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Discretising a structure into elements is a key step in finite element (FE) analysis. The discretised geometry used to formulate an FE model can greatly affect accuracy and validity. This paper presents a unified dimensionless parameter to generate a mesh of cubic FEs for the analysis of very long beams resting on an elastic foundation. A uniform beam resting on elastic foundation with various values of flexural stiffness and elastic supporting coefficients subject to static load and moving load is used to illustrate the application of the proposed parameter. The numerical results show that (a) Even if the values of the flexural stiffness of the beam and elastic supporting coefficient of the elastic foundation are different, the same proposed parameter "s" can ensure the same accuracy of the FE solution, but the accuracy may differ for use of the same element length; (b) The proposed dimensionless parameter "s" can indeed be used as a unified index to generate the mesh for a beam resting on elastic foundation, whereas the use of the same element length as a criterion may be misleading; (c) The errors between the FE and analytical solutions for the maximum vertical displacement, shear force and bending moment of the beam increase with the dimensionless parameter "s"; and (d) For the given allowable errors for the vertical displacement, shear force and bending moment of the beam under static load and moving load, the corresponding values of the proposed parameter are provided to guide the mesh generation. [ABSTRACT FROM AUTHOR]

The Gibbs phenomenon in Fourier series has long been recognized as a drawback in its applications, in particular when it is used to represent a function having discontinuities. One category, namely, intrinsic discontinuities, could be derived from the nature of the physical problems. Another, namely, inherent discontinuities, is created undesirably through the employment of Fourier series. To alleviate these drawbacks, two techniques are developed. The first aims at eliminating the inherent discontinuities. The size of the original domain [0, l] is first doubled with a virtual function [[Psi].sub.0] defined over the neighboring domain [-l, 0]. The augmented domain [-l, l] is then further extended periodically. The virtual function [[Psi].sub.0](y) is chosen so that continuities are achieved at y = 0, [+ or -] l, [+ or -] 2l,.... Consequently, no Gibbs phenomena will occur at the boundaries. The second aims at reproducing the intrinsic discontinuities in the representation function by incorporating piecewise cubic polynomials into the Fourier base function. The enlarged basis function, namely, the Gibbs-phenomenon-free-Fourier-series function, is able to represent accurately any specific boundary conditions and interior intrinsic discontinuous conditions. Examples of vibration and buckling analysis of complex beams show that the present method is versatile, accurate, and efficient.

Seismic design of reinforced concrete (RC) structures requires a certain minimum level of flexural ductility. For example, Eurocode EN1998-1 directly specifies a minimum flexural ductility for RC beams, while Chinese code GB50011 limits the equivalent rectangular stress block depth ratio at peak resisting moment to achieve a certain nominal minimum flexural ductility indirectly. Although confinement is effective in improving the ductility of RC beams, most design codes do not provide any guidelines due to the lack of a suitable theory. In this study, the confinement for desirable flexural ductility performance of both normal- and high-strength concrete beams is evaluated based on a rigorous full-range moment-curvature analysis. An effective strategy is proposed for flexural ductility design of RC beams taking into account confinement. The key parameters considered include the maximum difference of tension and compression reinforcement ratios, and maximum neutral axis depth ratio at peak resisting moment. Empirical formulae and tables are then developed to provide guidelines accordingly. [ABSTRACT FROM AUTHOR]

The remaining service life of a bridge is an important criterion for the bridge master to make decisions of maintenance and rehabilitation. In the assessment of fatigue problems of steel and composite bridges, a crucial step is to determine the fatigue stress spectra, which are usually obtained through field measurements. In this study, the standard fatigue vehicle spectrum of Ting Kau Bridge in Hong Kong is obtained from the dynamic weigh-in-motion system that monitors the traffic flow and volume and axle and gross vehicle weights. An advanced probabilistic loading model is proposed to simulate the vehicles running along the bridge based on measurements from the weigh-in-motion system considering not only the diurnal variations of traffic flow within different time intervals but also the rate of change of the annual traffic. The statistical fatigue reliability assessment at critical locations can then be carried out to estimate the remaining service life of the bridge. [ABSTRACT FROM AUTHOR]