PBL Group Ltd.

1. PBL Group Ltd. 8/11 Soi Viphavadi 44, Viphavadi-Rangsit Road, Lardyao, Jatujak, Bangkok 10900,Thailand. Design of Post-Tensioned Floor Systemswith the Case of Long Spansand Applicationsin High-Rise Buildings Presentation by Mr. Prapat Boonlualoah CEO, PBL Group Ltd., Bangkok

2. Introduction What is Pre-stressing? “Pre-stressing is a method of reinforcing concrete. Externally applied loads induce internal stresses (forces) in concrete during the construction and service phases of a member. The concrete is pre-stressed to counteract those anticipated stresses during the service life of the member” Source: Post-tensioning Institute (2006)

3. Introduction Methods of Pre-stressing Pre-tensioning Post-tensioning

4. Introduction Pre-tensioning • Steel tendons are stressed before the concrete is placed at a precast plant remote from the construction site.

5. Introduction Post-tensioning • Steel tendon are stressed after the concrete has been placed and gained sufficient strength at the construction site.

6. Introduction Benefits of Post-tensioning • Effective use of high strength materials • Better cost effectiveness • Thinner slab, lower mass, more attractive structures • Better deflection control • Better crack control • Better water-tightness • Improved seismic performance (due to lower mass of structure)

7. Introduction Post-tensioning vs. Typical RC Construction Faster floor construction cycle (typically 4-7 days cycle per floor) Lower floor weight (typically 1/5-1/3 less) Lower floor-to-floor height (no beams) Larger spans between columns (optimum 8-10 m for flat plate system) Reduced foundations Source: Post-tensioning Institute (2006)

8. Introduction Post-tensioning Applications • Office buildings • Car parks • Shopping centers • Hotels, apartments • Hospitals • Industrial buildings • Ground/rock anchors • Silos/water tanks/nuclear containments • Bridges/girders Source: Post-tensioning Institute (2006)

9. Introduction Cost comparison – flat plate

10. Introduction Cost comparison – one way slab with slab band

11. Introduction Post-tensioning Systems • Un-bonded Post-tensioning System • Bonded Post-tensioning Systems

12. Introduction Bonded vs. Unbonded Tendons • Bonded Source: The Concrete Society (1994)

13. Introduction Arrangement of Bonded Post-tensioning System

14. Introduction Bonded vs. Un-bonded Tendons • Unbonded Source: The Concrete Society (1994)

15. Introduction Arrangement of Unbonded Post-tensioning System

16. Design of PT Slabs Design Considerations and Selection of Suitable Floor Systems • Flat plate system • Flat plate with drop panels/caps • Slab with banded beams (one/two ways) • Slab with long span beam/other supporting structures

17. Design of PT Slabs Flat Plate Systems Common geometries* • Two-way system • Suitable span: 8 m • Limiting criterion: Punching shear • Rebar**: 1.08 kg/m2 • PT: 2.84 kg/m2 * for typical office/residential buildings using ACI/UBC requirements ** quantity assume no bottom reinforcement Source: Aalami & Bommer (1999)

18. Design of PT Slabs Flat Plate with Drop Panels Common geometries* • Two-way system • Suitable span: 12.2 m • Limiting criterion: Deflection • Rebar**: 2.94 kg/m2 • PT: 3.87 kg/m2 * for typical office/residential buildings using ACI/UBC requirements ** quantity assume no bottom reinforcement Source: Aalami & Bommer (1999)

19. Design of PT Slabs Slab with Banded Beams/slab bands Common geometries* • Two-way system • Suitable span: 13.4 m • Limiting criterion: Rebar congestion • Rebar**: 2.01 kg/m2 • PT: 4.16 kg/m2 * For typical office/residential buildings using ACI/UBC requirements ** case of slab band type Source: Aalami & Bommer (1999)

20. Design of PT Slabs SLAB with Long Span Beam/other Supporting Structures Common geometries* • One-way system • Beam spans: 18-20 m • Slab spans: 5.5-6.0 m • Slab thickness: 125-150 mm • Beam depth: 750-900 mm • Beam width: 400-460 mm * For typical office/residential buildings using ACI/UBC requirements Source: Aalami & Bommer (1999)

21. Design of PT Slabs Suitable Span Arrangements vs. Floor Thickness • Criteria of span combinations (internal/external/cantilever span) • Span-to-depth ratio of slab

22. Design of PT Slabs Criteria of Span Combinations (Internal/External/Cantilever Span) • Internal spans should be approximately equal. • External span should be approximately 0.8 times the length of the internal span. • Cantilevers should not exceed 0.3 times the length of the adjacent span. • Expansion joints – unless formed with double columns (completely separated slabs) should be approximately in the quarter span locations. 5. Size of slabs between expansion joints should be limited to a maximum of about 100m.

