Location Of Neutral Axis Research Articles

Elastic-Plastic Analysis of Bending Moment – Axial Force Interaction in Metallic Beam of T-Section

This study derives kinematic admissible bending moment – axial force (M-P) interaction relations for mild steel by considering elastic-plastic idealizations. The interaction relations can predict strains, which is not possible in a rigid perfectly plastic idealization. The relations are obtained for all possible cases pertaining to the locations of neutral axis. One commercial rolled steel T-section is considered for studying the characteristics of interaction curves for different models. On the basis of these interaction curves, most significant cases for the position of neutral axis which are enough for the establishment of interaction relations are suggested.

Kalman Filter based Neutral Axis tracking for damage detection in composites structures under changing axial loading conditions

Structural Health Monitoring (SHM) systems allow early detection of damage which allows maintenance planning and reduces the maintenance cost.Several researchers have proposed use of Neutral Axis (NA) location as a damage sensitive feature. It has been shown that through proper signal processing, NA location is insensitive to measurement noise and ambient temperature changes. This paper presents a methodology for successful NA tracking under changing axial loading conditions. The novel methodology is validated using numerical data as well as experimental results.This paper demonstrates the development of a Kalman Filter (KF) based NA tracking strategy under different loading conditions. The methodology was employed on a composite beam instrumented with fiber optic strain sensors. The stable NA tracking under changing loading conditions allows the application of the NA as a damage sensitive feature. The change in NA location is used to detect delamination in the beam. The method has been validated through a numerical model and experiments. The results show that the novel formulation of the KF for NA tracking allows more robust use of NA location as a damage sensitive feature in a wider range of applications.

Partial-composite behavior of sandwich beams composed of fiberglass facesheets and woven fabric core

In this study, thin-walled sandwich composites made of glass fiber-reinforced polymer (GFRP) facesheets and a three-dimensional (3D) woven fabric core were studied. A total of 30 small-scale sandwich beam specimens were manufactured across six unique beam varieties with dimensions of 50 mm in width, and 200 or 350 mm in length to be tested under four-point bending up to failure. The load-deflection behavior, load-strain behavior, moment-curvature behavior, and neutral axis location were analyzed. Based on the test results, the flexural stiffness, shear stiffness, core shear modulus of the sandwich beams were calculated. Also, an analytical model is presented to consider the effect of core shear modulus on deformation and composite action of the test specimens. The model is capable to quantify the degree of composite action based on the geometry and material properties of sandwich beams. Overall, the sandwich beams displayed a partial-composite behavior raging from 15% to 91% of full-composite behavior, which was a function of the relative stiffness of the facesheets and the core plus the length of the shear span. It was shown that compatibility between the mechanical properties of the facesheet and core is a key factor in optimizing sandwich panels made of the core. The results will be used for the design of thin-walled sandwich liners for the rehabilitation of underground infrastructure including existing highway culverts and large diameter drainage systems.

Flexural behavior of high-strength steel hybrid composite beams

In this study, hybrid utilization of high-strength steel in composite beams was proposed in order to maximize their flexural capacity and full-scale testing was conducted in two phases to investigate their flexural behavior. In fabricating specimens, high-strength steels were utilized for the bottom flange while normal-strength steels were used for the top flange and the web. In Phase I testing, however, all the high-strength steel bottom flange specimens were not able to reach their plastic moment by about 10–15% due to unexpected longitudinal shear failure along the beam axis, although sufficient shear studs were provided for full composite behavior and the plastic neutral axis location was limited within 15% of the total depth of the composite beam section. The specimens in Phase II testing designed with additional shear reinforcements showed no longitudinal shear cracking and developed their plastic capacity with reasonable deformability as intended in design. This implies that, different from the design of conventional composite beams, checking the longitudinal shear strength of composite concrete slab is crucial when designing hybrid composite beams utilizing high-strength steels. The nominal longitudinal shear strength was well predicted by the shear-friction based models in ACI 318-14 and AASHTO LRFD. The test results of this study show that when the limitation on the depth of the plastic neutral axis set forth by Eurocode 4 is satisfied along with sufficient longitudinal shear strength, the plastic stress design method can still be applied to the design of hybrid composite beams utilizing high-strength steels whose nominal yield strength is as high as 650 MPa.

