practical application of finite element analysis to the design of post-tensioned and reinforced...
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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, [email protected]