Showing papers on "Bending moment published in 1999"

Deployment dynamics of tape springs

Abstract: Tape springs are straight, thin–walled strips with a curved cross–section. Following recent proposals for large deployable structures exploiting the structural simplicity and robustness of such springs as deployment actuators, the paper investigates the dynamic deployment of a tape spring that is either coiled around a circular hub, or folded into a zig–zag pattern. It is shown that in both cases the spring deforms by forming an elastically deformed region with zero transverse curvature and uniform longitudinal curvature. The process of formation and growth of a fold belongs to a wide class of propagating instabilities. It is characterized by a high peak moment and a lower propagation moment. A compact characterization of the moment–rotation relationship for an elastic fold is presented. A key feature is that the bending moment on either side of a fold moving along a uniform tape spring, away from any end supports, is constant, whereas this moment increases near a support. Compact and accurate two–dimensional theories are developed to simulate the self–actuated deployment of tape springs. It is shown that conservative energy formulations are appropriate for coiled springs, where the velocity field is smooth, but not for springs with localized folds. To simulate the motion of such localized folds a non–conservative impulse–momentum formulation is proposed, and it is found that this model can accurately predict both the steady motion of the folds along the tape spring and their rebound against the end supports.

Fiber Element for Cyclic Bending and Shear of RC Structures. I: Theory

Abstract: After a few years of successful application of the fiber beam element to the analysis of reinforced concrete (RC) frames, the introduction of the mechanisms of shear deformation and strength appears to be the next necessary step toward a realistic description of the ultimate behavior of shear sensitive structures This paper presents a new finite-beam element for modeling the shear behavior and its interaction with the axial force and the bending moment in RC beams and columns This new element, based on the fiber section discretization, shares many features with the traditional fiber beam element to which it reduces, as a limit case, when the shear forces are negligible The element basic concept is to model the shear mechanism at each concrete fiber of the cross sections, assuming the strain field of the section as given by the superposition of the classical plane section hypothesis for the longitudinal strain field with an assigned distribution over the cross section for the shear strain field Transve

What determines the bending strength of compact bone

Abstract: The bending strength of a wide variety of bony types is shown to be nearly linearly proportional to Young's modulus of elasticity/100. A somewhat closer and more satisfactory fit is obtained if account is taken of the variation of yield strain with Young's modulus. This finding strongly suggests that bending strength is determined by the yield strain. The yield stress in tension, which might be expected to predict the bending strength, underestimates the true bending strength by approximately 40 %. This may be explained by two phenomena. (1) The post-yield deformation of the bone material allows a greater bending moment to be exerted after the yield point has been reached, thereby increasing the strength as calculated from beam formulae. (2) Loading in bending results in a much smaller proportion of the volume of the specimens being raised to high stresses than is the case in tension, and this reduces the likelihood of a weak part of the specimen being loaded to failure.

Moving Force Identification—A Frequency and Time Domains Analysis

Abstract: This paper addresses the problem of identifying a system of forces from vehicle crossing a guideway using only the vibration responses caused by the forces as the input without knowledge of the vehicle characteristics. The vehicle is modeled as a single axle and two-axle loads with fixed axle spacing moving on a simply supported beam with viscous damping. The equations of motion of the beam are obtained through modal coordinate transformation, and the resulting set of equations relating the Fourier transforms of the responses and the moving forces are converted into time domain by a new method proposed by the authors, Correctness of the identified forces are checked by the correproposed by the authors, Correctness of the identified forces are checked by the correlation between the measured responses and the responses reconstructed with the identified forces moving on the beam. Experimental result shows that the method is effective to give good correlation when both measured bending moment and acceleration are used, and it is faster and it gives more accurate estimate of the total mass of the vehicle than an existing method.

Collapse behavior of square thin-walled columns subjected to oblique loads

Abstract: The crush behavior of a square column subjected to oblique loads, which is undergoing both axial and bending collapses, is analyzed. Oblique load conditions in numerical simulations are realized by means of impacting the column on a declined rigid wall with no friction. Mean crush loads corresponding to load angles are investigated with such geometrical parameters as thickness, width and length. Results show that there is a critical load angle at which a transition takes place from the axial collapse mode to the bending collapse mode. The dimensionless mean crush load is employed by normalizing the mean crush load with the analytical axial mean crush load and bending moment equations. It is expressed as a function of only one variable, the load angle. Finally, the formulation for the mean crush load is developed in terms of geometrical parameters and the critical load angle. The equation of the critical load angle is expressed as a function of the ratio of l/b. The value of the mean crush load drops to about 40% of the mean crush load in pure axial collapse after the critical load angle. Some cases of thin-walled columns are examined to verify the formulas of the mean crush load, and the results of numerical simulations are in good agreement with the predicted mean crush loads.

