Radial Bending Moment Research Articles

Load variation of the wheel-mounted brake disc bolts of a high-speed train

The reliability of brake disc bolts is crucial to the operational safety of high-speed electrical multi-units (EMUs). It is of great significance to investigate the bolt loads to ensure the bolt service life. A theoretical analysis is completed according to the jointed structure and the service condition of the bolts. By establishing a finite element model of the wheel-rail contact, the bolt loads of the wheel-mounted brake disc under high-speed rotation are simulated. A field experiment is implemented to obtain the dynamic loads of wheel-mounted brake disc bolts of a Chinese high-speed train based on a load test technique. The tested bolt loads include the tensile force, radial bending moment and circumferential bending moment. The simulation results are compared with the field test data. It validates the finite element model. The results indicate that the bolt loads are closely related to the operation speed of the high-speed EMU. The theoretical calculation method and the finite element method both prove that the amplitude and the direction of the radial bending moment along the bolt are inconsistent. The extrema of the radial bending moments appear in the left, middle and right cross-sections. The radial bending moment at the left cross-section is larger than that at the right cross-section because of the asymmetry of the wheel structure.

Exact nonlocal solutions of circular nanoplates subjected to uniformly distributed loads and nonlocal concentrated forces

The nonlocal solutions of the bending problem of the circular elastic nanoplates subjected to uniformly distributed loads by using the Eringen’s nonlocal theory are approximate. Seeking for an exact solution of the concerning problem by adding a concentrated force; a specific concentrated force which depends on the nonlocal parameter and, therefore, vanishes in the local case, is obtained. In this context; starting from the local bending solution of the simply supported circular nanoplates under uniformly distributed loads and evolving the solution step by step, exact nonlocal solutions of the bending problem of the simply supported and clamped circular nanoplates subjected to uniformly distributed loads and the concerning nonlocal concentrated forces acting at the centers of the circular nanoplates are obtained with the expectation that the exact nonlocal solution is not very different than the corresponding exact local solution. The closed-form solutions are checked to satisfy exactly the equations of equilibrium, constitutive equations and the boundary conditions of the relevant nonlocal problem. The application of the concerning specific concentrated force, in addition to the uniformly distributed load, is seen to make the radial bending moments for the simply supported circular nanoplate and the deflections for the clamped circular nanoplate free from the effects of the nonlocality.

Response in piled raft foundation of tall chimneys under along-wind load incorporating flexibility of soil

The present paper deals with the numerical analysis of tall reinforced concrete chimneys with piled raft foundation subjected to along-wind loads considering the flexibility of soil. The analysis was carried out using finite element method on the basis of direct method of soil-structure interaction (SSI). The linear elastic material behavior was assumed for chimney, piled raft and soil. Four different material properties of soil stratum were selected in order to study the effect of SSI. The chimney elevation and the thickness of raft of piled raft foundation were also varied for the parametric study. The chimneys were assumed to be located in terrain category 2 and subjected to a maximum wind speed of 50 m/s as per IS:875 (Part 3)-1987. The along-wind loads were computed according to IS:4998 (Part 1)-1992. The base moments of chimney evaluated from the SSI analysis were compared with those obtained as per IS:4998 (Part 1)-1992. The tangential and radial bending moments of raft of piled raft foundation were evaluated through SSI analysis and compared with those obtained from conventional analysis as per IS:11089-1984, assuming rigidity at the base of the raft foundation. The settlements of raft of piled raft foundation, deflection of pile and moments of the pile due to interaction with different soil stratum were also evaluated. From the analysis, considerable reduction in the base moment of chimney due to the effect of SSI is observed. Higher radial moments and lower tangential moments were obtained for lower elevation chimneys with piled raft resting on loose sand when compared with conventional analysis results. The effect of SSI in the response of the pile is more significant when the structure-foundation system interacts with loose sand.

Bending of rectangular plates carried by vacuum cups

In order to carry thin plates, vacuum cups are frequently used. When the over-hang is large, the deflections and stresses of the plate have considerably large values. In this paper, the rectangular plate hung by circular vacuum cups is treated. The analysis is carried out for the plate, which is subjected to line loads and radial bending moments at the inner circular boundary and free at the outer rectangular boundary. In addition to these boundary conditions, the plate is subjected to different distributed loads on inner and outer domains. First, the general solutions for the deflections on each domain are obtained by using infinite series, which are expressed by the polar coordinate system. The several undetermined constants in these equations are decreased by the conditions of continuity at the inner boundaries. Satisfying the boundary conditions at the finite points on the outer edges of the plate, the deflections and stresses of the plate and the contact pressures between the plate and the vacuum cup are calculated. Typical results are presented in dimensionless graphical form for different parameters and vacuum cup edge conditions.

