MATHEMATICAL MODELS FOR LIMIT STATE AMPLITUDE OF DISPLACEMENT ANALYSIS OF RECTANGULAR PLATES

Abstract

Limit State Amplitude of Displacement is the limiting point or value of the amplitude of displacement beyond which the possibility of severe damage or failure is prominent. Understanding this level or point is key to determining the safety of plate structures. This work aims to derive the limit state expression that will help predict this limiting point or value for plate structures. The yield stress criterion equation was established. The yield stress was substituted with the stress equation in a plane using non-dimensional parameters.  The displacement shape function, w , in the equation, was replaced by the product of the amplitude of displacement, A, and the shape profile, h, and the equation evaluated by making, A, the subject of the equation. The resulting equation became the general limit state amplitude of displacement expression. Twelve plate types were considered and their shape profiles were evaluated and substituted into the general limit state amplitude of displacement equation to obtain the specific limit state amplitude of displacement expression for each plate type. Numerical applications were carried out to obtain the numerical values of the coefficient of the amplitude of displacement and the limit state amplitude of displacement for each plate type. From the new limit state equations, it was observed that the limit state amplitude of displacement is directly proportional to the length of the plate and inversely proportional to the thickness of the plate. This implies that the longer the plate's span the higher the amplitude of displacement, and the higher the thickness of the plate the lesser the amplitude of displacement. This relationship observed from the new equations conforms with the actual and practical behavior of structural elements such as plates, confirming the adequacy of the new equations. More so, the approach is easy and the equation can easily predict the amplitude of displacement of plates once the length of the plate and its thickness is known with the plate type determined. The work will help analysts and designers of plates with easy data to determine the limit of safety of plate structures based on amplitude of displacement, since the higher the amplitude of displacement, the higher the chances of failure or severity of damage. Hence, the conclusion is that these new equations are adequate for thin rectangular plate analysis for the amplitude of displacement and that the approach is simpler, understandable, and reproducible.

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KEYWORDS: Amplitude, Displacement, Limit state, Shape profiles, Rectangular plates