Showing papers on "Bending moment published in 1988"

On the calculation of energy release rates for cracked laminates

Abstract: A general method is given for calculating the energy release rate G from the local values of bending moments and loads in a cracked laminate. This total value is then partitioned into mode I and II components. Examples are given of the analysis of several test geometries including both variable and constant ratio mixed mode tests. Solutions for compression failures with buckling are also given. Finally there is some discussion of specimen compliances and stability criteria for fixed load and fixed displacement.

The Euler-Bernoulli beam equation with boundary energy dissipation

Abstract: : Many problems in structural dynamics involve stabilizing the elastic energy of partial differential equations such as the Euler-Bernoulli beam equation by boundary conditions. Exponential stability is a very desirable property such elastic systems. The energy multiplier method has been successfully applied by several people to establish exponential stability for various PDEs and boundary conditions. However, it has also been found that for certain boundary conditions the energy multiplier method is not effective in proving the exponential stability property. A recent theorem of F. L. Huang introduces a frequency domain method to study such exponential decay problems. In this paper, we derive estimates of the resolvent operator on the imaginary axis and apply Huang's theorem to establish an exponential decay result for an Euler-Bernoulli beam with rate control of the bending moment only. We also derive asymptotic limits of eigenfrequencies, which was also done earlier by P. Rideau. Finally, we indicate the realizability of these boundary feedback stabilization schemes by illustrating some mechanical designs of passive damping devices.

Dynamic wheel loads from bridge strains

Abstract: Earlier impact studies on a small span bridge under service loads gave impact fractions much higher than those specified by AASHTO. This paper represents the first stage of a programme to identify the high impact vehicles. It describes theoretical studies which use bridge measurements to estimate not only the equivalent static loads but also their dynamic variation with time. Acceptable estimates have been obtained. The use of measured bending moments gives better results than measured deflections. The correct selection of nodal spacing and arrangement is important (a).

Behaviour of diaphragm walls in clay prior to collapse

Abstract: Centrifuge model tests have been used in an attempt to gain a coherent view of the soil-structure interaction behaviour following the excavation of soil in front of a pre-constructed wall. Excavation was simulated by the removal of a suitably heavy fluid from a preformed cavity. The broad replication of stress magnitudes and stress paths permitted the full representation of wall deformation, soil strain and swelling, completing a 50 year full-scale lifespan in under 24 hours of continuous centrifuging. Measurements were made of soil displacement vectors, pore water pressures, wall displacements and bending moments together with forces in props when they were present. These have made possible the validation of simplified ‘geostructural mechanisms’ which offer the same degree of advantage to the designer as does the idealization of heam behaviour encapsulated in engineer's beam theory. A serviceability criterion for soil or wall displacements can be entered into simplified admissible strain fields appropria...

Response of the ligamentous lumbar spine to cyclic bending loads

Abstract: The effect of a "pure" cyclic flexion bending moment on the three-dimensional load-displacement behavior of fresh ligamentous lumbar spine was investigated. The load-displacement behavior, for 11 L1-sacrum specimens, pre- and post-cyclic fatigue bending tests were quantified using a Selspot II system. A special fixture was designed to mount the specimen within the MTS system to administer "pure" cyclic flexion bending, under displacement control, for 5 hours. The testing was accomplished in a 100% humidity chamber at 0.5 Hz. The maximum cyclic bending moment, based on the literature dealing with loads experienced by the spine during activities involving lifting, was set at 3.0 Nm. An increase in motion of the order of 10% in the extension loading mode was observed. The increase in motion in other loading modes was not significant. In the extension loading mode, the increase in the anteroposterior displacement (retrodisplacement) in general was higher than the corresponding rotation component. The results suggest that the bending moment of low magnitude, usually experienced by the spine during activities of daily living, alone may not trigger the mechanical failure processes in the disc. The presence of high axial compressive loads on the disc seems to be the main contributing factor in this process. The presence of bending moments and axial twist along with axial compressive load may accelerate the unstable processes leading to low back pain.

