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The dynamic stiffness matrix of a rectangular plate for the most general case is developed by solving the biharmonic equation and finally casting the solution in terms of the force-displacement relationship of the freely vibrating plate. Essentially the frequency dependent dynamic stiffness matrix of the plate when all its sides are free is derived, making it possible to achieve exact solution for free vibration of plates or plate assemblies with any boundary conditions. Previous research on the dynamic stiffness formulation of a plate was restricted to the special case when the two opposite sides of the plate are simply supported. This restriction is quite severe and made the general purpose application of the dynamic stiffness method impossible. The theory developed in this paper overcomes this long-lasting restriction. The research carried out here is basically fundamental in that the bi-harmonic equation which governs the free vibratory motion of a plate in harmonic oscillation is solved in an exact sense, leading to the development of the dynamic stiffness method. It is significant that the ingeniously sought solution presented in this paper is completely general, covering all possible cases of elastic deformations of the plate. The Wittrick-Williams algorithm is applied to the ensuing dynamic stiffness matrix to provide solutions for some representative problems. A carefully selected sample of mode shapes is also presented.

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In Standard CANICSA S16.1-M89, the contribution of the concrete to the flexural capacity of concrete-filled hollow structural sections is acknowledged as an alternative approach, but no method of assessing it is given. Preliminary studies had indicated that the concrete increased the ultimate moment capacity, the initial flexural stiffness, and the ductility, and delayed local buckling of the steel, thus enhancing the behaviour considerably. A series of four flexural tests on rectangular and square cold-formed hollow structural steel sections and twelve on concretefilled sections were undertaken to assess the general behaviour of these composite sections. The test specimens were selected to examine the effects of different ratios of depth to width and therefore of the proportions of steel and concrete in compression, and of different values of shear span to depth as related to the transfer of forces from one to the other when no direct means is provided for this transfer. The tests showed that the ultimate flexural strength of the concrete-filled sections is increased by about 10-30% over that of the bare steel sections, depending on the relative proportions of steel and concrete. The stiffness is also enhanced. In all cases, slip between the steel and concrete was not detrimental, even though shear-span-to-depth ratios as low as 1 were tested. Models are developed to predict the flexural strength of the composite section. Fully plastic stress blocks with the concrete at its maximum strength are used. The models are in excellent agreement with the test results.Key words: composite beams, concrete-filled, flexural behaviour, hollow structural sections. Dans la norme CANICSA S 16.1 -M89, l'apport du bCton B la rCsistance B flexion de profilks de charpente creux remplis de bCton est accept6 comme solution de rechange. Cependant, aucune mCthode d'Cvaluation n'est proposCe. Des Ctudes preliminaires ont dCmontrC que le bCton augmentait la capacitC de moment ultime, la rigidit6 en flexion initiale et la ductilitC, tout en retardant le flambage local de l'acier, amCliorant ainsi considerablement leur comporternent. Une sCrie de quatre essais en flexion de profilks d'acier de charpente creux formCs B froid de forrne carrCe et rectangulaire et une sCrie de douze essais de profilCs rernplis de bCton ont CtC rCalisCes afin d'Cvaluer le cornportement gCnCral de ces sections composites. Les Cchantillons d'essai ont CtC choisis afin d'exarniner les effets de diffCrents rapports hauteur-largeur et par consCquent des proportions d'acier et de bCton en compression ainsi que diverses valeurs de cisaillemeni-portCelhauteur en fonction du transfert de forces de l'un B l'autre lorsque ce transfert direct n'est assurC par aucun moyen direct. Les resultats ont indiquC que la rksistance B la flexion ultime des profilCs rernplis de bCton Ctait supCrieure d'environ 10 B 30% B celle des profilks d'acier nu, selon des proportions relatives d'acier et de bCton. La rigidit6 a Cgalement CtC accrue. Dans tous les cas, le glissernent entre I'acie...