Theoretical and experimental considerations on the neutral axis of wood beams with a hole in different locations

Abstract Holes contribute to the non-homogeneous nature of solid wood and shift the neutral axis of wood beams away from the centroid. Based on the plane-section assumption and idealized trapezoidal distribution, new calculating formulas will be presented in terms of the location of neutral axis for clear beams and wood beams with a hole at the center, compression zone and tension zone. To verify the results of theoretical analysis and formulas, four-point bending experiments of wood beams were performed by a digital image correlation (DIC) technique. There is a reasonable agreement between calculated and experimental results with a hole at the center or in the compression zone of the beams. Concerning a hole in the tension zone, on the other hand, the calculated locations of neutral axis are not in agreement with the experimental results, due to the plastic behavior on both the compression and tension zones of the beams in the inelastic stage.

Kalman filter based neutral axis tracking in composites under varying temperature conditions

Structural Health Monitoring (SHM) systems allow early detection of damage which allows maintenance planning and reduces the maintenance cost. There is a lot of active research in the area for SHM of civil and mechanical structures. The SHM system should be low cost, suitable for continuous monitoring, able to detect small levels of damage, and insensitive to ambient loading, changes in ambient temperature, and measurement noise. Change in Neutral Axis (NA) has been used by several researchers as a damage sensitive feature. It has been shown to be sensitive to small levels of damage, and independent of the ambient loading. This paper aims at showing the insensitivity of the NA to ambient condition changes. This paper demonstrates a methodology for overcoming the effect of temperature on the accurate tracking of the NA. A multi-rate Kalman Filter (KF) has been used for data fusion from temperature and strain sensors. The paper shows that through the use of KF one can easily compensate the effect of temperature on the observability of the NA. The work applies the methodology on a finite element (FE) model of a glass fiber- epoxy composite as well as validation through actual experiments. Based on the results obtained, it is apparent that the NA tracking using KF allows stable estimation even in changing temperature conditions and as such shows that NA location can indeed be used as a damage sensitive feature.

Elastic-plastic-creep response of multilayered systems under cyclic thermo-mechanical loadings

The modified Ohno and Abdel-Karim nonlinear kinematic hardening model considering cyclic hardening and creep effect are developed to investigate the deformation and residual stress of multilayered systems subjected to cyclic thermal and mechanical loads. Results reveal that, if the creep behavior is considered, significant stress relaxation takes place during about the first several cycles, and the accumulated strain of multilayered systems under deformation-controlled loads finally remains constant, which leads to shakedown. Remarkable changes of the residual stress, location of neutral axis and curvature of Si-Cu beams are observed during about the first 100 cycles. Therefore, the proposed model can be used for the engineering design of multilayered systems under complex loads.

Application of Kalman Filter based Neutral Axis tracking for damage detection in composites structures

Structural Health Monitoring (SHM) systems allow early detection of damage which allows maintenance planning and reduces the maintenance cost. The SHM system should be low cost, suitable for continuous monitoring, able to detect small levels of damage, and insensitive to ambient loading, changes in ambient temperature, and measurement noise. Neutral Axis (NA) location is a function of the condition of the structure alone and may be used as a damage sensitive feature. It has been shown that through proper signal processing, NA location is insensitive to measurement noise and ambient temperature changes. This paper aims at validating the use of NA as a damage sensitive feature through experimental study.This paper demonstrates the use of multi-rate Kalman Filter (KF) for accurate estimation of NA under different loading conditions. The methodology was employed on a composite beam instrumented with fiber optic strain sensors. Delamination was introduced in the beam and then progressively increased. The beam was subjected to different loading and temperature conditions for the different damage scenarios. The measured strains were then used for NA tracking. The results show that indeed the NA location may be used as a damage sensitive feature.Some of the loading scenarios were difficult to realise in the laboratory, so these loading scenarios were applied on a validated Finite Element (FE) model of the composite beam. The results indicate that under these dynamic loading scenarios, NA may be used for SHM. Based on the results it can be concluded that KF based NA tracking may be applied to structures for in-service SHM.

Flexural behavior of rectangular FRP-tubes filled with reinforced concrete: Experimental and theoretical studies

This paper presents experimental and theoretical investigations on the flexural behavior of rectangular concrete-filled fiber-reinforced polymer (FRP) tube (CFFT) beams with steel rebar. Seven full-scale CFFT beams, 3200mm long and 305×406mm2 cross section, were tested under a four-point bending load and were compared to two control steel-reinforced concrete (RC) beams. The CFFT beams had the same flexural steel reinforcement, but they had different wall thicknesses of filament-wound FRP tubes. The experimental results indicate an outstanding performance of the CFFT beams in terms of strength and energy absorption compared to the RC beams since their flexural strength and energy attained values 344% and 1052% higher than that of the RC beams, respectively. A strain compatibility/equilibrium model was developed to predict the moment-curvature response of the CFFT section addressing the issue of confinement and tension stiffening of concrete. The analytical results match well the experimental results in terms of moments, curvature, strains, and neutral axis location. Based on the model, the deflection can be predicted by integrating the curvatures along the span of the flexural member.