Large-amplitude undulatory fish swimming: fluid mechanics coupled to internal mechanics.

Abstract: The load against which the swimming muscles contract, during the undulatory swimming of a fish, is composed principally of hydrodynamic pressure forces and body inertia. In the past this has been analysed, through an equation for bending moments, for small-amplitude swimming, using Lighthill's elongated-body theory and a 'vortex-ring panel method', respectively, to compute the hydrodynamic forces. Those models are outlined in this review, and a summary is given of recent work on large-amplitude swimming that has (a) extended the bending moment equation to large amplitude, which involves the introduction of a new (though probably usually small) term, and (b) developed a large-amplitude vortex-ring panel method. The latter requires computation of the wake, which rolls up into concentrated vortex rings and filaments, and has a significant effect on the pressure on the body. Application is principally made to the saithe (Pollachius virens). The calculations confirm that the wave of muscle activation travels down the fish much more rapidly than the wave of bending.

Method and apparatus for separating non-metallic substrates utilizing a supplemental mechanical force applicator

Abstract: An apparatus and method for physically separating non-metallic substrates by forming a microcrack in the substrate and controllingly propagating the microcrack. An initial mechanical or pulsed laser scribing device forms a microcrack in the substrate. A scribe beam is applied onto the substrate on a separation line. A coolant stream intersects with, or is adjacent to, the trailing edge of the scribe beam. The temperature differential between the heat affected zone of the substrate and the coolant stream propagates the microcrack. Two breaking beams on opposing sides of the separation line follow the coolant stream. The breaking beams create controlled tensile forces that extend the crack to the bottom surface of the substrate for full separation. The scribe and break beams and coolant stream are simultaneously moved relative to the substrate. A preheat beam preheats the heat affected area on the substrate. The beams are formed by an arrangement of lasers and mirrors and lenses. A movable mirror selectively diverts a beam to form either the preheat beam or one or more of the break and scribe beams. Spherical aberration is introduced in the break and scribe beams to flatten their energy distribution profiles and evenly apply the beam energy. A supplemental mechanical force, applied by vertically movable wheels or by restraining the substrate against a curved frame, creates a bending moment to facilitate the separation process.

Strain distribution in the layered wall of the esophagus.

Abstract: The function of the esophagus is to move food by peristaltic motion, which is the result of the interaction of the tissue forces in the esophageal wall and the hydrodynamic forces in the food bolus. To understand the tissue forces in the esophagus, it is necessary to know the zero-stress state of the esophagus, and the stress-strain relationships of the tissues. This article is addressed to the first topic: the representation of zero-stress state of the esophagus by the states of zero stress-resultant and zero bending moment of the mucosa-submucosa and the muscle layers. It is shown that at the states of zero stress-resultant and zero bending moment, these two layers are not tubes of smaller radii but are open sectors whose shapes are approximately cylindrical and more or less circular. When the sectors are approximated by circular sectors, we measured their radii, opening angles, and average thickness around the circumference. Data on the radii, thickness-to-radius ratios, and the opening angles of these sectors are presented. Knowing the zero-stress state of these two layers, we can compute the strain distribution in the wall at any in vivo state, as well as the residual strain in the esophageal wall at the no-load state. The results of the in vivo states are compared to those obtained by a conventional approach, which treats the esophageal wall as a homogeneous material, and to another popular simplification, which ignores the residual strains completely. It is shown that the errors caused by the homogeneous wall assumption are relatively minor, but those caused by ignoring the residual strains completely are severe.

On transverse matrix cracking in cross-ply laminates loaded in simple bending

Abstract: A one-dimensional analysis of a cross-ply laminate, containing cracked transverse plies, loaded in flexure is presented. Simple bending theory is used in conjunction with a shear-lag analysis, to calculate the degraded longitudinal modulus of a cracked transverse ply, enabling the flexural modulus of the laminate to be determined. The solution is shown to agree well with a more sophisticated stress transfer model in the literature. The analysis is then extended to calculate the applied bending moment at transverse crack onset under flexural loading using a fracture mechanics approach. The results suggest that the in situ transverse ply stress at which matrix cracking commences for the beam loaded in flexure is very close to the stress level at which the same ply would crack if the laminate were loaded in tension.

