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Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E.

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Computer Assisted Design of Concrete Floors Types of programs available Advantages of each Why specialized finite element software is necessary for PT design

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Computer Assisted Design of Concrete Floors The design process using 3-D finite element analysis Project examples

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Types of Programs Available 2-D strip method 3-D finite element method Linear elastic Non-linear

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2-D Strip Method Structure analyzed with one model per beam, one-way slab, or two-way slab bay Equivalent frame method used for two- way slabs Easy to understand behavior Good for highly repetitive structures

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Flat Plate Example

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Transverse direction

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Longitudinal direction

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3-D finite element method Visual modeling / input Accuracy continuity effects (elastic reactions) load path complicated loads (including lateral) restraint effects torsion

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3-D finite element method Graphical presentation of results Less cumbersome – work with one model instead of numerous Easier to incorporate changes Loadings Concrete geometry Construction Issues »Low Concrete Strength »Broken Strands

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Las Olas River Condominiums 43 Story Fort Lauderdale, FL Suncoast Post- Tension

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Visual modeling / input Speed CAD like interface Reduce chances for input error Automatic mesh generation

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River City Apartments, Brisbane 1650 mm Transfer Slab

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River City Apartments – Tendons Robert Bird and Partners

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Accuracy of 3-D FE Analysis Continuity Effects Load Path Complicated Loads Generally leads to more optimal design

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Accuracy of 3-D FE Analysis Restraining Effects Torsion

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Continuity Effects

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Beam and Slab: Relatively straightforward load path

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Beam and Slab: More difficult load path

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Prestress tendon profile variations

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Bending moments …

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Loads ….. Self weight is automatically calculated Superimposed loadings easily input

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Straightforward line load

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Complicated point and line loads

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Restraining Effects Normally ignored by 2-D programs Can be calculated and accounted for by 3-D finite element programs Important for serviceability of structure Important for strength of structure (hyperstatic effects)

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Torsion Normally ignored by 2-D programs (potentially creating a conservative design) Can exist in 3-D finite element model and therefore should be designed for

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Torsion

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Graphical Presentation of Results

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Finite Element Basics Using shell elements to model concrete floors In plane forces Out of plane forces Related in irregular slabs (change of centroid)

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In Plane Forces

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Out of Plane Forces

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Plate Considerations Resolution of Txy Integrated forces in equilibrium with nodal loads

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Interaction of In Plane/Out of Plane Fx’ = Fx Vxy’ = Vxy Vxz’ = Vxz My’ = My - Fx d Mxy’ = Mxy - Vxy d

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Using Shell Elements to Model Beams Deep beam behavior Torsion stiffness of beams using shell elements Transfer of moment through large step

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Deep Beam Behavior

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Torsion Stresses

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Moment Transfer Through Step Beam

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Orthotropic Element Properties

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Hyperstatic (Secondary) effects …..

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Hyperstatic effects …

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Hyperstatic effects …..

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“Complete Secondary (Hyperstatic) Effects” Allan Bommer PTI Journal - January 2004

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Post-Tensioning Loadings Balance Loading Hyperstatic Loading

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The 3-D Finite Element Design Process Model the structure Apply the loads Lay out the tendons (if PT) Draw design strips (define cross-sections) Perform the design Process results

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Model the Structure

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Apply the Loads (Dead Loads)

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Apply the Loads (Live Loads)

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Lay Out Tendons (Banded)

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Lay Out Tendons (Distributed)

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Lay Out Tendons

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Deflection With Initial Tendon Layout

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Draw the Design Strips

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Perform the Design

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Process Results

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Special Considerations Lateral Analysis / Design Punching Shear Analysis / Design Restraining Effects Pour Strips, etc. Mat Foundations

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Punching Shear

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SR=1.25 Punching Shear …….. stress ratio exceeds unity

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Punching Shear …….. without penetrations, stress ratio < 1

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Mats

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48” Mat: DL + LL + WL Bearing pressure Max = 2560 psf Min = 690 psf

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24” Mat: DL + LL + WL Bearing pressure Max = 3450 psf Min = 0 psf (10 iterations)

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24” Mat: DL + LL + WL Bearing pressure Max = 3450 psf Min = 0 psf (10 iterations)

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Bridgewater Place, Leeds Mixed Use: Office / Residential Connell Mott McDonald Matthew Consultants

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Minneapolis Institute of Arts …….Soffit view Top view………

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Sheraton Keauhou Bay Resort Keauhou Kona, Hawaii

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Structural Systems (UK) Ltd

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Westbridge Wharf Leicester Strongforce / Laing O’Rourke

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3 residential buildings 9 levels each Westbridge Wharf

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St. Lucia Luxury Condominiums Destin, Florida Suncoast Post-Tension

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Royal Palm Plaza Boca Raton, FL Tendon Systems, Inc.

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Opus Architects and Engineers

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Jonathan Hirsch, P.E.

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