Multi-parametric MINLP optimization study of a composite I beam floor system

This paper deals with a comparative study of an optimal design regarding composite steel and concrete floor structures based on the performed multi-parametric mixed-integer non-linear programming (MINLP) approach, and Eurocode specifications. The optimization models COMBOPT (COMposite Beam OPTimization) were developed and cost optimizations of the structure alternatives were performed. A series of MINLP optimizations were executed over a wide range of various design parameters: different material unit prices, hourly labour costs, imposed loads, structure spans, steel and concrete grades, welded and standard steel sections, plastic and elastic cross-sectional resistances, different positions of the neutral axis and different locations of the centre of gravity axis of the transformed (all steel) section.The Modified Outer-Approximation/Equality-Relaxation (OA/ER) algorithm was applied. The minimal self-manufacturing costs of the structure, steel and concrete grades and standard sizes were obtained through each individual MINLP optimization. All the results were analysed and compared. Comparative diagrams and a recommended design for a composite floor system were determined. In addition, this study answered some questions regarding the influence of unit prices on the optimal design, the most suitable position of the neutral axis, the competitive spans of the structures with welded and standard steel sections, the competitiveness of the plastic cross-section resistance when compared to the elastic resistance, the spans and loads where the ultimate and the serviceability limit states are predominant and the adequate location of the centre of gravity axis of the transformed (all steel) section.

Nonlinear 3PB and 4PB Flexural Behavior and Softening Localization for Epoxy Resin E 863 Using Digital Image Correlation Technique

The effect of local strain and stress distribution in the polymeric material under out of plane loading is of interest in many applications. Flexural testing of the polymer resins is necessary to evaluate their mechanical behavior. In this paper, the flexural response of polymer resin Epon 863 mixed with the curing agent EPI-CURE 3290 using a 100/27 weight ratio has been investigated in threepoint bending (3PB) and four-point bending (4PB) at different strain rates. Beams with different lengths and span to depth ratios were tested. Results show a higher flexural strength for 4PB than 3PB. Strain fields within the polymer beam structure were determined using the digital image correlation (DIC) technique to study the evolution of softening localization in 3PB and 4PB setups. Results show that the length of the softening localization is less than half of the thickness throughout the loading. The DIC technique was used to obtain the location of the neutral axis in the nonlinear stage of the material behavior. Results indicate the nonlinear variations of the neutral axis location for epoxy resin Epon E 863. The results show that the DIC technique can accurately characterize the material response of an epoxy resin for flexural loading.

Highly bendable characteristics of amorphous indium–gallium–zinc-oxide transistors embedded in a neutral plane

The electromechanical response of an amorphous indium–gallium–zinc-oxide (a-IGZO) thin-film transistor (TFT) fabricated on a polyimide substrate was investigated as a function of the neutral axis location and strain history of the bending system. Here, we demonstrate the pronounced bending characteristics of a-IGZO TFTs and their backplane under extreme mechanical strain when they are embedded in a neutral plane (NP). After being subjected to tensile stress, the devices positioned near the NP were observed to function well against a cyclic bending stress of 2 mm radius with 100,000 times, while TFTs farther from the neutral surface exhibited modified electrical properties.

The neutral axis location for structural health monitoring: an overview

Structural health monitoring (SHM) is the process of continuously or periodically measuring structural parameters over time and the transformation of the acquired data into information about the actual structural behavior. The main goal of SHM is to provide quantitative and actionable information to infrastructure managers on a system-wide level. However, to achieve this goal, damage sensitive universal parameters need to be researched, identified, and implemented into SHM processes and data analysis. The neutral axis location has been identified as a potential parameter for damage detection, performance evaluation, and condition assessment of beam-like structures. This paper is intended to serve as a reference for researchers who are interested in the state of the art in evaluation of the neutral axis location, facts about the neutral axis behavior, and challenges associated with using the neutral axis for SHM purposes. Studies of the neutral axis in laboratory settings, controlled on-site testing, and on real structures in on-site conditions are presented and discussed. The main difficulties in using the neutral axis location for SHM purposes that are identified in this paper are: (1) its sensitivity to environmental effects such as temperature, humidity, and loading positions, (2) its natural variation in healthy cross-sections, (3) quantification of its sensitivity to damage, i.e. its damage detection capabilities in terms of the damage size and its distance from sensors, and (4) correlation between the neutral axis location and the capacity, performance, and condition of the monitored structure. The proof of concept has been provided with numerical modeling, and in the laboratory, and to some extent through controlled testing; however, a general on-site validation still remains a major challenge.

