Beam Of Rectangular Cross-section Research Articles

The Unified Solution for a Beam of Rectangular Cross-Section with Different Higher-Order Shear Deformation Models

The unified solution is studied for a beam of rectangular cross section. With the rotation defined in the average sense over the cross section, the kinematics with higher-order shear deformation models in axial displacement is first expressed in a unified form by using the fundamental higher-order term with some properties. The shear correction factor is then derived and discussed for the four commonly used higher-order shear deformation models including the third-order model, the sine model, the hyperbolic sine model and the exponential model. The unified solution is finally obtained for a beam subjected to an arbitrarily distributed load. The relation with that from the conventional beam theory is established, and therefore the difference is reasonably explained. A very good agreement with the elasticity theory validates the present solution.

Modal analysis of a rectangular variable cross-section beam with multiple cracks under different temperatures

A new method is proposed to calculate natural frequencies of a rectangular variable cross-section beam with multiple cracks under different temperatures. The temperature module is introduced through the elastic modulus, and cracks are modelled by bending springs without mass. Based on the transfer matrix method, the characteristic equation of the cracked beam is derived by the implementation of different boundary conditions. Examples are presented on cantilever beams having different non-uniformity parameters, and the influence of the temperature, the number and geometric parameters of cracks on natural frequencies is also investigated. Compared with results obtained using the Patran FEM method, good agreements are obtained and this analytical method is demonstrated to be feasible.

Warping stresses of a rectangular single leaf flexure under torsion

We describe a stress analysis of a single leaf flexure under torsion in which the warping effect is considered. The theoretical equations for the warping normal stress (oxx) and shear stresses (oxz and oxy) are derived by applying the warping function of a rectangular cross-sectional beam and the twist angle equation that includes the warping torsion. The results are compared with those of the non-warping case and are verified using finite element analysis (FEA). A sensitivity analysis over the length, width, and thickness is performed and verified via FEA. The results show that the errors between the theory of warping stress results and the FEA results are lower than 4%. This indicates that the proposed theoretical stress analysis with warping is accurate in the torsion analysis of a single leaf flexure.

Image Processing Algorithm for Fringe Analysis in Photoelasticity

Photoelastic fringe patterns recognition are carried out using a circular polariscope on a four point beam loaded by pure bending and they are processed with image processing algorithm in a personal computer. The aim of the present paper stress analysis of the photoelastic fringe in a rectangular cross section beam using digital image processing technology. An algorithm is developed to visualize the stress pattern acting in photoelastic models using fringe sharpening in conjunction with MATLAB software. Photoelasicity is a non-destructive experimental tool can be used for visual representation of stress patterns allowing for stress analysis. The present paper presents an image processing algorithm executed in a personal computer and obtained stress pattern recognition using digital image processing with histogram.

Retrofitting of Reinforced Concrete Beam by Ferrocement Technique

Background/Objectives: The aim of the present study was to examine the performance of reinforced concrete beams strengthened by ferro cement technique. Methods/Statistical Analysis: In this experimental investigation five beams of rectangular cross section were cast using M25 (1:1.48:2.52) normal mix and high strength deformed bars as longitudinal and shear reinforcement. The beams were retrofitted for two conditions. In one case, the beams were stressed to 70% of the failure load and than they were retrofitted. In second case, for overloading the unstressed beams were retrofitted. Findings: The results obtained indicate that the increase in ultimate load was 70% in overloading case and 45% in stressed beam, also there was reduction in rotation and deflection. Application/Improvements: It was concluded from the experimental investigation that the strengthening of reinforced concrete beams by ferro cement technique is practicable and has considerable advantages.

Analysis of the Vibrational Stress Relief for Reducing the Residual Stresses Caused by Machining

This research examines the use of vibratory methods to reduce residual stresses in structures. The main objective of this work is to seek a better knowing of the mechanism of the reduction of residual stresses of materials undergoing cyclic loading. Experiments have demonstrated that residual stresses can be largely relieved through vibratory stress relief (VSR) treatment. The factors that influence the reduction of residual stresses need to be understood to effectively apply the process. A mathematical model based on plasticity theorem with linear kinematic hardening is generated to explain the mechanism of reduction of residual stresses of materials experiencing cyclic loading. The numerical results from the mathematical model and the analytical results with existing experimental data for rectangular cross-section beams showed a similar trend.

