Structural Concrete - Hassoun

626 Chapter 17 Design of Two-Way Slabs
occurs along a truncated cone or pyramid around the column. The critical section is located at
a distance d/2 from the face of the column, column capital, or drop panel (Fig. 17.9a). If shear
reinforcement is not provided, the shear strength of concrete is the smaller of Eqs. 17.6 and 17.7:
φV c = φ
(
2 + 4 β
)
λ √ f ′ cb 0 d (17.5)
where
b 0 = perimeter of critical section
β = ratio of long side of column (or loaded area) to short side
( )
αs d
φV c = φ + 2 λ √ f
b
cb ′ 0 d (17.6)
0
where α s is 40 for interior columns, 30 for edge columns, and 20 for corner columns.
φV n ≤ φ(4λ √ f cb ′ 0 d)
When shear reinforcement is provided, the shear strength should not exceed
φV n ≤ φ(6 √ f ′ cb 0 d)
17.7.3 Shear Reinforcement in Two-Way Slabs without Beams
(17.7a)
(17.7b)
In flat-slab and flat-plate floor systems, the thickness of the slab selected may not be adequate to
resist the applied shear stresses. In this case, either the slab thickness must be increased or shear
reinforcement must be provided. The ACI Code allows the use of shear reinforcement by shearheads
and anchored bars or wires.
Shearheads consist of steel I-shapes or channel shapes welded into four cross arms and placed
in the slabs above the column (Figs. 17.9c, d). Shearhead designs do not apply to exterior columns,
where large torsional and bending moments must be transferred between slab and column. The ACI
Code, Section 22.6.9.10, indicates that on the critical section the nominal shear strength, V n , should
not exceed 4 √ f ′ cb 0 d, but if shearhead reinforcement is provided, V n should not exceed 7 √ f ′ cb 0 d.To
determine the size of the shearhead, the ACI Code, Section 22.6.9, gives the following limitations:
1. The ratio α v between the stiffness of shearhead arm, E s I, and that of the surrounding composite
cracked section of width, c 2 + d, must not be less than 0.15.
2. The compression flange of the steel shape must be located within 0.3d of the compression
surface of the slab.
3. The depth of the shear head must not exceed 70 times the web thickness.
4. The plastic moment capacity, M p , of each arm of the shearhead is computed by
φM p = V u
2n
[h v + α v
(
l v − c 1
2
)]
(ACI Code, Eq. 22.6.9.6) (17.8)
where
φ = strength reduction factor for tensioned control members
V u = factored shear force around periphery of column face
N = number of arms
h v = depth of shearhead
l v = length of shearhead measured from centerline of column
c 1 = dimension of rectangular, or equivalent rectangular, column
α v = ratio of flexural stiffness of shearhead arm to that of the surrounding composite slab