Application of Galerkin Approach for the Determination of the Optimum Buckling Value of a Prismatic Bar

Structural instability of the most used engineering material steel under the action of axially applied compressive load which thus actuates its failure has necessitated its study inquest to understand the contributory factors to such failure by buckling and the behavioural pattern of the material.This study was therefore based on the application of Galerkin's approach of the method of weighted residuals to determine the optimum buckling (deflection) value of a prismatic bar made of AISI 8620 alloy steel material.The percentage composition of the elements present in the material was determined using atomic absorption spectroscopy (AAS) machine.The mechanical properties of the material such as its compressive yield strength, elastic modulus, tensile and compressive strengths were experimentally determined with the aid of an Amatez EZ 250 tensile and compressive testing machine according to ASTM.The essential variables such as the cross-section area, moment of inertia, slenderness ratio, optimum buckling load, bending moment, position of the neutral axis, radius of gyration and critical stress were all evaluated using their appropriate formula.Analytical formula for calculating the deflections of a beam was equally employed to validate the results of Galerkin method.From the results obtained, the Galerkin's and analytical methods employed gave an optimum buckling (deflection) value of 2.8607mm and the results of the analytical method correlated well with that of the Galerkin's procedure.The material lost stability within its elastoplastic boundary before its plastic deformation.Therefore, this determined optimum buckling (deflection) value of AISI 8620 alloy steel material gave well-correlated values and should be referenced during structural/mechanical design of systems to ensure their safety and optimal performance characteristics.