Plate Bending of Steel Column Caps
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Transcript of Plate Bending of Steel Column Caps
Plate Bending of Steel Column Caps
Daniel Margolin MEng Structural EngineeringAbdul Al-Mishwat MEng Structural Engineering
MAE 5700 Final Project
What is a Column Cap?
Our Problem
10 ”
1 ”
Simplification
8 ”
Plate Theory
• Kirchhoff• Thin Plates
• Reissner-Mindlin• Thick Plates
- Assumes out-of-plane components are negligible.
- Normal to mid-surface remains normal after deformation.
- Thin plates: > t >
- Accounts for shear deformations.- Normal to mid-surface does not remain normal
after deformation.- Moderately thick plates: < t
Bi-Harmonic Equation of Plate Flexure:
Thin Plate Approximation:
WINT
WEXT
Linear Case Standard Displacement
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
ANSYS
Deflection: 6.337x10-3 in.
Stress:1854 psi
Element Performance
MATLAB
Maximum Deflection at Mid-Span: 1.56x10-4 m 6.14x10-3 in
Closed Form Solution
𝐷=𝑡 3𝐸
12(1−ν 2)
Rectangular Kirchhoff PlateSubjected to uniform loading
Maximum Deflection at Mid-Point: 6.266x10-3 in
Closed Form Solution
, κ=
𝜎 𝑥𝑥=6𝑡2𝑀 𝑥𝑥 𝜎 𝑦𝑦=
6𝑡 2𝑀 𝑦𝑦
Maximum In-Plane Stress: σxx 1839 psi
Final Results
%
Thank you !
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