Showing papers on "Bending moment published in 1995"

Impact Formulas for Vehicles Moving over Simple and Continuous Beams

Abstract: In this paper, a new set of impact formulas are developed for simple and continuous beams subjected to moving vehicle loads. By modeling a vehicle as sprung masses and a bridge structure by beam elements, a parametric study is performed for various simple and continuous beams traversed by five-axle trucks. Central to this study is the adoption of a nondimensional speed parameter s , which is defined as the ratio of the driving frequency of the vehicle, as represented by πv/L, with v denoting the velocity of the vehicle and L the characteristic length of the beam, to the fundamental frequency ω of the beam. From the numerical study, it is concluded that the impact factors for the deflections, bending moments, and shear forces at the midpoints of simple beams are linearly proportional to the speed parameter, and that these formulas can be multiplied by certain modification factors to yield results for continuous beams and support shears. Other parameters studied herein include the vehicle/bridge frequency r...

Analytical Model for Fictitious Crack Propagation in Concrete Beams

Abstract: An analytical model for load-displacement curves of concrete beams is presented. The load-displacement curve is obtained by combining two simple models. The fracture is modeled by a fictitious crack in an elastic layer around the midsection of the beam. Outside the elastic layer the deformations are modeled by beam theory. The state of stress in the elastic layer is assumed to depend bilinearly on local elongation corresponding to a linear softening relation for the fictitious crack. Results from the analytical model are compared with results from a more detailed model based on numerical methods for different beam sizes. The analytical model is shown to be in agreement with the numerical results if the thickness of the elastic layer is taken as half the beam depth. It is shown that the point on the load-displacement curve where the fictitious crack starts to develop and the point where the real crack starts to grow correspond to the same bending moment. Closed-form solutions for the maximum size of the fracture zone and the minimum slope on the load-displacement curve are given.

Extending Laser Bending for the Generation of Convex Shapes

Abstract: A summary about the present process understanding of the laser bending technology is given. Three different bending mechanisms are distinguished. Experimental results showing that at certain parameters an instability behaviour can occur are discussed. A bending mechanism is suggested which explains the stability behaviour. It is shown that laser bending can be extended in order to generate convex shapes, which means a bending away from the laser beam. The possibility of bending towards the laser beam or of bending away from the laser beam opens new ranges of applications, two of which are introduced in this paper.

A simple formulation for predicting the ultimate strength of ships

Abstract: The aim of this study is to derive a simple analytical formula for predicting the ultimate collapse strength of a single- and double-hull ship under a vertical bending moment, and also to characterize the accuracy and applicability for earlier approximate formulations. It is known that a ship hull will reach the overall collapse state if both collapse of the compression flange and yielding of the tension flange occur. Side shells in the vicinity of the compression and the tension flanges will often fail also, but the material around the final neutral axis will remain in the elastic state. Based on this observation, a credible distribution of longitudinal stresses around the hull section at the overall collapse state is assumed, and an explicit analytical equation for calculating the hull ultimate strength is obtained. A comparison between the derived formula and existing expressions is made for largescale box girder models, a one-third-scale frigate hull model, and full-scale ship hulls.

Exponential Stability of Coupled Beams with Dissipative Joints: A Frequency Domain Approach

Abstract: Two examples of coupled Euler-Bernoulli beams with a dissipative joint are considered. The joint placements that lead to exponential stability for these systems are characterized. The technique used shows input-output stability of a related controlled, observed system, and then shows that in these examples, input-output stability implies exponential stability. In the first example, the energy dissipation arises from a discontinuity in the shear at the joint. In the second example, the energy dissipation arises from a discontinuity in the bending moment at the joint. The analysis of this system involves a complete spectrum analysis of the zero dynamics of the associated controlled, observed system.

