Simple Beam Analysis Research Articles

Simultaneous extraction of tensile and shear interactions at interfaces

A simple beam analysis is developed that accounts for the tensile and shear interactions between the surfaces of two beams that have been brought into contact. The generally coupled differential equations for the relative normal and tangential displacements between the interacting surfaces and the normal and shear components of the traction between the two surfaces are decoupled when a balance condition involving the bending stiffness and height of each beam is satisfied. This condition also allows the normal and shear components of the J-integral and the crack tip displacement to be obtained from measurements of the applied loads along with load point displacement and rotation of each beam. As a result, the derivative of each component of the J-integral with respect to its associated crack tip displacement simultaneously provides both the normal and shear traction–separation relations at any value of the mode-mix without invoking any assumption on the particular form. As an application of this method, the normal and shear traction–separation relations for a silicon/epoxy interface were determined over nominal mode-mixes ranging from −53° to 87.5° using non-symmetric end-loaded split (ELS) and end-notched flexure (ENF) specimens. It is found that many of the assumptions made previously in developing traction–separation relations based on potential or damage-based approaches do not apply to this particular interface, which should motivate future theoretical developments.

Influence of Different Shank Distribution on Slip in Composite Beams

The beam model is modeled by simple beam analysis model. The finite element software ANSYS was used to analyze the model, and the two sets of models were not considered, and the shear deformation of the concrete and the steel was not taken into account. The model-one composite beam connection was adopted in the uniform arrangement of the model. The method of arrangement, comparing the results of the two groups, the value of the interface slip can be seen in the model two, due to the uniform arrangement of the way, the interface slip value is significantly reduced.

Failure initiation criterion in bonded joints with composites based on singularity parameters and practical procedure for design purposes

Composite to metal adhesively bonded joints generates critical points where geometry and material properties change abruptly. These points (multimaterial corners) are potential locations for failure initiation. There exist proposals predicting the initiation of failure at these multimaterial corners using a Fracture Mechanics approach, in which the Generalized Stress Intensity Factors (GSIFs) at the multimaterial corner control the failure initiation. The calculation of these GSIFs at anisotropic multimaterial corners involves not-straightforward calculations of the stress singularities and characteristic angular functions, numerical modeling of the joint and a careful postprocessing of the results. In this study a parametric Finite Element Analysis has been carried out allowing the generation of plots to calculate the GSIFs for unit values of the axial force, shear force and bending moment at one end of the overlap length. These results allow calculating the GSIFs at the multimaterial corners by a simple beam analysis of the joint, the use of these plots and the application of the superposition principle, for their use in the prediction of failure initiation by means of the singular parameters of the joint. Additionally, experiments have been carried out to propose an explicit failure criterion based on GSIF and Generalized Fracture Toughness values which fit very well with double-lap joint test results.

Analytical Method of Temperature Prediction in Reinforced Concrete Beams

The determination of temperature profile within a reinforced concrete (RC) beam is essential for carrying out structural analysis at elevated temperatures. The temperatures are usually estimated using sophisticated numerical techniques which require computational support. Since the determination of rebar temperature in RC beams is more important than the concrete temperature a reliable analytical method of temperature prediction can become a helpful tool in simple beam analysis problems which are employed for determining residual strength in fire. This paper presents the details of development of an empirical equation for the prediction of temperature of rebar in RC beams. The equation is also capable of predicting concrete temperatures at different locations within the beam. The predictions made by the equation were compared with the temperatures determined from experimental beam testing and finite element (FE) analysis. A good correlation of the predicted temperatures was found for the entire time-temperature history with both the observed data and the estimated temperatures by FE models.

Measurement of interface cohesive stresses and strains evolutions with combined mixed mode crack propagation test and Backface Strain Monitoring measurements

A Mixed Mode Bending (MMB) test is used to study the fracture process of an adhesively bonded specimen. Simple Beam analysis is proposed to estimate the Strain Energy Released Rate (SERR) from the evolution of specimen compliance. The effect of interface compliance on the process zone extension and specimen deformation is studied. Additionally, the Backface Strain Monitoring (BSM) technique is used to probe the peel and shear cohesive stresses along the bondline. With a simple analysis, a systematic procedure is proposed to evaluate the cohesive stresses as well as the peel and shear strain evolutions in the vicinity of the crack tip position during crack propagation experiment under mixed mode conditions.

