Variable Axial Load Research Articles

Analytical simulation of seismic collapse of RC frame buildings

Application of a fibre-element nonlinear modelling technique for seismic collapse capacity assessment of RC frame buildings in comparison with conventional lumped plasticity models is investigated in this paper. Constitutive material models of concrete and steel for fibre elements are adopted to enable simulation of the loss in vertical load carrying capacity of structural columns. Inclusion of the nonlinear second order P−Δ effects accelerated by degrading behaviour of steel and concrete materials in the fibre model allows prediction of the sidesway mode of collapse. The model is compared with nonlinear lumped plasticity models in which stiffness and strength degradation is replicated through degrading parameters in structural components. Static cyclic analyses of an example cantilever column and a portal frame indicate that the variation of axial loads in columns may result in accelerated degradation and failure of structural components which is not taken into account by lumped plasticity models. Moreover, incremental dynamic analysis of a ten-storey RC frame shows that the lumped plasticity model may overestimate building collapse capacity when vertical failure of structural components occurs prior to sidesway instability.

Chaotic motion of a parametrically excited microbeam

The complex sub and supercritical global dynamics of a parametrically excited microbeam is investigated with special consideration to chaotic motion. More specifically, for a microbeam subject to a time-dependent axial load involving a constant value together with a harmonic time-variant component, the bifurcation diagrams of Poincaré sections of the system near critical point are constructed when the amplitude of the longitudinal load variations is varied as the control parameter. In terms of modelling and simulations, the small-size-dependent potential energy of the system is constructed by means of the modified couple stress theory and constitutive relations. Continuous expressions for the kinetic energy and the energy dissipation mechanism are also constructed. A transformation to a high-dimensional reduced-order model is performed via use of an assumed-mode method as well as the Galerkin scheme. A direct time-integration method is employed to solve the reduced-order model. For different cases in the sub and supercritical regimes, but close to the critical mean axial force, the bifurcation diagrams of Poincaré sections are constructed as the amplitude of the axial load variations is chosen as the bifurcation parameter. The complex dynamical behaviour of the system is analysed more precisely through plotting time traces, fast Fourier transforms (FFTs), Poincaré sections and phase-plane diagrams.

Behavior of Rectangular Reinforced-Concrete Columns under Biaxial Cyclic Loading and Variable Axial Loads

AbstractThe behavior of reinforced-concrete (RC) elements subjected to axial loading variation in conjunction with cyclic biaxial bending is recognized as a very important research topic with a reduced number of experimental results available. Six full-scale RC rectangular columns were tested and analyzed to study the effects of variable axial load on the hysteretic behavior of RC building columns under biaxial horizontal loading. The experimental results are presented and discussed in terms of damage evolution, global hysteretic behavior, stiffness degradation, columns’ capacity, and energy dissipation. The global findings revealed the significant effects of the axial load variation on the hysteretic behavior of RC columns.

Performance of reinforced concrete columns under bi-axial lateral force/displacement and axial load

Accurate and realistic assessment of the performance of columns in general and those in critical locations that may cause progressive failure of the entire structure, in particular, is significantly important. This performance is affected by the load history, pattern and intensity. Current design code does not consider the effect of load pattern on the load and displacement capacity of columns. In the study reported here, monotonic material models, cyclic rule, and plastic hinge models have been utilized in a fiber-based analytical procedure, validated against experimental data. Comparison of the analytical predictions and experimental data, through moment–curvature and force–deflection analyses, confirmed the accuracy and validity of the analytical algorithm and models. The analytical model was then used in a parametric study considering the effects of axial load variation and lateral force/displacement paths on the flexural strength and energy dissipation capacity of reinforced concrete columns.

Numerical Modelling of RC Columns Subjected to Biaxial Horizontal Loading and Variable Axial Load

Annumerical study of RC columns subjected to variable axial load in conjunction with biaxial cyclic bending are presented in this article. The numerical models were built to simulate the response of all specimens using the computer program SeismoStruct and adopting three different modelling strategies, such as lumped plasticity and distributed plasticity (based in displacements and forces formulations) that were adopted in order to obtain the real behaviour of the RC columns. The efficiency of each modelling strategy is evaluated through the comparison between the experimental global hysteretic behaviour, stiffness degradation, columns capacity and energy dissipation and the numerical results.