Modified Stoney's Equation for Evaluation of Residual Stresses on Thin Film

In the article, a simple method for the modification of the Stoney's equation was presented. The Stoney's equation is proposed from the assumption of equi-biaxial residual stresses in thin films. In this present method, biaxial stresses are different in x-axis and y-axis on thin film. The location of neutral axis depends on the material parameters and the film thickness. The finite element method (FEM) was used to simulate the thermal stress on the thin film. The results of the modified methods are compared with the results of FEM and other literatures. The present method is more accurate than the Stoney's equation in the evaluation of such films.

Postbuckling and nonlinear free vibration of size-dependent prestressed FG nanobeams resting on elastic foundation based on nonlocal Euler-Bernoulli beam theory

AbstractVibrations of micro/nanobeams that are subjected to initial stresses due to mismatch between different materials or thermal stresses are important in some devices. The present study is an attempt to present nonlinear free vibration of simply supported size-dependent functionally graded (FG) nanobeams resting on elastic foundation and under precompressive axial force. It is assumed that the material properties of FG materials are graded in the thickness direction. The partial differential equation of motion, which is simplified into an ordinary differential equation using the Galerkin method, is derived based on Euler-Bernoulli beam theory, von Karman geometric nonlinearity, and Eringen’s nonlocal elasticity theory. The final ordinary differential equation is solved using the variational iteration method. The effects of geometrical parameters, small-scale parameter, elastic coefficient of foundation, precompressive axial force, and neutral axis location on dimensionless nonlinear natural frequencies are investigated. In this study, the buckling and postbuckling behavior of FG nanobeams and the effect of neutral axis location on buckling behavior are investigated as well. Results show that the effects of small scale on FG nanobeam frequencies change with the aspect ratio, the values of radius of gyration, and the values of compressive axial force. It is also found that the influence of neutral axis location on the nonlinear fundamental frequency of prestressed FG nanobeams is more than that of prestressed FG nanobeams resting on elastic foundation.

Effect of Island Configuration and Neutral Axis Location for Mechanical Bending Strain on a-IGZO Thin Film Transistors

In the electronic-device market, flexible displays using plastic substrates are considered to be one of the most promising alternatives for realizing the new functional needs of flat-panel displays. They are largely composed of a display element, thin film transistor (TFT) backplane, and a flexible substrate; the displays are an integrated system of these units. This means that the mechanical flexibility of each element to the physical stress while preserving the electrical stability is quite important because they reliably enable the overall flexibility of the integrated bending system. In this research, we report the effect of electromechanical and mechanical strain on coplanar amorphous indium-gallium-zinc-oxide (a-IGZO) thin film transistor regarding to the structural design of the device and the neutral axis location in bending. Here we show the highly reliable bending feature of the island structured (IS) device and its backplane after being subjected to an extreme cyclic bending stress [Fig.1]. The coplanar IS TFTs fabricated on polyimide (PI) substrate exhibit excellent bendability for an cyclic bending of 100,000 cycles with a radious less than 2 mm without a remarkable change of electrical properties although the coplanar device with the conventional structure shows an significant electrical failure at the same mechanical strain [Fig.2]. Competitive study of the device stability characterized by the neutral axis also reveals the strong effect of neutral plane (N.P) as well as the location from N.P for bending stress, which is also greatly assigned to the device configuration. That is, when the device is positioned close to the neutral plane using the sandwiched structure, the electrical characteristic of TFTs is quite stable for the induced mechanical bending without relying on the device configuration [Fig.3]. As the device is positioned apart from the neutral plane, the electrical performance is obiously degraded in the position about 30 μm from N.P on the device with the conventional structure as a function of bending cycles [Fig.4]. The onset of crack strain is also closely corresponds to that of the electrical failure of the device. On the otherhands, figure 4 clearly reveals that the positioning margin in the neutral zone is remarkably enhanced after emolying IS structure on a-IGZO devices for the extreme bending stress. IS TFTs achieved the stable electrical characterisic such as the mobility (μ) change less than 10 % compared to that of inital value (μo) for an cyclic bending of 100,000 cycles even they are subjcted to the mechanical tensile strain over 2.5 % without the cracks, which is corresponding to the device position in 50 μm far from N.P with a radius of 2 mm [Fig.4]. As a result, IS TFTs enable to bend until the radius of 1 mm thanks to the bendability enhancement, preserving μ decrease less than 20 % from μo. To our knowledge, this is one of the highest bendable feature adopting the inorganic TFT and its backplane which is also comparable with that of flexible organic device. Since the mechanical flexibility of the backplane component is one of key elements to achieve the integrated bending system as we discussed eariler, this result shows unique potential of IS TFT and its backplane to open new form factor flexible displays such as folding or rolling displays. Figure 1

