Showing papers on "Bending moment published in 2006"

DCB-specimen loaded with uneven bending moments

Abstract: A double cantilever beam specimen loaded with uneven bending moments (DCB-UBM) is proposed for mixed mode fracture mechanics characterisation of adhesive joints, laminates and multilayers. A linear elastic fracture mechanics analysis gives the energy release rate and mode mixity analytically for both isotropic and orthotropic materials. By varying the ratio between the two applied moments, the crack tip stress state can be varied from pure mode I to pure mode II for the same specimen geometry. The specimen allows stable crack growth. A special test fixture is developed to create uneven bending moments. As a preliminary example, the DCB-UBM specimen was used for characterising fracture of adhesive joints between two laminates of thermoset glass fibre reinforced plastic.

Behavior of Corrugated Web I-Girders under In-Plane Loads

Abstract: A theoretical formulation of the linear elastic in-plane and torsional behavior of corrugated web I-girders under in-plane loads is presented. A typical corrugated web steel I-girder consists of two steel flanges welded to a corrugated steel web. Under a set of simplifying assumptions, the equilibrium of an infinitesimal length of a corrugated web I-girder is studied, and the cross-sectional stresses and stress resultants due to primary bending moment and shear are deduced. The analysis shows that a corrugated web I-girder will twist out-of-plane simultaneously as it deflects in-plane under the action of in-plane loads. In the paper, the in-plane bending behavior is analyzed using conventional beam theory, whereas the out-of-plane torsional behavior is analyzed as a flange transverse bending problem. The results for a simply supported span subjected to a uniformly distributed load are presented. Finally, finite element analysis results are presented and compared to the theoretical results for validation.

Application of bi-adhesive in double-strap joints subjected to bending moment

Abstract: Generally, all failures in adhesively-bonded joints begin at the overlap ends because of the stress concentration occurring at the ends. The approach which reduces stress concentration at the overlap ends increases the load capacity and delays the failure. The lower the stiffness of the adhesive used, the lower the stress concentration, and the lower stress concentration gives rise to higher joint strength. In this work, the results of the application of two adhesives, one stiff and one flexible, with very different mechanical behaviors along the overlap length in double strap joints subjected to bending moment, were analyzed. A stiff adhesive was applied in the middle portion of overlap, while a flexible adhesive was applied towards the edges. The results show that the bi-adhesively-bonded joints carry more loads and have higher strength when compared with single-adhesively-bonded joints.

Effect of pitting corrosion on the ultimate strength of steel plates subjected to in-plane compression and bending

Abstract: Corrosion pits with a circular cone shape are typically observed on coated hold frames of aged bulk carriers which carry exclusively coal and iron ore. In order to ensure the safety of these types of bulk carrier, it is necessary to understand the effect of pitting corrosion on the local strength of hold frames. In order to investigate this effect, a series of nonlinear finite-element (FE) analyses has been performed with pitted plates subjected to in-plane compressive loads and bending moments. It has been shown that the ultimate compression load or bending moment of pitted plates is smaller than that of uniformly corroded plates in terms of average thickness loss, and that predictions of the ultimate strength using the average thickness loss at the minimum cross section would be conservative. In order to establish a method of evaluating strength reduction due to pitting corrosion, it is important to identify the failure mode that would be most detrimentally affected by pitting corrosion. It was found that the reduction of the ultimate compressive load or bending moment due to pitting corrosion is smaller than that of the tensile strength in terms of equivalent thickness.

