Showing papers on "Flexural rigidity published in 1988"

The growth of geological structures by repeated earthquakes, 1, conceptual framework

Abstract: In many places, earthquakes with similar characteristics have been shown to recur. If this is common, then relatively small deformations associated with individual earthquake cycles should accumulate over time to create geological structures. Following this paradigm, we show that existing models developed to describe leveling line changes associated with the seismic cycle can be adapted to explain geological features associated with a fault. In these models an elastic layer containing the fault overlies a viscous half-space with a different density. Fault motion associated with an earthquake results in immediate deformation followed by a long period of readjustment as stresses relax in the viscous layer and isostatic equilibrium is restored. Deformation is also caused as a result of the loading and unloading due to sediment deposition and erosion. In this paper, the parameters that control the growth of dip-slip structures are identified. We find that the flexural rigidity of the crust (or the apparent elastic thickness) provides the main control of the width of a structure. The loading due to erosion and deposition of sediment determines the ratio of uplift to subsidence between the two sides of the fault. The flexure due to sediment load is much more important in this respect than whether the fault is normal or reverse in character. We find that, in general, real structures are associated with apparent elastic thicknesses of 4 km or less and thus with very low flexural rigidities.

The Effects of Laminated Structure on Delamination Buckling and Growth

Abstract: Cylindrical postbuckling solutions are obtained for an arbitrarily structured laminate. The strains of the middle surface contain sinusoidal terms that are in-phase with the out- of plane deflection. Bendmg-stretching coupling significantly reduces the buckling load and enhances the postbuckling deformation. The effects may be characterized by introduc ing an equivalent bending rigidity. The postbuckling solutions for a laminate with clamped ends are applied first to a thin-film strip delamination in a base laminate subjected to uni form membrane loads and next to a mid-plane delamination in a symmetric laminate. The energy release rates at the crack tip are evaluated to determine the stability characteristics of delamination growth.

Flexural stiffness and modulus of elasticity of flower stalks from allium sativum as measured by multiple resonance frequency spectra

Abstract: Multiple resonance frequency spectra (MRFS) provide a rapid and repeatable method for determining the flexural stiffness and modulus of elasticity, E, of segments of plant stems and leaves. Each resonance frequency in a spectrum can be used to compute E, and removal of the distal portion of an organ produces characteristic shifts in spectra dependent upon the geometry of an organ. Hence, MRFS can be used to quantitatively determine the extent to which a particular leaf or stem morphology can be modelled according to beam theory. MRFS of flower stalks of Allium sativum L. are presented to illustrate the technique. The fundamental, f, and higher resonance frequencies, f2 . .. fn, of stems and the ratios of f2/f,, f3/f, and f3/f2 increase as stalk length is reduced by clipping. The magnitudes of these shifts conform to those predicted from the MRFS of a linearly tapered beam. Morphometric data confirm this geometry in 21 flower stalks. Based on this model, the average modulus equals 3.71 x 108 ? 0.32 x 108 N/M2, which compares favorably with values of E determined by static loading (3.55 x 108 ? 0.22 x 108 N/M2) and is in general agreement with ultrasonic measurements (3.8 x 108 to 4.4 x 108 N/M2). Data indicate that determinations of E from a single resonance frequency are suspect, since each resonance frequency yields slightly different values for E. Statistical evaluations from all the frequencies within a MRFS are more reliable for determining E and testing the appropriateness of beam theory to evaluate the biomechanical properties of plants. THE EXTENT to which a stem can support a weight at its tip or continue to grow vertically before buckling under its own weight depends upon its flexural stiffness and the modulus of elasticity of constituent tissues (McMahon, 1975; King, 1981; Givnish, 1982). Provided it can be modelled according to some beamlike geometry, the critical buckling weight and critical buckling length of a stem can be calculated from empirically determined values of the elastic modulus, E, which measures the proportionality between stress and strain for a structure (Silk, Wang, and Cleland, 1982; Niklas and O'Rourke, 1982, 1987). Consequently, a number of workers have devised methods to determine E. Among the most common is the Instron method of testing specimens under a ' Received for publication 1 October 1987; revision accepted 25 January 1988. The authors wish to thank Mr. William Holmes and Scott Copeland (Department of Theoretical and Applied Mechanics, Cornell University) for their technical assistance, Ms. Barbara Bernstein (Section of Plant Biology, Cornell University) for rendering figures from computer hard-copy printouts, and Professor Wolfgang H. Sachse and Mr. Howard J. Susskind (Theoretical and Applied Mechanics, Cornell University) for providing preliminary data from a longitudinal ultrasonic examination of flower stalks. Support from a National Science Foundation grant BSR 8320272 (KJN) is gratefully acknowledged. uniaxial, constant strain rate (Cleland, 1967, 1971, 1984). Although this technique provides rapid and repeatable measurements of E, the appropriateness of a beam geometry to model a particular stem morphology often remains conjectural. In addition, plant organs capable of supporting their own static weight can undergo dynamic mechanical failure. We present a technique for measuring the flexural stiffness and modulus of elasticity of plant stems which can also be used to evaluate the extent to which a particular stem morphology conforms to each of a variety of beam models. The technique is based on the mathematical relationship between the elastic properties and the multiple resonance frequencies of vibration of tapered or untapered beams with various transverse geometries (Timoshenko and Gere, 1961; Gorman, 1975; Blevins, 1979). A large body of empirical and theoretical studies underpin this approach, and to a limited extent it has been applied to examining the turgor pressure and rigidity of tissues (Virgin, 1955; Falk, Hertz, and Virgin, 1958). However, to our knowledge, multiple resonance frequency patterns have not been used to study plant organs in the method presented here. We have selected the flower stalk of Allium sativum L., to illustrate this method. Garlic

