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Jonathan Hirsch, P.E. PowerPoint Presentation
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Jonathan Hirsch, P.E.

Jonathan Hirsch, P.E.

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Jonathan Hirsch, P.E.

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

  2. Computer Assisted Design of Concrete Floors • Types of programs available • Advantages of each • Why specialized finite element software is necessary for PT design

  3. Computer Assisted Design of Concrete Floors • The design process using 3-D finite element analysis • Project examples

  4. Types of Programs Available • 2-D strip method • 3-D finite element method • Linear elastic • Non-linear

  5. 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

  6. Flat Plate Example

  7. Transverse direction

  8. Longitudinal direction

  9. 3-D finite element method • Visual modeling / input • Accuracy • continuity effects (elastic reactions) • load path • complicated loads (including lateral) • restraint effects • torsion

  10. 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

  11. Suncoast Post-Tension Las Olas River Condominiums43 StoryFort Lauderdale, FL

  12. Visual modeling / input • Speed • CAD like interface • Reduce chances for input error • Automatic mesh generation

  13. River City Apartments, Brisbane1650 mm Transfer Slab

  14. River City Apartments – TendonsRobert Bird and Partners

  15. Accuracy of 3-D FE Analysis • Continuity Effects • Load Path • Complicated Loads • Generally leads to more optimal design

  16. Accuracy of 3-D FE Analysis • Restraining Effects • Torsion

  17. Continuity Effects

  18. Continuity Effects

  19. Beam and Slab: Relatively straightforward load path

  20. Beam and Slab: More difficult loadpath

  21. Prestress tendon profile variations

  22. Bending moments …

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

  24. Straightforwardline load

  25. Complicatedpoint andline loads

  26. 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)

  27. 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

  28. Torsion

  29. Torsion

  30. Graphical Presentation of Results

  31. Graphical Presentation of Results

  32. Finite Element Basics • Using shell elements to model concrete floors • In plane forces • Out of plane forces • Related in irregular slabs (change of centroid)

  33. In Plane Forces

  34. Out of Plane Forces

  35. Plate Considerations • Resolution of Txy • Integrated forces in equilibrium with nodal loads

  36. Interaction of In Plane/Out of Plane Fx’ = Fx Vxy’ = Vxy Vxz’ = Vxz My’ = My - Fx d Mxy’ = Mxy - Vxy d

  37. Using Shell Elements to Model Beams • Deep beam behavior • Torsion stiffness of beams using shell elements • Transfer of moment through large step

  38. Deep Beam Behavior

  39. Deep Beam Behavior

  40. Torsion Stresses

  41. Moment Transfer Through Step Beam

  42. Orthotropic Element Properties

  43. Hyperstatic (Secondary) effects …..

  44. Hyperstatic effects …

  45. Hyperstatic effects …..

  46. Hyperstatic effects ….. “Complete Secondary (Hyperstatic) Effects” Allan Bommer PTI Journal - January 2004

  47. Post-Tensioning Loadings • Balance Loading • Hyperstatic Loading

  48. 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

  49. Model the Structure

  50. Model the Structure