The document discusses reinforcement in two-way slabs and footing design. It describes two types of shear failure in slabs: one-way shear and two-way shear. One-way shear results in inclined cracking and pull-out of negative reinforcement from the slab. Two-way shear can result in either inclined cracking or the slab sliding down the column. The critical perimeter for two-way shear is located at d/2 from the column face, where d is the effective depth of the slab. Formulas are provided to calculate the nominal shear resistance Vn of slabs under two-way shear with negligible moment transfer.

2. Direct Method

 Reinforcement in Two-way Slabs
 Footing Classification
 Footing Design

3. The reinforcement is for slabs without beams.

4. Look at Example 13-7
Design of a flat plate floor without spandrel
beams - Direct Design Method
Look at Example 13-9
Design of a Two-way slab with beams in both
directions.

5. Shear failure occurs when inclined cracks form due to flexural and
shearing stresses.
Two types of shear failure mechanism in 2-way slabs.
(a) One-way shear
(b) Two-way shear (Punching shear).

6. One-way shear Two-way shear

7. Inclined cracking Slab slides down column
Top (negative
reinforcement pulls out of
slab leaving no
connection to the
column
Inclined cracking

8. Critical perimeter is located d / 2 from column face, where d =
effective depth of slab

9. Critical perimeter is located d / 2 from column face, where d =
effective depth of slab
Slabs with Drop Panels

10. Two-way Shear with Negligible Moment Transfer
ACI Eqn. 11-1
Vu Vn
where, Vu =Factored shear force (tributary area
bounded by lines of zero shear)
Vn = Nominal shear resistance of slab
0.85

11. Two-way Shear with Negligible Moment Transfer
Vn Vc Vs
where, Vc =Shear resistance of concrete
Vs = Shear resistance of steel (in
most slabs, Vs = 0)

12. (a) Two-way Shear with Negligible Moment Transfer
For two-way shear in slabs (& footings) Vc is smallest
of
4 ACI 11-35
Vc 2 f c b0 d
c
where, = long side/short side of
c
column concentrated load
or reaction area
b0 =
length of critical perimeter
around the column

13. (b) Two-way Shear with Negligible Moment Transfer
d
s
ACI 11-36
Vc 2 f c b0 d
b0
where, = 40 for interior columns
s
30 for edge columns
20 for corner columns

14. (c) Two-way Shear with Negligible Moment Transfer
ACI 11-37
Vc 4 f c b0 d
Take smaller of (a), (b) and (c)

15. Tributary area for Vu calculations
Figure 13-41
MacGregor

16. If V Vn can be increased by:
,
Vc u
(1) Increase slab thickness
(2) Use drop panel
(3) Increase b0 by increasing column size or adding
a fillet or capital
(4) Add shear reinforcement