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Unformatted text preview: Lecture 27 Buckling of Elastic Columns Stability of Structures In the design of columns, crosssectional 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 PinEnded 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 = = &gt; = = &gt; ( ) ( ) 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 = = = = = &gt; = = &gt; 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.
 Spring '08
 PAPADOPOULOS
 Statics, Deformation, Stress

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