Longitudinal analysis of concrete U-girder bridge decks

U-shaped prestressed concrete bridge decks, simply supported, are now being increasingly used in railways and highways. Simplified methods of analysis are commonly used in design practice. In the longitudinal direction, the U-girder is modelled as a beam. However, under eccentric loading, simple beam analysis is found to yield unconservative estimates of longitudinal forces, mainly due to torsional warping. An understanding of U-girder bridge deck behaviour under torsional loading is facilitated by the application of Vlasov's thin-walled beam theory. This theory can be easily invoked as a substitute for simple beam analysis, resulting in vastly improved predictions of longitudinal stresses. The two U-girder decks have also been modelled in Structural Analysis Program software using shell elements, and the results of three-dimensional finite-element analysis validate the thin-walled beam theory. The scope of the study is limited to a straight and thin-walled U-girder bridge deck of uniform section. The effects of variation in load position have also been studied, and it is established that the thin-walled beam theory is well suited to estimate and design the U-girder for longitudinal stresses.

Based on ABQUS of Concrete Structure Nonlinear Finite Element Analysis

Based on the finite element analysis software ABAQUS, the nonlinear analysis of a reinforced concrete beam was carried out In this simple beam analysis, the concrete damage plasticity model in ABAQUS has been introduced thoroughly. Finally, the results of the experimentation and the ABAQUS analysis were compared in a diagram, accordingly reasons of the result difference between the two methods were discussed about, which can be a useful reference for the further study of the finite element analysis on ABAQUS.

Closed Form Solution for Deflection of Flexible Composite Bridges

Simply supported steel-concrete composite beams are widely used in bridge construction. Deflection is the significant parameter for serviceability limit state of bridges. A lot of computational effort is required for finite element analysis of bridges considering flexibility of shear connectors and shear leg effects. Neural network is presented for prediction of deflections, at service load, in simply supported steel-concrete composite bridges incorporating flexibility of shear connectors and shear lag effect. The training, testing and validation data sets for neural network are generated using finite element models. The finite element models have been developed using ABAQUS software. These models have been validated with available experimental results. Closed form solution is also proposed based on the developed neural network. The use of the neural network requires a computational effort almost equal to that required for the simple beam analysis (neglecting flexibility of shear connectors and shear lag effect). The neural network has been validated for number of bridges and the errors are found to be small. The network/closed form solution can be used for rapid prediction of deflection for everyday design.

Seismic Analysis for Safety of Dams

Geo-technical engineering as a subject has developed considerably in the past four decades. There has been remarkable development in the fields of design, research and construction of dam. India is capable of designing and constructing a dam that would withstand a seismic jolt. The country needs water and electricity to provide its people good living standards. Hydropower is the solution to the country's requirements, and this can be achieved by storing water in dams. In the past, earthquake effects may have been treated too lightly in dam design. Are such dams safe, and how have they fared in previous earthquakes, this Paper will be limited to the some of finding about one concrete types. What will happen to dams during severe earthquake shaking? It is obvious that at present engineers cannot answer this question with any certainty. But we are very much aware of the threat of disastrous losses of life and damage to property if dams should fail, and we are making great effort to increase our under standing of this complex topic. This Paper deals with the case study of totaladoh Dam Situated in Vidarbha Region of Maharashtra for Seismic Analysis by I.S.Code method (Simple Beam Analysis method). This also includes future scope of analyzing the same dam for Seismic safety by very accurate method i.e. finite element method. Keywords: Earthquake, The finite element method, Indian Standard codes(I.S.Code), horizontal seismic coefficient (αh ),Hydrostatic pressure, Seismic analysis, I. Introduction As of now, there are about 23,000 large dams in the world. A large dam is defined by the International Congress on Large Dams (ICOLD) as one which has a height of 33 metres and above: Of these dams, only four, namely Koyna (India), Kremesta (Greece), Kar iba (South Africa) and Singfenkiang (China), have experienced earthquakes of a moderate magnitude of between 6.0 and 6.5 on the Richter scale within a few years of building. Although no earthquake-related failure of a concrete dam has occurred to date, no large concrete dam with a full reservoir has ever been subjected to really severe ground shaking. Such a possibility has many groups concerned, including the Division of Safety of Dams(DSD), a California state agency responsible for assuring the safety of California dams. The Division of Safety of Dams (DSD) has the power to order an updated seismic check of a dam if new information rises or if better analysis techniques are developed by researchers. In the early 1970s, two events led the Division of Safety of Dams (DSD) to initiate a program to perform seismic checks on all major dams under its jurisdiction. The first event was the near collapse of Lower San Fernando Dam, a large earthen dam, during the 1971 earthquake; and the second was the development of the finite element method, a tool for computerized stress analysis. In this paper the methods of seismic Analysis of dam are discussed. A case study of Totaladoh Dam which is analyzed by simplified beam method. The Results obtained by this method will be compared by the results obtained by finite element method is the future scope of study. II. Methods for seismic analysis of Dam Concrete gravity dam design was, and still is, based on two-dimensional idealizations (as illustrated in the figure No.1) because gravity dams, which are generally located in wide river valleys, are long and nearly uniform in cross section. Water loading from the reservoir behind the dam seeks to overturn or slide the dam downstream; and the dam's own weight resists this action. A proper choice of dam cross section provides stability. In addition, since concrete is weak in tension and since no steel reinforcing is employed, engineers equated. The presence of tensile stresses with failure.If their computations showed tensile stress at any point, they redesigned the cross section. Stress analysis was performed by treating the dam cross section as a beam of variable thickness cantilevering from the valley floor.