Dependency of the tensile modulus on transverse dimensions, water potential, and cell number of pith parenchyma

Abstract: Uniaxial tensile tests of solid and hollow cylindrical plugs of pith parenchyma from potato tubers indicate the tensile modulus of elasticity, E, can vary significantly as a function of tissue transverse area and water potential. E increases from 1.2 to 19 MPa as *, changes from -1.4 to -0.4 MPa. E increases from 5 to 19 MPa as transverse area of solid tissue sample increases from 0.2 to 2.5 cm2. Variations in E accompanying changes in transverse area appear to be related to cell number along the radii of plugs. Hollow cylindrical plugs for which wall thickness is maintained but total tissue area is changed show constant values of E. It is suggested that shear stresses within tissue samples influence E and are dependent upon cell number and tissue water content. Material with these properties would be a "poor choice" for constructing plant organs experiencing repeated stress and periodic dehydration. However, ground tissue may act as a buffer against localized ovaling of stem and leaf cross sections under loading. PLANTS MUST BEAR their own weight during vertical growth, as well as the stresses induced by dynamic loading caused by wind and other forces (Fraser, 1962; Wainwright et al., 1976; Niklas, 1986). The extent to which they accomodate these stresses depends in large part upon the flexural rigidity of supporting tissues. Flexural rigidity is defined as the product of two parameters: the second moment of inertia (I) and the modulus of elasticity (E) (Timoshenko and Goodier, 1951; Gordon, 1978; cf. Silk, Wang, and Cleland, 1982). The second moment of inertia is a measure of the distribution of mass around the longitudinal axis of a structure and is dependent upon transverse geometry. E is defined as the proportionality constant relating stress to strain within the elastic range of a linearly elastic material (Sokolnikoff, 1956), and is a measure of material property. Theoretical treatments of inorganic, geometrically simple structures usually consider the values of E and I as constant. However, the value of E is known to vary in plant tissues as a function of water content (Robichaux, Holsinger, and Morse, 1986; Niklas and O'Rourke, 1987). Similarly, the transverse area of stems and leaves, and hence I, can vary due to the I Received for publication 1 April 1987; revision accepted 16 December 1987. The author wishes to thank two anonymous reviewers whose suggestions led to substantial improvements on the original version of this paper. This research was supported in part by NSF Grant BSR8320272. allometry of growth, or as a result of bending or injury (McMahon and Kronauer, 1976). Falk, Hertz, and Virgin (1958) presented data indicating the value of E, as measured by tensile stress, increases as the transverse area of solid cylinders of pith parenchyma from potato tubers increases. This phenomenon was most pronounced for tissue samples with a relatively high turgor pressure and was less evident in dehydrated tissue samples. Falk et al. (1958) speculated that the degree to which neighboring cells could move in response to shear stresses within the tissue was influenced by tissue water content and by the number of adjoining cells. Later studies ofithe mechanical properties of potato tubers, for example Finney and Hall (1967), failed to report a relationship between transverse area (hence cell number) and E, or involved corrections in area to accomodate inferred tissue damage (Somers, 1966). Consequently, the issue raised by Falk et al. (1958) has been largely ignored or forgotten. This paper repeats the experiments of Falk et al. (1958) and presents data on the relationships among the values of E, water potential and the wall thickness of hollow cylinders of pith parenchyma. In hollow cylinders, wall thickness can be maintained (thereby holding the number of cells in radial transect relatively constant) while varying the radius of the cylinder and hence the total cross-sectional area of tissue subjected to tension. In tandem, the results from solid and hollow cylinders indicate E changes as a function of cell number in

