ME85-Lecture27 - Lecture 27 Buckling of Elastic Columns Stability of Structures In the design of columns cross-sectional area is selected such that

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Unformatted text preview: Lecture 27 Buckling of Elastic Columns Stability of Structures In the design of columns, cross-sectional area is selected such that- allowable stress is not exceeded all A P =- deformation falls within specifications spec AE PL = After these design calculations, may discover that the column is unstable under loading and that it suddenly becomes sharply curved or buckles. Eulers Formula for Pin-Ended Beams Consider an axially loaded beam. After a small perturbation, the system reaches an equilibrium configuration such that 2 2 2 2 = + = = y EI P dx y d y EI P EI M dx y d Solution with assumed configuration can only be obtained if ( ) ( ) 2 2 2 2 2 2 2 r L E A L Ar E A P L EI P P cr cr = = > = = > ( ) ( ) s ratio slendernes r L tress critical s r L E A L Ar E A P A P L EI P P cr cr cr cr 2 2 2 2 2 2 2 = = = = = > = = > The value of stress corresponding to the critical load, Preceding analysis is limited to centric loadings. Human Spinal Column Cantilever column...
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This note was uploaded on 01/21/2012 for the course C 85 taught by Professor Papadopoulos during the Spring '08 term at University of California, Berkeley.

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ME85-Lecture27 - Lecture 27 Buckling of Elastic Columns Stability of Structures In the design of columns cross-sectional area is selected such that

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