Stresses and rate of twist in single-cell thin-walled beams with anisotropic walls

Abstract: The classical theory of elastic thin-walled beams of (assumedly) nondeformable cross section, familiar to aerospace structures engineers, is generalized to the case in which the walls are anisotropic. The assumed anisotropy is such as to allow coupling between cross-sectional shear flow and longitudinal strain and, reciprocally, between shear strain and longitudinal stress. The theory and several illustrative applications show that anisotropy of the walls can, as expected, lead to coupling phenomena not present in the classical theory, e.g., twist due to bending mements, bending due to torque, twist due to tension, and extension due to torque, thus confirming the well-known possibility of "tailoring" elastic behavior through the use of laminated composites. It is also shown that anisotropy of the walls can lead to a nonconstant rate of twist in uniform beams even if the cross-sectional torque and shears are constant. Another interesting outcome of the present theory is its prediction that the shear flows are independent of the coupling constant in the constitutive equations, i.e., the constant that defines the longitudinal strain due to shear flow and the shear strain due to longitudinal stress, and also independent of the elastic constant relating shear strain to shear flow.

An evaluation method of longitudinal stiffness of shield tunnel linings for application to seismic response analyses

Abstract: This paper presents a practical method to evaluate the longitudinal stiffness of shield tunnel linings which is of great importance in the seismic response analyses of shield tunnels. Linings of shield tunnels are constructed assembling a number of segments and joints, and have structural discontinuity in the longitudinal direction. In this paper, relationships between stress and deformation of segments-joints system, both for axial force and for bending moment, are formulated into the form of “equivalent stiffness”, i. e., the stiffness of uniform beam having the same stress-deformation relation as that of segments-joints system.Modeling the lining into a uniform beam with the equivalent stiffness, it makes possible to analyze behavior of shield tunnels by means of seismic deformation method as well as other pipe-like underground structures. Parameters which have influence on the equivalent stiffness are also discussed.

Damage‐Enhanced Creep in a Siliconized Silicon Carbide: Mechanics of Deformation

Abstract: Continuum mechanics methods were employed to analyze creep deformation of a grade of siliconized silicon carbide at elevated temperatures. Three loading modes (tension, compression, and bending) are considered in this analysis. In tension, deformation is accompanied by cavitation at stresses in excess of a temperature-dependent threshold level, resulting in bilinear power-law creep. In compression, greater applied stresses are required to achieve the same rate of strain, and although bilinear creep behavior is also observed, a single power-law creep equation was assumed to simplify the mathematical analysis of the flexure problem. Asymmetrical creep in siliconized silicon carbide leads to a number of unique features in flexural creep. At steady state, a threshold bending moment exists below which no damage occurs. The neutral axis shifts from the geometric center toward the compressive side of the specimen by an amount that depends on the level of applied stress. Cavitation zone shapes, which are predicted to develop in a four-point bend specimen as a function of load, are found to be in qualitative agreement with those obtained experimentally. For transient creep under bending, the time-dependent neutral axes for stress and strain do not coincide, although they do converge toward a single axis at steady state. Quantitative predictions are given for relaxation of tensile stresses at the outer fiber, reverse loading in the midplane region, and the growth of the damage zone toward the compressive side of the flexural specimen. This load redistribution leads to a prolonged transient stage as compared to its counterpart in uniaxial creep.

Thermal contraction and the state of stress in the oceanic lithosphere

Abstract: Nonuniform contraction of the oceanic lithosphere as it cools and thickens following its formation at the axis of a spreading center results in a complex three-dimensional state of deviatoric stress which can be separated into two parts: a thermal bending stress due to changes in the vertical temperature distribution and a thermal contraction stress due to lateral variations in the vertically averaged temperature. We examine thermal contraction stresses due to temperature changes in a thin, semi-infinite rectangular plate bounded by the spreading center axis. Two stress-free boundaries, representing transforms or fracture zones, define the plate width or ridge segment length L. With the bottom of the elastic plate defined by a prescribed temperature, the plate thickens as the square root of age, as expected for a thermal boundary layer due to vertical conductive cooling. Above this prescribed temperature, elastic stresses are assumed to relax quickly. Stresses are obtained by properly accounting for the rate of accumulation of the vertically averaged stress as initially stress-free material is added to bottom of the cooling, thickening plate. The state of thermal contraction stress calculated from this model is characterized by large tensile stresses at the boundaries of the plate and relatively low stresses in the plate interior. At the ridge axis, ridge-parallel tensile stresses are about 300 MPa, the same as if the plate were not allowed to contract in this direction. Along the transform boundary, the maximum transform-parallel tensile stress occurs at a distance L/2 from the ridge-transform intersection, where its magnitude is comparable to the stress at the ridge axis. The tangential stresses at the plate boundary decrease rapidly with distance from the boundary; at a distance of L/4 from the ridge axis the ridge axis parallel stresses are one tenth of their ridge axis magnitude. The stress magnitudes are independent of both spreading rate and ridge segment length. A large transform-parallel tensile stress may control the length of transform offsets. Thermal bending moments are influenced by the large thermal contraction stresses near the ridge axis. However, a short distance from the ridge these moments attain their free horizontal contraction values which previous studies have shown to cause observable bending of the plate and a geoid anomaly at fracture zones. Flexure due to thermal bending moments will concentrate bending stresses at a distance from the fracture zone determined by the flexural length of the plate, thus providing a natural length scale controlling the spacing of transforms.