Lithospheric bending at subduction zones based on depth soundings and satellite gravity

Abstract: A global study of trench flexure was performed by simultaneously modeling 117 bathymetric profiles (original depth soundings) and satellite-derived gravity profiles. A thin, elastic plate flexure model was fit to each bathymetry/gravity profile by minimization of the L(sub 1) norm. The six model parameters were regional depth, regional gravity, trench axis location, flexural wavelength, flexural amplitude, and lithospheric density. A regional tilt parameter was not required after correcting for age-related trend using a new high-resolution age map. Estimates of the density parameter confirm that most outer rises are uncompensated. We find that flexural wavelength is not an accurate estimate of plate thickness because of the high curvatures observed at a majority of trenches. As in previous studies, we find that the gravity data favor a longer-wavelength flexure than the bathymetry data. A joint topography-gravity modeling scheme and fit criteria are used to limit acceptable parameter values to models for which topography and gravity yield consistent results. Even after the elastic thicknesses are converted to mechanical thicknesses using the yield strength envelope model, residual scatter obscures the systematic increase of mechanical thickness with age; perhaps this reflects the combination of uncertainties inherent in estimating flexural wavelength, such as extreme inelastic bending and accumulated thermoelastic stress. The bending moment needed to support the trench and outer rise topography increases by a factor of 10 as lithospheric age increases from 20 to 150 Ma; this reflects the increase in saturation bending moment that the lithosphere can maintain. Using a stiff, dry-olivine rheology, we find that the lithosphere of the GDH1 thermal model (Stein and Stein, 1992) is too hot and thin to maintain the observed bending moments. Moreover, the regional depth seaward of the oldest trenches (approximately 150 Ma) exceeds the GDH1 model depths by about 400 m.

Modelling of the mechanical behaviour of a differential capacitor acceleration sensor

Abstract: A mechanical model and its mathematical solution are presented, which have been developed in order to calculate the sensitivity and frequency behaviour of an acceleration sensor. The sensor is built up as an interdigitated differential capacitor and is driven in a 'high frequency' detection circuitry with an overall electromechanical closed-loop configuration. It is fabricated using surface micromachining techniques and consists of 2 μm thick polysilicon beams. Due to the processes during manufacturing technology, the material contains an inherent tensile stress, such that the mechanical behaviour is not only determined by the restoring bending moments of the suspension tethers. The calculated deflection of the sensor element amounts to only 0.6 nm g−1; its resonance frequency is about 21 kHz. The results will be discussed and compared with the results obtained by finite-element analysis.

Vertical load distribution on a three-unit prosthesis supported by a natural tooth and a single Brånemark implant. An in vivo study.

Abstract: In vivo bite forces, implant axial forces and bending moments were measured on 5 patients with fixed posterior prostheses supported by a natural tooth and a single Brinemark implant. The results demonstrate that the vertical loads applied to the prostheses are shared between the tooth and the implant. The maximum bending moment transferred to the implant (10–15N.cm) was well below the acceptable load limits for the mechanical components (50–60N.cm), even at bite forces exceeding 100 N. The main reason for this load sharing seems to be the inherent bending flexibility of the implant screw joint, which matches the axial flexibility of the periodontal ligament of the tooth.

Structural Dynamic Loads in Response to Impulsive Excitation

Abstract: The modal approach is used to analyze the dynamic loads on a flexible structure due to local impulsive excitations such as that caused by store ejection from a flight vehicle. First-order, time-domain equations of motion in generalized coordinates are constructed for restrained and free-free structures, without and with unsteady aerodynamic effects. The dynamic loads associated with the structural response are expressed by the mode displacement (MD) and by the summation-of-forces methods. The MD approach is simpler and easier to apply, but requires the inclusion of more modes for obtaining results of acceptable accuracy. A rigorous comparison between the resulting loads shows that the performance of the MD method is especially poor when the excitation is local and impulsive. A dramatic improvement is obtained when the generalized coordinates are based on normal modes calculated with fictitious masses at the excitation points. Fictitious masses are also used to generate artificial load modes that yield simple and efficient expressions for integrated shear forces, bending moments, and torsion moments at various structural sections.