On large deflection effects in unsymmetric cross-ply composite laminates

Abstract: Static and dynamic behaviors of unsymmetric cross-ply laminates in cylindrical bending are investigated using von Karman large deflection theory. Due to the presence of bending- extension coupling, the effect of the large deflection term becomes pronounced even in the "small deflection" range. Further, the apparent laminate bending rigidity depends on the direction of deflection. It is also found that in free vibration at small amplitudes, large deflection theory may yield frequencies lower than linear theory.

Tepev Mons on Venus: Morphology and elastic bending models

Abstract: Tepev Mons is a large volcanic structure of about 250 km in diameter with an elevation of 5 km above the surroundings, located at the southwestern edge of Bell Regio. It is surrounded by a moat with a depth of about 0.5 km. If this moat is considered to be caused by bending of the lithosphere due to the load of the volcano, then elastic bending models give limits for the effective flexural rigidity FR and the effective elastic thickness of the lithosphere L: 2 x 1023 Nm ≲ FR ≲ 3 x 1024 Nm and 30 km ≤ L ≤ 100 km. High flexural rigidities are associated with small depressions and large thicknesses of the lithosphere and vice versa.

Effect of delamination on the flexural stiffness of composite laminates

Abstract: This paper presents the results of a study on the effect of delamination on the flexural stiffness of advancedcomposite laminates. Three- and four-point bending tests were conducted on graphite-epoxy laminates with embedded delaminations. The experimental results were corroborated with finite element method results as well as with simple beam theory models. The delaminations did not cause any degradation of the four-point bending stiffness. However, the three-point bending stiffness test showed that the delamination did degrade the stiffness by as much as 34%.

Bending beam for a door-stiffening rib, bumper, stiffening rib for a superstructure or the like

Abstract: A weight-optimised bending beam for door-stiffening ribs, bumpers, vehicle body stiffeners or the like is to be developed which has a maximum bending rigidity with a prescribed installation height h in the force application direction and as low a weight as possible, can be manufactured as a mass produced component and can be adapted to different load cases by slight modification. Bending beams for door-stiffening ribs, bumpers, vehicle stiffeners or the like consisting of a hollow profile with at least two plane-parallel deformation faces which are located opposite one another and arranged perpendicularly to the force application face in such a way that the deformation faces (2, 3) of the bending beam (1) are connected in positively and/or non-positively engaging fashion to at least one additional profile (4, 5), the centre of the additional profile coinciding approximately with the force application point and the ends extending to a point in which at least two thirds of the bending moment are reduced. Application in door-stiffening ribs, bumpers, vehicle body stiffeners or the like.

Solar cell sheet

Abstract: PURPOSE: To provide a solar cell sheet which can be bent freely and rolled up into a small diameter in the order of several centimeters, by producing a thin-film solar cell on a polymeric film substrate and composing the solar cell sheet of particular module sheets. CONSTITUTION: A solar cell sheet according to the invention consists of module sheets each comprising a thin film solar cell produced on a polymeric film substrate 21 and a protecting film layer 40 overlaid thereon through a buffering pressure-sensitive film 30. The module sheet has a thickness of 1000μm or less and flexural rigidity of 100kg.cm 2 or less when measured with a 5mm wide sample. In order to prevent properties and appearance of the solar cell from being changed when the module sheet is rolled or extended, the 5mm wide module should have flexural rigidity of 100kg.cm 2 or less, preferably of 10kg.cm 2 or less. In order that the sheet can be rolled up into a small diameter in the order of several centimeters without any problem, the module as a whole has flexural rigidity of 100kg.cm 2 or less and thickness of 100μm or less, more preferably of 400μm or less. COPYRIGHT: (C)1989,JPO&Japio

