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Strengthening T-joints of rectangular hollow steel sections against web buckling under brace axial compression using through-wall bolts

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THIN-WALLED STRUCTURES 2012年 56卷 71-87页

作者： Aguilera, Jose Shaat, Amr Fam, Amir Queens Univ Dept Civil Engn Kingston ON K7L 3N6 Canada

The effectiveness of through-wall bolts is examined for strengthening T-joints of rectangular hollow steel sections. This is accomplished by controlling the web outward budding of the chord under the brace axial load. The study examined the effect of the number and pattern of bolts, as well as the web height-to-wall thickness (h/t) ratio of the chord, on strengthening effectiveness. rectangular 203 x 76 x (3.09, 4.5, and 5.92) mm chord members were tested. The number of 8 mm diameter steel bolts varied from a single bolt to 15 bolts of various distributions. Holes were first drilled in the vertical walls of the chord member, and then bolts were inserted through one wall and anchored at the other wall. The joint strength increased by 29% for chords with (h/t) of 65. As (h/t) ratio reduced to 45 and 35, the gains were only 6.2% and 3.1%, respectively. The number and distribution of bolts had little effect on their effectiveness. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： HSS rectangular T-joint Chord Brace Local buckling Bolt

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Superconvergence for rectangular serendipity finite elements

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Science China Mathematics 2003年第1期46卷 1-10页

作者：陈传淼 Institute of Computation Hunan Normal University

Based on an orthogonal expansion and orthogonality correction in an element, superconvergenceat symmetric points for any degree rectangular serendipity finite element approximation to second order ellipticproblem is p... 详细信息

关键词： rectangular serendipity elements, superconvergence, symmetric points.

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Effects of a liquid layer on thickness-shear vibrations of rectangular AT-cut quartz plates

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IEEE TRANSACTIONS ON ULTRASONICS FERROELECTRICS AND FREQUENCY CONTROL 2002年第5期49卷 604-611页

作者： Lee, PCY Huang, R Princeton Univ Dept Civil & Environm Engn Princeton NJ 08544 USA

Thickness-shear vibrations of a rectangular AT-cut quartz with one face in contact with a layer of Newtonian (linearly viscous and compressible) fluid are studied. The two-dimensional (2-D) governing equations for vibrations of piezoelectric crystal plates given previously are used in the present study. The solutions for I-D shear wave and compressional wave in a liquid layer are obtained, and the stresses at the bottom of the liquid layer are used as approximations to the stresses exerting on the crystal surface in the plate equations. Closed form solutions are obtained for both free and piezoelectrically forced thickness-shear vibrations of a finite. rectangular AT-cut quartz in contact with a liquid layer of finite thickness. From the present solutions, a simple and explicit formula is deduced for the resonance frequency of the fundamental thickness-shear mode, which includes the effects of both shear and compressional waves in the liquid layer and the effect of the thickness-to-length ratio of the crystal plate. The formula reduces to the widely used frequency equation obtained by many previous investigators for infinite plates. The resonance frequency of a rectangular AT-cut quartz. computed as a function of the thickness of the adjacent liquid layer, agrees closely with the experimental data measured by Schneider and Martin.

关键词： compressibility crystal resonators elastic waves internal stresses liquid films quartz vibrations viscosity 1D shear wave 2D governing equations Newtonian fluid SiO/sub 2/ closed form solutions compressional wave compressional waves crystal plate thickne compression waves quartz plate Quartz rectangular internal stresses Viscosity Membranes-Liquid Compressibility Vibration resonant frequencies liquids Elastic waves crystal resonators

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Buckling and vibration analysis of non-homogeneous rectangular Kirchhoff plates resting on two-parameter foundation

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MECCANICA 2015年第4期50卷 893-913页

作者： Lal, Roshan Saini, Renu Indian Inst Technol Dept Math Roorkee 247667 Uttar Pradesh India

Effect of two parameter foundation has been analyzed on the transverse vibrations of non-homogeneous rectangular plates of uniform thickness when the two opposite edges are simply supported and these are subjected to linearly varying in-plane forces on the basis of Kirchhoff plate theory. The non-homogeneity of the plate material is assumed to arise due to the exponential variation in young's modulus and density of the plate material along one direction. Using Levy approach, the partial differential equation governing the motion of such plates has been reduced to an ordinary differential equation. Differential quadrature method has been used to obtain the frequency equations for two different combinations of clamped and simply supported boundary conditions at the other two edges. These frequency equations have been solved numerically using MATLAB. The lowest three roots of these equations have been reported as first three natural frequencies corresponding to the first three modes of vibration. The effect of various parameters such as foundation parameters, non-homogeneity parameter, density parameter, aspect ratio, in-plane force parameter and loading parameter has been investigated on the frequencies. By allowing the frequency to approach zero, the critical buckling loads for various value of different parameters have been computed. Three dimensional mode shapes for a specified plate for both the boundary conditions have been plotted. A comparison of results with those available in literature has been presented.