Characterization of the mechanisms producing bending moments in polysilicon micro-cantilever beams by interferometric deflection measurements

Abstract: Polysilicon micro-cantilever beams and doubly-supported beams are fabricated and conditioned with phosphorus doping and high-temperature anneal cycles to assess the effects of process history and geometry on polysilicon microstructure rigidity. Using a Linnik interferometer, deflection trends for series of beams are measured and compared for several process conditions. Two bending moments can induce beam deflection: the first due to the beam boundary support, and the second due to stress nonuniformity through the beam thickness. A comparison of polysilicon microstructure deflection behavior for doping and annealing conditions is presented and discussed. >

Bending-wave propagation by microtubules and flagella

Abstract: The movement of an elastic filament in a viscous medium can be computed from the fourth-order nonlinear partial differential equation obtained by balancing bending moments at all points along the length of the filament. These bending moments result from active forces, elastic resistance to bending, and viscous resistance to movement through the medium. I have studied numerical solutions obtained for two situations of biological interest: For the movement of individual microtubules, the active force is generated by interaction between the microtubule and the substratum over which it is moving, and is directed along the axis of the microtubule. The computations can reproduce the gliding movement of unrestrained microtubules, and also the periodic bending and bend propagation seen when the leading end of the microtubule is restrained. No modulation of active force is required to generate bending waves. For the movement of flagella, the active forces are generated internally as sliding forces between adjacent members of a cylinder of nine microtubular doublets. Without some additional control assumptions, the forces will be balanced and no bending moments will be generated. The problem faced by investigators of flagellar motility is to determine the control mechanisms that operate to make the system asymmetric, so that active bending moments are generated. Computations with models in which the curvature of the flagellum modulates the active-force generators have indicated that this control specification is sufficient to generate oscillation and bend propagation, but is insufficient to completely determine the movement.

Draw bar force sensing locomotive control system

Abstract: An improved strain sensor is disclosed utilizing a linear variable displacement transducer (LVDT) to precisely output the linear strain over a structural member. The LVDT is mounted utilizing a position apparatus having a similar coefficient of thermal expansion as the structural member, and effectively integrates the strain over the entire longitudinal dimension of the member by precisely measuring displacement under load. This assembly is readily incorporated in locomotive couplers and crane structures having a void or hollow coinciding with the neutral bending axis of the member being tested, as well as over relatively large spans, in pairs or singly, having bending moments present. A locomotive control system for increasing the strain on a locomotive coupler by monitoring the draw bar force with an associated generator speed and maximizing the draw bar force by manipulating the generator speed. A CPU interconnects the draw bar force sensor and the engine generator and makes comparisons and calculations necessary to set the generator speed in order to maximize draw bar force.

Method and apparatus for the bending of workpieces

Abstract: In a method for the bending of workpieces by swivel bending jaws, the bent-off part is to assume a predetermined bending angle with respect to the workpiece, for this purpose, in a first bending operation, at least one corresponding leg is to be bent off from the workpiece by means of the swivel bending jaws. Then, the swivel bending jaws are released from the leg and a springback of the leg or the actual bending angle is determined by direct measurements and compared with a set bending angle. Subsequently, an agreement is established between set bending angle and actual bending angle by a renewed bending operation, by a bending-over.

