Bijan O Aalami Emeritus Professor, San Francisco State University Principal, ADAPT Corporation

1. Design of Concrete Floors With Particular Reference to Post-Tensioning Bijan O Aalami Emeritus Professor, San Francisco State University Principal, ADAPT Corporation

2. DESIGN STEPS • Definition of geometry • Support conditions • Loading • Design criteria (building codes) • Structural Modeling • Analysis (determine moments, shear, axial) • Determine reinforcement • Detailing

3. Illustration of design concept for concrete floors through juxtaposition of its features with other materials: • Glass • Steel • Concrete • Post-Tensioned • Conventional

4. Design the plate using the following materials: • Glass • Steel • Concrete PARTIAL PLAN A DESIGN REGION C FREE EDGE B PLATE SUPPORT

5. MODELING OPTIONS OF A PLATE REGION A DESIGN REGION C FREE EDGE PLATE B SUPPORT (a) PARTIAL PLAN A A DETAILING TOP BARS C TOP BARS FOR DETAILING MAIN BOTTOM BARS MAIN TOP BARS B B (b) SPAN BETWEEN (c) CANTILEVER WALLS A AND B OVER WALL C

6. FLEXURAL DUCTILITY OF PRESTRESSED SECTIONS F DUCTILITY = mFu/Fy M n M M MOMENT M REBAR PT F F y u (a) FLEXURAL DUCTILITY F e a c 20 d e PT m REBAR 15 DUCTILITY 10 05 CODE PERMISSIBLE RANGE 0 0.1 0.2 0.3 0.4 0.5 c/d e (b) DUCTILITY AND REINFORCEMENT

7. ELASTIC AND DESIGN MOMENTS 2 M x M 1 y 1 2 (i) M ALONG 1-1 (ii) M ALONG 2-2 x y * (a) ELASTIC DISTRIBUTION OF MOMENTS 2 M x M y 1 1 2 (ii) M ALONG 2-2 (i) M ALONG 1-1 x y (b) DESIGN DISTRIBUTION OF MOMENTS * POISSON'S RATIO DISREGARDED

8. FINITE ELEMENT MESHING SCHEMES FOR CONCRETE AND OTHER MATERIALS INTEGRAL-DRIVEN MESHING (CONCRETE) STRESS-DRIVEN MESHING (GLASS)

9. STRESSES AND FORCE AT SECTIONS 1 Q A Q 1 1 1 (b) FEM MODEL (a) ACTUAL STRUCTURE 1 2P 3 P (c) ELEMENT A f 1 f 1 P 1 3 f 1 P P P a/2 F a/2 da f P F F = f a 1 fda = P (d) COMMON PROCEDURE (e) ALTERNATIVE PROCEDURE

10. CONSTRUCTION DETAILING WALL SUPPORT SLAB REBAR BAR "SIZE; LENGTH; SPACING" (i) BAR DESIGNATION ON STRUCTURAL DRAWING BAR "SIZE; LENGTH" (ii) BAR DESIGNATION ON SHOP DRAWING (a) DETAILING OF PRIMARY REINFORCEMENT 6d D H A R d D d OVERLAP (i) (ii) (iii) (b) BAR BENDING AND SPLICING

11. EXAMPLES OF "STRUCTURAL DETAILING" BOTTOM BARS CONCETRATED A LOAD BARS BELOW LOAD B (a) BARS FOR LOAD DISTRIBUTION SLAB EDGE AT RE-ENTRANT CORNER (b) CRACK CONTROL BARS

12. Additional Features Specific to Post-tensioned Floors

13. POST-TENSIONED DESIGN OPTION • Load Path (Tendon Layout) • Tendon Profile ? • Tendon Force ? TENDON 1 A SLAB C SLAB EDGE REBAR B 1 (a) PLAN TENDON REBAR WALL A WALL B (b) ELEVATION 1-1

14. Question • For the same floor geometry, • For the same loading, • For the same designated load path, • Will two engineers conclude with the same design? No • Reason • Solution depends on the additional assumptions of • Tendon profile. • Tendon force.