Component Dowel-Bar Model for Load-Transfer Systems in PCC Pavements

Abstract: A component dowel-bar model has been developed to simulate the doweled joint in portland-cement-concrete (PCC) pavements. The model consists of two bending beams of finite length, embedded in concrete, connected by a shear-bending beam. The objective is to model the dowel-bar load-transfer mechanism in PCC pavements. The new model can appropriately consider the interaction between concrete and embedded dowels. The model allows a rigorous numerical analysis without an increased number of unknowns. The model can be integrated into a finite-element program to predict the responses of the load transfer system, including distributions of bending moment, shear force and bearing stress of each dowel without using the assumption of effective length. A comparison between experimental and analytical results has verified that the component model can be used to reasonably predict the responses of a dowel bar load transfer system.

Shear Key Performance in Multibeam Box Girder Bridges

Abstract: This report describes a series of field tests of multibeam prestressed box girder bridges. The objective of the test was to investigate the in–situ performance of the grouted shear keys, located at the longitudinal joints between adjacent girders. The longevity of these joints can be a problem with this type of bridge; failure of the joint will typically not only compromise the load–sharing mechanism between adjacent girders, but also lead to the failure of the deck waterproofing system, with attendant corrosion problems. The tests consisted of monitoring relative displacements occurring across the intergirder joints, as well as bending strains in the girders themselves during passages of a preweighed tandem–axle dump truck, with axle loads typically in the range of 84.7kN (19 kips). Relative displacements were measured with an especially designed transducer, having a resolution on the order of 0.00254 mm (0.1 mil), which was bonded to the underside of the bridge across the intergirder joints. Bending strains in the girders were measured with conventional foil strain gauges, having a gauge length of 38 mm (1.5 in.) All bridges tested exhibited relative displacements across at least some of the joints, which indicated a fractured shear key.

Elastica of Simple Variable-Arc-Length Beam Subjected to End Moment

Abstract: This paper presents two methods to find the elastica of a bar or a beam of given span length, but unknown arc length. The beam is subjected to a moment at a hinged end that can slide freely over another support. In the first method the differential equation based on large-deflection theory is formulated and solved by using elliptic integrals. The method yields an exact closed-form solution. The critical or maximum applied moment the beam can resist is also obtained by this formulation. Further, the well-known small displacement solution can be obtained from the degeneration of the exact solution by considering small rotations. The second method is based on a variational formulation, which involves the bending strain energy and work done by the end moment. The finite-element discretization of span length instead of bar length is used to solve the problem. Numerical comparisons are given and results from the finite-element method show good agreement with the elliptic integrals solutions.

Torsional and stiffness properties of nickel–titanium K files

Abstract: The purpose of this study was to compare stiffness and resistance to fracture of four brands of nickel titanium K files. Instruments of sizes 15 to 40 were tested according to ANSI/ADA Specification No. 28. Resistance to fracture was determined by twisting and measuring the maximum torque and angular deflection at failure. Stiffness was determined by measuring the moment required to bend the instrument 45 degrees. The permanent deformation angle remaining between the tip and the flutes of the instruments after bending ceased was also recorded. Nickel titanium K files satisfied and far exceeded specification standards for stiffness. They also satisfied and exceeded the standards for angular deflection at failure. They met or exceeded the maximum torque at failure standards in all sizes except for the size 40 of the Maillefer Niti, and the size 30 of the MacSpadden Niti. Nickel titanium K files presented a null permanent deformation angle. Clinical studies are required to evaluate the influence of low bending moment on other properties such as breakage and canal transportation.