Stochastic Equivalent Linearization for 3‐D Frames

Abstract: Recent state-of-the-art reports emphasize the generality of stochastic equivalent linearization techniques in the nonlinear dynamic analysis of stochastically excited structures. When a three-dimensional frame is considered, it cannot be studied by decomposing the structure into several plane frames due to the impossibility of summing the effects that characterize nonlinear analyses. The equations of motion must be written for the whole structure. This is made possible by the knowledge of the constitutive law for the single story of the frame. Such a constitutive law can be identified from experimental data for regular buildings; otherwise, its dependence on the geometrical and mechanical properties of each structural element must be specified. This paper shows how the equations of motion can be written starting from the hysteretic constitutive law in the single potential plastic hinge in terms of the two bending moments and of the associate inelastic rotations. The generalization, including axial and shear forces and twisting moment in every beam section, is straightforward, but the dimension of the solving system for the equations quickly becomes impressive. Limitation to the bending moments provides the general features of the response and permits the analyzer to determine possible global torsional effects.

Wheel loads from bridge strains: laboratory studies

Abstract: Laboratory tests are described that explore the validity of using bridge measurements to determine not only equivalent static wheel loads but also their dynamic variation with time. A 12.2-m span composite girder was loaded with one to four dynamic loads fixed in location. Acceptable load predictions were obtained from measured strains and computed bending moments at the one-eighth points of the span. Estimates of dynamic load at a reduced accuracy were also obtained from measured deflections. Accurate dynamic calibration tests were necessary to find the equivalent beam-bending stiffness used in the dynamic interpretive analysis and also the strain-bending moment relationships.

On the bending moment capability of the pressurized abdominal cavity during human lifting activity.

Abstract: A theory has been developed for calculating the maximum bending moment which can be carried by the abdominal cavity pressurized by the intra-abdominal pressure. It is predicted that this bending moment is independent of the thickness of the abdominal wall and varies as pA 3/2, where p is the intra-abdominal pressure and A is the cross-sectional area of the abdominal cavity. An example has illustrated that the bending moment is capable of reducing the compressive load on the lumbar spine and the tensile load in the lower back muscles by about 20% during heavy lifting activity. Based on the theory an hypothesis is advanced to explain why certain types of lower back injury may occur during physical activity.

Hydraulic press platon support

Abstract: A hydraulic press for compacting materials with a large platen area has a platen support comprising of four hydraulic cylinders, one at each corner of a rectangular or square shaped platen. The cylinders are supplied with near equal fluid flows from commercially available hydraulic flow dividers. When an off-centered platen loading is encountered, the cylinders will respond with a higher restraining force from the cylinders nearest the load with relatively small bending moments transferred to the cylinder rods. The resulting platen structural load resembles a beam supported with pinned connections. The resulting press capacity can be significantly higher than that achievable with guided type platen supports of similar costs where the bending moment is restrained by the stiffness of the guides.

Stiffness Coefficients of Noncircular Curved Beams

Abstract: The stiffness coefficient matrix for a curved member of constant cross section considering the effect of flexural deformation is presented. This matrix relates the member-end rotations, vertical deflections, and horizontal translations to the internal bending moments, vertical shears, and horizontal thrusts. Expressions of the stiffness coefficients have been derived for noncircular curved beams of cycloidal, catenary, elliptic, and sine shapes. For curved beams of circular and parabolic shapes, expressions can be found from the writers' previous work. For a given curbed beam with the beam-height-to-span ratio known, the stiffness coefficients can be obtained from the derived expressions. Finally, with some modifications, this matrix can be applied to curved beams of variable moment of inertia.

Mechanical properties within the growth zone of corn roots investigated by bending experiments. II: Distributions of modulus and compliance in bending