Neural networks for prediction of deflection in composite bridges

Neural networks have been developed for prediction of deflections, at service load, in steel-concrete composite bridges incorporating flexibility of shear connectors, shear lag effect and cracking in concrete slabs. Three neural networks have been presented to cover simply supported bridges, two span continuous bridges and three span continuous bridges. The use of the neural networks requires a computational effort almost equal to that required for the simple beam analysis (neglecting flexibility of shear connectors, shear lag effect and cracking of concrete). The training and testing data for neural networks are generated using finite element software ABAQUS. The neural networks have been validated for number of bridges and the errors are found to be small. Closed form solutions are also proposed based on the developed neural networks. The networks/ closed form solutions can be used for rapid prediction of deflection for everyday design.

Characterisation of the rotational stiffness and strength of web-flange junctions of pultruded GRP WF-sections via web bending tests

Three-point flexure tests on the webs of 12 pultruded Glass Reinforced Plastic (GRP) Wide Flange (WF) specimens are described. The webs of the specimens were tested with their ends either simply or semi-rigidly supported. Dual knife-edge fixtures and rigid steel supports were designed and fabricated to simulate these support conditions. A series of low load tests were carried out on the webs of the WF specimens for both types of end conditions and deflections and strains were recorded at mid-span. Using simple beam analysis models in conjunction with the test data, both the transverse elastic modulus of the web and the rotational stiffness per unit length of the web-flange junctions of each specimen were determined. The webs of five of the specimens were failed under simply supported end conditions and the remaining seven under semi-rigid end conditions. From these failure tests the initial failure strengths of the web-flange junctions and the ultimate bending strengths of the webs were determined. The failure loads and modes of failure for both sets of end conditions have also been quantified.

Silicon Germanium Epitaxy: A New Material for MEMS

ABSTRACTA wide array of materials have been investigated as candidate fabrication templates for precision microelectromechanical structures, including boron-diffused silicon, boron-doped epitaxial silicon, polysilicon, silicon-on-insulator, and wafer-thick bulk structures. Here we present the latest fabrication results for epitaxial silicon-germanium alloys, a new class of materials which possess excellent crystalline structure, are compatible with non-toxic etchants in bulk micromachining, and are capable of on-chip integration with electronics. For MEMS applications, silicon-germanium alloy layers are grown using a graded buffer approach, resulting in very high quality micromachined structures. Very low defect densities are obtained through the use of these relaxed buffers. Original etch-stop studies determined that Ge doping provided a very weak selectivity in anisotropic etchants such as KOH and EDP. However, by extending the range of Ge concentration to over 20%, we have found extremely high etch selectivities in a variety of etchants. Unlike boron-doped layers, SiGe exhibits etch stop characteristics in the non-toxic, process compatible solution TMAH. The combination of independence from boron doping concentration and etchant compatibility make SiGe a material which is ideal for integration with on-chip electronics.In this work we present the latest fabrication data on comb-drive resonators built using SiGe epitaxial layers. Process compatibility issues related to wafer curvature, surface finish and reactive-ion-etching chemistries are addressed. An unexpected result of the fabrication process, curvature of released structures, is resolved by annealing wafers after the SiGe deposition. Changes in Young's modulus arising from the high atomic fraction of Ge in the device can be determined by simple beam analysis based on observed resonant frequencies. Overall, build precision for these devices is excellent. We conclude by addressing the remaining challenges for wide-scale implementation of silicon-germanium epitaxial MEMS.

