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 3𝐸12(1−ν 2)

Rectangular Kirchhoff PlateSubjected to uniform loading

Maximum Deflection at Mid-Point: 6.266x10-3 in

Closed Form Solution

, κ=

𝜎 𝑥𝑥=6

𝑡2𝑀 𝑥𝑥 𝜎 𝑦𝑦=

6

𝑡 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