Stress Distribution In Beams Research Articles

Effect of tapered-end shape of FRP sheets on stress concentration in strengthened beams under thermal load

Repairing and strengthening structural members by bonding composite materials have received a considerable attention in recent years. The major problem when using bonded FRP or steel plates to strengthen existing structures is the high interfacial stresses that may be built up near the plate ends which lead to premature failure of the structure. As a result, many researchers have developed several analytical methods to predict the interface performance of bonded repairs under various types of loading. In this paper, a numerical solution using finite - difference method (FDM) is used to calculate the interfacial stress distribution in beams strengthened with FRP plate having a tapered ends under thermal loading. Different thinning profiles are investigated since the later can significantly reduce the stress concentration. In the present theoretical analysis, the adherend shear deformations are taken into account by assuming a parabolic shear stress through the thickness of both beam and bonded plate. The shear correction factor for I-section beams is also included in the solution. Numerical results from the present analysis are presented to demonstrate the advantages of use the tapers in design of strengthened beams.

Effect of tapered-end shape of FRP sheets on stress concentration in strengthened beams

Bonding composite materials to structural members for strengthening purpose has received a considerable attention in recent years. The major problem when using bonded FRP or steel plates to strengthen existing structures is the high interfacial stresses that may be built up near the plate ends which lead to premature failure of the structure. As a result, many researchers have developed several analytical methods to predict the interface performance of bonded repairs. In this paper, a numerical solution using finite - difference method is used to calculate the interfacial stress distribution in beams strengthened with FRP plate having a tapered ends with different thinning profiles. These latter, can significantly reduce the stress concentration. In the present theoretical analysis, the adherend shear deformations are taken into account by assuming a parabolic shear stress through the thickness of both beam and bonded plate. Numerical results from the present analysis are presented to demonstrate the advantages of use the tapers in design of strengthened beams.

Non-linear analysis of two-layer beams with interlayer slip and uplift

A new mathematical model for the non-linear analysis of two-layer planar beams considering flexible connections is introduced and an effective, strain-based finite element numerical solution method derived. The model and the solution method account for the exact geometrically non-linear behaviour in each separate layer. Material is assumed homogeneous but can be different in each layer. The shear strains are neglected. The laws of contact in both tangent and normal directions are taken non-linear. Numerical examples verify the proposed approach. The comparisons with numerical and experimental results from literature are made and the effects of uplift on ductility and stress distribution in beams are systematically explored. The theoretical model, combined with the present numerical formulation, has been found to result in realistic behaviour, while the numerical method proves to be accurate, reliable and computationally effective.

Modeling and finite element analysis of mechanical behavior of flexible MEMS components

This paper describes the studies of the mechanical characteristics of flexible MEMS components including theoretical approach, finite element analysis and experimental investigations. Modeling and finite element analyses together with theoretical and experimental investigations are performed to estimate the mechanical behaviour of MEMS components as microcantilevers, microbridges and micromembranes. The finite element analysis of microcomponents deflections under different loading and the stress distribution in beams is determined and compared with the experimental measurements performed using atomic force microscope. The modeling of a micromembrane supported by four hinges that enable out-of-plane and in-plane motions is presented. Finite element analysis and experimental investigations are performed to estimate the deflection of the mobile plate of the micromembrane under an applied force and to visualize the distribution of the stress in hinges. In additional, this paper provides analytical relations for stiffness and stresses of the investigated flexible MEMS components.

On the Reduction of the Interfacial Stresses in a Repaired Beam with an Adhesively Bonded FRP Plate

Severe aging and deterioration of the transportation infrastructure has motivated extensive research in developing structural repair techniques using FRP or steel plates. As a result, previous researchers have developed several analytical methods to predict the interface performance of bonded repairs. An important feature of the reinforced beam is the significant stress concentration in the adhesive at the ends of FRP plate. In this paper, a numerical solution using a finite-difference method is used to calculate the interfacial stress distribution in beams strengthened with FRP plate having a tapered ends. These latter, can significantly reduce the stress concentrations. Numerical results from the present analysis are presented to demonstrate the advantages of use the tapers in design of strengthened beams.

Effect of strain hardening on residual stress distribution in beams determined using the crack compliance method

This work used the crack compliance method for the determination of residual stresses in beams subjected to prior straining before the introduction of residual stresses through bending. The paper also introduces a support system that allows free movement of specimens during cutting by electric discharge machining. The experimental testing and verification procedure considered factors such as different materials and strain hardening levels. The results obtained provide a quantitative demonstration of the effect of prior strain hardening on residual stress distribution in beams.

