practical application of finite element analysis to the design of post-tensioned and reinforced...
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![Page 1: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/1.jpg)
Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete FloorsJonathan Hirsch, P.E.
![Page 2: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/2.jpg)
Computer Assisted Design of Concrete Floors
• Types of programs available
• Advantages of each
• Why specialized finite element software is necessary for PT design
![Page 3: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/3.jpg)
Computer Assisted Design of Concrete Floors
• The design process using 3-D finite element analysis
• Project examples
![Page 4: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/4.jpg)
Types of Programs Available
• 2-D strip method
• 3-D finite element method• Linear elastic• Non-linear
![Page 5: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/5.jpg)
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
![Page 6: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/6.jpg)
Flat Plate Example
![Page 7: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/7.jpg)
Transverse direction
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Longitudinal direction
![Page 9: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/9.jpg)
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
![Page 11: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/11.jpg)
Las Olas River Condominiums
43 StoryFort 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, Brisbane1650 mm Transfer Slab
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River City Apartments – TendonsRobert 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
![Page 16: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/16.jpg)
Accuracy of 3-D FE Analysis
• Restraining Effects
• Torsion
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Continuity Effects
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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 loadpath
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Prestress tendon profile variations
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Bending moments …
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Loads …..Self weight is automatically calculatedSuperimposed loadings easily input
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Straightforwardline load
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Complicatedpoint andline 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)
![Page 27: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/27.jpg)
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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Torsion
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Graphical Presentation of Results
![Page 31: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/31.jpg)
Graphical Presentation of Results
![Page 32: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/32.jpg)
Finite Element Basics
• Using shell elements to model concrete floors
• In plane forces
• Out of plane forces
• Related in irregular slabs (change of centroid)
![Page 33: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/33.jpg)
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
![Page 38: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/38.jpg)
Deep Beam Behavior
![Page 39: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/39.jpg)
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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Hyperstatic effects …..
“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
![Page 50: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/50.jpg)
Model the Structure
![Page 51: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/51.jpg)
Model the Structure
![Page 52: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/52.jpg)
Apply the Loads (Dead Loads)
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Apply the Loads (Live Loads)
![Page 54: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/54.jpg)
Lay Out Tendons (Banded)
![Page 55: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/55.jpg)
Lay Out Tendons (Distributed)
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Lay Out Tendons
![Page 57: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/57.jpg)
Deflection With Initial Tendon Layout
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Draw the Design Strips
![Page 59: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/59.jpg)
Draw the Design Strips
![Page 60: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/60.jpg)
Draw the Design Strips
![Page 61: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/61.jpg)
Draw the Design Strips
![Page 62: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/62.jpg)
Draw the Design Strips
![Page 63: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/63.jpg)
Draw the Design Strips
![Page 64: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/64.jpg)
Perform the Design
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Perform the Design
![Page 66: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/66.jpg)
Perform the Design
![Page 67: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/67.jpg)
Perform the Design
![Page 68: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/68.jpg)
Process Results
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Process Results
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Process Results
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Process Results
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Process Results
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Process Results
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Process Results
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Process Results
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Process Results
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Process Results
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Process Results
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Process Results
![Page 80: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/80.jpg)
Process Results
![Page 81: Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors Jonathan Hirsch, P.E](https://reader031.vdocuments.us/reader031/viewer/2022012315/56649c805503460f949383f0/html5/thumbnails/81.jpg)
Process Results
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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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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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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, LeedsMixed Use: Office / Residential
Connell Mott McDonaldMatthew Consultants
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Minneapolis Institute of Arts
…….Soffit view
Top view………
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Sheraton Keauhou Bay ResortKeauhou Kona, Hawaii
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Structural Systems(UK) Ltd
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Westbridge WharfLeicester
Strongforce / Laing O’Rourke
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3 residential buildings9 levels each
Westbridge Wharf
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St. Lucia Luxury CondominiumsDestin, Florida
Suncoast Post-Tension
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St. Lucia Luxury CondominiumsDestin, FloridaSuncoast Post-Tension
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Royal Palm PlazaBoca Raton, FL
Tendon Systems, Inc.
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Royal Palm PlazaBoca Raton, FL
Tendon Systems, Inc.
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OpusArchitects and Engineers
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Jonathan Hirsch, [email protected]