Nonlinear analysis of concrete shells including effects of normal and transverse shear stresses

The previously developed numerical model of the authors for the analysis of conventional reinforced and prestressed concrete shells under short‐term and long‐term loading was improved by including the effects of transverse shear stresses on the shell failure. The 9‐node degenerated shell element with the layered material model through the thickness of the shell was used. The reinforcement was modelled as a separate layer. To include the effect of transverse shear stresses on the shell failure, the failure criterion for concrete and longitudinal reinforcement was defined by a relation of transverse shear stresses and normal stresses in two mutually perpendicular vertical planes. The total transverse shear bearing capacity of the shell cross‐section is obtained by summing up the concrete and reinforcement contributions. The developed numerical model and appropriate software were verified based on experimental tests.     

Intensity of Local Effects at the Core Junctions in Sandwich Panels

Local effects that occur in the vicinity of junctions between different cores in sandwich panels subjected to the in-plane axial force and bending moment are considered. These local effects manifest themselves in a rise of locally induced bending normal stresses in the sandwich faces and shear and normal stresses in the cores in the near vicinity of the core junctions. Intensity of the local effects is measured experimentally for a representative sandwich beam subjected to both types of loadings. The numerical simulations are performed using Finite Element Analysis, and they reveal significant rates of stress concentrations in the faces and cores adjacent to the core junctions. The intensity of the local effects is dependable on the geometry and elastic properties of the sandwich faces and a degree of dissimilarity of elastic properties of the adjoined cores.     

Extension of MITC to higher‐order beam models and shear locking analysis for compact,thin‐walled,and composite structures

A class of mixed interpolated beam elements is introduced in this paper under the framework of the Carrera Unified Formulation to eliminate the detrimental effects due to shear locking. The Mixed Interpolation of Tensorial Components (MITC) method is adopted to generate locking‐free displacement‐based beam models using general 1D finite elements. An assumed distribution of the transverse shear strains is used for the derivation of the virtual work, and the full Gauss‐Legendre quadrature is used for the numerical computation of all the components of the stiffness matrix. Linear, quadratic, and cubic beam elements are developed using the unified formulation and applied to linear static problems including compact, laminated, and thin‐walled structures. A comprehensive study of how shear locking affects general beam elements when different classical integration schemes are used is presented, evidencing the outstanding capabilities of the MITC method to overcome this numerical issue. Refined beam theories based on the expansion of pure and generalized displacement variables are implemented making use of Lagrange and Legendre polynomials over the cross‐sectional domain, allowing one to capture complex states of stress with a 3D‐like accuracy. The numerical examples are compared to analytic, numerical solutions from the literature, and commercial software solutions, whenever it is possible. The efficiency and robustness of the proposed method demonstrated throughout all the assessments, illustrating that MITC elements are the natural choice to avoid shear locking and showing an unprecedent accuracy in the computation of transverse shear stresses for beam formulations.     

A novel numerical model of debonding of FRP-plated concrete beam

Accurate modeling is required to estimate the debonding in a plated fiber-reinforced polymer (FRP) concrete beam. In the present investigation, a numerical method is developed to model a crack in the FRP–concrete interface. An initial notch is located at the mid-span of the concrete beam. A modified crack closure integral method is implemented to model Mode-I fracture in the concrete. In the present research, a special interface element is formulated to simulate and to predict the distribution of interfacial shear stresses by using drilling degrees of freedom in the nodes of interface elements. Cohesive forces in the nodes of interface elements are formulated by finite element methods. A crack propagation criterion is presented to evaluate when the crack grows in FRP–concrete interface. If the principal stress in the node at the tip of an interface element reaches the maximum shear stress along the FRP–concrete interface, debonding happens. The model is robust, accurate, independent of mesh size, and it is able to model the crack growth in the concrete and debonding of the FRP–concrete interface, simultaneously. The model presented in this study showed acceptable similarity to previous research data.     

Probabilistic analysis of delamination onset in linear anisotropic elastic and viscoelastic composite columns

Previously developed deterministic and stochastic combined load invariant failure criteria are used to determine the onset of delamination in elastic and viscoelastic columns. The analysis includes the effects of initial imperfections as well as offset column loads and transverse shear contributions. The delamination predictions are found to be sensitive to the magnitude of applied loads and of initial imperfections. Illustrative numerical examples are presented for elastic and viscoelastic columns with random combined failure stresses in bending, shear, compression and with normal interlaminar stresses. Probabilities of delamination onset are established for various axial loads and initial imperfections and in the viscoelastic columns additionally as a function of lifetime. Since the failure theories consider the combined effects of bending, shear, compression and normal interlaminar stresses, delamination onset is predicted at smaller axial loads than the critical buckling loads in the elastic case and at shorter viscoelastic lifetimes compared to equivalent columns with no delamination effects.     

