Transcript Slide 1
Practical Application of Finite Element Analysis to the Design of Post-Tensioned and Reinforced Concrete Floors
Jonathan 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 Story Fort Lauderdale, FL Suncoast Post Tension
Visual modeling / input
• Speed • CAD like interface • Reduce chances for input error • Automatic mesh generation
River City Apartments, Brisbane 1650 mm Transfer Slab
River City Apartments – Tendons Robert 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 load path
Prestress tendon profile variations
Bending moments …
Loads …..
Self weight is automatically calculated Superimposed loadings easily input
Straightforward line load
Complicated point and line 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
Punching Shear …….. stress ratio exceeds unity
SR=1.25
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, Leeds Mixed Use: Office / Residential Connell Mott McDonald Matthew Consultants
Minneapolis Institute of Arts
Top view……… …….Soffit view
Sheraton Keauhou Bay Resort Keauhou Kona, Hawaii
Structural Systems (UK) Ltd
Westbridge Wharf Leicester Strongforce / L aing O’Rourke
Westbridge Wharf 3 residential buildings 9 levels each
St. Lucia Luxury Condominiums Destin, Florida Suncoast Post-Tension
St. Lucia Luxury Condominiums Destin, Florida Suncoast Post-Tension
Royal Palm Plaza Boca Raton, FL Tendon Systems, Inc.
Royal Palm Plaza Boca Raton, FL Tendon Systems, Inc.
Opus Architects and Engineers
Jonathan Hirsch, P.E.