Effect of earthquake‐induced axial load fluctuations on asymmetric frame–wall–rocking foundation systems

SummaryFluctuations in axial load imposed on a rocking footing will affect its moment capacity, the shape of its moment–rotation hysteresis, and potentially the system's seismic performance. Structural asymmetry increases the likelihood of axial load variation during earthquake excitations. To investigate this issue, a unique centrifuge testing program was carried out on low‐rise frame–wall–rocking foundation systems. In this paper, the seismic behaviors of asymmetric and symmetric models from this test program are systematically compared. Experimental results reveal that placing the lateral force resisting shear wall outboard produces significant axial load fluctuation, which in turn greatly deteriorate the lateral load‐carrying capacity of a foundation rocking dominated frame–wall system, particularly in its weak direction. However, it strengthens the system when loading is towards the shear wall, leading to a highly asymmetric hysteretic response. During earthquake loading, all asymmetric rocking foundation systems observe smaller peak roof accelerations, but larger peak and permanent roof drifts compared with the symmetric systems. Despite these differences in response, the axial load fluctuation and structural asymmetry do not significantly change the relative energy dissipated by the rocking foundations and inelastic structural components within each frame–wall–rocking foundation model. Copyright © 2015 John Wiley & Sons, Ltd.

Optimal control for a vibrating string with variable axial load and damping gain

Abstract We consider an optimal control problem for a vibrating string with multiplicative distributive control. Multiplicative control is the coefficient u ( x, t ) of velocity term y t . Using multiplicative control, we bring the state solution to the desired profile under a quadratic cost of control.We prove the existence of optimal control. Criterion for characterization of the unique optimal control is provided in the form of optimality system.

An Analytical Approach to Vibration Analysis of Beams with Variable Properties

In this paper, an approach is proposed for determination of vibration frequencies of variable cross-section Timoshenko beams and of non-prismatic Euler beams under variable axial loads. In each case, the governing differential equation is first obtained and, according to a harmonic vibration, is converted into a single-variable equation in terms of location. Integral equations for the weak form of governing equations are derived through repetitive integrations. Mode shape functions are approximated by a power series. A system of linear algebraic equations is obtained by substitution of the power series into the integral equation. Using a non-trivial solution for system of equations, natural frequencies are determined. The presented method is formulated for beams having various end conditions and is extended for determination of the buckling load of non-prismatic Euler beams. The effectiveness and accuracy of the method is shown through comparison of the numerical results to those obtained using available finite element software.

Capacity Assessment of V-Shaped RC Bridge Bents

AbstractAssessment of the flexural and shear capacity of two V-shaped RC bridge bents has been validated against experimental results from tests on 1:3-scale specimens. A numerical procedure based on iterative analyses taking into account the variation of vertical loads in the bents’ columns provides a satisfactory prediction of the bents’ overall performance. Based on its general agreement with the experimental data, the numerical model was also used to investigate the uneven distribution of axial load and shear force between the two columns of each bent. Three models were compared for the assessment of the shear capacity of the specimens. All the models identified the compression column as the most critical in terms of shear capacity, as confirmed by the experimental results. The University of California at San Diego (UCSD) model, which introduces an additional contribution due to the compression strut along the column length, appears to be less sensitive to axial load variations and to provide a reliab...

Resistance to Lateral Luxation of Two Canine Total Elbow Replacement Systems Under Variable Mechanical Loads

To measure the loads required to induce lateral luxation of the Iowa State University (ISU) elbow implant, a modified elbow implant, and the normal canine elbow with the ligaments and joint capsule removed. Mechanical testing on cadaveric specimens Twelve thoracic limbs were harvested from adult, medium sized dogs that had been euthanatized for reasons unrelated to the study. The torque needed for luxation was identified on potted cadaver elbows under variable axial load and compared to ISU implants and modified implants. Shear force needed to induce medial and lateral luxation were collected for the 2-implant designs at 10, 109, 209, and 342 N of axial load based on. Shear force needed to induce lateral luxation were collected for the normal elbows (with and without an anconeal process) at 10 N of axial load. The modified implant had 5× higher torque at luxation than the ISU implant and cadavers elbows for both internal and external rotation. Luxation during shear testing was significantly higher in cadaver elbows when compared to either implant but the modified implant was 4-7× more resistant then the ISU implant. The modified total elbow replacement implant may reduce lateral luxation in vivo by increased resistance to shear and torsional forces.