Numerical model for composite structures with experimental confirmation

The paper briefly presents a numerical model for the simulation of composite structures. The main structure is modeled with two‐dimensional plane finite elements. The composite surface is modeled with two‐dimensional interface elements for the continuous connection simulation and modified beam elements for the discrete connection simulation. The applied material model’s primary purpose is the simulation of reinforced concrete structures. It includes the most important nonlinear effects of reinforced concrete behavior: yielding in compression and opening and propagation of cracks in tension, with tensile and shear stiffness of cracked concrete, as well as the nonlinear behavior of reinforced steel. It also includes nonlinear behavior of the composite surface and the connection elements. The model was confirmed in experimental tests of composite concrete Omnia slabs, which are in common usage. The achieved test results were compared with the results obtained through the developed numerical model.     

STRESSES DUE TO CONCENTRATED LOADS IN RESTRAINED BENDING TESTS

The paper describes an analytical method using finite element techniques for evaluating the "pinching" stresses in a beam subjected to opposing concentrated forces acting on upper and lower faces. These conditions arise in restrained modulus of rupture tests on concrete beams when it is required to know the magnitude of these local stress concentrations in relation to the normal "straight line" flexural stress field.
The analytical values are compared with results taken from a photo-elastic model with suitably simulated loading conditions. There is excellent correlation between the patterns of principal shear contours as plotted from the finite element solution and the isochromatic lines observed in the loaded model.     

Stress analysis of steel beams strengthened with a bonded hygrothermal aged composite plate

In this paper, the problem of interfacial stresses in steel beams strengthened with bonded hygrothermal aged composite laminates is analyzed using linear elastic theory. The analysis is based on the deformation compatibility approach developed by Tounsi (Int. J. Solids Struct. 43:4154–4174, 2006) where both the shear and normal stresses are assumed to be invariant across the adhesive layer thickness. The adopted model takes into account the adherend shear deformations by assuming a linear shear stress through the depth of the steel beam. This solution is intended for application to beams made of all kinds of materials bonded with a thin composite plate. For steel I-beam section, a geometrical coefficient ξ is determined to show the effect of the adherend shear deformations. This research is helpful for the understanding on mechanical behaviour of the interface and design of such structures.     

Cohesive zone model for the prediction of interfacial shear stresses in a composite-plate RC beam with an intermediate flexural crack

In this paper, an analytical method is developed to predict the distribution of interfacial shear stresses in concrete beams strengthened by composite plates. Accurate predictions of such stresses are necessary when designing to prevent debonding induced by a central flexural crack in a FRP-plated reinforced concrete (RC) beam. In the present analysis, a new theoretical model based on the bi-linear cohesive zone model for intermediate crack-induced debonding is established, with the unique feature of unifying debonding initiation and growth. Adherent shear deformations have been included in the present theoretical analyses by assuming a parabolic shear stress through the thickness of the adherents, verifying the cubic variation of the longitudinal displacement function, whereas all existing solutions neglect this effect. The results obtained for interfacial shear stress distribution near the crack are compared to the Jialai Wang analytical model and the numerical solutions are based on finite element analysis. Parametric studies are carried out to demonstrate the effect of the mechanical properties and thickness variations of FRP, concrete and adhesive on interface debonding. Indeed, the softening zone size is considerably larger than that obtained by other models which neglect adherent shear deformations. However, loads at the limit of the softening and debonding stages are larger than those calculated without the thickness effect. Consequently, debonding at the interface becomes less apparent and the lifespan of our structure is greater.     

Warping shear stresses in nonuniform torsion by BEM

 In this paper a boundary element method is developed for the nonuniform torsion of simply or multiply connected prismatic bars of arbitrary cross section. The bar is subjected to an arbitrarily distributed twisting moment, while its edges are restrained by the most general linear torsional boundary conditions. Since warping is prevented, beside the Saint–Venant torsional shear stresses, the warping normal and shear stresses are also computed. Three boundary value problems with respect to the variable along the beam angle of twist and to the primary and secondary warping functions are formulated and solved employing a BEM approach. Both the warping and the torsion constants using only boundary discretization together with the torsional shear stresses and the warping normal and shear stresses are computed. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy. The magnitude of the warping shear stresses due to restrained warping is investigated by numerical examples with great practical interest. Received: 13 November 2001 / Accepted: 2 October 2002     