Pile Behavior Due to Excavation-Induced Soil Movement in Clay. I: Stable Wall

Abstract: A series of centrifuge model tests has been conducted to investigate the behavior of a single pile subjected to excavation-induced soil movements behind a stable retaining wall in clay. The results reveal that after the completion of soil excavation, the wall and the soil continue to move and such movement induces further bending moment and deflection on an adjacent pile. For a pile located within 3 m behind the wall where the soil experiences large shear strain (>2%) due to stress relief as a result of the excavation, the induced pile bending moment and deflection reach their maximum values sometime after soil excavation and thereafter decrease slightly with time. For a pile located 3 m beyond the wall, the induced pile bending moment and deflection continue to increase slightly with time after excavation until the end of the test. A numerical model developed at the National University of Singapore is used to back-analyze the centrifuge test data. The method gives a reasonably good prediction of the induced bending moment and deflection on a pile located at 3 m or beyond the wall. For a pile located at 1 m behind the wall where the soil experiences large shear strain (>2%) due to stress relief resulting from the excavation, the calculated pile response is in good agreement with the measured data if the correct soil shear strength obtained from postexcavation is used in the analysis. However, if the original soil shear strength prior to excavation is used in the analysis, this leads to an overestimation of the maximum bending moment of about 25%. The practical implications of the findings are also discussed in this paper.

A finite element model for bending behaviour of conducting polymer electromechanical actuators

Abstract: Emerging conducting polymer electromechanical actuators (CPEA) have many potential applications ranging from biomedical to micro/nano manipulation systems In order to make use of their potential, it is needed to establish a valid mathematical model to provide enhanced degrees of understanding, predictability, control and efficiency in performance Although it is known that the mechanism behind their operation is quite straightforward; establishing a mathematical model to predict their behaviours and quantify their performance is hampered by many mechanical, electrical and chemical parameters With this in mind, the aim of this study is to establish and experimentally validate a lumped-parameter model of bending-type polypyrrole (PPy) actuators for use in improving their displacement and force outputs With reference to their operation principle, we draw an analogy between the thermal strain and the real strain in the PPy actuators due to the volume change to set up the mathematical model, which is a coupled structural/thermal model The finite element method (FEM) is used to solve the model The effect of propagation of the ion migration into the PPy layers is mimicked with a temperature distribution model Theoretical and experimental results demonstrate that the model is practical and effective enough in predicting the bending angle and bending moment outputs of the PPy actuators quite well for a range of input voltages, and the PPy layer thicknesses

On the calculation of energy release rates for cracked laminates with residual stresses

Abstract: Prior methods for calculating energy release rate in cracked laminates were extended to account for heterogeneous laminates and residual stresses. The method is to partition the crack tip stresses into local bending moments and normal forces. A general equation is then given for the total energy release rate in terms of the crack-tip moments and forces and the temperature difference experienced by the laminate. The analysis method is illustrated by several example test geometries. The examples were verified by comparison to numerical calculations. The residual stress term in the total energy release rate equation was found to be essentially exact in all example calculations.

A methodology towards geometry optimization of high performance polypyrrole (PPy) actuators

Abstract: This paper focuses on a geometry optimization methodology based on a lumped-parameter mathematical model, which accepts the voltage as the input, and bending angle and bending moment as the outputs, for a trilayer bending-type polymer actuator. An analogy is made between thermal strain and the real strain in the actuator to establish the mathematical model, which is solved using the finite element method in order to obtain theoretical results. The polypyrrole (PPy) actuator, which consists of five layers of three different materials, operates in a non-aquatic medium, i.e., air, as opposed to its predecessors. With reference to its operation principle, the movement or propagation of dopant ions and solvent molecules into the PPy layers is mimicked with a temperature distribution model to improve the accuracy of the model. Theoretical and experimental results presented suggest that the model is valid to predict the bending angle and bending moment outputs of the PPy actuators quite well for a range of input voltages and actuator thicknesses. The model has been employed to determine the actuator geometry, resulting in improved/higher bending angle and bending moment outputs. The geometry optimization results for an actuator with a constant length and width demonstrate that the thicker is the root of the actuator, where it is clamped, the higher is the bending moment, as compared to an actuator with a uniform thickness.

