1. Lecture 33 - Design of Two-Way Floor Slab System
April 10, 2001
CVEN 444

2. Lecture Goals
One-way and two-way slab
Slab thickness, h

3. Comparison of One-way and Two-way slab behavior
One-way slabs carry load in one direction.
Two-way slabs carry load in two directions.

4. Comparison of One-way and Two-way slab behavior
One-way and two-way slab action carry load in two directions.
One-way slabs: Generally, long side/short side > 1.5

5. Comparison of One-way and Two-way slab behavior
Two-way slab with beams
Flat slab

6. Comparison between a two-way slab verses a one-way slab
For flat plates and slabs the column connections can vary between:

7. Comparison of One-way and Two-way slab behavior
Flat Plate
Waffle slab

8. Comparison of One-way and Two-way slab behavior
The two-way ribbed slab and waffled slab system: General thickness of the slab is 2 to 4 in.

9. Comparison of One-way and Two-way slab behavior Economic Choices
Flat Plate suitable span 20 to 25 ft with LL= psf
Advantages
Low cost formwork
Exposed flat ceilings
Fast
Disadvantages
Low shear capacity
Low Stiffness (notable deflection)

10. Comparison of One-way and Two-way slab behavior Economic Choices
Flat Slab suitable span 20 to 30 ft with LL= psf
Advantages
Low cost formwork
Exposed flat ceilings
Fast
Disadvantages
Need more formwork for capital and panels

11. Comparison of One-way and Two-way slab behavior Economic Choices
Waffle Slab suitable span 30 to 48 ft with LL= psf
Advantages
Carries heavy loads
Attractive exposed ceilings
Fast
Disadvantages
Formwork with panels is expensive

12. Comparison of One-way and Two-way slab behavior Economic Choices
One-way Slab on beams suitable span 10 to 20 ft with LL= psf
Can be used for larger spans with relatively higher cost and higher deflections
One-way joist floor system is suitable span 20 to 30 ft with LL= psf
Deep ribs, the concrete and steel quantities are relative low
Expensive formwork expected.

13. Comparison of One-way and Two-way slab behavior
ws =load taken by short direction
wl = load taken by long direction
dA = dB
Rule of Thumb: For B/A > 2, design as one-way slab

14. Two-Way Slab Design Static Equilibrium of Two-Way Slabs
Analogy of two-way slab to plank and beam floor
Section A-A:
Moment per ft width in planks
Total Moment

15. Two-Way Slab Design Static Equilibrium of Two-Way Slabs
Analogy of two-way slab to plank and beam floor
Uniform load on each beam
Moment in one beam (Sec: B-B)

16. Two-Way Slab Design Static Equilibrium of Two-Way Slabs
Total Moment in both beams
Full load was transferred east-west by the planks and then was transferred north-south by the beams;
The same is true for a two-way slab or any other floor system.

17. General Design Concepts
(1) Direct Design Method (DDM)
Limited to slab systems to uniformly distributed loads and supported on equally spaced columns. Method uses a set of coefficients to determine the design moment at critical sections. Two-way slab system that do not meet the limitations of the ACI Code must be analyzed more accurate procedures

18. General Design Concepts
(2) Equivalent Frame Method (EFM)
A three dimensional building is divided into a series of two-dimensional equivalent frames by cutting the building along lines midway between columns. The resulting frames are considered separately in the longitudinal and transverse directions of the building and treated floor by floor.

19. Equivalent Frame Method (EFM)
Transverse equivalent frame
Longitudinal equivalent frame

20. Equivalent Frame Method (EFM)
Perspective view
Elevation of the frame

21. Method of Analysis (1) Elastic Analysis
Concrete slab may be treated as an elastic plate. Use Timoshenko’s method of analyzing the structure. Finite element analysis

22. Method of Analysis (2) Plastic Analysis
The yield method used to determine the limit state of slab by considering the yield lines that occur in the slab as a collapse mechanism.
The strip method, where slab is divided into strips and the load on the slab is distributed in two orthogonal directions and the strips are analyzed as beams.
The optimal analysis presents methods for minimizing the reinforcement based on plastic analysis

23. Method of Analysis (3) Nonlinear analysis
Simulates the true load-deformation characteristics of a reinforced concrete slab with finite-element method takes into consideration of nonlinearities of the stress-strain relationship of the individual members.

24. Column and Middle Strips
The slab is broken up into column and middle strips for analysis

25. Minimum Slab Thickness for two-way construction
The ACI Code specifies a minimum slab thickness to control deflection. There are three empirical limitations for calculating the slab thickness (h), which are based on experimental research. If these limitations are not met, it will be necessary to compute deflection.

26. Minimum Slab Thickness for two-way construction
(a) For
fy in psi. But not less than 5 in.

27. Minimum Slab Thickness for two-way construction
(b) For
fy in psi. But not less than 3.5 in.

28. Minimum Slab Thickness for two-way construction
(c) For
Use the following table

29. Minimum Slab Thickness for two-way construction
Slabs without interior beams spanning between supports and ratio of long span to short span < 2
See section For slabs with beams spanning between supports on all sides.

30. Minimum Slab Thickness for two-way construction
The definitions of the terms are:
h = Minimum slab thickness without interior beams
ln =
b =
am=
Clear span in the long direction measured face to face of column
the ratio of the long to short clear span
The average value of a for all beams on the sides of the panel.

31. Definition of Beam-to-Slab Stiffness Ratio, a
Accounts for stiffness effect of beams located along slab edge reduces deflections of panel adjacent to beams.

32. Definition of Beam-to-Slab Stiffness Ratio, a
With width bounded laterally by centerline of adjacent panels on each side of the beam.

33. Beam and Slab Sections for calculation of a

34. Beam and Slab Sections for calculation of a

35. Beam and Slab Sections for calculation of a
Definition of beam cross-section
Charts may be used to calculate a Fig

36. Minimum Slab Thickness for two-way construction
Slabs without drop panels meeting and ,
tmin = 5 in
Slabs with drop panels meeting and ,
tmin = 4 in

37. Example
A flat plate floor system with panels 24 by 20 ft is supported on 20 in. square columns. Determine the minimum slab thickness required for the interior and corner panels. Use fc = 4 ksi and fy = 60 ksi

38. Example
The floor system consists of solid slabs and beams in two directions supported on 20 in square columns. Determine the minimum slab thickness required for an interior panel. Use fc = 4 ksi and fy = 60 ksi

39. Example
The cross-sections are:

40. Example
The resulting cross section: