Composite Beam Theory Research Articles

Prediction of sectional collapse of thin-walled structure under pure bending by nonlinear composite beam theory

Brazier (1927) found that when one dimension of the beam cross-section was relatively smaller than the others, large in-plane displacements over the cross-section might occur, even though the strains could remain very small. Under this circumstance, the so-called Brazier effect refers to the cross-sectional ovalization, which leads to nonlinear bending buckling and collapses. This paper studies the Brazier effect by the nonlinear Variational Asymptotic Beam Sectional Analysis (VABS) theory which considers finite cross-sectional deformations. Nonlinear VABS reduces three-dimensional (3D) continuum to a one-dimensional (1D) beam analysis and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities without unnecessary kinematic assumptions. The present theory is implemented using the finite element method (FEM) in the VABS code, a general-purpose beam cross-sectional analysis tool. An iterative method is applied to solve the finite warping field for the classical-type model using the Euler–Bernoulli beam theory. The deformation gradient tensor is directly used to deal with finite deformation, various strain definitions, and several types of material laws. Numerical examples demonstrate the capabilities of VABS to predict the sectional collapse of thin-walled structures under pure bending.

Evaluation and prediction of bending properties of glulam beams made from young plantation-grown Eucalyptus nitens

ABSTRACT Interest in making glulam from plantation-grown Eucalyptus nitens has increased, but current structural timber standards were not designed for species grown in plantations. Additionally, the applicability of classical composite beam theory remains uncertain due to the unique features of this species. This study was designed to assess the hypothesis that the bending performance of glulam made from young plantation-grown E. nitens is reliable and predictable. We tested the hypothesis through experimental procedures and theoretical and statistical analyses. First, we assessed the bending performance of 20 glulam beams, which were manufactured in five configurations. Second, we compared our experimental results with predictive values to evaluate the accuracy of methods in current standards. Third, in our pursuit of improved predictive tools, we developed theoretical and parametric models using mechanical properties of the board elements. Our improved models showed a decreased deviation in both stiffness and strength values. A Monte Carlo simulation was used to determine the distribution for both stiffness and strength. The results validated that this product can be allocated a GL grade using current standards and the bending performance is predictable. The study enhances confidence in incorporating E. nitens into glulam products and offers valuable data for future specification modifications.

Static hydroelastic study of composite T-foils with beam and lifting line models

Well-designed hydrofoils improve ship resistance and seakeeping by lifting the hull above the water. With greater speeds come greater loads, and the two-way interaction of structural deflections of lifting surfaces on the hydrodynamics must be considered. Tailored structural anisotropy can improve hydrodynamic and structural efficiency of lifting surfaces compared to rigid counterparts by exploiting the layup of composite materials. Structural efficiency here means reduced risk of structural failure for a given amount of material, and hydrodynamic efficiency means lower drag. A T-foil is a prototypical multi-component appendage, consisting of the foil wing and the strut, which we investigate in this work. We use simple composite beam and lifting line theory to explore the static fluid-structure interaction of a composite T-foil for a variety of fiber angles (θf = 0˝ , ˘15˝ ). We apply a simple approximation on lift coefficient at infinite Froude number (F n) to model the free-surface effects, which is valid at high depth-based Froude numbers (F nh ą10a h/c) when CL is independent of F nh and the inertial effects dominate. Results for the moth rudder T-foil geometry studied here indicate that aligning composite fibers towards the leading edge results in a more hydrostructurally efficient foil and that free-surface effects are minor because of the large submergence for this flow condition.

Fabrication and structural characterisation of hybrid timber-cardboard sandwich beams

This paper develops a novel class of timber-cardboard sandwich (TCS) panels, consisting of low-cost timber facings and a block-laminated corrugated cardboard core. Experimental and analytical studies are conducted to characterise the flexural performance of TCS beams made from recycled or waste materials. TCS beams made from scrap cardboard cores have the exceptional characteristic of being made mostly from waste, up to 91% by volume or 76% by weight, and are demonstrated to have equivalent performance to beams made with recycled cores. TCS beam flexural behaviour is found to be primarily governed by timber face sheets, with very strong composite action and no observed core shear or debonding failure. The strength, stiffness, and dominant failure mode of TCS beams are thus shown to be accurately predicted using composite sandwich beam theory and cross-sectional analysis. TCS beam bending strength is also found to be significantly higher than conventional foam-core structurally-insulated panels with comparable densities, making them highly viable as a bio-based structural alternative. These research findings enhance the capacity and confidence by which cardboard can be used as a construction feedstock, supporting societal progression toward a greener and more circular economy.

The Influence of the Flexibility of a Polymeric Adhesive Layer on the Mechanical Response of a Composite Reinforced Concrete Slab and a Reinforced Concrete Beam Girder.

This study addresses the challenges of modeling flexible connections in composite structures employing a polymeric adhesive layer. These types of connections provide a more uniform stress distribution compared to conventional rigid connectors. However, they lack standardized design rules and still require much research to sufficiently comprehend their properties. The novelty of this research lies in proposing an analytical solution to address these issues. Its aim is to investigate the influence of the stiffness of the polymer adhesive on the girder's deflection and on the maximum stresses in both the adhesive and concrete. The analyzed composite structure consists of a reinforced concrete (RC) slab and an RC beam connected with a layer of flexible polyurethane (FPU) adhesive. Analytical and numerical approaches for the description of the mechanical response of a composite bridge girder are presented. Another objective is to validate the analytical design formulas using 3D nonlinear numerical analysis, both in the case of uncracked and cracked concrete. Seven types of FPUs are tested in the uniaxial tension test, each examined at five strain rates. The obtained data is used to predict the mechanical response of the considered girder using finite element analysis (FEA) as well as with a simplified one-dimensional composite beam theory. Fair agreement is found between the FEA results and theoretical predictions. A comparison of the results obtained for these two models is performed, and the similarities and discrepancies are highlighted and discussed.

Effect of depth-absorbed dose distribution on the flexural modulus of carbon fiber–reinforced plastics in a radiation environment in radio-astronomical satellite orbit

Carbon fiber–reinforced polymers (CFRP) are used as structural materials for spacecraft due to their excellent physical properties. However, exposure in space to environmental factors, such as radiation, ultraviolet radiation, and thermal cycling, would alter these properties. Therefore, in order to ensure the safety and reliability of the spacecraft and the feasibility of the mission, it is necessary to evaluate the material’s space-environment resistance.The space environment consists of various types of energy and radiation, resulting in a non-uniform depth-absorbed dose distribution. This means that the absorbed dose is significantly higher at the surface of the material and lower with depth. However, reproducing this distribution in a ground-based test facility that typically uses a single energy irradiation is challenging. To overcome this challenge in ground-based testing, it is recommended that multiple radiation types and energies be irradiated to simulate the depth-absorbed dose distribution in a real space environment. However, there is a lack of understanding about the agreement between the depth-absorbed dose distribution obtained in real space environments and in ground-simulated tests. Additionally, the degree to which each depth region of the absorbed dose distribution affects material degradation is unknown. Hence, a faithful reproduction of the depth-absorbed dose distribution in a real space environment requires not only massive test facilities with significant financial investment but also a significant amount of time spent on irradiating those materials containing radiation that have practically no effect on material degradation.This study focused on analyzing the changes in the mechanical properties of CFRP due to radiation degradation using composite beam theory and mathematical models while considering the non-uniform depth-absorbed dose distribution in real space environments. The results of this study provide insight into which depth region of the depth-absorbed dose distribution is dominant for radiation-induced changes in mechanical properties when the CFRP plate thickness varies.

Analytical theory of composite beams with CSWs using the state space method

Based on the zig-zag theoretical model of corrugated steel web beam (CSW), the governing equations in the form of state equations are derived and their analytical solutions are obtained for different loads, variable cross-sections and boundary conditions. Through numerical examples, it is verified that the bending moment, deflection and stresses predicted by the present analytical method have a good agreement with the results of the three-dimensional finite element model. The applicability of the present method for non-prismatic continuous beams with CSWs under different loads is also demonstrated. Meanwhile, it is found that the quasi-plane assumption is still valid in non-prismatic continuous beams with CSWs. Through quantitative analysis of the flexural stresses in the top and bottom slabs, it is confirmed that the zig-zag theory in this study can well reflect the accordion effect of CSWs. Because of the inclined bottom slabs in the non-prismatic beams with CSWs, the Resal effect on the shear stresses in the CSWs and bottom slabs, which is caused by the vertical component of the axial force in the bottom slab, is discussed. A refined shear formulation is developed for more accurate shear stresses in the CSWs and bottom slabs, which provides fundamental theoretical support for the strength prediction of the non-prismatic beam with CSWs.

Mechanical Characterization of Bi-Layer Environmental Barrier Coatings Under Tension and Bending Using Acoustic Emission and Digital Image Correlation

Abstract Fracture characteristics of bi-layer environmental barrier coatings (EBC) deposited on a woven ceramic matrix composite (CMC) substrate using air plasma spray processes were investigated under uni-axial tension and bend tests at room temperature. Health monitoring techniques such as acoustic emission (AE) and digital image correlation (DIC) were employed to better understand the cracking behavior of the coating and its progression. Post-test microscopy was performed to correlate the coating cracks with DIC and AE location. The results indicate that multiple transverse cracks first occurred in the coating, followed by substrate transverse cracks and additional coating cracks. DIC analysis was able to highlight the formation and location of these cracks. The fracture strength of the coating was estimated assuming the composite beam theory.

Verification of Composite Beam Theory with Finite Element Model for Pretensioned Concrete Members with Prestressing FRP Tendons.

Composite beam theory was previously developed to establish an analytical solution for determining the transfer length of prestressed fiber-reinforced polymers (FRP) tendons in pretensioned concrete members. In the present study, a novel finite element (FE) modeling approach is proposed to provide further verification of the developed analytical method. The present FE model takes into account the friction coefficients obtained from pull-out tests on the FRP tendons and prestressed concrete members. Convergence analysis of two numerical simulations with different mesh densities is carried out as well. The results demonstrated that the transfer length predicted by the fine FE model with a friction coefficient of α = 0.3 for high pretension is in good agreement with the measured values and the analytical solutions. The consistency between the analytical solution and FE simulation not only further proves the reliability of composite beam theory but also demonstrates the importance of the bond-slip relationship in predicting the transfer length of pretensioned concrete members prestressed with FRP tendons.

Experimental, numerical and analytical investigation of bending performance of bolted demountable composite beams with profiled steel decking

This paper presents the results of a detailed experimental, numerical and analytical study to investigate the flexural bending performance of prefabricated demountable composite beams (PDCBs) with bolted shear connectors. Four full–scale tests were carried out for two profiled steel decking configurations (parallel and perpendicular to the steel section) with two different degrees of shear connection. The experimental results were used to validate a numerical simulation model established by the ABAQUS platform. A detailed parametric study was then performed using the validated numerical model to evaluate the effects of using different numbers of bolted shear connectors. The experimental results show that the final failure modes of the demountable composite beams are the same as conventional composite beams using welded shear studs, and the demountable composite beams behavior is ductile. The results of a comparison of load carrying capacity and elastic stiffness of the demountable beams calculated using the analytical equations for conventional composite beams against the experimental and numerical simulation results for the demountable composite beams confirm that the conventional composite beam theory can be used for the demountable composite beams. However, the experimental results indicate that longitudinal cracking in the grout between concrete slabs along the steel beam can happen, due to unsymmetrical location of the shear studs. Anti-cracking mesh would be necessary in practical applications for crack control.

Monitoring of Allowable Bending Stress Overload in Glass‐Fiber‐Reinforced Polymer Composites Using Magnetostrictive Fe–Co Fibers

For the safe operation of glass‐fiber‐reinforced polymer (GFRP) laminates, evaluating the applied stress and the health of composite structures is crucial. Magnetostrictive materials are functional materials that can be applied to structural health monitoring as sensor materials. Herein, a method for detecting whether the maximum stress of GFRP laminates under bending exceeds the allowable stress using magnetostrictive fibers is proposed. First, magnetostrictive Fe–Co alloy fibers are embedded in GFRP laminates. Then, four‐point bending tests are conducted. Magnetomechanical coupled modeling based on the composite beam theory is then applied to the experimental results. The effects of the position of Fe–Co fibers on the magnetostrictive behavior and mechanical properties of the prepared composites are evaluated. A concept for monitoring the relationship between the maximum bending stress and the allowable stress of the composite materials is proposed.

The appropriacy of the analytical models for calculating the shear capacity of cross-laminated timber (CLT) under out-of-plane bending

Rolling shear, an inherent property of cross-laminated timber (CLT) due to the weak shear strength of cross layers, is always the determinant of load-bearing capacity for short-span CLT members subjected to out-of-plane bending. Many analytical models were developed to calculate the shear capacity of CLT members. Because of the difficulty to precisely model the complicated shear failure mechanisms, however, no model was universally accepted. This paper aims to study the appropriacy of the commonly used analytical models, namely, composite beam theory, shear analogy method, Gamma method, and simple beam theory, by tests and analytical calculations. A composite beam theory-based simplified method was proposed. Three-point loading tests for the short-span CLT panels with 3 and 5 layers were conducted, and the shear capacities of the test specimens were calculated using the above-mentioned analytical methods. Shear strength and modulus of cross layers of the test specimens, which were used as the inputs for calculating the shear capacities, were tested by modified planar shear method. By comparing the calculation results obtained from different analytical models and the test results as well, it can be concluded that: (1) composite beam theory, shear analogy method, and the proposed simplified method give almost the same calculation results, therefore, the proposed simplified method can be used as the replacement for the other models; (2) Gamma method is more appropriate for calculating the shear capacity in case the input shear strength is determined by planar shear test; (3) the simple beam theory that is used in CSA O86 provides significantly lower shear capacity predictions than those obtained by the other methods.

Flexural performance of Metal-Reinforced glass Beams: Numerical and analytical investigation

Reinforced glass beam (RG beam) is a promising but under-researched structural typology. Existing analytical models for RG beams have provided unsafe residual resistance predictions, indicating the need for better theoretical methods.As a basis for the theoretical model, this paper conducts a numerical study and validates the applied finite element method (FEM) with previous experiments. To improve computational efficiency, a simplified 2D modelling method is proposed that applies equivalent material models for both laminated glass and adhesive layers, for in-plane flexural behaviour. The applied 2D finite element (FE) model is verified against experimental data.The effects of reinforcement ratio, reinforcement material, adhesive performance, and shear span to depth ratio on the in-plane flexural performance of the RG beam are then extensively investigated using the proposed FEM model. Numerical results help understanding the failure mechanisms of different failure modes, with an emphasis on the significance of adhesive behaviour.Adopting the composite beam theory, an analytical method is proposed to address different limit states of the RG beams and is validated against the FEM and experimantal results.