Non-linear inplane deformation and buckling of rings and high arches

Abstract: A non-linear theory is presented for stretching and inplane-bending of isotropic beams which have constant initial curvature and lie in their plane of symmetry. For the kinematics, the geometrically exact one-dimensional (1-D) measures of deformation are specialized for small strain. The 1-D constitutive law is developed in terms of these measures via an asymptotically correct dimensional reduction of the geometrically non-linear 3-D elasticity under the assumptions of comparable magnitudes of initial radius of curvature and wavelength of deformation, small strain, and small ratio of cross-sectional diameter to initial radius of curvature ( h/R ). The 1-D constitutive law contains an asymptotically correct refinement of O (h/R) beyond the usual stretching and bending strain energies which, for doubly symmetric cross sections, reduces to a stretch–bending elastic coupling term that depends on the initial radius of curvature and Poisson’s ratio. As illustrations, the theory is applied to inplane deformation and buckling of rings and high arches. In spite of a very simple final expression for the second variation of the total potential, it is shown that the only restriction on the validity of the buckling analysis is that the prebuckling strain remains small. Although the term added in the refined theory does not affect the buckling loads, it is shown that non-trivial prebuckling displacements, curvature, and bending moment of high arches are impossible to calculate accurately without this term.

In-Plane Buckling and Design of Steel Arches

Abstract: Many design codes do not give methods for designing steel arches against in-plane failure. The few that do provide methods that are essentially based on a linear interaction equation for the in-plane strengths of an equivalent beam-column, which uses the maximum elastic bending moment and axial compression in the arch. However, the linear interaction equation for a beam-column may not be suitable for an arch because it does not consider the strength characteristics of steel arches. This paper studies the in-plane buckling of arches in uniform compression and uses a nonlinear inelastic finite-element model to develop a method for designing steel arches against uniform compression, and also to develop an interaction equation for the design of steel arches against nonuniform in-plane compression and bending. Analytical solutions for the buckling loads of shallow arches in uniform compression are obtained. It is found that the design equation for steel columns cannot be used directly for steel arches in uniform compression, nor can the design interaction equations for steel beam-columns be used directly for steel arches under nonuniform compression and bending. The proposed design equations provide close predictions for the in-plane buckling strengths of both shallow and nonshallow steel arches in uniform compression. The modified interaction equation proposed provides good lower bounds for the in-plane strengths of both shallow and nonshallow steel arches in bending and compression because it considers the nonuniform distributions of the bending moment and axial compression around the arch, the behavior of shallow arches, and the favorable moment redistribution after the first hinge forms.

Metal culvert response to earth loading: performance of two-dimensional analysis

Abstract: The results of finite-element analyses conducted before and after testing of a 9.5-m span low-profile metal arch culvert are presented here. A two-dimensional procedure that models the elastic-plastic response of both structure and soil during backfilling has been used. A plasticity-based procedure to provide an upper bound for the effect of soil compaction on metal culvert response during side filling is introduced and used in the analysis of field response. The procedure involves application of passive earth pressures after layer placement to simulate the highest values of residual horizontal earth pressure. The pretest and posttest analyses are compared with measurements of field response previously published by Webb et al. Predictions for culvert deformation and bending moments generated during backfilling were excellent. The new procedure to include the effects of compaction during construction was effective in capturing culvert peaking during placement of the side fill and increases in bending moment. Both pre- and posttest predictions for deformation and moment successfully captured the culvert response during burial and the effect of backfill soil density. The posttest predictions include consideration of the top-loading applied during placement of the side fill. The predictions of deflection follow measured values during application and subsequent removal of those temporary surcharge loads. Estimates of soil stresses acting normal to the external surface of the culvert were shown to be close to those measured in the field. The analysis indicates that shear strength is fully mobilized in wedge-shaped zones of the backfill adjacent to the culvert. Those zones diminish in size once backfill is placed over the crown. The residual horizontal earth pressures that are modeled during compaction act to reduce the size of the plastic zones.

