Showing papers on "Flexural rigidity published in 1979"

Effects of flexural rigidity of plates on bone healing.

Abstract: The effect of bone-plate flexural rigidity on the strength of healing bone was explored. Plates with similar shapes and a range of flexural rigidities (from 1.4 to 16.8 Nm2) were prepared from fiberpolymer composites or selected from among commercially available metal plates and applied to the anterolateral surface of osteotomized femora in dogs. At sixteen weeks, the plated femora and contralateral control femora were removed Bone specimens (composed of cortex and callus) were removed from the area beneath the plate and from the opposite side of the same femur as well as from the anterobateral surface of the contralateral control femur. The strengths of these specimens were determined in bending tests. Bone strength increased with decreasing rigidity of the plate, and the effects were more marked in the specimens taken from the side of the femur opposite that of the plate The results indicate that control of the bending * Read at the Annual Meeting of the Orthopaedic Research Society, Las Vegas, Nevada, February 3, 1977. t Division of Orthopedic Surgery, University of Utah Medical Center, Salt Lake City, Utah 84132. Please address reprint requests to Dr. Dunn. t National Bureau of Standards, Washington, D.C. 20234. § University of Utah Research Institute, Salt Lake City, Utah 84108. 1 Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 841 12. loads to which bone is subjected during healing may be an important aspect of fracture treatment. CLINICAL RELEVANCE: Initial fracture healing appears to be enhanced by rigid internal fixation. However, the ultimate strength of the bone depends not only on this phase of fracture healing but also on the remodeling that occurs. Traditional metallic plates have been shown to have unfavorable effects on bone remodeling because they prevent the underlying bone from being subjected to the stresses that are normally present. Remodeling studies have demonstrated that when the normal forces to which living bone is exposed are removed, decreased cortical thickness and increased osteoporosis ensue. These changes have been shown to be a function of plate flexibility or stiffness. The present study, utilizing flexible plates made from fiber-reinforced composite materials, indicates that the presence of more normal stress may be beneficial in early fracture healing as well as remodeling. We suggest that so-cabled stress-shielding caused by rigid metallic plates can be diminished through the use of plates constructed from more flexible composite materials. Bone is a living tissue which responds to its mechanical environment. It has been shown that mechanical stresses are needed to minimize undesirable remodeling of FIG. I EFFECTS OF FLEXURAL RIGIDITY OF PLATES ON BONE HEALING 867 VOL. 61-A, NO 6. SEPTEMBER 1979 bone, but the effects of loading and movement during fracture healing have been explored less thoroughly’3. The optimum mechanical environment for fracture healing has not been delineated, a fact that is well demonstrated by present-day clinical use of such widely divergent treatments as cast-bracing and internal fixation. We studied the response of fracture healing to various mechanical environments provided by bone plates with a wide range of flexural rigidities, and in this report we describe our experimental approach and initial findings. In studies of bone remodeling, it has been noted that use of conventional metal fixation plates results in a bone plate-bone mechanical mismatch in which the relatively rigid plates ‘ ‘shield ‘ ‘ the bone from the stress to which it is ordinarily exposed. It has been demonstrated that this socabled stress-shielding results in bone remodeling causing cortical thinning or osteoporosis, or both2’9”#{176}”3. It has also been shown that the magnitudes of these changes are functions of flexural stiffness of the plate. For exampie, Woo and co-workers, using intact canine femora, compared the effects of a conventional metallic plate with the effects of