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.
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The menacing effects of global warming, rising cost of cement, high energy requirements for the production of cement, and the mitigation of environmental pollution have led researchers towards using locally available materials to partially replace cement in concrete or mortar. The concrete produced from such locally available material is called Green Concrete. Few researches have been reported on the usage of Oyster Shell Powder (OSP) to partially replace the Ordinary Portland Cement (OPC). However, none of those reports has reflected the response of such Green Concrete made with Oyster Shell Powder to Splitting Tensile load. In this research, OPC is partially replaced with OSP at the rate of 0%, 5%, 10%, 15%, 20% and 25% in concrete. A total of 72 number of cylindrical metal moulds of 150mm diameter and 300mm height are used to cast the concrete, demoded after 24 hours and cured for 3, 7, 14 and 28 days with three replicates for each curing age and each replacement percentage. The properties of fresh and hardened concrete were quantified. The results show that the increase of OSP from 0% up to 25% delays the initial and final setting times of cement paste by 25mins and 40mins respectively. It also improves workability by an additional slump of 19mm. In addition, the Splitting Tensile Strength decreased from 1.706N/mm2 for 0% replacement to 1.011N/mm2 for 25% replacement after a three-day curing period, as well as from 2.076.N/mm2 for 0% to 1.388N/mm2 for 25% replacement, after a 28-day curing period. In as much as the Splitting Tensile Strength of concrete is known to be very low relative to its compressive strength; this study has reflected the extent of vulnerability of OSP-Cement concrete to tensile cracking and stress due to loads. Hence, this will result in safer design and loading of such concrete.
Keywords: Concrete, Cement, Oyster Shell Powder, Splitting Tensile Strength, Partial Replacement.
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