Deflection and flexural rigidity of ferrocement i- and box beams

Abstract: Etude experimentale et theorique (methodes ACI et CEB), pour diverses geometries et types de renforcement

Effect of flexural rigidity on cable tension estimated by vibration method

Abstract: The estimating method of tension imposed on bridge cables by measuring their natural frequency, so-called vibration method, is very convenient on the construction site of structures with cables. However, there still exist several problems concerning the flexural rigidity of cables that have to be overcomed so as to get reliable and accurate estimation as follows:(1) The flexural rigidity of the cable is needed to be obtained beforehand, but few data have been reported in regard to the property.(2) The accuracy of estimated cable tension, affected by the flexural rigidity in particular, is necessary has to be analysed theoretically.(3) A simple method of estimating the flexural rigidity of cables on the construction site is desired.In this paper, the above mentioned problems are theoretically and experimentally studied.

A study on ultimate compressive strength properties of longitudinally stiffened continuous plates under uniaxial compression

Abstract: This paper clarifies the ultimate strength properties of longitudinally stiffened continuous plates simply supported by transverse stiffeners with sufficient flexural rigidity under uniaxial compression. By means of the elasto-plastic finite displacement theory, in which much reduction of degree of freedom of analytical models and computer time can be greatly expected by introducing a technique similar to the usual modal analysis making use of generalized coordinates into the conventional finite element method, many models of stiffened plates with various values of parameters are efficiently analized. Moreover, the numerical results are compared with the strength curves specified by several design codes, and then the safety margin included in these design codes are discussed.

Measuring instrument for large deformation bending characteristic

Abstract: PURPOSE:To easily measure bending rigidity in a large deformation bending area by arranging a measurement cloth mount plate which is coupled directly with a force meter below the pressure plate of an elevation member which moves up and down at a constant speed. CONSTITUTION:The elevation member 1 is so formed as to move up and down by a motor 5 through pulleys 9 and 10 and the flat pressure plate 2 is formed at the lower end of the elevation member 1. Measurement cloth 8 is folded and mounted on the measurement cloth mount plate 3 and the pressure plate 2 is lowered to cause bending deformation by a large quantity. Then the current bending rigidity is detected and measured by the force meter 7. At this time, the distance between the pressure plate and measurement cloth mount plate, the thickness of the cloth to be measured, and curvature of bending to be measured are controlled by a small computer 11 incorporated in a measuring instrument and a measured value is outputted to an X-Y recorder which indicates the bending rigidity applied to the lower plate and displacement of the upper plate on respective axes.

Extraction-molded pipe

Abstract: PURPOSE:To enable obtaining of an extraction-molded product whose straightness and uniformity in bending rigidity are high, by a method wherein a tow of a reinforced fiber to at least a unidirectional reinforced layer of which a twist has been given is used and a kind of fibers is made of carbon. CONSTITUTION:A tape 2 of bias cloth forming an inner layer is shaped cylindrically on a mandrel 3 and a carbon fiber tow 1 forming a unidirectional layer is obtained by giving a twist of 20T/m to a tow of 6,000fil. These are arranged concentrically around a mandrel 3 at an inlet of a mold by an arrangement guide 4. In other wards, it follows that the tows do not piled up partially each other and a thickness of a unidirectional layer is formed uniformly as the tows of twisted threads are used for the unidirectional reinforced layer. A pipe obtained hereupon possesses sufficient high straightness of 1mm extending over a length of 1m and uniformity in bending rigidity falls within a range of 5% of an average value of the same whatever direction and part may be taken.

On several problems for lateral instability of cantilever plates

Abstract: The present article researches several problems about the lateral instability, of cantilever plates by means of the energy method, in which we discuss the minimum critical load of cantilever rectangular plates under a concentrated force, a uniformly distributed load, a distributed load in triangular form and a concentrated couple, respectively, when the lateral buckling takes place.