STATIC BEHAVIOUR OF DIFFERENT TYPES OF R.C BEAM-COLUMN CONNECTIONS AS AFFECTED BY BOTH VALUE OF ACTING AXIAL NORMAL FORCE AND GRADE OF USED CONCRETE (THEORETICAL STUDY)

This paper describes a theoretical study of the effect of both acting axial loads and grade of concrete on the static behaviour of (32) thirty two Reinforced Concrete (RC) Beam-column joints. ABAQUSCAE version 6.7, a nonlinear finite element analysis software package, was developed specifically for the analysis of reinforced concrete structures under plane stress conditions. Variable axial loads were applied and increased gradually with constant lateral load, which was applied maintaining at the top of the column at internal and external beam-column joint only the ultimate and cracking axial loads were recorded as well as the corresponding versus vertical displacement, the maximum joint shear stresses, axial, stresses strains, and absorbed energy, mode of failure using different grades of concrete C250, C400, C600 and C1200 were evaluated and recorded.

Experimental studies on structural load monitoring using piezoelectric transducer based electromechanical impedance method

In general aerospace, civil and mechanical (ACM) structures are often subjected to some or the other forms of loading during their service life. It has been reported that about 75% of aerospace structures fail due to fatigue cyclic loading. The civil-structural components are subjected to some form of axial and transverse loading which continuously deteriorates the health of the structure. Mechanical components are also subjected to stresses due to contact pressures between several components. Thus for ACM structures, effective monitoring through-out the entire life is required as these often involve public life and huge investments. Owing to such necessity, researchers around the world are continuously working on the development of smart sensor based effective monitoring techniques. Piezo electric (PZT) transducer based electromechanical impedance (EMI) is one such technique which was developed for structural health monitoring (SHM). In this technique, PZT transducers are usually attached to the structure to be monitored and are then subjected to unit sinusoidal electric voltage to generate the electromechanical (EM) admittance signatures when interrogated to the desired frequency range of excitations. These signatures consist of real (conductance) and imaginary (susceptance) parts which serve as indicator to predict the structural health. Any deviations in these signatures during the monitoring period indicate disturbance in the structure. However, the EMI technique was not widely explored for structural load monitoring (such as fatigue cyclic load, monotonous load, axial and transverse load) compared to damage detection. In this paper, systematic experiments were presented on the specimens for axial load variations, transverse load variations, monotonous and fatigue load variation with discussions on boundary effect and buckling effects. For axial, fatigue, monotonic load, the conductance was found to be effective where as for transverse load monitoring susceptance was found to be effective. This paper summarizes different types of loading effects related to EMI.

Assessment and Design Procedure for the Seismic Retrofit of Reinforced Concrete Beam-Column Joints using FRP Composite Materials

In this study, an analytical procedure for the evaluation of the expected performance of existing reinforced concrete (RC) beam-column joints before and after being retrofitted using fiber-reinforced polymer (FRP) composite materials is presented. Focus is given on the evaluation of the shear-strength versus deformation properties of the panel zone region either in the as-built or FRP-retrofitted configuration. Based on experimental and numerical evidence as well as on physical models representing the mechanics of the joint region, principal tensile stresses versus joint shear deformation relationships are adopted and preferred to more traditional nominal shear-strength rules, to evaluate, within a step-by-step iterative procedure, the combination of the joint shear contribution provided by the FRP composite material and that provided by the concrete core alone. The use of principal stresses allows one to directly account for the effects of variation of axial load, typically neglected in the assessment and retrofit of beam-column joints. The hierarchy of strength and sequence of events (damage mechanisms) expected within a beam-column subsystem are visualized via M-N interaction performance domains, used as a basis for a performance-based retrofit philosophy. Specific limit states or design objectives are targeted, with attention given to both strength and deformation limits. The proposed analytical procedure is validated on the results of a set of experimental tests available in the literature. With the intention to provide a simple design tool that can be easily implemented by practicing engineers, a worked example for the evaluation of the expected performance of an FRP retrofitted beam-column joint is provided and used as a basis for a parametric study to illustrate the effects of different strengthening schemes on the behavior of strengthened exterior joint panels under various axial load levels.

