Design of rectangular reinforced concrete slabs supported on all the sides with a short discontinuous edge

Bending moment coefficients for the design of rectangular reinforced concrete panels supported on four sides with a short discontinuous edge are derived using the strip theory. The moment fields resulting from the use of proposed coefficients are examined in terms of the moment volume for possible savings in reinforcement and compared with other codified procedures. The strip coefficients averaged over the corresponding sides of the panel, besides resulting in considerable savings in reinforcement, are found to be identical with the coefficients predicted by simple yield line theory using an orthotropic layout of reinforcement.

Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates

This paper presents a unified exact analysis for the statics and dynamics of a class of thick laminates. A three-dimensional, linear, small deformation theory of elasticity solution is developed for the bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates. All the nine elastic constants of orthotropy are taken into account. The solution is formally exact and leads to simple infinite series for stresses and displacements in flexure, forced vibration and "beam-column" type problems and to closed form characteristic equations for free vibration and buckling problems. For free vibration of plates, the present analysis yields a triply infinite spectrum of frequencies instead of only one doubly infinite spectrum by thin plate theory or three doubly infinite spectra by Reissner-Mindlin type analyses. Some numerical results are presented for plates and laminates. Comparison of results from thin plate, Reissner and Mindlin analyses with these yield some important conclusions regarding the validity and effects of the assumptions made in the approximate theories.

Vibration of rectangular orthotropic plates

An approximate analytical procedure has been given to solve the problem of a vibrating rectangular orthotropic plate, with various combinations of simply supported and clamped boundary conditions. Numerical results have been given for the case of a clamped square plate. Nomenclature 2a, 2b sides of the rectangular plate h plate thickness Eprime x , Eprime y , EPrime, G elastic constants of te orthotropic material D x Eprime x h 3/12 D y Eprime y h 3/12 H xy EPrimeh 3/12+Gh 3/6 D x , D y and H xy are rigidity constants of the orthotropic platergr mass of the plate per unit area ngr Poisson's ratio W deflection of the plate p circular frequency gamma b/a ratio X m , Y characteristic functions of the vibrating beam problem -lambda rgrp 2 a 2 b 2/H xy the frequency parameter.

An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates

A three-dimensional linear, small deformation theory of elasticity solution by the direct method is developed for the free vibration of simply-supported, homogeneous, isotropic, thick rectangular plates. The solution is exact and involves determining a triply infinite sequence of eigenvalues from a doubly infinite set of closed form transcendental equations. As no restrictions are placed on the thickness variation of stresses or displacements, this formulation yields a triply infinite spectrum of frequencies, instead of only one doubly infinite spectrum by thin plate theory and three doubly infinite spectra by Mindlin's thick plate theory. Further, the present analysis yields symmetric thickness modes which neither of the approximate theories can identify. Some numerical results from the two approximate theories are compared with those from the present solution and some important conclusions regarding the effect of the assumptions made in the approximate theories are drawn. The thickness variations of stresses and displacements are also discussed. The analysis is readily extended for laminated plates of isotropic materials. Numerical results are also given for three-ply laminates, and are used to assess the accuracy of thin plate theory predictions for laminates. Extension to general lateral surface conditions and forced vibrations is indicated.

Limit analysis of rectangular R.C. slabs on ground

A method is presented for obtaining lower bound on the carrying capacity of reinforced concrete foundation slab-structures subject to non-uniform contact pressure distributions. Functional approach suggested by Vallance for simply supported square slabs subject to uniform pressure distribution has been extended to simply supported rectangular slabs subject to symmetrical non-uniform pressure distributions. Radial solutions, ideally suited for rotationally symmetric problems, are shown to be adoptable for regular polygonal slabs subject to contact pressure paraboloids with constant edge pressures. The functional approach has been shown to be well suited even when the pressure is varying along the edges.