关键词： rectangular Non-homogeneous Buckling Pasternak foundation Differential quadrature method

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Design recommendations for bolted rectangular HSS flange-plate connections in axial tension

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ENGINEERING JOURNAL-AMERICAN INSTITUTE OF STEEL CONSTRUCTION INC 2003年第1期40卷 15-24页

作者： Willibald, S Packer, JA Puthli, RS Univ Karlsruhe Versuchsanstalt Stahl Holz & Steine Karlsruhe Germany Univ Toronto Dept Civil Engn Toronto ON Canada

The results of an experimental investigation of four bolted flange-plate connections between rectangular hollow structural sections, with bolts on all four sides, have been presented. A brief overview of different design methods for bolted flange-plate connections for square and rectangular hollow structural sections under tension load has also been given. A comparison of the load predictions of the various methods for the specimens in the experimental program supports the use of the design procedure that can be found in the AISC HSS Connections Manual (AISC. 1997). However, this is provided that the flange-plate width/height is used to calculate the bolt pitch. Unfortunately, the AISC HSS Connections Manual illustrates the (more conservative) use of the HSS width/height instead of the flange-plate width/height for determining the bolt pitch, but the latter is hereby advocated. Moreover, the results of this experimental study on rectangular HSS connections suggest that the connection strength should be calculated for both the short and long side individually, using the minimum of both values as the actual connection resistance. Provided that the edge distance, a, and the distance from bolt line to tube face. b. are the same for the short and long side of the connection, the side having the smaller bolt pitch p will govern. Using the \"averaged\" values for the bolt pitch p will always result in slightly less conservative predictions for the connection resistance. It might be conceivable to use the \"averaged\" bolt pitch instead, considering that the load predictions for all test specimens were done with all resistance factors removed in the calculations. For design purposes the bolt capacity as well as the flange-plate capacity are reduced by the inclusion of resistance factors. φ = 0.75 and φ_p = 0.9 respectively, providing a fair safety margin. All the given design recommendations should be restricted to the range of experimental verification, which is for up to

关键词： rectangular Bolt design process bolted joints load forecasting

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Thermal Casimir effect in ideal metal rectangular boxes

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EUROPEAN PHYSICAL JOURNAL C 2008年第4期57卷 823-834页

作者： Geyer, B. Klimchitskaya, G. L. Mostepanenko, V. M. Univ Leipzig Inst Theoret Phys Leipzig Germany N W Tech Univ St Petersburg Russia Noncommercial Partnership Sci Instruments Moscow Russia

The thermal Casimir effect in ideal metal rectangular boxes is considered using the method of zeta functional regularization. A renormalization procedure is suggested which provides the finite expression for the Casimir free energy in any restricted quantization volume. This expression satisfies the classical limit at high temperature and leads to zero thermal Casimir force for systems with infinite characteristic dimensions. In the case of two parallel ideal metal planes the results, as derived previously using thermal quantum field theory in Matsubara formulation and other methods, are reproduced starting from the expression obtained. It is shown that for rectangular boxes the temperature-dependent contribution to the electromagnetic Casimir force can be both positive and negative depending on side lengths. Numerical computations of the scalar and electromagnetic Casimir free energy and force are performed for cubes.

关键词： FINITE-TEMPERATURE ZETA-FUNCTIONS BOUNDARY CONSTRAINTS CAVITIES VACUUM ENERGY FIELDS rectangular Constraint Zeta function Energy sources Casimir effect Vacuum

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Influences of Boundary Conditions on Laminar Natural Convection of Bingham Fluids in rectangular Enclosures With Differentially Heated Side Walls

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HEAT TRANSFER ENGINEERING 2014年第9期35卷 822-849页

作者： Turan, Osman Poole, Robert J. Chakraborty, Nilanjan Univ Liverpool Sch Engn Liverpool L69 3BX Merseyside England Karadeniz Tech Univ Dept Mech Engn Trabzon Turkey Newcastle Univ Sch Mech & Syst Engn Newcastle Upon Tyne NE1 7RU Tyne & Wear England

Two-dimensional steady-state simulations of laminar natural convection in rectangular enclosures with differentially heated side walls have been conducted for a range of different aspect ratios (height/length) for both constant wall temperature and constant heat flux boundary conditions. The rectangular enclosures are considered to be completely filled with a yield-stress fluid obeying the Bingham model. Yield-stress effects on heat and momentum transport are investigated for nominal values of Rayleigh number in the range 10(4)-10(6) and the aspect ratio range 1/8 to 8 for a single nominal Prandtl number (= 500). It is found that the mean Nusselt number increases (decreases) with increasing values of Rayleigh (Bingham) number irrespective of the boundary condition. For the constant wall temperature boundary condition, the aspect ratio at which the maximum mean Nusselt number occurs is found to decrease with increasing Rayleigh number. In contrast, the value of mean Nusselt number increases monotonically with increasing aspect ratio in the case of the constant wall heat flux boundary condition. Detailed physical explanations are provided for these aspect ratio effects. New correlations are proposed for the mean Nusselt number in both the constant wall temperature and wall heat flux boundary conditions, which are shown to satisfactorily capture the simulation results.

