CRITICAL LATERAL LOAD ANALYSIS OF RECTANGULAR PLATE CONSIDERING SHEAR DEFORMATION EFFECT

Abstract

This work present flexural analysis of rectangular plate subjected to uniform distributed transverse loads using displacement and third-order shear deformation theory. The aim of this study is to establish the formula’s for calculation of the critical lateral imposed load of the plate before deflection reaches the specified maximum specified limit q𝑖𝑤 and critical lateral imposed load before plate reaches an elastic yield point q𝑖𝑝. The essence is to ensure that deflection does not exceed specified maximum limit and the plate shear not exceeding the elastic yielding point. Furthermore, this approach overcomes the challenges of the conventional practice in the structural analysis/design which involves checking of deflection and shear; the process which is proved unreliable. Total potential energy equation of a thick plate was formulated from the static elastic theory of the plate. The formulated potential energy was in the same way used by the method of direct variation to obtain the coefficient of deflection and shear deformation. This expression was applied to solve bending problem of two different types of rectangular thick plates. The plates has one edge clamped and other three edges simply supported (CSSS). From the result obtained in this work among the two types of plate, it is observed that the value of q𝑖𝑝 if greater than that of q𝑖𝑤. It can be said that the failure of plate in q𝑖𝑤 is like a warning requesting maintenance whereas failure in q𝑖𝑝 means total failure and cannot be maintained. Hence, failure in deflection (q𝑖𝑤) is seen in the plate into consideration. The numerical analysis obtained, it is found that if the value of critical lateral imposed load (q𝑖𝑤 and q𝑖𝑝) increase as the specified thickness (t) of plate increases and decrease as the length to width ratio increases. This implies that as we increase the thickness and allowable deflection improve the safety in the plate, whereas an increase in the span (length) of the plate increases the failure tendency of the plate structure. Furthermore, effects of aspect ratio of the critical lateral load of isotropic plates are investigated and discussed. It is concluded that the values of critical lateral load obtained by this theory achieve accepted transverse shear stress to the thickness of plate variation and satisfied the transverse flexibility of the condition of the plate while predicting the be characteristics for the CSSS isotropic rectangular thin or thick plate.