Modeling of steel-concrete composite beams under negative bending

Abstract: Negative bending moments acting in the support regions of continuous composite beams generate tensile stresses in the concrete slab and compressive stresses in the lower steel profile. As a result the mechanical behavior of these beams is strongly nonlinear even for low stress levels, due not only to the slip at the beam-slab interface, but also to cracking in the slab. Therefore, an adequate theoretical modeling should take account of the interactions between the structural steel and the concrete slab by shear connectors and also between steel rebars and concrete in tension by bond phenomenon. In this paper a model of steel and concrete composite beams subjected to negative bending is presented. It accounts for the slip occurring at both the beam-slab interface and the steel reinforcement-concrete interface. Some numerical results, obtained using a suitable numerical procedure, are discussed to show the capacity of the model.

The effects of lifting speed on the peak external forward bending, lateral bending, and twisting spine moments

Abstract: Lifting tasks that involve twisting have been repeatedly implicated as contributing to the onset of occupational back injuries in epidemiological studies. The objective of this work was to quantify the three directional external moments acting on the spine during a sagittally symmetric and two asymmetric lifting tasks. A total of 15 subjects participated in the three lifting tasks. All tasks were performed at two qualitatively defined lifting speeds, 'slow' and 'fast', and with two load magnitudes: 10 and 20% of the subject's body weight. The mid-sagittal plane lifts were performed using two horizontal reach distances: 40 and 60 cm. A four-camera, two-forceplate motion and force measurement system were used to obtain the kinematic and kinetic data as the lifts were performed. A dynamic link-segment biomechanical model was used to quantify the reaction forces and moments at the ankle, knee, and hip and L5/S1 joints. Results from all tasks showed increased sagittal plane (forward bending) spine moments with the heavier load and at the faster lifting speed (p < 0.001). Spine lateral bending and twisting moments increased during the mid-sagittal plane lifts with the greater reach distance and the faster lifting speed, respectively. The twisting moments on the spine were greatest as subjects lifted from in front and placed the load to the side but were dependent upon the lifting speed and the load magnitude. The lateral bending moments increased during this same task with the heavier load. However, the spine lateral bending moments were greatest when lifting from one side to the other.

Mechanical Engineering Science

Abstract: Preface. Note On SI Units. 1. Statics. 2. Moment. Couple And Torque. 3. Polygon Of Forces Frameworks. 4. Friction. 5. Work And Power. 6. Machines. 7. Motion Velocity And Acceleration. 8. Force Amd Acceleration. 9. Momentum And Energy. 10. Uniform Motion In A Circular Path Satellites. 11. Stress And Strain. 12. Shear Force And Bending Moment. 13. Heat Engines. 14. Temperature And Heat. 15. Expansion And Compression Of Gases. 16. Fuels Combustion, Energy Release. 17. Steam. 18. Energy, Heat And Work. 19. Heat Exchangers Power Generation Emissions. 20. The Prime Mover. 21. Fluids. Index.

Limit Loads for Pipe Elbows Subjected to In-Plane Opening Moments and Internal Pressure

Abstract: The purpose of this study is to determine limit loads for pipe elbows subjected to in-plane bending moments that tend to open the elbow (i.e., increase its radius of curvature), and the influence of internal pressure on the value of the limit load. Load-deflection curves were obtained, and from these curves plastic collapse and instability loads at various values of internal pressure were determined. This was done for different pipe bend factors (h = Rt/r 2 ) using the nonlinear finite element analysis code (ABAQUS) with its special elbow element. A set of limit curves was generated from the results. These curves show the variation of collapse and instability loads with internal pressure for different elbows. Collapse loads were found to increase and then decrease with increasing pressure for all the elbow geometries studied. Instability loads were difficult to reach because of the large stiffening effect of the elbow cross-sectional deformation, and they were generally found to decrease with increasing pressure.

Arch action in reinforced concrete beams--a rational prediction of shear strength

Abstract: A rational expression, developed to predict the shear strength of reinforced concrete beams, is derived from the relationship between shear and the rate of change of bending moment along a beam coupled with experimental findings for the arch action. Eight reinforced concrete simple span beams without web reinforcement were tested statically up to failure to investigate quantitatively the arch action. Variables included four shear span-to-depth ratios (2, 2.5, 3, and 4) and two longitudinal steel ratios (1% and 2%). On the basis of the experimental findings, an equation is proposed to predict the internal moment arm length, which then leads to a shear strength equation that combines beam action and arch action. The proposed ultimate shear strength equation, arising from analytical premises and then calibrated with experimental data, is a similar form to the American Concrete Institute (ACI) 318 equation derived mainly from an empirical approach. The proposed ultimate shear strength equation applied to existing test data and the results were compared with those predicted by the ACI 318 equation and the Zsutty's equation.

