Comparison of Range of Applicability of Rayleigh-Ritz Method and Method of Weighted Residual for Calculating the Deflection of Simply Supported Beam with Central Loading Condition

A beam is a structural element that is primarily resists the transverse load or laterally applied loads to the beam’s axis. Beams are traditionally descriptions of building or structural elements, but any structures such as automotive automobile frames, aircraft components, machine frames, and other mechanical or structural systems contains beam structures that are designed to carry transverse loads. In engineering, deflection is the result to which a structural element is displaced under load. There are many method s to find out the deflection of a beam such as virtual work method, direct integration, Castiglione’s method. Macaulay’s method or the direct stiffness method but Leonhard Euler and Daniel Bernoulli in 1750, first time developed a theory for finding the deflection of beam. Though recent studies argue that Leonardo da Vinci was the first to make a observation but he couldn’t develop a theory due to lack of Hooke’s law and calculus. There is also different approximate methods were developed to calculate the deflection such as Point collaboration method, Sub-domain collaboration method, Galerkin Method, method of least square etc. In this investigation an attempt to be made a comparison of range of applicability of Rayleigh-Ritz method and above mentioned method of Weighted Residual to calculate the deflection of a simply supported beam under central loading. From the investigation, it is concluded that Rayleigh –Ritz method gives the accurate deflection result of the subjected beam.