Mechanism and Application of Layered Grouting Reinforcement for Fractured Coal and Rock Roadway

This paper takes the ZF3806 working face of Shuiliandong Coal Mine in Binxian County, Shaanxi Province as the engineering background. Aiming at the problems of the development of surrounding rock cracks and roof breakage encountered in the process of roadway excavation and support and based on the composite beam theory, the method of layered grouting reinforcement of roadways is proposed according to the deformation and failure of the roadway roof and the internal drilling conditions. At the same time, combined with the splitting grouting mechanism, the roadway is strengthened and supported by layered grouting of “shallow bolt grouting + deep cable grouting”. The “shallow” and “deep” form a complete and stable composite beam support structure. After grouting, the bending moments of “shallow” and “deep” support beams decrease by 20.78 × 106 N·m and 26.50 × 106 N·m, respectively. The support scheme is applied to the field test, and the grouting effect is analyzed and monitored. The research results show the layered grouting support scheme of “shallow bolt grouting + deep cable grouting” can significantly improve the structural integrity of the roadway roof. The displacement of the two sides is within the controllable range, and the support role of the bolt and cable is entirely played through grouting. The roof displacement of the roadway is reduced by 65% on average, and the bolt failure and steel belt fracture are significantly reduced, which effectively controls the deformation and damage of the roadway and reduces the maintenance cost of the roadway while ensuring safe mining. The study’s findings could be useful in treating broken surrounding rock in other coal mine roadways.

Two-dimensional model for composite beams and its state-space based mixed finite element solution by DQM

Most one-dimensional composite beam theories are based on simplified shear deformation assumptions, or even ignore shear deformation, which have limitations in analyzing multilayer beams with significant material differences. Therefore, this paper firstly proposed a two-dimensional analytical model for composite beams through the equivalent transformation of cross section. Based on the mixed variational principle, the state equations are then derived by finite element meshing and interpolation along the length of the beam, with nodal displacements and their energy-conjugated stresses as state variables. Subsequently, the differential quadrature method (DQM) is introduced to solve the equations and a two-dimensional analysis method for composite beams is established. Due to the use of displacements and stresses as fundamental variables in the state equations, various transfer characteristics of displacements and stresses at the interlayer interfaces of composite beams can be conveniently handled. This method is finally verified by numerical examples of steel-concrete composite beams and concrete beams with corrugated steel webs. Since no assumptions of displacement and stress distributions along the thickness of beams are required, the present method can provide benchmarks for various one-dimensional beam theories.

Exact series solutions of composite beams with rotationally restrained boundary conditions: static analysis

The structural performance of composite beams is sensitive to load distribution as well as actual boundary conditions. Although the composite beam theory has been solidly established and exact solutions have been readily developed for various loading and boundary conditions, almost all of them are limited to classical boundary conditions (free, pinned and clamped) and there has been little discussion about the actual support conditions in real structures. The general representation of actual boundary conditions can be defined as rotationally restrained edges. In this research, an analytical model with exact series-type solutions was developed for composite beams with rotationally restrained edges. The model and displacement solutions were validated by other analytical methods and numerical results. The influence of rotational and end-slip restraints was investigated. It was found that the deflection and interface slip of composite beams are highly affected by both restraints introduced by the actual boundary conditions. The current model can be used as a benchmark for future design methods considering the realistic boundary conditions of composite beams.

Evaluation of Laminated Composite Beam Theory Accuracy.

Carbon fiber-reinforced polymer (CFRP) has been widely implemented in electric vehicle bodies and aircraft fuselage structures. The purpose of CFRP is to reduce the weight and impart rigidity in the final product. A beam structure is typically used to bear the structural load, and the rigidity of the beam can be changed by arranging the laminated fibers at different angles. In this study, a composite I-beam is used as an example in engineering components. Because the theoretical model of the superimposed composite I-beam is established, the theoretical formula is based on the theoretical assumptions of the two-dimensional composite beam, and is combined with the traditional composite plate theory to analyze the maximum bending stress, strain, and deflection. During the theoretical derivation, it is assumed that the flanges of the I-beams are divided into narrow and wide flanges. The beams are considered as structures of beams and flatbeds. When a narrow flange is loaded in the side, the wide flange has no lateral deformation, and the lateral moments are neglected. Therefore, the accuracy of this formula needs to be verified. The purpose of this study is to verify the accuracy of theoretical solutions for the deflection and stress analysis of composite beams. A finite element analysis model is used as the basis for comparing the theoretical solutions. The results indicate that when the aspect ratio of the beam is >15, the theoretical solution will have better accuracy. Without the addition of the material, when 0° ply is placed on the outermost layer of the flange of the nonsymmetric beam, the effective rigidity of the beam is increased by 4–5% compared with the symmetrical beam. The accuracy range of the theoretical solution for the composite beams can be accurately defined based on the results of this study.