关键词： ASPECT RATIO Enclosures rectangular wall temperature Boundary conditions wall heat flux Rayleigh number SIDEWALL Boundary non-Newtonian fluids Nusselt number constant heat flow Natural convection

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Three-dimensional natural vibration analysis and energy considerations for a piezoelectric rectangular plate

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JOURNAL OF SOUND AND VIBRATION 2005年第3-5期283卷 1093-1113页

作者： Cupial, P Cracow Univ Technol Inst Appl Mech PL-31864 Krakow Poland

The paper presents results of the exact three-dimensional analysis of the natural frequencies and mode shapes of a rectangular piezoelectric plate poled along the direction perpendicular to the plate middle plane. The solutions are obtained in non-dimensional form for flexural modes of vibration of a plate simply supported along the plate edges and two types of electrical boundary conditions on the plate faces, namely for the case of short and open circuit. A numerically stable algorithm is described, which allows the calculation of the natural frequencies and mode shapes of the piezoelectric plate. The details of the algorithm have been found to be especially important in the case of equal wavelengths along the two plate edges (e.g. for the lowest flexural mode of a square plate). The natural frequencies of a rectangular plate are given for a rectangular and square plate for the case of short-circuited and open-circuit plate faces, together with the through-thickness distributions of the mechanical and electric fields. Energy balance for piezoelectric continua is used to derive two equivalent formulae which extend the Rayleigh quotient used in free vibration analysis of elastic continua. These expressions are used to verify the consistency of the results and to obtain additional insight into the phenomenon of electromechanical coupling in a vibrating piezoelectric plate. (c) 2004 Elsevier Ltd. All rights reserved.

关键词： piezoelectric plate rectangular modal response flexural mode Vibration analysis Electromechanical coupling Vibrations modes Rayleigh quotient thickness distribution Short circuits Natural frequencies rectangular PLATES

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Optimum design of broadband n-way rectangular power dividers with arbitrary power division and impedance matching

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IET MICROWAVES ANTENNAS & PROPAGATION 2011年第12期5卷 1447-1454页

作者： Oraizi, H. Ayati, S. -A. Iran Univ Sci & Technol Tehran Iran

A novel n-way rectangular power divider is presented, which has the capability of design for arbitrary power division among its output ports and arbitrary specification of impedances at all its terminal ports. Consequently, the impedance matching is also realised by its configuration. An accurate equivalent circuit is derived for the power divider, which is used to develop a design procedure by the method of least squares. Two prototype models, namely a three-way and a four-way dividers are fabricated and measured for different terminal impedances and power division ratios. The agreement among the results from the proposed design procedure, full-wave computer simulation and measurement is noteworthy.

关键词： impedance impedance matching power dividers Optimal design rectangular design process Division output ports Arbitrary Energy sources division

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Study on the flexural vibration of rectangular thin plates with free boundary conditions

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JOURNAL OF SOUND AND VIBRATION 2001年第5期239卷 1063-1071页

作者： Shuyu, L Shaanxi Normal Univ Appl Acoust Inst Xian 710062 Peoples R China

An analytical method is presented for the flexural vibration of rectangular thin plates with Free boundary conditions. Based on the apparent elasticity method, the flexural vibration of a rectangular thin plate is reduced to two one-dimensional flexural vibrations of slender rods. Then the two-dimensional flexural vibration of a rectangular thin plate with free boundary conditions is considered as the coupling of these two equivalent flexural vibrations with different equivalent elastic constants. It should be noted that these two equivalent flexural vibrations are different from the traditional one-dimensional flexural vibrations of slender rods. They are coupled to each other by the introduced mechanical coupling coefficient. The analytical solutions for the isotropic rectangular thin plate in flexural vibration are derived and the resonance frequency equation is obtained. The natural vibrational mode is analyzed and the frequency spectra are calculated. It is found that the normal modes and the natural frequencies of the rectangular thin plate in flexural vibration are abundant. Theoretical analysts show that one-dimensional flexural vibration of a slender rod based on the classical elementary flexural theory, as well as the stripe mode vibration of a rectangular thin plate is a limiting vibrational mode of rectangular thin plates. Experiments show that the measured resonance frequencies are in good agreement with the calculated results, and the displacement nodal line pattern is also observed experimentally. (C) 2001 Academic Press.

关键词： THIN PLATES Flexural vibration rectangular Boundary conditions resonant frequencies Frequency spectra Vibrations modes

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