Interfacial stresses in externally FRP-plated concrete beams

In this paper, an analytical method is developed to predict the distributions of interfacial stress in concrete beams strengthened by composite plates. Accurate predictions of such stresses are prerequisite for designing against debonding failures of the FRP plate from the RC beam. In the present analysis, a simple theoretical model to estimate shear and peel-off stresses is proposed, including the variation in FRP plate fibre orientation. Numerical results from the present analysis are presented both to demonstrate the advantages of the present solution over existing ones and to illustrate the main characteristics of interfacial stress distributions in beams.

Stress Fields in Fiber Reinforced Laminate Beams Due to Bending and Torsion Moments

A model of fiber reinforced composite laminate beam with sections of orthogonal shape is presented, in which the stresses due to simultaneously applied torsional and bending moments are found by an analytical solution. The technique followed is based on Sokolnikoff ’s approach in conjunction with the theory of anisotropic elasticity. The results derived permit the evaluation of the off-axis-strength elastic constants for the material. The evaluation of 3-D stress distributions in beams with sections characterized by various aspect ratios reveals variations of stresses, which depend on the warping combined with flexure in these laminate composite beams. In addition, useful information gained from the study of variation of the elastic properties as well as torsional rigidity for fiber reinforced laminate beams leads to further knowledge for the profile of stress distribution allover the beam. Specifically, the results have revealed that the torsional rigidity of the fiber reinforced laminate composite beam reaches an optimal value at a -lamination angle between 20° and 30°. Thus, the normal stresses vary in higher values versus the lamination angle of the composite than the shear stresses do. Also, the stresses allover the beam become so intensive as the bending-to-torsion moments ratio increases.

Interfacial Stresses in Beams and Slabs Bondedwith Thin Plate

A new popular method for retrofitting reinforced concrete beams and slabs is to bond fiber-reinforced plastic (FRP) plates to the soffit. An important failure mode for such strengthened members is the debonding of the FRP plate from the member due to high interfacial stresses near the plate ends. Accurate predictions of the interfacial stresses are a prerequisite for designing against debonding failures. In this paper, a theoretical interfacial stress analysis is presented for simply supported beams and slabs bonded with a thin FRP composite or steel plate and subjected to a uniformly distributed load in combination with a uniform bending moment. The analysis leads to an exact closed-form solution, in which a plane stress model is used for beams and a plane strain model is used for slabs. The salient features of the new analysis include the consideration of nonuniform stress distributions in and the satisfaction of the stress boundary conditions at the ends of the adhesive layer. Numerical results from the present analysis are presented both to demonstrate the advantages of the present solution over existing ones and to illustrate the main characteristics of interfacial stress distributions in beams and slabs.

Photoelastic Investigation of Shearing Stress Distribution in Beams Having a Rectangular Cross-Section

Photoelastic Investigation of Shearing Stress Distribution in Beams Having a Rectangular Cross-Section

Bending and transverse shear stresses in fiber-composite beams by the transformed-section method

A method to determine bending and transverse shear stress distributions in beams composed of fiber-composite layers is presented. The method is based on the transformed-section concept and takes into account the effects of Poisson's ratios and in-plane shear coupling. To demonstrate the feasibility of the transformed-section model, numerical solutions are presented for three rectangular and I-shaped cross-sections. It is shown that for bending moments the transformed-section model presented herein is entirely consistent with the lamination theory. The model can also be used to determine the transverse shear stresses, and it is shown that the accuracy of the results may be significantly affected when the effects of Poisson's ratios and in-plane shear are neglected in the analysis.

Closure to “Discussion of ‘Prediction of Creep-Deflection and Stress Distribution in Beams From Creep in Tension’” (1956, ASME J. Appl. Mech., 23, p. 133)

Closure to “Discussion of ‘Prediction of Creep-Deflection and Stress Distribution in Beams From Creep in Tension’” (1956, ASME J. Appl. Mech., 23, p. 133)

Prediction of Creep-Deflection and Stress Distribution in Beams From Creep in Tension

Abstract A method of predicting creep in bending from data on creep in tension has been derived and applied to creep of a canvas laminate. Both creep deflections and stress distribution were derived. The deflections compared favorably with test data. It was shown that the stress distribution remained constant during creep in bending when creep in tension and compression were equal and the coefficient of the time-dependent term was equal to the time-independent term. Methods of determining creep deflections of beams having nonuniform bending moments are described.