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

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

Computer Assisted Design of Concrete Floors

• Types of programs available

• Advantages of each

• Why specialized finite element software is necessary for PT design

Computer Assisted Design of Concrete Floors

• The design process using 3-D finite element analysis

• Project examples

Types of Programs Available

• 2-D strip method

• 3-D finite element method• Linear elastic• Non-linear

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

Flat Plate Example

Transverse direction

Longitudinal direction

3-D finite element method

• Visual modeling / input

• Accuracy• continuity effects (elastic reactions)• load path• complicated loads (including lateral)• restraint effects• torsion

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

Las Olas River Condominiums

43 StoryFort Lauderdale, FL

Suncoast Post-Tension

Visual modeling / input

• Speed

• CAD like interface

• Reduce chances for input error

• Automatic mesh generation

River City Apartments, Brisbane1650 mm Transfer Slab

River City Apartments – TendonsRobert Bird and Partners

Accuracy of 3-D FE Analysis

• Continuity Effects

• Load Path

• Complicated Loads

• Generally leads to more optimal design

Accuracy of 3-D FE Analysis

• Restraining Effects

• Torsion

Continuity Effects

Continuity Effects

Beam and Slab: Relatively straightforward load path

Beam and Slab:

More difficult loadpath

Prestress tendon profile variations

Bending moments …

Loads …..Self weight is automatically calculatedSuperimposed loadings easily input

Straightforwardline load

Complicatedpoint andline loads

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)

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

Torsion

Torsion

Graphical Presentation of Results

Graphical Presentation of Results

Finite Element Basics

• Using shell elements to model concrete floors

• In plane forces

• Out of plane forces

• Related in irregular slabs (change of centroid)

In Plane Forces

Out of Plane Forces

Plate Considerations

• Resolution of Txy

• Integrated forces in equilibrium with nodal loads

Interaction of In Plane/Out of Plane

Fx’ = Fx Vxy’ = Vxy Vxz’ = Vxz

My’ = My - Fx d Mxy’ = Mxy - Vxy d

Using Shell Elements to Model Beams

• Deep beam behavior

• Torsion stiffness of beams using shell elements

• Transfer of moment through large step

Deep Beam Behavior

Deep Beam Behavior

Torsion Stresses

Moment Transfer Through Step Beam

Orthotropic Element Properties

Hyperstatic (Secondary) effects …..

Hyperstatic effects …

Hyperstatic effects …..

Hyperstatic effects …..

“Complete Secondary (Hyperstatic) Effects”

Allan Bommer

PTI Journal - January 2004

Post-Tensioning Loadings

• Balance Loading

• Hyperstatic Loading

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

Model the Structure

Model the Structure

Model the Structure

Apply the Loads (Dead Loads)

Apply the Loads (Live Loads)

Lay Out Tendons (Banded)

Lay Out Tendons (Distributed)

Lay Out Tendons

Deflection With Initial Tendon Layout

Draw the Design Strips

Draw the Design Strips

Draw the Design Strips

Draw the Design Strips

Draw the Design Strips

Draw the Design Strips

Perform the Design

Perform the Design

Perform the Design

Perform the Design

Process Results

Process Results

Process Results

Process Results

Process Results

Process Results

Process Results

Process Results

Process Results

Process Results

Process Results

Process Results

Process Results

Process Results

Process Results

Special Considerations

• Lateral Analysis / Design

• Punching Shear Analysis / Design

• Restraining Effects

• Pour Strips, etc.

• Mat Foundations

Punching Shear

Punching Shear

SR=1.25

Punching Shear …….. stress ratio exceeds unity

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

Mats

Mats

48” Mat: DL + LL + WL

Bearing pressure

Max = 2560 psf

Min = 690 psf

24” Mat: DL + LL + WL

Bearing pressure

Max = 3450 psf

Min = 0 psf

(10 iterations)

24” Mat: DL + LL + WL

Bearing pressure

Max = 3450 psf

Min = 0 psf

(10 iterations)

Bridgewater Place, LeedsMixed Use: Office / Residential

Connell Mott McDonaldMatthew Consultants

Minneapolis Institute of Arts

…….Soffit view

Top view………

Sheraton Keauhou Bay ResortKeauhou Kona, Hawaii

Structural Systems(UK) Ltd

Westbridge WharfLeicester

Strongforce / Laing O’Rourke

3 residential buildings9 levels each

Westbridge Wharf

St. Lucia Luxury CondominiumsDestin, Florida

Suncoast Post-Tension

St. Lucia Luxury CondominiumsDestin, FloridaSuncoast Post-Tension

Royal Palm PlazaBoca Raton, FL

Tendon Systems, Inc.

Royal Palm PlazaBoca Raton, FL

Tendon Systems, Inc.

OpusArchitects and Engineers

Jonathan Hirsch, P.E.Jonathan.Hirsch@bentley.com