Green's function of a thin circular plate with elastically supported edge

The Green's function that is suitable for immediate computations, is obtained for a thin circular Poisson–Kirchhoff plate of a uniform thickness. The plate's edge is elastically supported so that the boundary values of the radial bending moment equal zero, while the shear force is directly proportional to the deflection function on the boundary. The extended version of the classical method of eigenfunction expansion is used with partial summation of the resultant Fourier expansion. The ‘singular’ component of the Green's function is analytically split off. This makes the representation accessible for engineering computations.

Some New Results on the Bending of a Circular Plate Subject to a bansverse Point Force

Two influence functions of a unit transverse point force are obtained for a thin circular Poisson Kirchhoff plate. One of these functions is constructed for a plate whose edge is elastically clamped in such a way that the edge's slope is zero, while the shear force on the edge is directly proportional to the deflection function. The other influence function is obtained for a plate that is elastically supported, with the deflection being zero and the radial bending moment being directly proportional to the slope on the plate's edge. The plates of a uniform thickness are built of an elastic isotropic homogeneous material. The extended version of the classical method of eigenfunction expansion is used. The singular components of the influence functions are explicitly split off, while their regular components are obtained in the form containing uniformly convergent trigonometric series.

Deformation of simply supported circular plate by central pressure pulse

Bending of a circular simply supported plate subjected to a central pressure pulse is investigated theoretically; the plate is assumed to be rigid perfectly-plastic and follows the Tresca yield condition. Results are presented for a central pulse of constant pressure and brief duration. If the blast pressure is sufficiently large the radial bending moment changes sign between the region of loading and the periphery of the plate. Previous analyses of pulse loading on a simply supported rigid-plastic plate gave bending moments that satisfied the yield condition only if the pressure magnitude was not very large. The present analysis extends the previous analyses into the range of large pressures.

Acoustic scattering from a fluid-loaded cylindrical shell with discontinuities: Double plate bulkhead

The far-field acoustic scattered pressure from a fluid-loaded cylindrical shell with two internal plate bulkheads is determined from knowledge of the junction forces between the shell and the internal plate structures. Results are shown for the circumferential modes n equals 0 and 2. This paper follows a previous paper in which a single internal plate bulkhead was considered. The approach used to solve for the junction forces is the same as that used in the previous paper. However, the results for the far-field scattered pressure show interesting features that can be associated with the acoustic and structural interaction between the two bulkheads. The interaction is due to both acoustic coupling and structural coupling. The scattered pressure associated with the radial forces at the bulkheads show an interference pattern with high and low intensity regions. The high intensity regions correspond to locations with constructive interference between the components of the scattered pressure by each bulkhead, which have dipolelike radiation characteristics. The low intensity regions correspond to locations with destructive interference. The same type of interference pattern is obtained in the scattered pressure component associated with the radial bending moments. The components of the scattered pressure associated with the bending moment at each bulkhead have quadrupolelike radiation characteristics. However, the contributions of these components is small compared to the other contributions. The scattered pressure components associated with the supersonic, axial longitudinal, and tangential shear waves do not show much of an interference pattern and this is mainly attributed to the fact that the scattering from these supersonic waves has preferred directions of propagation. All components of the scattered pressure show areas of high intensity at very specific frequencies which can only be attributed to structural interaction through the shell between the two internal bulkheads. The far-field scattered pressure results are presented for both bistatic and monostatic scattering.

Mechanical Properties of Human Cranium and Effect of Cranial Fractures on Extradural Hematoma.

The purpose of this study is to understand the mechanical properties of the human cranium in order to develop a FEM simulation model of the head. Craniectomy samples, autoclave bone flaps and dry cadaver skulls were tested using values of radial bending moment considered typical in the case of head injury. In this study, we developed a procedure for estimation of the mechanical properties of the cranium by assuming a proportional relation between the bone mineral density and Young's modulus. The mechanical properties of the human cranium have been determined from the three-point bending test and the bone mineral density measured by the dual energy X-ray absorptiometry. The human cranium consisted of inner and outer tables (cortical bones) and a diploe (a cancellous bone). The stress on the cortical and the cancellous bones in the field of bending stress was assumed that the cranium was a beam in which two different materials were combined. The experiment showed that fresh cranial fractures start at the inner table and the diploe and then propagate to the outer table. The fracture of a cranium taken out of a human being will exhibit elastic-plastic fractures. This fact implies that the inner table and the diploe fractures can occur even if no fracture is detected using plain X-rays in cases of acute extradural hematomas (EDH).

Axially symmetric deformations and stability of a geometrically nonlinear circular plate subjected to multiparametrical static loading

Axially symmetric deformations and stability of a geometrically nonlinear circular plate subjected to multiparametrical static loading systems are investigated by means of a so-called deformation map. The deformation map was further used for stability considerations of geometrically nonlinear shells, see Shilkrut [1, 2]. The map reveals the complete picture of the axially symmetric deformations and the stability of the investigated structure. The equilibrium differential equations for the above mentioned circular plate were derived by Timoshenko [3]. The boundary value problem of the investigated structure is transformed to an initial value problem (Cauchy's problem). Then the Runge-Kutta (R. K.) method can be used to solve numerically the equilibrium equations. The geometrically nonlinear, simply supported circular plate subjected to uniform radial force and uniform radial bending moment acting along the supported edge is investigated as example, and some new qualitative and quantitative results are obtained. This approach can be used without essential difficulties for the investigation of axially symmetric deformations and stability of a geometrically nonlinear circular plate subjected to multiparametrical static loading systems in elastic and non-elastic fields.