a fiber-reinforced-polymer composite plate which was geometrically similar to the metallic plate but was one-tenth as stiff. Less cortical thinning was observed with the more compliant plate. Similarly, Tonino and associates noted less remodeling beneath an even more compliant non-reinforced-polymer plate than beneath a metal plate with which it was compared. The effect of flexurab stiffness of the plate on fracture healing has been explored to some extent”36. Fracture healing is a complex continuing process, but to facilitate understanding it can be considered as composed of phases. The first phase is characterized by proliferation of callus and the second, by bone remodeling. When considering the effects of plates in bight of these healing phases, one can hypothesize two conflicting requirements during the service life of a plate. First, it must have sufficient flexural rigidity to prevent excessive motion at the fracture site, to maintain alignment and allow initial fracture healing (calbus proliferation) to occur. Subsequently, the plate should have sufficient compliance to minimize stress-shielding and the undesirable aspects of remodeling such as cortical thinning and bone resorption. We performed this preliminary study to explore the effect on fracture healing of varying the flexural rigidity of bone plates from about 4 to 40 per cent of the rigidity of the bone to be plated. It is possible to measure many aspects of the biological response of bone to the mechanical environment present during fracture healing. We chose to determine bone strength because it is of direct clinical interest. Our findings indicate that within the limits explored, decreasing the flexurab rigidity of the plate increased the strength of the healing bone. Materials and Method One class of materials available for the fabrication of internal fixation devices is composed of polymers reinforced with continuous fibers 1,3.6.5,13 These materials can be used to produce devices such as bone plates by laminating layers of the materials in a heated die under pressure. A spectrum of mechanical properties can be achieved in devices of similar geometric configuration by using different materials and lamination patterns. For our project, geometrically similar plates with a range of flexural rigidities were obtained. Some were selected from clinically used stainless-steel plates, while others were fabricated from commercially available graphite-polysulfone and glass-epoxy laminates as well as from laboratoryprepared graphite-polypropylene composites . All composite materials were tested for biocompatibility in agaroverlay tissue-culture tests and were shown to produce responses similar to those produced by samples of the USP Negative Control Plastic Reference Standard . Examples of the fabricated plates and of a stainless-steel plate are shown in Figure 1. Examples of the plates used to stabilize the femoral osteotomies. Top graphite-polysulfone; middle glass-epoxy; bottom conventional 316L-type stainless steel. The plates were approximately I 15 millimeters long, and depending on the properties desired they were fabricated with widths between about eleven and thirteen millimeters and thicknesses between 2.5 and 6.3 millimeters. All plates were approximately 1 15 millimeters long, with six screw-holes located in the same positions as in the standard steel plates. The desired spectrum of flexural rigidity was achieved not only by varying the plate materiabs but also by varying the plate widths from eleven to thirteen millimeters and the thicknesses from 2.5 to 6.3 millimeters. The flexural rigidities ranged from I .45 to 16.8 Nm2, while the axial stiffnesses were more nearby the same. The eleven plates that were more flexible had axial stiffnesses that ranged from approximately I .4 x bO” to 2.8 x lO Nm2, and the six stiffer plates had axial stiffnesses that ranged as high as 10.8 x l0 Nm2. The flexural rigidities were determined by four-point bending tests, while the axial stiffnesses were determined in compression tests. The flexural rigidities were calculated using the