Effects of Modeling Soil Nonlinearity and Wall Installation on Back-Analysis of Deep Excavation in Stiff Clay

Abstract: This paper describes the application of two relatively simple models: a linear elastic–perfectly plastic Mohr–Coulomb and a nonlinear “brick” model for simulating the top–down construction of a multipropped excavation in the overconsolidated stiff–fissured Gault clay at Lion Yard, Cambridge, with and without wall installation effects modeled. Numerical results are evaluated through comparisons with the comprehensive case record at Lion Yard, Cambridge. The objectives of the comparisons are to illustrate the effects of modeling wall installation and soil nonlinearity inside the yield surface on geotechnical designs. These comparisons are thus focused on aspects in which the practicing engineers are most interested, including the bending moments and deflections of the diaphragm wall, the strut loads, and the ground movements around the excavation. The results of the comparison demonstrate that the use of a Mohr–Coulomb model with a “wished–in–place” wall can reasonably predict the maximum bending moments and deflections of the wall for design purposes once the input soil parameters are correctly estimated. However, it significantly overestimates strut loads and fails to estimate the general ground deformation pattern.

Analysis of cantilever sheet-pile walls in cohesionless soil

Abstract: A revised method is proposed for the analysis and design of cantilever retaining walls in homogeneous cohesionless soil. Like the current limit-state design methods, the revised method is based on assumed linear pressure distributions but does not require the artificial simplifications inherent in those methods. Furthermore, these pressure distributions provide equilibrium without being directly dependent on assumed limit states in the passive earth support regions. They are dependent, however, on one empirical parameter for which a suitable value is determined, from the results of centrifuge model tests, within very narrow limits. The revised method gives critical depths of excavation closer to those observed in centrifuge tests than the current methods, and it is shown to yield complete bending moment distributions, with magnitude and position of maximum bending moments reasonable close to those observed. Finally, simple equations and design curves are presented to facilitate safe design, their use is illustrated with a typical example, and comparisons are made with the current methods.

Vibration of Thin-Walled Box-Girder Bridges Excited by Vehicles

Abstract: This paper presents a procedure for obtaining the dynamic response of thin-walled box-girder bridges due to truck loading. The box-girder bridge is divided into a number of thin-walled beam elements. Both warping torsion and distortion are considered in the study. The analytical vehicle is the American Association of State Highway Transportation Officials (AASHTO) HS20-44 truck simulated as a nonlinear vehicle model with 11 independent degrees of freedom. Four different classes of road-surface roughness generated from power spectral density function for very good, good, average, and poor roads are used in the analysis. The proposed procedure has been checked against the folded-plate method studied by former investigators. The comparison between these two methods is very good. The analytical results show that the dynamic response of vertical bending moment is caused mainly by several vibration modes, and that of torsion and distortion is greatly affected by the higher modes.

Orthopedic bone plate bending irons

Abstract: The present invention is a simple machine that permits the concentrated application of a bending moment to a stiff metallic bone plate. The present invention permits bends along three orthogonal torsional axes. The present invention can be scaled so that modest sized operators can bend the most stout bone plates. The bending moments are transmitted to the bone plates through the edges of curved apertures so that the built in transverse curvature of the plate is not crushed with resulting weakening of the plate. Finally, the apertures are rotated and angled to provide comfortable hand clearance and to permit efficient application of muscle force by the operator.

Relationship between file size and stiffness of nickel titanium instruments

Abstract: The purpose of this study was to evaluate the relationship existing between file size and stiffness for 3 endodontic files made of nickel titanium. Three groups of instruments with different cross-sections were tested: a triangular cross-section, a square cross-section and a modified triangular cross-section. The instruments were tested from size 15 to size 40 or 60 according to ANSI/ADA specification no. 28 for binding moment evaluation. There was a statistically significant difference between the 3 groups: the square cross-section K files presented a larger bending moment than the triangular cross-section K files, which presented a larger bending moment than the modified cross-section K files. Like the stainless steel instruments, there was an exponential relationship between file size and bending moment for triangular and square cross-section K files, but a linear relationship between file size and bending moment for the files with a modified triangular cross-section.