Flexure of orthotropic rotating disks

The influence of off-set in mounting the blades on the disk, termed “eccentricity”, and the centrifugal stiffening on the stresses and deflection induced in laterally loaded orthotropic disks of variable thickness is analysed. The analysis is based on a series solution for the differential equation governing the deflection of the disk. Numerical results showing the effects of anisotropy, eccentricity and rotation on the stresses and deflection of the disk are presented graphically. It is shown that the stress due to radial bending moment reduces significantly with the increase in the degree of anisotropy.

Dynamical bending of rigid-plastic annular plates

Dynamical bending of circular rigid-plastic annular plates, fixed along the exterior boundary and free on the interior boundary, when subjected to instantaneously applied transverse uniformly distributed blast-type load[1], is investigated in this paper. It is shown that annular plates are preferable to plates without holes, since their load capacity increases while residual deflections decrease. A so-called boundary parameter is introduced to estimate the effect of boundary conditions on the radial bending moment. A procedure for determining the residual deflections at every point of a plate is developed for use on an electronic computer. Numerical examples are given. In the end of the paper, the particularities of solution of our problem for annular plates, corresponding to the setting of Wang[2], Wang and Hopkins[3] for plates without holes are discussed.

Model Studies of Multicell Curved Box-Girder Bridges

A model study on the static response of curved box-girder bridges is presented, and a close agreement is found between the test and analytical results. The prototype bridge was a four-cell reinforced concrete design, 33 ft 10 in. (10.31 m) wide, 4 ft 10 in. (1.47 m) deep, and had a radius of curvature of 282 ft (86 m). A 1/29 scale aluminum model was studied for spans of 60 in. (1,500 mm), 45 in. (1,140 mm), and 30 in. (760 mm), with or without a midspan radial diaphragm. The quantities measured were: (1) Boundary reactions; (2) strains at a radial section close to midspan; and (3) deflections at selected points. The data were reduced by computer, and distribution graphs of tangential plate forces, radial bending moments, and deflections were plotted by Calcomp plotter. Based on the model data, some general observations are made regarding the behavior of curved box-girder bridges.

Estimation of higher natural frequencies of polar orthotropic annular plates

A method based on an assumption that the radial bending moment is zero at a nodal circle is shown to yield accurate estimates of natural frequencies corresponding to higher modes of transversely vibrating polar orthotropic annular plates for various combinations of clamped, simply supported and free edge conditions. This method is found to be convenient for the determination of locations of nodal circles as well. Numerical investigations revealed that for small holes, nodal circles tend to move towards the outer edge with increasing number of nodal diameters. For large holes, it has been shown that the plate behaves like a long rectangular strip.

Nonlinear Filtering for Random Signals in Statistically Unknown Noise

resultants are plotted for various R/a ratios at 9 •= 0. Figure 4 shows that the tangential bending moment stress resultants along the hole diminish by roughly a factor of two for each added increment in the R/a ratio. To determine the accuracy of the results obtained, an error analysis was performed. First, a residue was calculated to see how well the boundary conditions (w and M) were satisfied at each of the fourteen points along the outer boundary. Then a measure of the maximum value of the error was found for the calculated deflections and bending moment stress resultants by taking the ratio of the value of deflection or radial bending moment stress resultants at the outer edge on 9 = 0, to their respective maximum values within the plate. The deflection and bending moment residues were of the order of 10 ~, while the values of the error ratios were of the order of 10~, indicating a high degree of accuracy.

Analysis of circular plates with symmetrically stiffened perforations

A method of analysis for plates with stiffened perforations is developed. Square and triangular patterns of perforations are considered under both uniform radial stress and uniform radial bending moment. The analysis derives the effective elastic modulus of the plate and the maximum stress concentration factors in terms of a “stiffening factor” which is a measure of the effectiveness of the perforation stiffener. Results of the analysis are compared with results obtained by other forms of analysis.

A Tabular Method of Propeller Blade Stress Analysis

A tabular, trial-and-error method of evaluating the steadybending stresses in a rotating propeller blade is developed and examples of its application are given. The bending moment at a shank section of the blade is estimated and, by tabular integration, the corresponding radial bending moment distribution is calculated. Additional trials with appropriately revised shank section bending moment estimates are made until the correct distribution is found, having the physically required moment value of zero a t the blade tip. Tilted blades and blades whose section centers of gravity do not in general fall on the blade axis are shown to be readily analyzed. Because the final analysis can be quickly checked on a calculating machine and because the method is easily learned, versatile, and fast, its general adoption by the propeller industry is advocated.