Aeroelastic characteristics of magneto-rheological fluid sandwich beams in supersonic airflow

Supersonic aeroelastic instability of a three-layered sandwich beam of rectangular cross section with an adaptive magneto-rheological fluid (MRF) core layer is investigated. The panel is excited by an airflow along it’s longitudinal direction. The problem formulation is based on classical beam theory for the face layers, magnetic field dependent complex modulus approach for viscoelastic material model and the linear first-order piston theory for aerodynamic pressure. The classical Hamilton’s principle and the assumed mode method are used to set up the equations of motion. The validity of the derived formulation is confirmed through comparison with the available results in the literature. The effects of applied magnetic field, core layer thickness and constraining layer thickness on the critical aerodynamic pressure are studied. The onset of instability in terms of the critical value of the nondimensional aerodynamic pressure for the sandwich beam is calculated using the p-method scheme. Simply supported, clamped–clamped and clamped-free boundary conditions are considered. The results show that the magnetic field intensity and thickness ratios have significant effects on the instability bounds.

Laser Non-Uniform Heating of Moving Thin Wires Below the Biot Number Criterion of Uniform Temperature

An analytic solution is obtained for three-dimensional quasi-steady state temperature distribution during laser heating of moving thin wires. The wire moves at a constant speed through a vacuum chamber, which is back-filled with an inert gas such as argon, and a laser beam of rectangular cross-section is incident on the wire. The ambient gas provides a convection heat transfer mechanism, which yields a Biot number, Bi, for the heating process to determine whether the temperature distribution would be uniform or nonuniform in the cross-section of the wire. Generally, the criterion of Bi less than 0.1 is applied to assume spatially uniform temperature distribution in a solid. The temperature distribution is determined for different Bi numbers and the variation of the temperature in the azimuthal direction is analyzed. The method of solution involves the Fourier transform in the azimuthal direction and the Hankel transform in the radial direction for a three-dimensional quasi-steady state heat conduction equation containing an advection term that accounts for the motion of the wire. The thermal and optical properties of the material is assumed to be constant in the temperature range of this study. The heat loss due to radiation heat transfer between the wire surface and the surrounding environment is neglected due to the small laser-heated surface area. Using this model, the temperature profile is studied for different process parameters such as the incident laser power, laser beam profile, Biot number, and wire speed.

Dynamic stability of cracked multi-bay frame structures

ABSTRACTThe effects of crack depth and crack location on the in-plane static and dynamic stability of cracked multi-bay frame structures subjected to periodic loading have been investigated numerically by using the finite element method. For the rectangular cross-section beam, a crack element is developed by using the principles of fracture mechanics. In addition, the effect of the number of spans and static and dynamic load parameters on static and dynamic stability analysis are also investigated. For buckling and dynamic stability analyses, the results obtained by using the present model are presented in three-dimensional graphical forms and tables.

Application of the Contact Layer in the Solution of the Problem of Bending the Multilayer Beam

The article deals with solution for stress-strain state of multilayer composite beams of rectangular cross-section, which is bended by the normally distributed load . The interaction between layers is accomplished by the contact layer, in which the substances of adhesive and substrata are mixed.

On Vibrodiagnostics of the Presence of a Closing Edge Crack in a Beam with Amplitude-Dependent Damping Capacity Under Superharmonic Resonance

The paper summarizes the results of approximate calculation of the influence of amplitudedependent damping capacity of a vibrating system on vibrodiagnostic parameters of the presence of a closing mode I edge crack in a cantilever beam of rectangular cross section for various methods of excitation of the second-order resonance in the lowest natural bending mode.

The Influence of Amplitude-Dependent Damping on Vibrodiagnostic Parameters of the Presence of a Closing Crack in a Beam Under Subharmonic Resonance

The paper summarizes the results of approximate calculation of the influence of amplitudedependent dissipation of energy on vibrodiagnostic parameters of the presence of a closing mode I edge crack in beams of rectangular cross-section for different end restrain conditions and different cases of harmonic excitation of subharmonic resonance in any natural mode.

Crack Assessment by FEM of AMMC Beam Produced by Modified Stir Casting Method

Aluminium metal matrix composite (AMMC) are now recognized as important structural materials. It offers attractive properties such as low density, good manufacturability and high specific strength. The samples of AMMC were prepared with modified stir casting method and used for crack analysis. Since the structural parts/components made up of AMMC is more susceptibility for crack failure, a finite element method (FEM) is used to analyze the crack failure. FEM analysis is conducted using rectangular cross-sectional cantilever beam for crack at predetermined positions. The deferent mode shapes and natural frequency of the said beam are analyzed to know the behaviour of the AMMC as a beam structures. The result of crack analysis for AMMC is very encouraging so it can be utilize as the structural material in different applications.