Noninvasive measures of bone bending rigidity in the monkey (M. nemestrina).

Abstract: The in vivo bending rigidity and bone mineral content of monkey ulnae and tibiae were measured. Bending rigidity in the anteroposterior plane was measured by an impedance probe technique. Forced vibrations of the bones were induced with an electromechanical shaker, and force and velocity at the driving point were determined. The responses over the range of 100–250 Hz were utilized to compute the bending rigidity. Bone mineral content in the cross section was determined by a photon absorption technique. Seventeen male monkeys (Macaca nemestrina) weighing 6–14 kg were evaluated. Repeatability of the rigidity measures was 4%. Bone mineral content was measured with a precision of 3.5%. Bending rigidity was correlated with the mineral content of the cross section,r=0.899. Two monkeys were evaluated during prolonged hypodynamic restraint. Restraint produced regional losses of bone most obviously in the proximal tibia. Local bone mineral content declines 17 to 24% and the average bending rigidity declines 12 to 22%. Changes in bones leading to a reduction in mineral content and stiffness are discussed.

Isostasy and flexure of the lithosphere under the Hawaiian Islands

Abstract: Previous flexural studies on Hawaii were done under the assumption that the amount of deflection caused by the loading of the islands is equivalent to the change in Moho depth. Crustal profiles based on seismic refraction suggest an alternative measurement of deflection as the change in depth of the boundary between the basement and oceanic layers. This alternative implies the existence of an unflexed portion of the crust that represents the difference between the basement-oceanic and Moho displacements and that effectively lessens the load due to its buoyancy. This material represents either a phase change of mantle to crustal material or intrusion into the lower crust. From the basic equations of flexure and Airy isostasy a more general form of equilibrium equation is developed and can be interpreted as an addition of an elastic flexure term to the isostatic equations or an addition of a term accounting for changes in the crustal column to the presently used flexure equations. The study of simple models indicates that the most reliable parameter in estimating flexural rigidity is the wavelength of the flexure. When elastic flexure and buoyancy of added crust are considered in relation to the Hawaiian Ridge at Oahu, a plausible case is made for the presence of both. A flexural rigidity of about 1.2×1023 N m for an unfractured lithosphere is derived for the Hawaiian Islands; this value agrees favorably with results of other studies.

Manufacture of curved fiberrreinforced resin laminate

Abstract: PURPOSE:To manufacture the title laminate having improved strength and flexural rigidity, by laminating continuous fibrous materials impregnated with an uncured resin on a rotating drum under tension, and by cutting the cured material. CONSTITUTION:A plurality of prepreg sheets 1 fed by the guide rolls 3 under tension are heated by the preheater 4 at about 50-150 deg.C, fed to the rotating drum 5, and laminated by the roll 7 while removing the air between the sheets 1 in the vacuum chamber 8. The laminated sheet 1' is then pressed by the rolls 9 under a pressure of about 1-5 kg/cm heated by the main heater 10 at about 100-200 deg.C, shaped and cured into a curved form of desired thickness along the surface of the rotary cutters 11 (longitudinal and lateral cutters 11L and 11T) on the drum 5 in the longitudinal and lateral directions to give the desired fiber-reinforced resin laminate 1'''.

28—the bending behaviour of a helical filament part i: the rigidity of the helix

Abstract: The large-scale bending of a helical filament is considered. It is shown that, in many cases likely to be of interest in textile applications, the bending rigidity of the helix calculated from small-deflexion theory provides a good approximation to the large-deflexion case. The cross-section of the deformed helix and the position of the neutral axis are also discussed.

Fibre reinforced concrete in pure torsion and in combined bending and torsion.

Abstract: The paper studies the influence of steel fibres on the torsional and flexural rigidity of concrete beams. Ultimate load tests were carried out on square beams subjected to pure torsion and on rectangular beams subjected to combined bending and torsion. Steel fibres with a length/diameter ratio of 150 were used and the increases in torsional capacity and tensile strength were studied. Fibre reinforced beams were found to have a considerable post-ultimate reserve and pronounced ductility in torsion and in combined bending and torsion. Flexural loads did not cause any reduction in torsional capacity. Satisfactory predictions of ultimate torque were obtained by using sand-heap analogy and a reduced value for the tensile strength of concrete. (a) (TRRL)

Estimation of the Distributing Cross Sectional Asymmetry along the Rotor Axis

Abstract: A method is presented for estimating the asymmetry of flexural rigidity which varies along a rotor axis. The rotor is pendulously suspended with a couple of ropes and a pair of natural frequencies on two principal planes are measured. Such experimental results are combined with numerical ones for estimating asymmetry. The procedure is discussed in detail and proved to be useful with a simple asymmetric shaft model. The amount of asymmetry on an actual turbogenerator is also estimated and verified to be a sufficiently wide margine for the limit of unstable vibration.

Concrete Beams with Prestressed Elements

Abstract: The tests on 16 simply supported rectangular concrete beams reinforced with precast elements were undertaken to provide information on general charactertistics such as cracking and ultimate strength, flexural rigidity, effect of roughness of surface of elements, effective residual prestress, change in behavior of these beams when reinforced with combination of mild steel, and effectiveness of prestressing wire and the element to failure. The collapse loads calculated on the basis of the simple plastic theory gave safe and conservative values for the ultimate load capacities of the composite beams. Test data of seven symmetrically loaded two-span continuous rectangular concrete beams confirmed the ability of support hinges to redistribute the moments. A method for computing the magnitude of plastic rotation at the hinge sections along with moment-curvature relationship is proposed.