Axial–shear–flexure interaction hysteretic model for RC columns under combined actions

This paper proposes a coupled axial–shear–flexure interacting (ASFI) hysteretic model that can capture the nonlinear interactive behavior of RC columns under combined action of shear, bending moment and variable axial load. The model utilizes a novel concept of normalization to parameterize the primary curves at different axial load levels in addition to the consideration of shear–flexure interaction. An axial load independent stress level index is developed and used with a two-step loading approach to enable the transition between different reloading and unloading branches corresponding to variable axial load levels during seismic shakings. The proposed model has been implemented and calibrated in a displacement-based finite element program. It is able to realistically simulate the pinching behavior, strength deterioration and stiffness softening under combined actions. The validation against the experimental results of columns subject to varying axial loads shows very good agreement. Particular factors affecting the ASFI behavior of RC columns, such as the arrival time and amplitude of vertical ground motions, are also evaluated. Finally, the seismic responses of a realistic prototype bridge are conducted to demonstrate the effects of vertical ground motion on the lateral displacement and force demands.

Thrust Bump Air Foil Bearings with Variable Axial Load: Theoretical Predictions and Experiments

Thrust air foil bearings are critical components in high-efficiency turbomachinery, such as two-stage compressors subjected to large and irregular axial forces. In this article, a model of thrust bump foil bearings that predicts deflection with variable axial load is developed assuming no tilting effect of the thrust collar. To predict the air clearance, deflection of the elastic foundation was used in the air film height equation. Combined Dirichlet and Neumann-type boundary conditions were used for static load performance predictions. To verify the theoretical model, tests were performed with three different thrust air foil bearings with outer radii of 45, 50, and 55 mm. The rotating speed ranged from 10,000 to 25,000 rpm. From the test results, the model using nonlinear stiffness was in better agreement with the experimental results than the model using linear stiffness.

Section Discretization of Fiber Beam-Column Elements for Cyclic Inelastic Response

AbstractThe paper presents studies of the effect of the number of material integration points at the monitored sections of fiber beam-column elements on the local response of typical structural cross sections under an extensive set of cyclic biaxial load conditions with constant and variable axial load. The study covers wide-flange steel sections and rectangular reinforced concrete sections. The integration over the section uses the midpoint rule and shows that a standard section discretization with relatively few fibers is a good compromise between accuracy and economy of means. The proposed coarse section discretization schemes are computationally efficient while ensuring the accurate representation of important aspects of the three-dimensional response of structural members, such as interaction of axial force with biaxial bending moment, effect of residual stress in steel members, and effect of cracking in reinforced concrete members. The local strain response is also represented with good accuracy by ...

Assessment of RC columns subjected to horizontal and vertical ground motions recorded during the 2009 L’Aquila (Italy) earthquake

In the aftermath of recent earthquakes there has been substantial field evidence demonstrating that the collapse of several existing structures was caused by the effects of the vertical component of seismic ground motions. Such field evidence has not yet been supported by comprehensive analytical assessment and experimental tests. The present work focuses on preliminary analyses of the seismic response of reinforced concrete (RC) members subjected to horizontal (HGMs) and vertical (VGMs) ground motions recorded during the 2009 L’Aquila (Italy) earthquake. Normalised axial loads in beam–columns as well as the peak ground acceleration ratios between horizontal and vertical ground accelerations are emphasised as they are considered parameters of paramount importance for the assessment of structural components and systems subjected to combined horizontal and vertical ground motions (HVGMs). Results of extensive parametric nonlinear dynamic analyses carried out on simplified structural models are discussed in detail. The sample models comprise cantilever RC columns and a two-storey, two-bay plane frame designed for gravity loads. The structural response quantities for the performed analyses are expressed in terms of axial loads, axial deformations, bending moment-axial load interaction and shear demand/capacity ratios. It is found that the variation of axial loads is significant in columns under HVGMs, especially in compression. For values of normalised axial loads ( ν ) corresponding to actual RC columns in framed building structures, e.g., normalised axial load ν > 0.10 , the average increase of the compression load ranges between 174% ( ν = 0.20 ) and 59% ( ν = 0.50 ). For high values of normalised axial loads the computed axial load-bending moment pairs lie beyond the threshold interaction curves and, in turn, the RC members may fail. The shear demand-to-supply ratio is also detrimentally affected by the high fluctuations of axial loads in the columns. Net tensile forces were computed for columns with low-to-moderate axial gravity preload. In multi-storey framed buildings, the response of central columns is significantly affected by the HVGMs. Reliable seismic performance assessment of framed systems requires that combined HGMs and VGMs should be accounted for in the analyses. Further experimental and numerical research is needed to formulate efficient mechanical models to evaluate the shear capacity of structural members of existing RC framed buildings under earthquake loading.

