scholarly journals Eurocodes for bridge design versus mechanics

2013 ◽  
Vol 12 (2) ◽  
pp. 031-038
Author(s):  
Sławomir Karaś ◽  
Wioleta Czubacka

Regulations on which designers base their process of designing of any engineer structures should  include and combine mechanics, loads and dimensioning. It is not always the case as far as eurocodes are concerned. Ambiguities appear everywhere, which  sometimes leads to  incorrect understanding of a norm. The authors meticulously analysed  basic mechanical terms. Their digressions began with  the concepts of strain and deformation that have discrepant definitions in sources from other countries. The next part of article discusses the concept of „shear lag”. It is treated as an elementary concept in the eurocodes, although is has not been defined yet. Other sources define it as cooperating width and shear strain in the beam flanges or as stretching. Polish translation mentions the effect of „wide stripes”. The authors focused also on dynamics – especially while discussing first natural frequencies denoted as “n0”. They scrutinised  the norm EN 1991-2 in which dynamic problems of bridges are understood as effects of service load when the  environmental impact is not included. As always, in a situation when there is a doubt, it is possible apply the to accurate mechanics rules. To sum up, Polish versions of bridge eurocodes should be corrected to be unambiguous and useful in a design.

2011 ◽  
Vol 305 ◽  
pp. 57-60
Author(s):  
Da Lei Li ◽  
Yue Feng Yin ◽  
Fang Fang Ding

The conical spring is one critical part of DANA MHR-3200 series Transmission, its structure is compact and it has good stability and used for bearing larger load and vibration attenuation. Using SolidWorks Simulation to conduct simulation analysis for the stiffness and modality of conical spring, acquire the deformation law of spring under service load, the stiffness curve with nonlinear characteristics, the first four orders natural frequencies and its modal shape, which will lay a foundation for the RE design of conical spring and provide basis for its reconfiguration and repair after lose efficacy.


Author(s):  
Wenshuo Ma ◽  
Yan Xie ◽  
Jingjun Yu ◽  
Xu Pei

Dynamic performance is of great importance to compliant mechanisms which are employed in dynamic applications, especially if the dynamic problems in DOC (degree of constraint) directions are to be met. An investigation on the dynamic characteristics of a 2R compliant mechanism is presented. Based on the substructure techniques, the in-plane dynamic model of the preceding compliant mechanisms is developed. The natural frequencies and sensitivities are then analyzed. The numerical result verifies the validity of the proposed method. Finally, optimal design of compliant mechanism is investigated.


Author(s):  
C. C. Chao ◽  
T. P. Tung ◽  
Y. C. Chern

Abstract Axisymmetric free vibration of moderately thick polar orthotropic hemispherical shells are studied under the various boundary conditions of sliding, guided pin, clamped and hinged edges. Based on the improved linear elastic shell theory with the transverse shear strain and rotatory inertia taken into account, the dynamic equilibrium equations are formulated and transformed into the displacement form in terms of mid-surface meridian and radial displacements and parallel circle cross-section rotation. These partial differential equations are solved by the Galerkin method using proper Legendre polynomials as admissible displacement functions with the aid of the orthogonality and a number of special integral relations. Numerical results of the present theory compare well with existing data, which is available only in the isotropic theories. Good convergence is obtained for natural frequencies and mode shapes. Study of the effects of thickness and modulus ratio reveals higher frequencies for the thicker and/or stiffer shells with E\ oriented parallel to the meridians. Ranking of the natural frequencies descends in the order of guided pins, sliding, clamped and hinged edges in general. Also seen are the effects of transverse shear strain from the mode shapes with clamped and sliding edges on the slant. For the guided pin and sliding edges, frequencies increase fast as thickness increases so that new fundamental modes are generated in filling up the “frequency gap”. These are the new discoveries in the field of anisotropic shells, as a result of polar orthotropy of shell material and construction.


1987 ◽  
Vol 109 (2) ◽  
pp. 180-185 ◽  
Author(s):  
A. D. Kerr ◽  
M. A. El-Sibaie

The accuracy of the new equations for the rail-tie structure, derived by Kerr and Zarembski and recently generalized for dynamic problems by Kerr and Accorsi, is studied. This is done by comparing the natural frequencies based on the new equations with those calculated using a finite element method for a range of fastener stiffness values and a variety of rail spacings. The comparison revealed very close agreement. The findings confirm the suitability of the new equations for dynamic analyses of cross-tie tracks in the lateral plane.


2019 ◽  
Vol 21 (1) ◽  
pp. 13-30
Author(s):  
Marin Grbac ◽  
Dragan Ribarić

A four-node finite element is developed for modeling plates according to the Mindlin plate theory and it is constructed with the assumed shear strain approach. The element is previously verified in a static analysis on the benchmark problems of moderately thick and extremely thin plate models and compared to the other elements known from the literature. As starting interpolations, a complete cubic polynomial for the transverse displacement field and quadratic polynomials for the two rotation fields are used, and they are problem dependent at the same time. Some unfavorable terms are excluded from the derived shear strain expression to avoid locking phenomena in the thin geometry conditions. In this paper, the proposed element is tested for the dynamic analysis calculating the natural frequencies of plate vibrations with the uniformly distributed mass. The influence of the element consistent mass matrix is analyzed on the first 12 vibration modes. The results are verified on the circular plate model and compared to the existing analytical solutions as well as the results of other four-node elements from the literature. The goal of this paper is to demonstrate the efficiency of the proposed assumed strain element also in the dynamic analysis of plane structures.


1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.


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