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Practical Application of Finite ElementAnalysis 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 cumbersomework 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 ApartmentsTendons
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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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 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-Dfinite element programs
Important for serviceability of structure
Important for strength of structure (hyperstaticeffects)
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Torsion
Normally ignored by 2-D programs(potentially creating a conservativedesign)
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
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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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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
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Model the Structure
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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)
O T d (Di ib d)
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Lay Out Tendons (Distributed)
L O t T d
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Lay Out Tendons
D fl i Wi h I i i l T d
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Deflection With Initial Tendon Layout
D th D i St i
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Draw the Design Strips
D th D i St i
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Draw the Design Strips
D th D i St i
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Draw the Design Strips
D th D i St i
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Draw the Design Strips
D th D i St i
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Draw the Design Strips
D th D i St i
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Draw the Design Strips
P f th D i
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Perform the Design
Perform the Design
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Perform the Design
Perform the Design
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Perform the Design
Perform the Design
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Perform the Design
Process Results
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Process Results
Process Results
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Process Results
Process Results
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Process Results
Process Results
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Process Results
Process Results
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Process Results
Process Results
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Process Results
Process Results
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Process Results
Process Results
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Process Results
Process Results
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Process Results
Process Results
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Process Results
Process Results
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Process Results
Process Results
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Process Results
Process Results
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Process Results
Process Results
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Process Results
Process Results
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Process Results
S i l C id ti
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Special Considerations
Lateral Analysis / Design
Punching Shear Analysis / Design
Restraining Effects
Pour Strips, etc.
Mat Foundations
P hi Sh
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Punching Shear
Punching Shear
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Punching Shear
Punching Shear ..
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SR=1.25
Punching Shear ..
stress ratio exceeds unity
Punching Shear ..
ith t t ti t ti
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without penetrations, stress ratio
< 1
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Mats
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Mats
48 Mat: DL + LL + WL
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Bearing pressure
Max = 2560 psf
Min = 690 psf
24 Mat: DL + LL + WL
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Bearing pressure
Max = 3450 psf
Min = 0 psf
(10 iterations)
24 Mat: DL + LL + WL
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Bearing pressure
Max = 3450 psf
Min = 0 psf
(10 iterations)
Bridgewater Place Leeds
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Bridgewater Place, LeedsMixed Use:
Office / Residential
Connell Mott McDonald
Matthew Consultants
Minneapolis Institute of Arts
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Minneapolis Institute of Arts
.Soffit view
Top view
Sheraton Keauhou Bay Resort
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Sheraton Keauhou Bay Resort
Keauhou Kona, Hawaii
Structural Systems
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Structural Systems
(UK) Ltd
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Westbridge Wharf
Leicester
Strongforce / Laing ORourke
Westbridge Wharf
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3 residential buildings
9 levels each
St. Lucia Luxury
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Condominiums
Destin, Florida
Suncoast Post-Tension
St. Lucia Luxury
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Condominiums
Destin, Florida
Suncoast Post-Tension
Royal Palm Plaza
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Boca Raton, FL
Tendon Systems,Inc.
Royal Palm Plaza
Boca Raton, FL
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Boca Raton, FL
Tendon Systems,Inc.
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Opus
Architects and Engineers
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Jonathan Hirsch, [email protected]