Lithospheric flexure and deformation-induced gravity changes: effect of elastic compressibility and gravitation on a multilayered, thick-plate model

Abstract: SUMMARY An approach is formulated by which the theoretical admittance can be evaluated for the flexure of a multi-layered elastic plate overlying an inviscid fluid. The multi-layered elastic and compressible plate is subjected to well-posed boundary conditions. Gravitational body force, elastic compressibility and elastic coupling at the interfaces with elastic modulus contrast are fully accounted for. The elastic field solution was obtained by the propagator matrix technique. The contribution to gravity change from local density perturbation within the compressible plate is also included. Our calculation shows that the density perturbation component is smaller than the Bouguer component by at least an order of magnitude over the compensated waveband. The thin-plate approximation can be used with an effective flexural rigidity evaluated from the thickness-averaged values of the elastic moduli. If there is significant elastic coupling between the crust and the mantle, the discrepancy between our results and the incompressible, thick-plate model can be quite appreciable due to the different isostatic compensation mechanisms operative within the crust. Preliminary calculations show that similar conclusions would apply to the response functions for the sub-surface loading case. Our technique can also be used to compute the stress distribution in a multilayered plate. The numerical results show that the stresses can be appreciably different from that in a homogeneous plate.

Thermal gradient effects on the vibration of prestressed rectangular plates

Abstract: The effect of a thermal gradient on the transverse vibration of a prestressed rectangular plate is investigated by the method of matched asymptotic expansions. This class of heated plate is characterised by changing its Young's modulus with temperature. Analytical results for the eigenvalues are presented for fully-clamped and fully-hinged rectangular plates when the bending rigidity is small compared to the in-plane loading. To leading order in ɛ (where ɛ2 denotes the normalized bending rigidity), the eigenvalues of an ideal membrane are obtained, independent of thermal effects.

Composite of concrete or the like having flexural tensile strength and forms left embedded

Abstract: PURPOSE: To obtain a main body having excellent tensile strength and corrosion resistance, and besides, excellent appearance by integrating a plane outer layer material comprising fiber reinforced plastics and having protrusions with heads in its inner surface, in the outer surface of at least region to be applied with flexural tensile strength of a main body having compression strength and comprising concrete or the like. CONSTITUTION: In the outer surface of the region 2 of a main body 1, a built-in mold frame is integrated, which has in its inner surface T-shaped cross-sectional protrusions 3 with heads A for improving adhesiveness and flexural rigidity of concrete, mortal, ice or the like, and a plane outer layer material 4 being a main body made of fiber reinforced plastics having flexural tensile strength, and corrosion resistance comprising forms left in place being constituted integrally. Accordingly, it has sufficiently toughness and resisting force of flexural strength and flexural rigidity through the plane outer layer material 4 comprising FRP, even if the flexural tensile strength is applied on a region 2 by a force in an arrow direction. Furthermore, the protrusions 3 with heads 3A is integrated firmly with the main body 1 of concrete or the like in biting into it under the condition of being engaged by heads 3A thereof, and since the protrusions 3 with heads 3A fulfill the function of reinforcing ribs, the flexural rigidity or torsional rigidity can be improved. COPYRIGHT: (C)1990,JPO&Japio

Uniform strength design of beams with non-zero minimum flexural rigidity under multiple loadings

Abstract: The analytical method for uniform strength design (U.S.D.) of statically indeterminate beams is extended to deal with a preassigned constraint of non-zero minimum flexural rigidity and multiple load cases. And a numerical method of finding the U.S.D. is presented. Therefore we have a uniform procedure of solution of U.S.D. to beams with arbitrary cross-sectional shape and acted upon by several loadings and subjected to the constraint of minimum flexural rigidity.

Minimum Weight of a Sandwich Panel

Abstract: The least‐weight problem of a sandwich panel with a truncated, hollow, hexagonal core, and subjected to a given bending moment along each edge is analyzed in this paper. In order to meet the practical manufacturing requirements and be within allowable stress limits, constraints are placed on the geometrical dimensions of the structural parts of the sandwich panel as well as on the physical strength, such as the allowable stresses. Upper and lower limiting values are assigned for each of the design variables. Through the use of the penalty function, the minimization problem subjected to a set of twenty inequality constraints is changed to a sequence of unconstrained ones. The modified Fletcher‐Powell method is used by a proper choice of the penalty parameter and the reduction factor. The methodology presented here can be extended to include multiple loading conditions, bending rigidity, and shear rigidity requirements, which present no additional difficulties except to increase the number of constraints.