23. Design of PT Slabs Span-to-depth Ratio of Slab * Recommended by The Concrete Society ** Recommended by The Post-Tensioning Institute

24. Design of PT Slabs Design Principles • Equivalent frame method • Finite element analysis • Load balancing of effective pre-stressing forces • Pre-stress losses • The concept of banded/distributed tendon system • Moment redistribution • Strength of section (flexure &shear)

25. 1 CONCRETE OUTLINE AND SUPPORTS 2 DESIGN OPTIONAL PATH LOADING REQUIREMENTS (a) 3 STRUCTURAL STRUCTURAL SYSTEM AND MODELING LOAD PATH SELECTION (c) (b) ANALYSIS OPTION 5 6 4 FINITE SIMPLE EQUIVALENT ELEMENTS FRAME FRAME 7 CALCULATION OF REBAR FOR DESIGN SECTIONS DESIGN 8 STRUCTURAL DETAILING 9 CONSTRUCTION (SHOP DRAWINGS) DETAILING Design of PT Slabs Flowchart for PT Floor Slab Source: Aalami (a)

26. Design of PT Slabs Design Steps Sizing • Span • Thickness Cover to reinforcement and tendons • Corrosion • Wear • Fire Loading • Dead • Live • Prestressing Sizing Cover to reinforcement and tendons Loading Structural system Analysis Design Source Aalami and Jurgens (2001)

27. Design of PT Slabs Structural System • Structure • One-way • Two-way • Model Pre-stressing Analysis • Elastic theory • Gross cross-section • Redistribution of moments due to limited plasticity • Two-way systems • Simple frame • Equivalent frame • Finite Elements Design • Serviceability • Crack control • Deflection control • Safety • Add passive reinforcement if necessary Design Steps Sizing Cover to reinforcement and tendons Loading Structural system Analysis Design Source Aalami and Jurgens (2001)

28. Design of PT Slabs Design Steps Source: The Concrete Society (1994)

29. Design of PT Slabs Design Steps • For given:     • Structural geometry and boundary conditions • Material properties • Loading There is a unique design for nonprestressed concrete members Added information is needed for prestressed members • Tendon profile • Average precompression • Percentage of loading to balance Based on added information, a multitude of design alternatives are possible

30. REBAR A S (a) NONPRESTRESSED BEAM TENDON ? ? (ii) FORCE (i) TENDON SHAPE ? REBAR A (iii) TENDON DRAPE S (b) POST-TENSIONED BEAM Design of PT Slabs Initial Assumptions for Post-Tensioning Design Source: Aalami (a)

31. Design of PT Slabs Design Focus • Crack control in service condition • Safety against overload • Durability Source: Aalami and Jurgens (2001)

32. Design of PT Slabs Equivalent Frame Method • The equivalent frame method is currently the most common method of analyzing and designing concrete floor systems, including post-tensioned floors. It is flexible and efficient, equally suited for both regular and irregular floor systems Source: Aalami and Bommer (1999)

33. Design of PT Slabs Column stiffness representation using equivalent frame modeling Source: Aalami and Bommer (1999)

34. Design of PT Slabs Structural model for gravity Source: Aalami and Bommer (1999)

35. Design of PT Slabs Break down of floor into design strips in two directions Source: Aalami and Bommer (1999)

36. COLUMN SLAB OPENING WALL SLAB EDGE BEAM Y X Design of PT Slabs Plan of Floor Slab Source: Aalami (b)

37. A B Support line C D E F Y X G Design of PT Slabs Support Lines in X-direction Source: Aalami (b)

38. 2 1 3 4 5 Y X Design of PT Slabs Support Lines in Y-direction Source: Aalami (b)

39. 6 A 8 5 3 B 1 2 4 9 C 7 D E F Y X G Design of PT Slabs Selection of Design Strips Source: Aalami (b)

40. 2 3 4 5 1 A B C D E F Y X G Design of PT Slabs Design Strips Tributaries (X-axis) Source: Aalami (b)

41. 2 1 3 4 5 A B C D E F Y X Design of PT Slabs Design Strips Tributaries (Y-axis) Source: Aalami (b)

42. 2 3 5 4 1 A B C D E DESIGN SECTION F Y X Design of PT Slabs Design Sections for Design Strips B and E Source: Aalami (b)

43. 1 2 3 4 5 0.8 9 10 10 9.2 B (a) DESIGN STRIP IN PROTOTYPE 0.8 9 10 10.6 10.5 B (b) STRAIGHTENED DESIGN STRIP IDEALIZED B ACTUAL (c) IDEALIZED TRIBUTARY FOR DESIGN Design of PT Slabs Construction of Design Strip in Plan Source: Aalami (b)

44. 1 2 3 4 5 Design of PT Slabs Design Strips in Elevation Source: Aalami (b)

45. Design of PT Slabs Finite Element Analysis • In the FEM analysis, the plate is subdivided into a number of small parts, referred to as elements. • The elements are connected at reference points called nodes • The force assume at the nodes are generally Mx, My, and Fz whendealing with the flexural respond of the plate • The force assume at the nodes are generally Mx, My, Fz, Fx and Fy when the plate respond is due to both flexure and stretching (membrane action)

46. Design of PT Slabs Finite element for plate bending Source: Aalami and Bommer (1999)

47. Design of PT Slabs Flexural and membrane actions for elements in PT slabs Source: Aalami and Bommer (1999)

48. Design of PT Slabs Discretization of floor slab Source: Aalami (b)

49. Y Design of PT Slabs Diagram of load flow under service condition Source: Aalami (b)

50. A B C D E F Y G X Design of PT Slabs Zero line of shear transfer in Y-direction Source: Aalami (b)