Dynamics and stability of transverse vibrations of nonlocal nanobeams with a variable axialload

This paper investigates the natural frequency, steady-state resonance and stability for thetransverse vibrations of a nanobeam subjected to a variable initial axial force, includingaxial tension and axial compression, based on nonlocal elasticity theory. It is reported thatthe nonlocal nanoscale has significant effects on vibration behavior, which results in a neweffective nonlocal bending moment different to but dependent on the correspondingnonlocal bending moment. The effects of nonlocal nanoscale and the variation of initialaxial force on the natural frequency as well as the instability regions are analyzed by theperturbation method. It concludes that both the nonlocal nanoscale and the initial tension,including static and dynamic tensions, cause an increase in natural frequency,while an initial compression causes the natural frequency to decrease. Instabilityregions are also greatly influenced by the nonlocal nanoscale and initial tensionand they become smaller with stronger nonlocal effects or larger initial tension.

Electromechanical Modeling and Nonlinear Analysis of Axially Loaded Energy Harvesters

To maximize the electromechanical transduction of vibratory energy harvesters, the resonance frequency of the harvesting device is usually tuned to the excitation frequency. To achieve this goal, some concepts call for utilizing an axial static preload to soften or stiffen the structure (Leland and Wright, 2006, “Resonance Tuning of Piezoelectric Vibration Energy Scavenging Generators Using Compressive Axial Preload,” Smart Mater. Struct., 15, pp. 1413–1420; Morris et al., 2008, “A Resonant Frequency Tunable, Extensional Mode Piezoelectric Vibration Harvesting Mechanism,” Smart Mater. Struct., 17, p. 065021). For the most part, however, models used to describe the effect of the axial preload on the harvester’s response are linear lumped-parameter models that can hide some of the essential features of the dynamics and, sometimes, oppose the experimental trends. To resolve this issue, this study aims to develop a comprehensive understanding of energy harvesting using axially loaded beams. Specifically, using nonlinear Euler–Bernoulli beam theory, an electromechanical model of a clamped-clamped energy harvester subjected to transversal excitations and static axial loading is developed and discretized using a Galerkin expansion. Using the method of multiple scales, the general nonlinear physics of the system is investigated by obtaining analytical expressions for the steady-state response amplitude, the voltage drop across a resistive load, and the output power. These theoretical expressions are then validated against experimental data. It is demonstrated that in addition to the ability of tuning the harvester to the excitation frequency via axial load variations, the axial load aids in (i) increasing the electric damping in the system, thereby enhancing the energy transfer from the beam to the electric load, (ii) amplifying the effect of the external excitation on the structure, and (iii) enhancing the effective nonlinearity of the device. These factors combined can increase the steady-state response amplitude, output power, and bandwidth of the harvester.

Simplified uni-axial hysteretic damage model for panel zone of structural steel under earthquake loads

In structural systems, it is a very important issue to predict damage levels of structural components subjected to earthquakes. To appreciate ultimate behaviors and fracture mechanism on the panel zone of structural steels under earthquake loads, it is essential to comprehend damage levels quantitatively. Thus, simple damage models are needed to predict structural components behaviors for random earthquakes effectively. This study proposes a simplified uni-axial hysteretic damage model for panel zone, which is applicable to multi-axial cyclic loading. To confirm the validity of the model, experimental tests are performed under the cyclic shear loading with constant or variable axial loading. The results from the tests are compared with those of the proposed hysteretic model considering the effect of damage. Though limitations are given to the application of this model, this model can predict well the hysteretic behavior of general panel zone applied to multi-axial cyclic loading.