Evaluation of the mechanical contribution of wood degraded by insects in old timber beams through analytical calculations and experimental tests

Existing timber structures are often affected by peripheral degradation due to insect attack. The contribution of the degraded areas of the beam cross-section to the load bearing capacity is usually neglected, leading to an over-conservative approach to the structural verification of historic wooden constructions. This work analyses timber elements dismantled from a nineteenth century building by means of a comprehensive geometrical survey, the evaluation of the degraded portion of the cross-section and by destructive bending tests. An iterative procedure based on the linear elastic theory of composite beams was set up to define a reduction coefficient of the mechanical properties of degraded wood, in order to include the contribution of the degraded parts during the structural calculation. The analytical procedure proved to be effective only for timber elements without localised major defects or anomalies, such as woodworking or internal decay, which may alter the linear elastic flexural behaviour of the beam. The values obtained of the reduction coefficient ranged from 1.7 to 5.0 and were successfully verified by numerical models.

Zig-zag theory for concrete beams with corrugated steel webs

Owing to the large difference between the longitudinal and transverse stiffness of corrugated steel webs (CSWs), concrete beams with CSWs are idealized as sandwich beams with an orthotropic core in this study. A zig-zag displacement is then assumed to describe the deformation along the beam thickness along with a layer-wise parabolic distribution of the transverse shear stress. A new composite beam theory for a concrete beam with CSWs is finally developed, and the governing equations are derived using the variational principle of mixed energy. The transverse shear stress in the proposed theory automatically satisfies the traction-free condition at both the top and bottom surfaces of the beam. The continuity conditions of the displacements and shear stresses at the interfaces between two adjacent layers are also maintained, and thus there is no need to introduce a shear correction factor. Finally, analytical solutions for CSWs under four common boundary conditions are derived. These solutions are verified by numerical methods, and the results show that the proposed theory in this study can predict the deformation and stress of the concrete beams with CSWs more accurately.

Scaling the dynamic response and stability of composite hydrodynamic lifting surfaces

Imperfectly scaled models are commonplace in aerodynamics and hydrodynamics because few facilities can meet all the flow and structural scaling requirements. The objectives of this work are to (1) derive and numerically validate scaling relations for the steady-state and dynamic hydroelastic response and stability of hydrodynamic composite lifting surfaces and (2) to investigate the effect of imperfect scaling on the steady-state and dynamic response, as well as hydroelastic stability of said surfaces. We derive proper scaling laws and validate them through numerical simulations using unsteady potential flow and composite beam theory. We investigate the prediction of inception of a new, low-frequency mode that only develops at sufficiently high speeds using scaled models. We demonstrate scaling effects on the modal frequencies, damping coefficients, and hydroelastic instability boundaries by comparing cases with fully enforced scaling laws and cases with relaxed similarities. Using the same material for both the prototype and reduced length-scale models results in imperfect scaling; the steady-state and dynamic hydroelastic responses are not scaled, and smaller length-scale models exhibit delayed hydroelastic instabilities. The conclusion is that using appropriate materials for model scale tests to satisfy Cauchy number similarity is necessary for similar steady-state response, but dynamic similarity additionally requires similar solid-to-fluid added mass ratio. Proper scaling allows one to accurately interpret and assess the performance and stability of full-scale flexible composite lifting surfaces such as foils, propulsors, turbines, fins, rudders, energy saving devices, and energy harvesters.