On minimum-area convex shapes of given torsional and flexural rigidity

Abstract: This paper uses a rapidity convergent series to establish the shapes giving minimum cross-sectional area for a convex section subjected to minimum constraints on second moment of area about an arbitrary centroidal axis and on torsional rigidity. In the formulation, some properties of the solution established by earlier workers are assumed. The results give upper bounds on the minimum area which are lower than those previously available and extend solutions to the full range of design parameters. The convexity constraint becomes active for ratios of torsional to bending stiffness of 1.575 and lower.

Coupling mechanism for connecting with flexural rigidity profile beams

Abstract: not available for EP0165932Abstract of corresponding document: DE3332916Connection of profile beams (92, 98) particularly in steel hall constructions, wherein the ends of the profile beams (92, 98) are connected by a rigid frame fishplate (100) arranged on one side and enabling an adjustment motion between the profile beams (92, 98).

Monosurface, polygonal, curved bar structure

Abstract: In a bar structure consisting of structural bars (1) and polygonally curved in at least one direction, to increase the dimensional stability of the bar structure despite the low flexural rigidity of the structural bars (1) and of the bar bending points (nodes 3, 3'), in each case two bar bending points (3 and 3' respectively) are connected to one another, leaving out a bar bending point (3' and 3 respectively) lying between them, by prestressed tension members (2, 2', 5). In order to damp vibrations of the bar structure, the tension members (2, 2', 5) can be assigned spring damping elements (4, 6), which may simultaneously serve for prestressing the tension members (2, 2', 5). … …

The Assessment of Fabric Wear and Handle Caused by Increments of Accelerator Abrasion in Dry Conditions Part I: Changes in Some Fabric Mechanical Properties as a Result of Abrasion

Abstract: In this paper, sane aspects of the physical and mechanical properties of woven fabrics, such as mass, thickness, stiffness, air-permeability, and compression, are considered as criteria for assessing the effects of damage caused by changes in frictional abrasion when the Accelerator Tester is used. Two 100% cotton woven fabrics were used in the experiment. Results show that changes occurred in fabric properties as a result of incremental wear. The mass per square metre, coercive couple, and flexural rigidity show a consistent decrease, while thickness, air–permeability, and compression show inconsistent increases with increasing time of abrasion.

Vibration isolating device

Abstract: PURPOSE:To adjust natural frequency with a simple structure by installing an inside case on either of an equipment setting face and the base of an equipment and an outside case on the other and connecting said cases with a suspending member of a small flexural rigidity. CONSTITUTION:An outside case 4 is fixed to a base 1 and an inside case 5 is fixed to a floor face 2 with bolts 7 and these cases 4, 5 are connected by means of suspending members 6 having a small flexural rigidity such as a wire, a chain, etc. Accordingly, the structure can be made simple while facilitating the adjustment of the natural frequency of a system, enabling the isolation of vibration at the time of an earthquake or transportation irrespective of the weight of equipment.

Method for detecting downward warpage of material to be rolled

Abstract: PURPOSE:To calculate the downward warpage quantity of the leading end of a material to be rolled, by measuring the impact force of the material to be rolled acting on two table rollers in front of or in the rear of a rolling machine to estimate the angle of collision of the leading end of the material to be rolled to the table rollers CONSTITUTION:The angle theta0 of collision of a downward warpage part 1a at the time of the collision with a table roller 3 can be shown by theta0=cos (1-S/R) when downward warpage quantity is set to S and the radius of the roller is set to R When it is supposed that the speed of a steel plate in the horizontal direction thereof is equal to the peripheral speed of the roller, the pressing force F of the steel plate can be expressed by F=F1R[(theta0-theta)-(sintheta0-sintheta)] (wherein K1 is a definite value showing the bending rigidity of the roller and theta is the angle from the upper end of the roll to a material contact point) The bending force W of the steel plate can be expressed by W=K2/K1)R(costheta-costheta0) (wherein K2 is a definite value showing the rigidity of a rolled material) On the basis of these relational expressions, the angle theta of collision is calculated from the pressing force F or the bending force W and substituted into theta0=cos(1-S/R) to make it possible to calculate the downward warpage quantity S