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