ME3180_Columns_01172012 - Analyze Buckling and Determine...

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Design of Columns Gregg Larson ME 3180, Section A Spring 2012
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Design of Columns Columns can fail in compression or due to buckling. “Short” columns will fail in compression. “Long” or “medium” columns will buckle at stresses well below the yield strength of the material. Image from efunda.com (10/8/2010) Image from aplaceofsense.com (10/8/2010)
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What’s Long? What’s Short? The determination of whether a column is “long” or “short” is based upon the slenderness ratio, S r S r is the ratio of the length, l , to the radius of gyration, k I is the moment of inertia A column is “short” if S r ≤ 10 4 64 2 4 d A d I A I k k l S r
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Buckling of Columns For long columns, calculate the critical load to predict failure potential. Below the critical load, the column is safe. At the critical load, the column will buckle. Column experiences Bending Compression http://www.youtube.com/ watch?v=TUE7DKNBIrU
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Sectioned View of Column
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Unformatted text preview: Analyze Buckling and Determine the Critical Load . cos sin : : 2 1 2 1 2 2 2 2 conditions boundary upon depend C and C x EI P C x EI P C y of form the has Solution y EI P dx y d yields Combining Py M dx y d EI M Experimental Demonstration of Buckling of Columns (http://en.wikipedia.org/wiki/File:Buckledmodel.JPG) Rounded-rounded Ends ,... 3 , 2 , 1 sin : 2 # : 1 # 1 2 n where n l EI P for true is This l EI P C l x at y BC C x at y BC Lowest Critical Load (n=1) The critical load is a function of: Youngs modulus (material property) Cross-sectional geometry Length The strength of the material is NOT a factor. 2 2 l EI P cr Rewriting in terms of the critical load/area: 2 2 2 2 2 2 2 2 2 2 r cr r r cr S E A P k l S Ak I A I k S EA l EAk l EI P...
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This note was uploaded on 02/08/2012 for the course ME 3180 taught by Professor Staff during the Spring '08 term at Georgia Institute of Technology.

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ME3180_Columns_01172012 - Analyze Buckling and Determine...

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