Deformation and Fracture Behavior of Stator Windings Subjected to Cyclic Bending Loading

Abstract: This paper presents the deformation and fracture behavior of stator windings under cyclic bending loading In this study, two different kinds of stator windings, which are impregnated with epoxy and polyester resins, are examined The flexural stiffness and tan? characteristics of the stator windings are measured, applying cyclic loading to the stator nd-windings of up to 107 load cycles Their variations are revealed under various strain amplitudes, and the failure mechanism of the stator windings under cyclic loading is discussed The breakdown voltage is also measured in the last stage of each test, and the correlation between the reduction rates in the breakdown own voltage and the flexural stiffness is clarified The failure criterion on the mechanical strength of the stator windings under cyclic loading is proposed

Forced vibration of a prestressed rectangular membrane: Near resonance response

Abstract: Using singular perturbation the near resonance behavior of anisotropically prestressed thick rectangular membranes is analysed to determine the effects of viscous damping, bending rigidity, prestress anisotropy and aspect ratio.

Stator iron core for rotary armatures

Abstract: PURPOSE:For reducing vibration amplitude and noise, to uniform flexural rigidity by laminating stator iron core plates having notches on the outer circumference thereof, said iron core plates being shifted circumferentially so that said notches may be dispersed in lamination direction

On Interlaminar Shear and Flexural Strengths of Composite Beam

Abstract: The interlaminar shear strength and the flexural strength are usually determined by means of the three-points flexural test because of its simplicity. These strengths are defined as the maximum stress values predicted by elementary beam theory based on Euler-Bernoulli hypotheses. However, in the three-points flexural test on composite materials, especially with high anisotropy, the stress distribution in the vicinity of central loading point is not so simple as that given by the elementary beam theory. In the present paper, the multi-axial stress distributions in the three-points flexural test and the influences of various factors such as span/depth ratio and shape of load distribution on beam are analysed in order to discuss the validity of these fracture strengths and to propose a reasonable testing method. Consequently, it is found that the local stresses at the maximum bending moment region are very high, and that, in the case of small span/depth ratio, the stress distribution differs extremely from that based on the elementary beam theory. The validity of these analytical results is confirmed by using the finite element method analysis. The initial failure behaviors can be explained by these analytical results.

Highhspeed rotary cylinder

Abstract: PURPOSE:To increase the rated number of revolutions by specifying the position of a bellow portion, axial length and bending rigidity to reduce a dangerous number of revolutions.

Uściślony opis drgań wymuszonych linii wałów z uwzględnieniem asymetrii sztywności na zginanie i podatności fundamentów

Abstract: The paper deals with linear vibrations of shaftings at periodic excitations. The derived formulae are describing the influence of an internal damping, constant axial force, shear forces and rotary inertia on flexural Vibrations. There are also given the formulae concerning with longitudinal and torsional vibrations with an internal damping taken into account. The solution method for a flexural vibrations problem in flexible supported, geared shaft systems with flexural rigidity asymmetry is presented. The possibility of applying, the deformable (or stiff) finite element technique is illustrated for the case of a crankshaft. It is assumed that each node (or stiff finite element) has 6 degrees of freedom. The size of system matrices is reduced by means of transfer matrices related to solution coefficients for adjacent shaft pieces or by use of transfer matrices referred to one crank when the finite element technique is applied.

Rotor of rotary machine

Abstract: PURPOSE:To circumferentially uniformalize the bending rigidity of a rotor without reducing the space factor of a magnetic pole section by applying an axial groove in the magnetic pole section of the rotor core and laminating and inserting a number of thin steel plates into it through a plate type matter with small wear coefficient CONSTITUTION:The groove 2a which is same as or similar to the slot 1 of the coil slot section 1a is axially arranged in the magnetic pole section 2 of the rotary core in such rotary core machines as two-pole machines The laminated thin steel sheet 9 is inserted into the groove 2a through a plate type member 11 with small wear coefficient and pressed by the wedge 10 This permits the space factor of the magnetic pole section 2 not to decrease Since the rigidity of the thin steel sheet 9 is small, the effect of the existence of the groove 2a cannot be dicreased and bending rigidity can be uniformalized