Plates are important structural elements used to model bridge decks, retaining walls, floor slabs, spacecraft panels, aerospace structures, and ship hulls amongst. Plates have been modelled using three dimensional elasticity theory, Reissner's theory, Kirchhoff theory, Shimpi's theory, Von Karman's theory, etc. The resulting plate equations have also been solved using classical and numerical techniques.In this research, the Galerkin-Vlasov variational method was used to present a general formulation of the Kirchhoff plate problem with simply supported edges and under distributed loads. The problem was then solved to obtain the displacements, and the bending moments in a Kirchhoff plate with simply supported edges and under uniform load. Maximum values of the displacement and the bending moments were found to occur at the plate center. The Galerkin Vlasov solutions for a rectangular simply supported Kirchhoff plate carrying uniform load was found to be exactly identical with the Navier double trigonometric series solution.
This work studies the dynamic characteristics of simply supported rectangular thin plates undergoing natural transverse vibrations in harmonic motion. The governing partial differential equation for the free transverse vibration of the plate was solved by the Galerkin-Vlasov variational technique. The assumption of free harmonic motions reduced the governing equation to an algebraic eigen value eigenvector problem, which was solved in the space domain to obtain the eigen frequencies and modal shape functions of the vibrating Kirchhoff plate. The eigen frequencies and modal shape functions obtained were found to be identical with the results obtained by the classical methods of Navier and Levy for the same problem.
In this work, the Fourier transform method has been applied to the determination of stresses induced by infinitely long line loads on semi-infinite homogeneous elastic soils. Airy's stress functions of the Cartesian coordinates system were used to express the governing equations of plane strain elasticity for a semi-infinite homogeneous soil as a biharmonic problem. The fourth order partial differential equation was then solved by an exponential Fourier transform technique, with respect to the space valuable x where x; and the resulting solutions made subject to the stress-boundary conditions. The stresses obtained were found to be exactly identical with solutions obtained by integrating Boussinesq's solutions for a point load which are available in the technical literature. The stresses determined in the present study were also exactly identical with the Flamant's solution for the same problem; obtained by assuming a stress function in terms of the cylindrical coordinates.
This work investigated the effect of partial replacement of sand with quarry dust on the This work investigated the effect of partial replacement of sand with quarry dust on the This work investigated the effect of partial replacement of sand with quarry dust on the This work investigated the effect of partial replacement of sand with quarry dust on the compressive strength, compressive strength, compressive strength,
This research is centered on the investigation of the implication of abandonment on the strength of exposed steel and concrete in an abandoned project; as most abandoned project are continued without due consideration to the current strength of the structural members, which may lead to eventual collapse, if the structural members have failed in strength. Six abandoned project sites were investigated: three in Port Harcourt, Rivers state and the other three in Lagos, Lagos state, Nigeria. Thus limiting the investigation to Southern region of Nigeria where the temperature ranges between 23°C and 32°C and precipitation/rainfall ranged between 36mm and 410mm.The Periods of the abandonment ranges from three to thirty-five years. All structural members were cast in-situ. Visual inspections were carried out on site, rebound hammer test was done, concrete samples were cored and steel reinforcement bars were cut from site. Laboratory test and analysis were carried on te cored samples as well as tensile test carried out on the steel samples. Data obtained from both field and laboratory analysis, were analyzed using Excel regression analysis and a model was obtained to help determine the estimated steel strength of exposed steel reinforcement bars after a period of abandonment in the region considered.
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