Orji, Godswill Christopher2026-03-212026-03-212020-01Orji, G. C. (2020). Pure bending analysis of thin rectangular flat plates using euler-bernoulli residual force approach [Unpublished Master'sThesis]. Federal University of Technology, Owerri, Nigeriahttps://repository.futo.edu.ng/handle/20.500.14562/2434This thesis is for the award of Master of engineering (M. Eng) in Civil Engineering (Structure)This study investigated pure bending analysis of thin rectangular flat plate using EulerBernoulli residual force equilibrium equation. The study derived from first principle; the total potential energy functional of a thin rectangular plate based on Kirchhoff’s assumption. The study carried out direct differentiation of the equation with respect to the displacement function, w (x, y) to obtain the general Euler-Bernoulli residual force equilibrium equation for the plate. The study used direct integration to solve the Euler-Bernoulli residual force equilibrium equation of plates to obtain the exact general deflection equation with unknown coefficients. The boundary conditions (simple support designated with S and clamp support designated with C) of the plates were satisfied in the general solution to obtained particular solutions that are products of unknown coefficients and exact shape functions. The plates include SSSS (all edges simply supported), CCCC (all edges clamped), CSCS (two opposite edges simply supported and the other two edges clamped), CSSS (one edge simply supported and the other three edges clamped), CCCS (one edge simply supported and the other three edges clamped) and CCSS (two adjacent edges clamped the remaining two adjacent edges simply supported). The exact particular shape functions were substituted into the Euler-Bernoulli equation of equilibrium to obtain the exact coefficients of deflection of the plates for the boundary conditions considered. With the exact shape functions and their corresponding exact coefficients obtained, the study went on to determine the exact central deflection, exact maximum bending moments and exact maximum shear forces for the plates considered. To check the exactness of the approach used, the study obtained the values of residual forces from Euler-Bernoulli approach (the present study) and from other classical method considered (Ibearugbulem, 2014), for the selected plate types. This was done by substituting the integrands of the shape functions from the present study and Ibearugbulem, 2014, approaches into the Euler-Bernoulli governing partial differential equation determined from this study. The results of residual forces from the present study gave zero while the results from Ibearugbulem, 2014 did not give zero. This shows that the results from the present study are exact while the results from the other classical methods considered violate the law of equilibrium of forces which postulates that the forces must be as such that they cancel out. The results obtained herein showed that the average percentage differences between the present study and Ibearugbulem, 2014, recorded for SSSS, CCCC, CSCS, CSSS, CCSS and CCCS were 23.73%, 3.36%, 14.21%, 18.01%, 12.46% and 7.94% respectively. The method is simple and devoid of complexity.enAttribution-NonCommercial-ShareAlike 4.0 InternationalEuler-Bernoulli residual forceweighted residual forceshape functioncoefficient of deflectionpartial differential equationDepartment of Civil EngineeringMaster’s Thesis