Fatigue Crack Growth Behavior in Mullite/Alumina Functionally Graded Ceramics

Mullite/Al2O3 functionally graded ceramics (FGCs) have been obtained by sequential slip casting and subsequently firing at 1650°C in air. Functionally graded layered dense (similar/congruent99% of the theoretical density) compacts, with five different layers with thickness ranging from 670 to 850 µm, were obtained. The layer composition was gradually changed from 100% mullite to 80% mullite/20% alumina. The elastic modulus, the flexure strength, and the fatigue life of the monolithic (80% mullite/20% alumina) and mullite/alumina FGCs were measured by means of four‐point bending tests. The mullite/alumina FGCs exhibited lower strength than the monolithic material but the fatigue resistance and reliability were improved in the high cycle fatigue regime. These results were rationalized in terms of the residual stress distribution in the FGCs, which was computed using a description of stresses and strains in the multilayer composite based on the simple beam analysis. The tensile residual stresses which developed in the surfaces were responsible for the lower strength, while the compressive residual stresses within the bulk arrested the fatigue crack and improved the fatigue life of the FGC material.

Interfacial crack propagation in a thin viscoelastic film bonded to an elastic substrate

Edge decohesion along the interface of a thin viscoelastic film bonded to an elastic substrate under tensile residual stresses is considered. The tensile residual stress in the film is replaced by a combination of edge loads, and an explicit relation of strain energy with respect to time is obtained through simple beam analysis. The strain energy function is discretized into time steps which are assumed to be very small so that the dissipation effects over the time steps can be neglected. The energy release rate is then calculated using a Griffith type energy balance. An analytical model is developed to predict the crack growth and its velocity. Extent of crack growth along the interface is prediced based on a fracture criteria. The analytical predictions are compared with results from a viscoelastic finite element analysis.

Thin-walled composite beams under bending, torsional, and extensional loads

Symmetric and antisymmetric layup graphite-epoxy composite beams with thin-walled rectangular cross sections are fabricated using an autoclave molding technique and tested under bending, torsional, and extensional loads. The bending slope and elastic twist at a station are measured using an optical system, and the results correlated with predicted values from a simple beam analysis as well as a refined finite element analysis. A symmetric ply layup results in bending-twist coupling whereas an antisymmetric layup causes extension-twist coupling. Simple analytical results with plane-stress assumption agree better with measured data as well as finite element predictions than with plane-strain assumption. For symmetric layup beams, the bending-induced twist and torsion-induced bending slope are predicted satisfactorily using simple analytical solution. Correlations with measured data, however, are generally improved using a finite element solution. For antisymmetric beams, axial force-induced twist is predicted satisfactorily by both methods.

A Simplified Racking Analysis of a Car Carrier by Using Symbolic Calculations

In this paper a simplified analysis is proposed for the selection of structural systems of a car carrier, whose transverse structural system has wise variations such as a partial bulkhead system and a strong web frame system depending on the relevant design philosophies. Introducing a simple beam model, which can be solved by a symbolic manipulation procedure, one can observe that the racking deformation of the transverse section is mainly influenced by the non-dimensional shearing rigidity defined in the present analysis. Comparing the partial bulkhead and strong web frame systems, the shearing rigidities at the bulkhead sections having the latter system is considerably small, and correspondingly is racking deformation obtained by the simplified analysis is several times larger than that of the former system. In order to predict the racking deformation of actual ships having various transverse rigidities, an effective method is proposed, where the simple beam analysis using symbolic calculations is combined with the numerical data obtained by precise three-dimensional structural analyses of ships having similar principal dimensions. The validity of the proposed method is confirmed by comparing the predicted values with the precise numerical results.