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Plate Bending of Steel Column Caps Daniel MargolinMEng Structural Engineering Abdul Al-MishwatMEng Structural Engineering MAE 5700 Final Project

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What is a Column Cap?

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Our Problem 10 ” 1 ”

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Simplification 8 ”

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Plate Theory Kirchhoff Thin Plates Reissner-Mindlin Thick Plates

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Bi-Harmonic Equation of Plate Flexure: Thin Plate Approximation:

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W INT W EXT

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Linear Case Standard Displacement

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Parameters PLATE PROPERTIES: -DIMENSIONS: 8”- 8”- 0.1” -MODULUS OF ELASTICITY (E): 29,000 KSI -Poisson’s Ratio (ν): 0.3 -Applied load: 1 psi -SUPPORT CONDITIONS: SIMPLY SUPPORTED

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ANSYS Deflection: 6.337x10 -3 in. Stress: 1854 psi

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Element Performance

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MATLAB Maximum Deflection at Mid-Span:1.56x10 -4 m 6.14x10 -3 in

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Closed Form Solution Rectangular Kirchhoff Plate Subjected to uniform loading

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Closed Form Solution

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Final Results %

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Thank you !

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References -M. Suneel Kumar “ULTIMATE STRENGTH OF SQUARE PLATE RECTANGULAR OPENING UNDER AXIAL XCOMPRESSION” Journal of Naval Architecture and Marine Engineering, June 2007 -Alexander G. Losilevich “AN ANALYSIS OF FINITE ELEMENTS FOR PLATE BENDING PROBLEMS” Massachusetts Institute of Technology, 1996 -A.J.M Ferreira “MATLAB CODES FOR FINITE ELEMENT ANALYSIS” Universidade do Porto, Portugal, 2008 -Niels Ottosen & Hans Peterson “INTRODUCTION TO THE FINITE ELEMENT METHOD” University of Lund, Sweden, 1992 -Thomas J.R.Hughes “THE FINITE ELEMENT METHOD-LINEAR STATIC AND DYNAMIC FINITE ELEMENT ANALYSIS” Stanford University, 1987

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