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Critical Length (critical + length)
Selected AbstractsThe eigenvalues of isolated bridges with transverse restraints at the end abutmentsEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 8 2010Nicos Makris Abstract This paper examines the eigenvalues of multi-span seismically isolated bridges in which the transverse displacement of the deck at the end abutments is restricted. With this constraint the deck is fully isolated along the longitudinal direction, whereas along the transverse direction the deck is a simple-supported beam at the end abutments which enjoys concentrated restoring forces from the isolation bearings at the center piers. For moderate long bridges, the first natural period of the bridge is the first longitudinal period, while the first transverse period is the second period, given that the flexural rigidity of the deck along the transverse direction shortens the isolation period offered by the bearings in that direction. This paper shows that for isolated bridges longer than a certain critical length, the first transverse period becomes longer than the first longitudinal period despite the presence of the flexural rigidity of the deck. This critical length depends on whether the bridge is isolated on elastomeric bearings or on spherical sliding bearings. This result is also predicted with established commercially available numerical codes only when several additional nodes are added along the beam elements which are modeling the deck in-between the bridge piers. On the other hand, this result cannot be captured with the limiting idealization of a beam on continuous distributed springs (beam on Wrinkler foundation),a finding that has practical significance in design and system identification studies. Finally, the paper shows that the normalized transverse eigenperiods of any finite-span deck are self-similar solutions that can be represented by a single master curve and are independent of the longitudinal isolation period or on whether the deck is supported on elastomeric or spherical sliding bearings. Copyright © 2009 John Wiley & Sons, Ltd. [source] Kinematic response functions and dynamic stiffnesses of bridge embankmentsEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 11 2002Jian Zhang Abstract Recognizing that soil,structure interaction affects appreciably the earthquake response of highway overcrossings, this paper compares approximate analytical solutions and finite element results to conclude on a simple procedure that allows for the estimation of the kinematic response functions and dynamic stiffnesses of approach embankments. It is shown that the shear-wedge model yields realistic estimates for the amplification functions of typical embankments and reveals the appropriate levels of dynamic strains which are subsequently used to estimate the stiffness and damping coefficients of embankments. The shear-wedge model is extended to a two-dimensional model in order to calculate the transverse static stiffness of an approach embankment loaded at one end. The formulation leads to a sound closed-form expression for the critical length, Lc, that is the ratio of the transverse static stiffness of an approach embankment and the transverse static stiffness of a unit-width wedge. It is shown through two case studies that the transverse dynamic stiffness (,spring' and ,dashpot') of the approach embankment can be estimated with confidence by multiplying the dynamic stiffness of the unit-width wedge with the critical length, Lc. The paper concludes that the values obtained for the transverse kinematic response function and dynamic stiffness can also be used with confidence to represent the longitudinal kinematic response function and dynamic stiffness, respectively. Copyright © 2002 John Wiley & Sons, Ltd. [source] The relationship between temperature and the size and age of larvae and peri-metamorphic stages of Pleuronectes flesusJOURNAL OF FISH BIOLOGY, Issue 2 2004S. Hutchinson Laboratory observations of live animals were used to describe the developmental sequence of the flounder Pleuronectes flesus. Developmental state was related to age and total length (LT) from hatching, through metamorphosis, to the juvenile form. By following animals at 7, 11 and 15° C it was found that, whilst the LT at metamorphosis was the same for all the temperature regimes and was not temperature-dependant, the time taken to reach this stage was related to rearing temperature. It was also observed that animals could be induced to metamorphose by transfer to reduced salinity but only if they were close to the critical length for metamorphosis. [source] Frozen in time: a new method using cryo-scanning electron microscopy to visualize root,fungal interactionsNEW PHYTOLOGIST, Issue 2 2006Steve Refshauge Summary ,,A new method of sample preparation for cryo-scanning electron microscopy was used to visualize internal infection of wheat (Triticum aestivum) roots by the pathogenic fungus Rhizoctonia solani AG-8. The new method retained fungal hyphae and root cells in situ in disintegrating root tissues, thus avoiding the distortions that can be introduced by conventional preparation by chemical fixation, dehydration and embedding. ,,Infected roots frozen in liquid nitrogen were cryo-planed and etched (sublimed) at ,80°C for a critical length of time (up to 9 min) in the microscope column to reveal plant and fungal structures in three dimensions. ,,Root and fungal structures were well preserved irrespective of infection severity. Root and hyphal cell walls were clearly seen and hyphal architecture within and between root cells was preserved. ,,This rapid method permits three-dimensional in situ visualization of fungal invasion within roots and has broad application for examination of diseases caused by other necrotrophic fungi. [source] Temperature conditions control embryo growth and seed germination of Corydalis solida (L.) Clairv., a temperate forest spring geophytePLANT BIOLOGY, Issue 6 2009F. Vandelook Abstract Spring is often the most suitable period for seedling establishment of temperate woodland species. Different physiological mechanisms resulting in spring emergence have evolved in seeds of such plants. The aim of this study was to determine the requirements for breaking dormancy and for seed germination of the European perennial spring geophyte Corydalis solida (Fumariaceae). Ripe seeds of C. solida contain an underdeveloped embryo, consisting of no more than a clump of cells. As a consequence, the embryo has to differentiate and grow to a critical length before germination can occur. In nature, seeds are dispersed in spring, while growth of the embryo starts in the autumn and continues in winter. Germination starts in late winter, immediately after embryo growth is completed, resulting in seedling emergence in the following spring. Experiments in controlled conditions showed that temperature is the main factor controlling dormancy and germination. Incubation at autumn temperatures (15/6 °C; 20/10 °C) for at least 8 weeks is required to initiate embryo growth, while a transfer to 5 °C is needed for completion of embryo growth and germination. Growth of the embryo of C. solida occurs at different temperatures over an extended period, a feature typical of temperate forest herbs. Our results indicate that the dormancy mechanism in seeds of C. solida is very similar to mechanisms in other Corydalis species studied thus far, suggesting that stasis in the dormancy trait has occurred. [source] Rotational motion of a discretized buckled beamPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006H. Troger We study a simple discretized model of a vertical cylindrical beam with circular cross-section which is clamped at its lower end and free at its upper end. If the beam is longer than a critical length the initially straight configuration will loose its stability and the beam will buckle due to its own weight. Now the base of the buckled beam is rotated about its vertical axis. Several different families of steady state motions are detected for the undamped system. Their stability is investigated. Moreover it is shown that there is a big difference in the behavior of the discretized model of the beam whether internal damping is included in the model or not. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | |||||||||||||