Predicting fracture of mortar beams under three-point bending using non-extensive statistical modeling of electric emissions

Weak electric signals termed as “Pressure Stimulated Currents, PSC” are generated and detected while cement based materials are found under mechanical load, related to the creation of cracks and the consequent evolution of cracks’ network in the bulk of the specimen. During the experiment a set of cement mortar beams of rectangular cross-section were subjected to Three-Point Bending (3PB). For each one of the specimens an abrupt mechanical load step was applied, increased from the low load level (Lo) to a high final value (Lh), where Lh was different for each specimen and it was maintained constant for long time. The temporal behavior of the recorded PSC show that during the load increase a spike-like PSC emission was recorded and consequently a relaxation of the PSC, after reaching its final value, follows. The relaxation process of the PSC was studied using non-extensive statistical physics (NESP) based on Tsallis entropy equation. The behavior of the Tsallis q parameter was studied in relaxation PSCs in order to investigate its potential use as an index for monitoring the crack evolution process with a potential use in non-destructive laboratory testing of cement-based specimens of unknown internal damage level.The dependence of the q-parameter on the Lh (when Lh<0.8Lf), where Lf represents the 3PB strength of the specimen, shows an increase on the q value when the specimens are subjected to gradually higher bending loadings and reaches a maximum value close to 1.4 when the applied Lh becomes higher than 0.8Lf. While the applied Lh becomes higher than 0.9Lf the value of the q-parameter gradually decreases. This analysis of the experimental data manifests that the value of the entropic index q obtains a characteristic decrease while reaching the ultimate strength of the specimen, and thus could be used as a forerunner of the expected failure.

Tailoring the second mode of Euler-Bernoulli beams: an analytical approach

In this paper, we study the inverse mode shape problem for an Euler-Bernoulli beam, using an analytical approach. The mass and stiffness variations are determined for a beam, having various boundary conditions, which has a prescribed polynomial second mode shape with an internal node. It is found that physically feasible rectangular cross-section beams which satisfy the inverse problem exist for a variety of boundary conditions. The effect of the location of the internal node on the mass and stiffness variations and on the deflection of the beam is studied. The derived functions are used to verify the p-version finite element code, for the cantilever boundary condition. The paper also presents the bounds on the location of the internal node, for a valid mass and stiffness variation, for any given boundary condition. The derived property variations, corresponding to a given mode shape and boundary condition, also provides a simple closed-form solution for a class of non-uniform Euler-Bernoulli beams. These closed-form solutions can also be used to check optimization algorithms proposed for modal tailoring.

FLEXURAL BEHAVIOURAL STUDY ON RC BEAM WITH EXTERNALLY BONDED ARAMID FIBER REINFORCED POLYMER

This paper presents the flexural behaviour of Aramid fiber reinforced polymer (AFRP) strengthened reinforced concrete (RC) beams of M25 grade of concrete. The experimental program included strengthening and testing of simply supported rectangular cross section beam of size 100mm x 150mm x 1200 mm strengthened with Aramid fiber polymer sheets. Total twenty specimens were tested out of which two beam specimens were tested as control beams and remaining for various damage degrees (i.e. 0%, 70%, 80%, 90%, and 100%). The effects of strengthening on load carrying capacity and effect of damage degree are discussed in detail. The results indicate that the load carrying capacity of beams was significantly increased as the number of layer increased. The validation of the experimental results was done by using ANSYS software. In order to study the flexural behaviour of the beam, the specimens were only subjected to two point loading mechanism only. The beams were wrapped with AFRP sheets in single layer and double layers along the length at the bottom face of the beam. The present work includes Effect of damage degree of the beam and effect of number of layers. Thus it is a feasible method for strengthening and retrofitting of RC beams.

