1. ANALYSIS OF TWO-WAY SLABS WITH BEAMS

2. ANALYSIS OF TWO-WAY SLABS WITH BEAMS
In this lecture the moments are determined by the direct design method for an exterior panel of a two-way slab with beams. It is felt that if you can handle this problem, you can handle any other case that may arise in flat plates, flat slabs, or two-way slabs with beams using the direct design method.
The requirements of the Code are so lengthy and complex that in Example 16.4, which follows, the steps and appropriate Code sections are spelled out in detail. The practicing designer should obtain a copy of the CRSI Design Handbook, because the tables therein will be of tremendous help in slab design.

3. ANALYSIS OF TWO-WAY SLABS WITH BEAMS
Example 16.4
SOLUTION

4. ANALYSIS OF TWO-WAY SLABS WITH BEAMS

5. ANALYSIS OF TWO-WAY SLABS WITH BEAMS

6. ANALYSIS OF TWO-WAY SLABS WITH BEAMS

7. ANALYSIS OF TWO-WAY SLABS WITH BEAMS

8. ANALYSIS OF TWO-WAY SLABS WITH BEAMS

9. ANALYSIS OF TWO-WAY SLABS WITH BEAMS

10. ANALYSIS OF TWO-WAY SLABS WITH BEAMS

11. ANALYSIS OF TWO-WAY SLABS WITH BEAMS

12. ANALYSIS OF TWO-WAY SLABS WITH BEAMS

13. ANALYSIS OF TWO-WAY SLABS WITH BEAMS

14. ANALYSIS OF TWO-WAY SLABS WITH BEAMS

15. ANALYSIS OF TWO-WAY SLABS WITH BEAMS

16. ANALYSIS OF TWO-WAY SLABS WITH BEAMS

17. TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS
AND COLUMNS

18. TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS
On many occasions the maximum load that a two-way slab can support is dependent upon the strength of the joint between the column and the slab. Not only is the load transferred by shear from the slab to the column along an area around the column, but also there may be moments that have to be transferred as well. The moment situation is usually most critical at the exterior columns.
If there are moments to be transferred, they will cause shear stresses of their own in the slabs, as will be described in this section. Furthermore, shear forces resulting from moment transfer must be considered in the design of the lateral column reinforcement (that is, ties and spirals), as stated in Section of the Code. When columns are supporting slabs without beams (that is, flat plates or flat slabs), the load transfer situation between the slabs and columns is extremely critical. Perhaps if we don’t have the flexural reinforcing designed just right throughout the slab as to quantities and positions, we can get by with it; however, if we handle the shear strength situation incorrectly, the results may very well be disastrous.

19. TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS
The serious nature of this problem is shown in Figure 16.20, where it can be seen that if there is no spandrel beam, all of the total exterior slab moment has to be transferred to the column. The transfer is made by both flexure and eccentric shear, the latter being located at a distance of about d/2 from the column face. Section of the Code states that for moment transfer between the slab and edge column, the gravity load moment to be transferred shall be 0.3Mo (where Mo is the factored statical moment).
When gravity loads, wind or earthquake loads, or other lateral forces cause a transfer of an unbalanced moment between a slab and a column, a part of the moment equal to γfMu shall be transferred by flexure, according to ACI Section Based on both tests and experience, this transfer is to be considered to be made within an effective slab width between lines that are located 1.5 times the slab or drop panel thickness outside opposite faces of the column or capital. The value γf is to be taken as

20. TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS

21. TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS

22. TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS

23. TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS

24. TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS
Example 16.5

25. TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS
Example 16.5
SOLUTION

26. TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS
Example 16.5
SOLUTION

27. TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS
Example 16.5
SOLUTION

28. TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS
Example 16.5
SOLUTION

29. TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS
Example 16.5
SOLUTION

30. TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS
Example 16.5
SOLUTION

31. Factored Moments in Columns and Walls
TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS
Factored Moments in Columns and Walls
If there is an unbalanced loading of two adjoining spans, the result will be an additional moment at the connection of walls and columns to slabs. The Code ( ) provides the approximate equation listed at the end of this paragraph to consider the effects of such situations. This particular equation was derived for two adjoining spans, one longer than the other. It was assumed that the longer span was loaded with dead load plus one-half live load and that only dead load was applied to the shorter span.

32. Factored Moments in Columns and Walls
TRANSFER OF MOMENTS AND SHEARS BETWEEN SLABS AND COLUMNS
Factored Moments in Columns and Walls
If there is an unbalanced loading of two adjoining spans, the result will be an additional moment at the connection of walls and columns to slabs. The Code ( ) provides the approximate equation listed at the end of this paragraph to consider the effects of such situations. This particular equation was derived for two adjoining spans, one longer than the other. It was assumed that the longer span was loaded with dead load plus one-half live load and that only dead load was applied to the shorter span.