1. Lecture 39 - Design of Two-Way Floor Slab System
CEN 347

2. Lecture Goals
Example of DDM

3. Example –Two-way Slab (Panels)
Using the direct design method, design the typical exterior flat-slab panel with drop down panels only. All panels are supported on 20 in. square columns, 12 ft long. The slab carries a uniform service live load of 80 psf and service dead load that consists of 24 psf of finished in addition to the slab self-weight. Use fc = 4 ksi and fy = 60 ksi

4. Example –Two-way Slab (Panels)
The thickness of the slab is found using

5. Example –Two-way Slab (Panels)
From the ACI Code limitation:
For panels with discontinuous edges, end beams with a minimum a equal to 0.8 must be used; otherwise the minimum slab thickness calculated by the equations must be increased by at least 10%.
When drop panels are used without beams, the minimum slab thickness may be reduced by 10 %. The drop panels should extend in each direction from the centerline of support a distance not less than one-sixth of the span length in that direction between center to center of supports and also project below the slab at least h/4. 1. 2.

6. Example –Two-way Slab (Panels)
From the ACI Code limitation:
Regardless of the values obtained for the equations, the thickness of two-way slabs shall not be less than the following: 3. 1. 2. 3.
For slabs without beams or drop panels, 5 in.
for slabs without beams but with drop panels, 4 in.
for slabs with beams on all four sides with am > 2.0, 3.5 in. and for am < 2.0, 5 in. (ACI Code 9.5.3)

7. Example –Two-way Slab (Panels)
Therefore, the panel thickness is
The panel half width are at least L/6 in length.

8. Example –Two-way Slab (Panels)
Therefore, the drop down panel thickness is 10 in. and has 7 ft x 8 ft.

9. Example –Two-way Slab (Panels)
The load on the slab is given as:
The load on the panel is

10. Example –Two-way Slab (Panels)
The drop panel length is L/3 in each direction, then the average wu is

11. Example –Two-way Slab (Panels)
The punch out shear at center column is

12. Example –Two-way Slab (Panels)
The punch out shear at center column is

13. Example –Two-way Slab (Panels)
The punch out shear at panel is

14. Example –Two-way Slab (Panels)
The punch out shear at panel is
One way shear is not critical.

15. Example –Two-way Slab (Panels)
Moment Mo for the two directions are:
Long direction
Short direction

16. Example –Two-way Slab (Panels)
The column strip will be 10 ft. (20 ft /4 = 5ft), therefore the middle strips for long section is 10 ft and the middle strip for the short section will be 14 ft.
The average d for the panel section
The average d for the slab section

17. Example –Two-way Slab (Panels)
The factored components of the moment for the beam (long) is similar to an interior beam.
Negative – Moment
Positive + Moment

18. Example –Two-way Slab (Panels)
Components on the beam (long) interior.
Column Strip
Negative – Moment
Positive + Moment

19. Example –Two-way Slab (Panels)
Components on the beam (long) interior.
Negative – Moment
Positive + Moment
Middle Strip

20. Example –Two-way Slab (Panels)
Computing the reinforcement uses:

21. Example –Two-way Slab (Panels)
Compute the reinforcement need for the internal moment in long direction. Strip width b =120 in. (10 ft) d =8.5 in. and Mu = k-ft

22. Example –Two-way Slab (Panels)
Compute the reinforcement need for the internal moment in long direction. Strip width b =120 in. (10 ft) d =8.5 in. and Mu = k-ft

23. Example –Two-way Slab (Panels)
The area of the steel reinforcement for a strip width b =120 in. (10 ft), d = 8.5 in., and h = 10 in.

24. Example –Two-way Slab (Panels)
The area of the steel reinforcement for a strip width b =120 in. (10 ft), d = 8.5 in., and As = 4.76 in2. Use a #5 bar (Ab = 0.31 in2 )
Maximum spacing is 2(h) or 18 in.
So 7.5 in. < 18 in. OK

25. Example –Two-way Slab (Panels)
The long direction

26. Example –Two-way Slab (Panels)
The short direction