Abstract: A bending technique was used to infer the spatial distributions of rheological properties within the growth zone of the root of corn, Zea mays. "Bending modulus" (ratio of stress to strain, calculated from engineering theory of bending) falls from 20 MPa near the root tip (3 mm from the tip) to 6 MPa at the location 6 mm from the tip and then remains uniform through the basal region of the growth zone. Where growth stops, at 11-12 mm, there is a sharp rise in bending modulus. The profile of bending moduli is not changed by root incubation temperature during the growth period prior to bending, but it is shifted to the left in roots growing more slowly than the average at either of two temperatures (19 and 29 C). The spatial distribution of "compliance" (reciprocal of bending modulus and a measure of tissue extensibility) resembles the distribution of swelling in response to osmotic perturbation. The distribution of compliance does not parallel that of growth rate. Attempts to explain the discrepancy between compliance and growth rate lead us to examine the theoretical basis for the calculations and to suggest that the dependence of compliance on rate of stretching is physiologically important. PLANT ORGANS grow as their cell walls extend under an internal hydrostatic pressure. The mechanical properties of cell walls have been the subject of much study because of their important role in growth (reviewed in Cleland, 1971; Taiz, 1984; Cosgrove, 1986). Over the past 60 years several techniques have been used to analyze wall properties. In early investigations, deflections of plant tissue segments hung with weights characterized tissue extensibility (Heyn, 1931). In later work, an instron stressstrain analyzer permitted examination of forcedisplacement-time relationships and resulted in a characterization of the extensibility of plant walls under various environmental conditions (Cleland, 1967; Haughton and Sellen, 1969; Masuda et al., 1974). These studies clarified the effects of hormones on plant growth mechanics. In recent review articles, Silk (1984) and Cosgrove (1986) emphasized the importance of refining the earlier studies to include a consideration of the distribution of extensibility within the growth zone. In most organs, growth is distributed over less than a centimeter oftissue; and an understanding ofgrowth I Received for publication 13 May 1987; revision accepted 17 September 1987. Supported in part by NSF grants DCB-841704 and RII8503652. 2 Current address: Department of Information and Computer Science, University of California, Irvine, California 92717. 3Send reprint requests to this address. dynamics requires a knowledge of tissue extensibility on a spatial scale of millimeters. A newer approach, the pressure probe, shows promise for resolving the spatial distribution of wall extensibility within the plant organ (Cosgrove, 1985; Van Volkenburgh and Cleland, 1986). Here we report the results of a complementary technique, based on the physics of beam bending, to estimate the intraorgan distribution of mechanical properties. We evaluate the spatial distribution of local curvature which develops in response to an imposed bending moment and use the engineering theory of bending to infer the distribution of mechanical properties which might be related to growth. MATERIALS AND METHODSExperimental conditions for growing seedlings of corn (Zea mays crow single cross hybrid WF9 x HO 17) and the apparatus for bending roots were described in a companion paper (Silk and Beusmans, 1988). "Swell and shrink" experiments were conducted to verify the distribution of compliance computed from the bending experiments. Root tips were excised and marked with a pen at approximately millimeter increments and were placed in distilled water for two minutes, photographed, placed in -10 bar mannitol solution for two minutes and rephotographed. Root images were enlarged 20-fold, and percent length change was calculated from digitized photographs of the marked roots.

Internal-pressure-bearing female screw

Abstract: An internal-pressure-bearing female screw adapted to be applied with a varying composite load due to variation of an internal pressure, in which the thread contact heights of the female screw are formed so as to be successively lowered along the direction of an applied tensile load, whereby the bending moments per unit length at the bottom of valleys of the respective female screw threads are equalized to reduce the maximum bending moment and the bending moment amplitude.

A new finite element scheme for bending plates

Abstract: Using a mixed formulation a new finite element for bending plates is suggested. It appears as an extension of numerical scheme used in fluid mechanics. One of its advantages is that both triangular and quadrangular element can be used. Furthermore, it implies an accuracy O( h 2 ) on the bending moments or the transverse shear for a low cost. Finally, the element works for arbitrary boundary conditions.

Torsional damping device

Abstract: A description is given of a torsional damping device, in particular a spiral-spring damper for motor-vehicle friction clutches/brakes, the said torsional damping device having an input part and an output part arranged coaxially, rotatable about the same axis and capable of twisting to a limited extent relative to one another, and having at least one spiral-spring arm, the inner end of which is attached to the hub flange of the output part and the outer end of which is attached to the input part. The essential feature here is that the radial cross-section (height) of the spring arms (23, 28, 33) is designed to match the load (bending moment), which varies along the arms, the smallest cross-section being provided in the transition zone (26) in which the point of contraflexure (M = 0) occurs. This provides the advantage that the spring arm is particularly elastic and has a large work storage capacity, that a saving is made on materials, and that uniform loading of the material and a favourable mass moment of inertia etc. are achieved. The spring elements can be designed as individual arms or as a multi-armed spiral-spring ring (21) and combined with others to form an assembly.