced concrete composite beams were tested: 10 of them were the RCCB subjected to two-phase uniformly distributed load, the other 2 were the comparative reinforced concrete beams cast at the same time as the RCCB subjected to one-phase uniformly distributed load. The interface of precast unit and recast concrete was natural and rough. The test range of the main composite factors: the ratio of precast section depth to composite section depth was from 0.35 to 0.65, the ratio of first-phase load moment to precast section ultimate bearing moment was from 0.25 to 0.65. Based on the test results, the stresses of the longitudinal reinforcements and stirrups, the load-bearing properties of the interface, the crack state and the failure characteristics of the RCCB under uniformly distributed load are discussed. The effects of the stirrups, the concrete strength and the composite factors on the shear resistance of the RCCB are analyzed, and the method for evaluating the shear resistance of the RCCB is proposed.

Nonlinear Absolute Nodal Coordinate Formulation of a Flexible Beam Considering Shear Effect

Nonlinear modeling of a flexible beam with large deformation was investigated. Absolute nodal cooridnate formulation is employed to describe the motion, and Lagrange equations of motion of a flexible beam are derived based on the geometric nonlinear theory. Different from the previous nonlinear formulation with Euler-Bernoulli assumption, the shear strain and transverse normal strain are taken into account. Computational example of a flexible pendulum with a tip mass is given to show the effects of the shear strain and transverse normal strain. The constant total energy verifies the correctness of the present formulation.

CALCULATION ANALYSIS OF SHEARING SLIP FOR STEEL-CONCRETE COMPOSITE BEAM UNDER CONCENTRATED LOAD

The strain difference of steel and concrete under vertical concentrated load was analyzed on the basis of elastic theory, and was compared with ideal solution of steel and concrete under vertical uniform load. The results indicate that the computing formula concluded from the paper is believable. The practical structure usually bears concentrated load, so it can be used in the practical engineering.

SHEAR STRESS ANALYSIS OF TIMOSHENKO'S BEAM WITH MULTIPLY CONNECTED CROSS SECTION

In this paper, a finite element method is developed to numericallyevaluate the shear coefficient of Timoshenko's beam with multiplyconnected cross section. With focus on analyzing shear stressesdistributed at the neutral axis of the beam, an improved definitionof the shear coeffi- cient is presented. Based on this definition, aGalerkin-type finite element formulation is proposed to analyze theshear stresses and shear deflections. Numerical solutions of theexamples for some typical cross-sections are compared with thetheoretical results. The shear coefficient of tower sections of theTsing Ma Bridge is calculated by use of the proposed approach, sothat the finite element modeling of The bridge can be developed withthe accurate values of the sectional properties.

Shear strengthening of pre-damaged reinforced concrete beams with carbon fiber reinforced polymer sheet strips

This paper presents the results of an experimental investigation on the response of pre-damaged reinforced concrete (RC) beam strengthened in shear using applied-epoxy unidirectional carbon fiber reinforced polymer (CFRP) sheet. The reasearch included four test rectangular simply supported RC beams in shear capacity. One is the control beam, two RC beams are damaged to a predetermined degree from ultimate shear capacity of the control beam, and the last beam is left without pre-damaged and then strengthened with using externally bonded carbon fiber reinforced polymer to upgrade their shear capacity. We focused on the damage degree to beams during strengthening, therefore, only the beams with side- bonded CFRPs strips and horizontal anchored strips were used. The results show the feasibility of using CFRPs to restore or increase the load-carrying capacity in the shear of damaged RC beams. The failure mode of all the CFRP-strengthened beams is debonding of CFRP vertical strips. Two prediction available models in ACI-440 and fib European code were compared with the experimental results.