Formulation Of The Total Potential Energy Functional Relevant To The Stability Analysis Of A Doubly Symmetric Single (DSS) Cell Thin- Walled Box Column In Line With Raleigh- Ritz Method

Purpose: This work is concerned with the formulation of peculiar Total Potential Energy Functional (TPEF) for a Doubly Symmetric Single (DSS) cell Thin -walled Box Column (TWBC).  The formulated Energy Functional Equations support the stability analysis of a DSS cell thin-walled box (closed) column cross-section using Raleigh - Ritz Method (RRM) with polynomial shape functions. Methodology: This present formulation is based on the governing TPEF developed by Nwachukwu and others (2017). The polynomial shape functions (only the first two coordinate polynomial shape functions) for different boundary conditions were generated first, and then followed by the formulation of TPEF for different boundary conditions of the DSS cell TWBC. Findings: The Raleigh- Ritz based formulated TPEF equations are found suitable, handy and simple to be used in the Flexural(F) , Flexural- Torsional(FT)  and Flexural- Torsional- Distortional(FTD) buckling/stability analysis of DSS cell TWBC cross-section where data obtained (critical bulking loads) will be compared with the works of other authors in subsequent papers. Conclusion: Henceforth it is recommended that additional work should be done using more than first two coordinate polynomial shape functions in order to increase the accuracy of RRM.