Pile Behavior Due to Excavation-Induced Soil Movement in Clay. II: Collapsed Wall

Abstract: A series of centrifuge model tests has been conducted to investigate the behavior of a single pile behind a retaining wall that eventually fails due to soil excavation in front of the wall. All the piles are located at 3 m behind the wall where the soil experiences large shear strain (>2%). The induced bending moment and deflection on the pile as well as the soil and wall movements are monitored at regular intervals throughout the tests. It is found that the pile performance depends greatly on the degree of wall instability. After a critical excavation depth, active wedge slip plane and tension cracks developed in the vicinity of the pile. The limiting soil pressure profile deduced from the measured maximum induced pile bending moment profile is established to be much lower than that of a conventional laterally loaded pile. Using the measured soil movements at the pile location as the input data, the calculated pile bending moment obtained using an existing numerical model generally show fair agreement with the measured values when the back-analyzed limiting soil pressures acting on the pile are employed in the back-analysis. The practical implications of the findings are discussed in the paper.

Reducing stem bending increases the height growth of tall pines

Abstract: The hypothesis was tested that upper limits to height growth in trees are the result of the increasing bending moment of trees as they grow in height. The increasing bending moment of tall trees demands increased radial growth at the expense of height growth to maintain mechanical stability. In this study, the bending moment of large lodgepole pine (Pinus contorta Dougl. Ex Loud. var. latifolia Engelm.) was reduced by tethering trees at 10 m height to counter the wind load. Average bending moment of tethered trees was reduced to 38% of control trees. Six years of tethering resulted in a 40% increase in height growth relative to the period before tethering. By contrast, control trees showed decreased height growth in the period after tethering treatment. Average radial growth along the bole, relative to height growth, was reduced in tethered trees. This strongly suggests that mechanical constraints play a crucial role in limiting the height growth of tall trees. Analysis of bending moment and basal area increment at both 10 m and 1.3 m showed that the amount of wood added to the stem was closely related to the bending moment produced at these heights, in both control and tethered trees. The tethering treatment also resulted in an increase in the proportion of latewood at the tethering height, relative to 1.3 m height. For untethered control trees, the ratio of bending stresses at 10 m versus 1.3 m height was close to 1 in both 1998 and 2003, suggesting a uniform stress distribution along the outer surface of the bole.

Structural mechanism of traditional wooden frames by dynamic and static tests

Abstract: This paper deals with the structural mechanism of traditional wood frames to evaluate the seismic performance of wooden buildings like Japanese temples. The outline of shaking table tests and static tests using several scale models is described and typical experimental results are discussed. From experiments, it is found that the horizontal restoring force of wooden frame without walls depends mainly on the bending moment resistance from tie beams and the restoring force due to column rocking. The equilibrium relationship between the total restoring force and all the bending moments involved is established and verified. Using this equilibrium relationship, it is possible to evaluate the restoring force due to column rocking. The restoring force due to column rocking is the major part of the total restoring force when the frame deformation is small. The bending moments from tie beams become dominant as the deformation increases. The traditional wooden frame has the large flexibility and deformability. It is essential to take advantage of the structural mechanisms found from this study in the seismic and enhancement design of traditional wooden buildings. Copyright © 2005 John Wiley & Sons, Ltd.

Wave-current interactions in marine current turbines:

Abstract: The influence of waves on the dynamic properties of bending moments at the root of blades of tidal stream vertical-axis rotors is reported. Blade element-momentum theory for wind turbines is combined with linear wave theory and used to analyze this influence. Experiments were carried out with a 350 mm diameter rotor to validate the simulation and the comparison shows the ability of the theoretical approach to predict the blade root bending moments. It can be concluded that, in steep waves, linear theory underestimates the dynamic behaviour of bending moments. However, in long waves, linear theory works well. Bending moments at roots of rotor blades fluctuate with significant amplitudes (as much as 50 per cent of mean value for out-of-plane bending moment and 100 per cent of mean value for in-plane bending moment), which will be important for design of tidal stream rotors.

Methods and apparatus for balancing a rotor

Abstract: A method for balancing a rotor of a rotary machine, wherein the rotor includes at least two rotor blades and a rotor shaft, includes receiving at least one measurement of either a load, an acceleration, or a displacement that pertains to at least one bending moment acting on the rotor shaft, determining at least one value of the at least one bending moment acting on the rotor shaft based, at least in part, on the received at least one measurement, and determining a pitch offset angle value of at least one rotor blade that facilitates reducing the at least one bending moment acting on the rotor shaft.

