Structural failure is discovered to be attributed to the inability of the designer to determine the structural load (critical load) that causes it. The aim of this study is to develop a mathematical model for calculation of the critical lateral imposed load of the plate before deflection reaches the maximum specified limit and its corresponding critical lateral imposed load before plate reaches an elastic yield point . Total potential energy equation of a thick plate was formulated from the static elastic theory of the plate. Direct variation method of analysis was adopted by minimizing the total potential energy obtained to determine the expression for the deflection and shear deformation. By solving the formulated expression, the effect of stress and load distribution analysis of a mild steel rectangular plate with one edge clamped, free at the other and the other opposite edge simply supported (CSFS) are analyzed and discussed. From the established equation, a new model for determination of the critical lateral imposed load of the plate is developed. The result showed that: (i) as the specified thickness of the plate increases, the value of critical lateral imposed load increase (ii) the critical lateral imposed load decrease as the plates span increases. iii) the critical lateral imposed load increase as the plate thickness increases. (iv) increase in the value of the allowable deflection value required for the analysis of the plate reduces the chances of failure of a structural member. It is concluded that the values of critical lateral load obtained by this theory achieve accepted vertical shear stress to the thickness of plate variation and satisfied the transverse flexibility of the condition of the plate while predicting the flexural characteristics for an isotropic rectangular CSFS plate. Numerical comparison was conducted to verify and demonstrate the efficiency of the present theory. The results obtained are in good agreement with those in the literature. This approach is recommended to the practicing engineers as it 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.
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