%0 Journal Article %1 citeulike:5946616 %A Keller, Joseph %D 1960 %J Archive for Rational Mechanics and Analysis %K 74g60-bifurcation-and-buckling %N 1 %P 275--285 %R 10.1007/bf00252909 %T The shape of the strongest column %U http://dx.doi.org/10.1007/bf00252909 %V 5 %X Abstract The problem of determining that shape of column which has the largest critical buckling load is solved, assuming that the length and volume are given and that each cross section is convex. The strongest column has an equilateral triangle as cross section, and it is tapered along its length, being thickest in the middle and thinnest at its ends. Its buckling load is 61.2\% larger than that of a circular cylinder. For columns all of whose cross sections are similar and of prescribed shape-not necessarily convex—the best tapering is found to increase the buckling load by one third over that of a uniform column. This result, which was independently obtained by H. F. Weinberger, is originally due to Clausen (1851). For a uniform column, triangularizing is shown to increase the buckling load by 20.9\% over that of a circular cylinder. The results lead to isoperimetric inequalities for the buckling loads of arbitrary columns.

@article{citeulike:5946616, abstract = {{Abstract The problem of determining that shape of column which has the largest critical buckling load is solved, assuming that the length and volume are given and that each cross section is convex. The strongest column has an equilateral triangle as cross section, and it is tapered along its length, being thickest in the middle and thinnest at its ends. Its buckling load is 61.2\% larger than that of a circular cylinder. For columns all of whose cross sections are similar and of prescribed shape-not necessarily convex—the best tapering is found to increase the buckling load by one third over that of a uniform column. This result, which was independently obtained by H. F. Weinberger, is originally due to Clausen (1851). For a uniform column, triangularizing is shown to increase the buckling load by 20.9\% over that of a circular cylinder. The results lead to isoperimetric inequalities for the buckling loads of arbitrary columns.}}, added-at = {2017-06-29T07:13:07.000+0200}, author = {Keller, Joseph}, biburl = {https://www.bibsonomy.org/bibtex/27a9db823c15929621b9c8797882c0f27/gdmcbain}, citeulike-article-id = {5946616}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/bf00252909}, citeulike-linkout-1 = {http://www.springerlink.com/content/16j672065h876831}, comment = {(private-note)`Our method is inspired by and extends J. Keller's classic treatment of the Euler buckling problem with a beam of nonuniform cross section' (Chen \& Brenner 2008)}, day = 1, doi = {10.1007/bf00252909}, interhash = {fe5f1889e53df12eeab4400ff75ef4bb}, intrahash = {7a9db823c15929621b9c8797882c0f27}, journal = {Archive for Rational Mechanics and Analysis}, keywords = {74g60-bifurcation-and-buckling}, month = jan, number = 1, pages = {275--285}, posted-at = {2009-10-15 23:24:29}, priority = {2}, timestamp = {2017-06-29T07:13:07.000+0200}, title = {{The shape of the strongest column}}, url = {http://dx.doi.org/10.1007/bf00252909}, volume = 5, year = 1960 }