Evaluation and formulation of raleigh- ritz based peculiar total potential energy functional for doubly symmetric multi (dsm) cell and mono symmetric multi (msm) cell thin- walled box column (twbc) cross- sections

Knowing the critical buckling load would put the designer in better stead to carry out efficient design. This work is concerned with the evaluation and formulation of peculiar Total Potential Energy Functional (TPEF)for Doubly Symmetric Multi (DSM) cell and Mono Symmetric Multi (MSM) cell Thin -walled Box Column (TWBC) cross-sections in preparation for the eventual stability analysis in subsequent papers. This present study is a follow up of the works by Nwachukwu and others (2017) and Nwachukwu and others (2021). For each of the cross – section under consideration, the cross –sectional properties are evaluated first to obtain the cross-sectional areas and moment of inertia. This is followed by the formulation of the TPEF for the cross- sections for different boundary conditions..The Raleigh- Ritz based formulated TPEF equations are found suitable, handy and simple to be used in the proper stability/buckling analysis (in future publications) where critical bucking loads will be obtained. The audience is therefore advised to look forward towards future publications, where these equations will be transformed in the stability analysisof DSM and MSM TWC.