Fiber Element for Cyclic Bending and Shear of RC Structures. II: Verification

Abstract: The fiber beam element with shear modeling developed in the companion paper is calibrated and verified by comparison with test data. The verification is carried out for the material constitutive behavior and for single beam and column elements using available test results from literature. A structural analysis of a shear sensitive viaduct pier subjected to ground input motion is presented. Details of the algebraic expressions used for the concrete and steel constitutive behaviors are provided.

Metal V-belt

Abstract: The relation of the length h1 of the V surface of each metal element to the saddle primary thickness h2 is determined such that the strength of the metal element for the Hertz's pressure generated on the V surface 2 from the normal force P which acts on the V surface 2 when the element engages in the V-shaped groove of a pulley and the strength for the bending moment which is produced by the normal force P on the saddles 1 of the metal element are made substantially equal to each other. Also, the relation of the length of the V surface to the saddle primary thickness is determined such that the fatigue life by the Hertz's pressure which acts on the V surface and the fatigue life by the bending moment which acts on the saddles are made substantially equal to each other. The length h1 of the V surface, which is determined in the above mentioned ways, can be about 0.26-1.0 of the saddle primary thickness h2. Thus, the miniaturization and lightening of the element is achieved by this rational method which equalizes the fatigue life for the whole body of the element while providing the element with necessary strengths.

Modeling of the electro-mechanical (e/m) impedance response of a damaged composite beam

Abstract: The electro-mechanical (E/M) impedance method has gained acceptance as an effective technique for structural health monitoring, damage detection, and failure prevention. In spite of extensive experimental validation of this novel method, very little work has been dedicated to its modeling. This paper develops a model of the E/M impedance response of a damaged composite beam interrogated by a PZT wafer active sensor. The electro- mechanical model for the interaction between the beam and the active sensor is developed from first principles. The effective axial force and bending moments induced by the PZT wafer into the beam are considered. Equations of motion for the flexural vibrations of a composite beam under moment excitation are developed. Solution in terms of normal modes with internal damping is obtained. The resulting response and the applied force are utilized to deduce general expressions for pointwise dynamic stiffness and pointwise dynamic compliance. Effective stiffness of the PZT wafer is also calculated, and the complex stiffness ratio for the PZT-structure interaction is determined. Hence, the complex electro-mechanical impedance and admittance are deduced. A numerical example is given to illustrate the method and test its effectiveness. It is found that the real part of the effective pointwise dynamic stiffness interacts at par with the PZT stiffness at structural resonance frequencies. The imaginary part of the complex stiffness ratio directly reflects the pointwise structural resonances. Consequently, the real part of the electro- mechanical impedance directly reflects the pointwise structural resonances too. The same behavior is also found in the electro- mechanical admittance. Thus, the real part of the E/M impedance and the real part of the E/M admittance are found to be direct measures of the structural response, reflective of damage presence.

Lateral buckling strengths of cold-formed Z-section beams

Abstract: This paper is concerned with the inelastic lateral buckling strengths of cold-formed Z-section (CFZ) beams. The point symmetry of the cross-section of a CFZ beam introduces characteristics that are not encountered in a doubly symmetric I-beam. Firstly, the effective section rotates after yielding, so that a CFZ beam under in-plane bending about the geometrical major principal axis is subjected to bending moments about the effective minor axis and bimoments. Secondly, the minor axis bending and warping strain distributions and therefore the lateral inelastic buckling behaviour and strengths of CFZ beams are related to the twist rotation and minor axis displacement directions. The stress–strain curves, residual stresses, initial imperfections, and lipped flanges of CFZ beams are all different to those of hot-rolled I-beams. This paper develops a realistic finite element model for the analysis of CFZ beams and uses it to investigate the elastic lateral-distortional buckling, inelastic behaviour, and strengths of CFZ beams with residual stresses and initial imperfections. The results of the study are used to develop improved design rules which are suitable for CFZ beams. The effects of moment distribution and load height on the lateral buckling strengths are also studied.