Nonlinear dynamic analysis of beams with layered cross sections under moving masses

This paper considers the nonlinear dynamic analysis of moving masses applied on beams with layered cross sections. This mechanical system is often used in passenger transportation systems, such as high-velocity trains and magnetic levitation transport vehicles. The structural systems are modeled numerically with the aid of a formulation based on the Finite Elements Method. The main objective of this paper was to present an original numerical approach for a mass-beam system using the concept of positional geometric nonlinearity, which uses nodal positions rather than nodal displacements to describe the finite elements kinematics. By using this methodology, analyses can be performed for moving masses traveling with constant or variable velocity in dimensionless or physical problems. For the analyzed problems, sets of results are presented for the mechanical behavior analyses, such as the moving mass trajectories along the mass-beam coupled system. Moreover, a comparative study is performed on beams with rectangular and rail cross sections. After the passage of the moving masses, the elastoplastic rectangular cross-sectional beam presents a higher stiffness than the elastoplastic rail cross-sectional beam, as a result of the double plasticity that occurs at the extreme surfaces. Another original numerical example presents a beam made of two different materials under the action of a moving mass.

Torsional Shear Strength and Size Effect in Laminated Veneer Lumber

Abstract This study investigates the effect that specimen depth has on the torsional shear strength of full-size Eastern Species Laminated Veneer Lumber (LVL). Characterization of this effect is valuable for structural design purposes as well as for use in constitutive modeling when predicting member strength of one depth based on member strength of a different depth derived from testing. To this end, torsion tests were carried out on three depths (140, 184, and 235 mm) of 1.98 m long by 44 mm thick 1.9E Eastern Species LVL. The shear strength of each depth was determined based on homogeneous, orthotropic theory for beams of rectangular cross-section. Despite a perceptible trend of slightly decreasing shear strength with increasing depth, an analysis of variance test indicated that no statistically significant depth effect exists as it relates to torsional shear strength. Further, a three dimensional finite element model of the 44 mm by 140 mm specimen indicated that stresses are uniform within the shear span of 2 times the depth plus the grip distance away from each end of the specimen. The predicted average maximum shear stress in this region compared well to the maximum shear stresses obtained experimentally.

Bending Analysis of Functionally Graded Materials Beam Considering Different Shear Deformation Theory

Static bending analysis of functionally graded materials(FGM) beam of rectangular cross section considering different shear deformation theory are presented. The FGM beams are assumed to be made of ceramics and metal, and the equivalent parameters of FGM are continuously variation across the beam thickness with a simple power law. Based on the principle of minimum potential energy, the differential equations for the FGM beam are obtained, in which the unknown functions are deflection, axial displacement and rotation angle. For simply supported FGM beam, considering 5 kinds of shear deformation theory, the curves of deflection, axial displacement and rotation angle of FGM beam are obtained respectively by the Fourier series method. The effect of length-to-height ratios and gradient index of the FGM beam on the bending deformation are discussed. The distribution characteristics of the shear stress and normal stress of FGM beams under different shear deformation theory are investigated. Then the static bending behaviors of beam with FGM and homogeneous material are compared. The curves between the neutral axis location and gradient index of FGM beam are given. The properties of the curves are analyzed.

Piezoresistive Sensing of Strain and Damage in Carbon/Epoxy Rectangular and I-shaped Cross-section Beams in Flexure

The strain and damage sensing capabilities of a carbon fiber/epoxy composite subjectedto monotonic and incremental cyclic flexural loading is investigated using theelectrical resistance approach. The piezoresistive sensitivity of the carbon fiber/epoxycomposites were first characterized using rectangular cross-section specimens andthen application of the electrical resistance approach was extended to an I-shapedcross-section laminated composite. The change in the electrical resistance of the specimenswas simultaneously monitored on both the tensile and compressive sides whilethe specimens were tested under flexural loading. On the tensile side, the positive electricalresistance change (ΔR) showed a linear trend for small deformations (less than0.3% strain) and increased in a nonlinear fashion for larger deformations. In contrast tothe tensile side, ΔR on the compressive side showed a nonlinear and non-monotonicbehavior. Initially, ΔR decreased for low values of deformation (less than 0.3% strain),leveled off at the onset of the specimen’s compressive failure, and then increased upto complete failure. Correlations between abrupt changes in ΔR and indications ofcomposite damage are confirmed with scanning electron microscopy. Carbon fibersin both rectangular and I-shaped cross-section carbon/epoxy specimens are capableof sensing tensile and compressive strain, and adequately capture the onset and progressionof failure by fiber micro-buckling, formation of kink bands, and delamination.The cross-section properties (e.g. stiffness and layup sequence) affect the piezoresistiveand damage sensitivity, with the stiffer I-shaped cross-section being less sensitiveto ΔR than standard specimens of rectangular cross-section. ΔR under cyclic flexuralloading for both tensile and compressive sides showed a permanent change with applieddeformation after each cycle, indicating first the release of residual stresses andthen damage.