BUCKLING OF A RECTANGULAR COLUMN ON THE BASIS OF MURNAGHAN'S FORMULA FOR STRAIN ENERGY

Buckling criteria are derived for a rectangular column for large two-dimensional strains, using a strain energy density function suggested by Murnaghan. This function is analogous to the classical density function in that it involves two elastic constants but is simpler in certain respects. Despite the apparent simplicity, the evaluation proved more difficult than the equivalent analysis using the classical function. As expected, Murnaghan's density function leads to smaller values of critical strains than does the classical but the difference is slight for slender columns. For infinitely thick columns, the critical strain is found to range between 0.344 to 0.372 depending upon the ratio of elastic constants as compared to 0.5 for the classical formula independent of this ratio. (Author)