Linear stress relations for a metal matrix composite sandwich beam with any core material

In this paper, it is shown that shear stresses are developed in the interface between the facing material and the core of a sandwich beam. The sandwich beam is composed of a core of any suitable material sandwiched between an upper unreinforced metal facing and a bottom facing made from metal matrix composite (MMC) material. The shear stress is shown to be a consequence of the differences in the core and facing elastic moduli. The magnitude of the shear stress increases as the core stiffness is made to diminish. The shear stress can exceed the bond strength between facing and core, resulting in delamination. Consequently, structural materials using this type of construction and particularly flexural experiments should contain a relatively stiff core. The magnitude of the facing stresses is shown to be relatively insensitive to the assumption or neglect of these shear stresses. In the worst case considered, neglecting the interfacial shear stresses results in an overestimation of the compressive and tensile stresses by less than 5%.     

Analysis of shear transfer and gap opening in timber–concrete composite members with notched connections

In timber–concrete composite members with notched connections, the notches act as the shear connections between the timber and the concrete part, and have to carry the shear flow necessary for composite action. The shear transfer through the notches generates shear and tensile stresses in both parts of the composite member, which may lead to brittle failure and to an abrupt collapse of the structure. Although simplified design formulas already exist, some structural aspects are still not clear, and a reliable design model is missing. This paper summarizes current design approaches and presents analytical models to understand the shear-carrying mechanism, to estimate the shear stresses acting in the timber and concrete, and to predict failure. The analysis concentrates on three problems: the shearing-off failure of the timber close to the notch, the shear failure of the concrete, and the influence of the shear flow on the gap opening between the timber and concrete. Parts of the model calculations could be compared to experimental observations. The conclusions of this paper contribute to improving current design approaches.     

Evaluation of Stresses in Reinforced-Concrete Beam Elements,Their Strength,and Crack Resistance

We develop a procedure for the evaluation of strength and crack resistance of reinforced-concrete beam elements based on the approaches of fracture mechanics. A model for the numerical analysis of stresses is proposed and the formulas for finding normal stresses in the reinforcement and compressed concrete fibers are deduced by taking into account the inelastic zones in the vicinity of the crack tip. The established relations are checked experimentally and compared with the formulas proposed by SNiP 2.03.01-84.     

变截面梁的应力计算及其分布规律研究

为了合理计算预应力混凝土变截面箱形梁的剪应力,客观反映其应力分布状况,首先推导了任意变截面梁剪应力计算的一般公式,在此基础上,考虑箱形梁的梁高、底板厚度、腹板厚度沿跨度的变化,导出了变截面箱形梁的剪应力实用计算公式。应用导出的公式,结合矩形及箱形变截面悬臂梁算例,分析了变截面梁的应力分布状况。研究结果表明,变截面梁横截面上的最大剪应力并不发生在截面重心轴处,而是在重心轴以下区域或梁底缘处;变截面箱形梁的底板受有很大剪应力作用,为了合理设计变截面箱形梁,不应采用薄底板,而且应加强其配筋及构造处理。     

New designs of adhesive joints for thick composite laminates

New joint designs are proposed for adhesive bonding of thick multilayered composite adherends. The objective is to reduce or eliminate the failure modes associated with delamination and tensile and/or shear failure of the surface plies that are often observed in lap joints, and provide for a better stress distribution in the adhesive. In contrast to lap-joint designs, which transfer in-plane tensile stresses and other loads from the adherends to doubler plates by out-of-plane shearing of the surface plies, the new joint configurations transfer most of the load by in-plane shear and normal stresses, through bonded inserts or interlocking interfaces which have the same thickness as the laminate adherends. Doublers will transfer a calculated percentage of the load. Finite-element evaluations of the internal stresses in laminates, joined in both the conventional lap method and the new manner, suggest that the proposed load-transfer mechanism may improve joint efficiency by substantially increasing the size of adhesively bonded areas, and by making the stresses in the adherends nearly uniform through the thickness of the laminate. Some of the designs allow for selected ratios of shear to normal stresses in the adhesive layers. The stress concentrations often found in conventional designs, in the adherend surface plies and the adhesive layer at the leading edges of the doublers, are substantially reduced.     