Parametrically Excited Vibration of a Timoshenko Beam on Random Viscoelastic Foundation jected to a Harmonic Moving Load

Abstract: The vibration response of a Timoshenko beam supported by a viscoelastic foundation with randomly distributed parameters along the beam length and jected to a harmonic moving load, is studied. By means of the first-order two-dimensional regular perturbation method and employing appropriate Green's functions, the dynamic response of the beam consisting of the mean and variance of the deflection and of the bending moment are obtained analytically in integral forms. Results of a field measurement for a test track are utilized to model the uncertainty of the foundation parameters. A frequency analysis is carried out and the effect of the load speed on the response is studied. It is found that the covariance functions of the stiffness and the loss factor both have the shape of an exponential function multiplied by a cosine function. Furthermore, it is shown that in each frequency response there is a peak value for the frequency, which changes inversely with the load speed. It is also found that the peak value of the mean and also standard deviation of the deflection and bending moment can be a decreasing or increasing function of the load speed depending on its frequency.

A closed form solution for the dynamic response of finite ribbed plates

Abstract: A simple and closed form solution for the vibration response of finite ribbed plates to point force/moment excitations is presented in this paper This solution shows that input mobilities of finite ribbed plates are bounded by the input mobilities of the uncoupled plate and beam that form the ribbed plate It is found that point force input mobilities of a finite ribbed plate are controlled by the plate bending stiffness when the excitation force is more than a quarter wavelength away from the beam The input mobilities are mainly dominated by the beam flexural stiffness when the force acts on or very close to the beam, and when the beam flexural stiffness is far greater than the plate bending stiffness A similar result is found in the moment excitation case when the moment axis is perpendicular to the beam neutral axis (bending moment excitation) In contrast, the input mobilities of the ribbed plate do not vary much from that of the corresponding uncoupled plate when the moment axis parallels to the beam’s neutral axis (torsional moment excitation) where the input mobilities are mainly dominated by the plate bending stiffness The reductions in plate kinetic energy due to beam insertions are discussed

Bending stability of multiwalled carbon nanotubes

Abstract: This paper reports the results of an investigation on bending stability of an individual multiwalled carbon nanotube. Based on the point of view of continuum modeling, a multilayer shell model is presented for the pure bending buckling of an individual multiwalled carbon nanotube, in which the effect of van der Waals forces between adjacent two tubes is taken into account. Here, the critical bending moment and the bending buckling mode for three types of multiwalled carbon nanotubes with different layer numbers and ratios of radius to thickness are calculated. Results carried out show that the bending buckling mode corresponding the critical bending moment is unique, which is obviously different from the purely axial compression buckling of an individual multiwalled carbon nanotube. It is also seen from numerical examples that the distribution of the critical bending strain for each tube of multiwalled carbon nanotubes under bending is dependent on the radius-to-thickness ratio and the layer number of the multiwalled carbon nanotubes. The new features and interesting numerical results in the present work are helpful for the application and the design of nanostructures in which multiwalled carbon nanotubes act as basic elements.

A closed form solution for the dynamic response of finite ribbed plates

Abstract: A simple and closed form solution for the vibration response of finite ribbed plates to point force/moment excitations is presented in this paper. This solution shows that input mobilities of finite ribbed plates are bounded by the input mobilities of the uncoupled plate and beam that form the ribbed plate. It is found that point force input mobilities of a finite ribbed plate are controlled by the plate bending stiffness when the excitation force is more than a quarter wavelength away from the beam. The input mobilities are mainly dominated by the beam flexural stiffness when the force acts on or very close to the beam, and when the beam flexural stiffness is far greater than the plate bending stiffness. Similar result is found in the moment excitation case when the moment axis is perpendicular to the beam neutral axis (bending moment excitation). In contrast, the input mobilities of the ribbed plate do not vary much from that of the corresponding uncoupled plate when the moment axis parallels to the beam’s neutral axis (torsional moment excitation) where the input mobilities are mainly dominated by the plate bending stiffness. The reductions in plate kinetic energy due to beam insertions are discussed.