Effect of Island Configuration and Neutral Axis Location for Mechanical Bending Strain on a-IGZO Thin Film Transistors

The effect of electromechanical and mechanical strain was studied on amorphous indium-gallium-zinc-oxide (a-IGZO) thin film transistor regarding to the structural design of the device as well as the location from neutral plane (N.P) for bending stress. Here we show a highly reliable bending feature of the island structured (IS) device and its backplane against the mechanical strain after being subjected to an extreme tensile cyclic bending stress. The IS TFTs fabricated on polyimide (PI) substrate exhibit an pronounced bendability for an cyclic bending of 100,000 cycles with varying radii to a radius less than 2 mm with the electro-mechanical integrity. The onset of crack strain also closely corresponds to that of the electrical degradation of the device. The backplane array composed of IS TFTs clearly reveals that the island configuration remarkably reduce the bending stress accumulation on the sheets of inorganic stacked layers along to the uniaxial on plastic substrate.

Effect of measurement uncertainties on strain-based damage diagnostics for highway bridges

Diagnostic load rating of highway bridges using distributed strain transducers is one of the more prominent strategies applied for both periodic and continuous monitoring of highway bridges. Techniques for load rating structures using experimental measurements of neutral axis locations, girder distribution factors, and dynamic increase factors have been suggested for structural health monitoring and damage detection applications. However, practical considerations related to the influence of measurement uncertainties on the reliability of these diagnostic measures in the presence of damage have only been examined recently. This paper extends uncertainty propagation formulae previously derived for neutral axis measurements to girder distribution factors. The significance of measurement uncertainties on damage-sensitive features are then explored using experimental data from a real bridge subjected to progressive, prescribed damage. The experimental results suggest that both apparent neutral axis locations and girder distribution factors exhibit sensitivity to the damage mechanisms introduced that exceeds the measurement uncertainty. In addition, girder distribution factors are found to demonstrate the ability to locate the damage. Comparisons with finite element simulations underline the challenges associated with faithfully modeling the effects of structural damage and emphasize the need for continued full-scale validation of structural health monitoring approaches on real structures.

Analytical investigation of hybrid composite precast beams with modified strain compatibility for entire history of nominal flexural capacity

SummaryThe strain compatibility documented in Chapter I of the American Institute of Steel Construction 360‐10 (AISC, 2010) was modified to provide accurate analytical solution for hybrid composite precast beams. In the proposed method, locations of neutral axis of the section are investigated to formulate all possible equilibrium equations of stress fields of composite sections. The only neutral axis satisfying all stress fields is then found for composite sections for entire loading history including yield and maximum load limit state and between those limit states. Finally, the nominal moment capacity of hybrid composite precast beam is calculated based on the correct neutral axis. Experimental study was conducted to verify the accuracy of the proposed method. The test results for hybrid composite precast beams agreed very well with the analysis results. The capacity difference between them is less than 4.8%. This study also compares the proposed design method with the conventional strength addition method, showing that the conventional method underestimated structures leading to over‐design. It was found that the new approach predicted the behaviors of hybrid composite precast beams more accurately than the conventional methods. Copyright © 2015 John Wiley & Sons, Ltd.

Detecting minute damage in beam-like structures using the neutral axis location

The neutral axis is the curve within a cross-section of a beam under loading at which the normal stress and strain vanish. The neutral axis is correlated with the centroid of stiffness which depends on material and geometric properties of the beam cross-section. The centroid is sensitive to changes in area and stiffness of the cross-section, i.e. damage. The neutral axis is a universal parameter in beam-like structures, and since the majority of structural systems is based on beams, the neutral axis location can be used as a damage sensitive feature in a variety of structures. In this paper the sensitivity of the neutral axis location to minute damage is studied through a test structure with induced artificial damage. The structure was equipped with long-gauge fiber-optic strain sensors in three cross-sections, one with partial delamination in the concrete, one with a small crack, and one with no damage (healthy). The structure was monitored during lifting and transport, and dynamic tests were performed in close-to-real conditions. A detailed uncertainty analysis was performed both on the evaluations of the centroid location and the neutral axis measurements. A Z-score hypothesis test was used to set thresholds and determine whether the damage was detected or not. The results show that the neutral axis location is sensitive to minute damage, and that the latter can be detected within the uncertainty limits in on-site conditions.