Adhesively-bonded Patch Repair with Composites

Adhesively-bonded composite patch repairs over cracked or corrosion-damaged metallic aircraft structures have shown great promise for extending life of ageing structures. This study presents the numerical investigation into the interface behaviour of adhesively-bonded cracked aluminum alloy substrate patched with fibre-reinforced composite material. The adhesive is modelled as an elasto-plastic bilinear material to characterise the debond behaviour, while the defective substrate is regarded as linear elastic continuum. Two typical patch shapes were selected based on information available in the literature. Geometric and material nonlinear analyses for square and octagonal patches were performed to capture peel and shear stresses developed between the substrate and the patch to examine the possibility of interface delamination/debonding. Parametric studies on adhesive thickness and patch thickness were carried out to predict their infuence on damage tolerance of repaired structures.

Adhesively-bonded Patch Repair with Composites

Adhesively-bonded composite patch repairs over cracked or corrosion-damaged metallic aircraft structures have shown great promise for extending life of ageing structures. This study presents the numerical investigation into the interface behaviour of adhesively-bonded cracked aluminum alloy substrate patched with fibre-reinforced composite material. The adhesive is modelled as an elasto-plastic bilinear material to characterise the debond behaviour, while the defective substrate is regarded as linear elastic continuum. Two typical patch shapes were selected based on information available in the literature. Geometric and material nonlinear analyses for square and octagonal patches were performed to capture peel and shear stresses developed between the substrate and the patch to examine the possibility of interface delamination/debonding. Parametric studies on adhesive thickness and patch thickness were carried out to predict their infuence on damage tolerance of repaired structures.

A rectangular laminated anisotropic shallow thin shell finite element

This report contains the details of the development of the stiffness matrix for a rectangular laminated anisotropic shallow thin shell finite element. The derivation is done under linear thin shell assumptions. Expressing the assumed displacement state over the middle surface of the shell as products of one-dimensional first-order Hermite interpolation polynomials, it is possible to insure that the displacement state for the assembled set of such elements, to be geometrically admissible. Monotonic convergence of the total potential energy is therefore possible as the modelling is successively refined. The element is systematically evaluated for its performance considering various examples for which analytical or other solutions are available

An experimental study of suddenly expanded rectangular jet flow field

Flow through a rectangular Passage which is expanded suddenly into another rectangular duct of larger Cross-sectional area has been studied experimentally with stagnation Pressures from 3.5 atmospheres to 1.25 atmospheres. The length to height ratio of the enlarged duct varied from 5.769 to 1.923 and three models with length to height ratios 5.769, 3.846, and 1.923 were studied. The influence of stagnation Pressures and length to height ratio of the enlarged duct on base pressure and flow field mean pressures in the enlarged duct is discussed. The results of the present investigation indicate that the oscillatory nature of the mean pressure flow field in the enlarged portion with rectangular cross-section is appreciably different from that for circular cross-section at similar flow conditions.

Analytical prediction of break-out noise from a reactive rectangular plenum with four flexible walls

This paper describes an analytical calculation of break-out noise from a rectangular plenum with four flexible walls by incorporating three-dimensional effects along with the acoustical and structural wave coupling phenomena. The breakout noise from rectangular plenums is important and the coupling between acoustic waves within the plenum and structural waves in the flexible plenum walls plays a critical role in prediction of the transverse transmission loss. The first step in breakout noise prediction is to calculate the inside plenum pressure field and the normal flexible plenum wall vibration by using an impedance-mobility approach, which results in a compact matrix formulation. In the impedance-mobility compact matrix (IMCM) approach, it is presumed that the coupled response can be described in terms of finite sets of the uncoupled acoustic subsystem and the structural subsystem. The flexible walls of the plenum are modeled as an unfolded plate to calculate natural frequencies and mode shapes of the uncoupled structural subsystem. The second step is to calculate the radiated sound power from the flexible walls using Kirchhoff-Helmholtz (KH) integral formulation. Analytical results are validated with finite element and boundary element (FEM-BEM) numerical models. (C) 2010 Acoustical Society of America. DOI: 10.1121/1.3463801]