Mechanics of bonds in an FRP bonded concrete beam

Fibre-reinforced plastic (FRP) materials have been recognised as new innovative materials for concrete rehabilitation and retrofit. Since concrete is poor in tension, a beam without any form of reinforcement will fail when subjected to a relatively small tensile load. Therefore, the use of the FRP to strengthen the concrete is an effective solution to increase the overall strength of the structure. The attractive benefits of using FRP in real-life civil concrete applications include its high strength to weight ratio, its resistance to corrosion, and its ease of moulding into complex shapes without increasing manufacturing costs. The speed of application minimises the time of closure of a structure compared to other strengthening methods. In this paper, a simple theoretical model to estimate shear and peel-off stresses is proposed. Axial stresses in an FRP-strengthened concrete beam are considered, including the variation in FRP plate fibre orientation. The theoretical predictions are compared with solutions from an experimentally validated finite element model. The results from the theory show that maximum shear and peel-off stresses are located in the end region of the FRP plate. The magnitude of the maximum shear stress increases with increases in the amount of fibres aligned in the beam's longitudinal axis, the modulus of an adhesive material and the number of laminate layers. However, the maximum peel-off stress decreases with increasing thickness of the adhesive layer.     

On the reduce of interfacial shear stresses in fiber reinforced polymer plate retrofitted concrete beams

One major problem when using bonded fiber reinforced polymer (FRP) plate is the presence of high interfacial shear stresses near the end of the composite (edge effect) which might govern the failure of the strengthening schedule. It is known that the decrease of plate thickness reduces the magnitude of stress concentration at plate ends. Another way is to use a plate end tapering. In this paper, the analytical solution of interfacial shear stresses obtained has been extended by a numerical procedure using the modal analysis of finite element method (FEM) in a retrofitted concrete (RC) beam with the FRP plate with tapered end, which can significantly reduce the stress concentration. This approach allows taking into consideration the variation of elastic properties of adhesive and plate as well as the complicated geometrical configurations and effects of thermal loads.     

Strength of shear connection in composite bridges with precast decks using high performance concrete and shear-keys

In this paper, a connection between precast beam and precast slabl to be used in decks of precast composite bridges is studied. The difference between this connection and the common connection used in bridge construction is that in this paper the steel connector is associated with a shear-key which is formed on the top face of the precast beam, and a high, performance concrete is used to fill out the shear pockets. The connector is formed by steel bars bent in a hoop form, which are inserted in pockets of the precast slab. The connection is made filling out the shear pockets with steel fiber reinforced concrete. Push-out tests were carried out to evaluate the strength of the shear connection. From these tests expressions based on a shear-friction model are proposed to evaluate the strength of the shear connection taking into account the compressive strength of the concrete cast in the pocket, the diameter of the connector and the addition of steel fibers to cast-in-place concrete. These expressions were shown to be appropriate to evaluate the strength of a shear connection, since the failure of precast concrete is avoided near the connection.     

Stresses on and around fibres in a composite

Abstract

The widely used shear-lag theory for the stresses and displacements in a short fibre composite is discussed and compared with more exact theories in the literature. A simple modification of shear-lag theory, using stress functions, is proposed that allows prediction of radial stresses in the fibre, while being easy to use for calculations. Predictions from the present theory are compared with those from the shear-lag theory and with some of the more exact theories. At low fibre concentrations, the present theory underestimates the radial stress at the fibre ends while predicting shear stresses comparable with those from shear lag. At high fibre concentrations both radial and shear stresses are overestimated.

MST/635     

An assessment of five modeling approaches for thermo-mechanical stress analysis of laminated composite panels

 A study is made of the effects of variation in the lamination and geometric parameters, and boundary conditions of multi-layered composite panels on the accuracy of the detailed response characteristics obtained by five different modeling approaches. The modeling approaches considered include four two-dimensional models, each with five parameters to characterize the deformation in the thickness direction, and a predictor-corrector approach with twelve displacement parameters. The two-dimensional models are first-order shear deformation theory, third-order theory; a theory based on trigonometric variation of the transverse shear stresses through the thickness, and a discrete layer theory. The combination of the following four key elements distinguishes the present study from previous studies reported in the literature: (1) the standard of comparison is taken to be the solutions obtained by using three-dimensional continuum models for each of the individual layers; (2) both mechanical and thermal loadings are considered; (3) boundary conditions other than simply supported edges are considered; and (4) quantities compared include detailed through-the-thickness distributions of transverse shear and transverse normal stresses. Based on the numerical studies conducted, the predictor-corrector approach appears to be the most effective technique for obtaining accurate transverse stresses, and for thermal loading, none of the two-dimensional models is adequate for calculating transverse normal stresses, even when used in conjunction with three-dimensional equilibrium equations. Received 14 September 1999