15. FLOW CHART FOR CONCRETE FLOOR DESIGN 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

16. EXAMPLE OF A LOAD PATH DESIGNATION • Analysis using Equivalent Frame Method • Analysis using Finite Element Method

17. PLAN OF FLOOR SLAB COLUMN SLAB OPENING WALL SLAB EDGE BEAM Y X

18. DESIGNATION OF LINES OF SUPPORT IN X-DIRECTION A B Support line C D E F Y X G

19. DESIGNATION OF LINES OF SUPPORT IN Y-DIRECTION 2 3 5 1 4 Y X

20. SELECTION OF DEMARCATION POINTS FOR TRIBUTARIES (DESIGN STRIPS) 6 A 8 5 3 B 1 2 4 9 C 7 D E F Y X G

21. TRIBUTARIES FOR DESIGN STRIPS IN X-DIRECTION 2 3 4 5 1 A B C D E F Y X G

22. TRIBUTARIES FOR DESIGN STRIPS IN Y-DIRECTION 2 3 5 1 4 A B C D E F Y X

23. DESIGN SECTIONS FOR DESIGN STRIPS B AND E DESIGN SECTION 2 3 5 4 1 A B C D E F Y X

24. CONSTRUCTION OF DESIGN STRIP IN PLAN 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

25. DESIGN STRIP IN ELEVATION 1 2 3 4 5

26. DISCRETIZATION OF FLOOR SLAB

27. DIAGRAM OF LOAD FLOW UNDER SERVICE CONDITION Y X

28. ZERO LINE OF SHEAR TRANSFER IN Y-DIRECTION A B C D E F Y G X

29. ASSUMED DESIGN STRIPS SUPERIMPOSED ON NATURAL TRIBUTARIES IN X-DIRECTION 0 0 0 A 0 0 0 0 0 0 0 0 -250 0 B B 0 0 0 0 -250 0 0 0 0 0 0 0 0 0 C C 250 0 0 250 -250 0 0 0 0 0 0 -250 -250 -250 0 D 0 0 0 0 0 0 250 0 0 0 0 -250 E 0 0 0 -250 0 0 -250 250 -250 250 250 0 250 0 F 0 Y 0 0 0 0 X 0 G 0 250

30. PARTIAL VIEW OF IN-SERVICE MOMENTS My FOR DESIGN STRIP B OF PROSPERITY SLAB 2 1 A -12.1 kN 19.9 kN -15.2 kN 21.4 kN 4.88 kN B -281 kN-m -74.8 kN-m DESIGN STRIP 128 kN-m -83.2 kN + -8.61 kN -2.52 kN 3.99 kN 1.37 kN 6.86 kN Y X CONTOURS AT 20kN INTERVALS

31. Thank you for your attention.

32. Design_concept2 • - 11-30-00 reviewed • move the slides 31 through 35 to PT_des_tech • - Renee should look at the slides and improve them • 3-7-01 reviewed it looks ok

33. Example of post-tensioned waffle slab during construction.

34. WAFFLE SLAB MODELING OPTION COLUMN (a) ACTUAL SLAB B Y DESIGN STRIPS X B b b e e (b) DESIGN STRIPS IN X-DIRECTION ADP-728

35. STRUCTURAL MODELING OF WAFFLE UNITS COLUMN CENTERLINE RIB ATTACHMENT (b ) w SOLID DIRECTION CAP/DROP b OF FRAME b w w (a) THREE WAFFLE SOLID SUPPORT CAP h h f DIRECTION c OF FRAME b B= b w e (b) IDEALIZED RIB ATTACHMENTS PARALLEL BEAM CAP/PANEL DIRECTION B OF FRAME TRANSVERSE BEAM b e (c) PLAN OF IDEALIZED STRUCTURAL MODEL ADP-726

36. CROSS-SECTION OF A WAFFLE SLAB c = b f b f h h f 12 1 b BASIC w STRUCTURAL UNIT DESI-122

37. Concluding Remarks: • Load path designation is an integral part of floor design • Structural detailing is essential for satisfactory performance