The moment gfMunb is transferred over an effective slab width that extends 1.5 times the slab thickness outside each side face of the column or column capital support. The existing reinforcement in the column strip may be concentrated over this effective width or additional bars may be added.

The fraction of unbalanced moment not transferred by flexure gv (gv = 1 — gf) is transferred through eccentricity of shear that acts over an imaginary critical section perimeter located at a

FIGURE 7.15 Flat plate.

FIGURE 7.15 Flat plate.

distance d/2 from the periphery of the column support (see Figure 7.16). Shear stress at the critical section is determined by combining the shear stress due to the direct shear demand Vu (which may be obtained from tributary loading) and that from the eccentricity of shear due to the unbalanced moment:

Ac Jc where the concrete area of the critical section Ac = b0d = 2d(c1 + c2 + 2d), and Jc is the equivalent polar moment of inertia of the critical section

J _ d(ci + d)3 (ci + d)d3 d(c2 + d)(ci + d)2 Jc " 6 + 6 + 2 ( 3)

The maximum shear stress vu on the critical section must not exceed the shear stress capacity defined by f vn = f Vc/bod (7.34)

The concrete shear capacity Vc for two-way action is taken to be the lowest of the following three quantities:

where bc is the ratio of long side to short side of the column. The factor as is 40 for interior columns, 30 for edge columns, or 20 for corner columns.

If the maximum shear stress demand exceeds the capacity, the designer should consider using a thicker slab or a larger column, or increasing the column support area with a column capital. Other options include insertion of shear reinforcement or shearhead steel brackets. Detailing of Flat Plates

Refer to Figure 7.17 for minimum extensions for reinforcements. All bottom bars in the column strip should be continuous or spliced with a Class A splice. To prevent progressive collapse, at least two of the column strip bottom bars in each direction should pass within the column core or be anchored at the end supports. This provides catenary action to hold up the slab in the event of punching failure.

7.13.3 Flat Slabs with Drop Panels and/or Column Capitals

The capacity of flat plates may be increased with drop panels. Drop panels increase the slab thickness over the negative moment regions and enhance the force transfer in the slab-column connection. The minimum required configuration of drop panels is given in Figure 7.18. The minimum slab thickness is given in Table 7.8 and should not be less than 4 in.

Alternatively, or in combination with drop panels, column capitals may be provided to increase capacity (see Figure 7.19). The column capital geometry should follow a 45° projection. Column capitals increase the critical section of the slab-column force transfer and reduce the clear span lengths. The design procedure outlined for flat plates in the previous sections are applicable for flat slabs detailed with drop panels or column capitals.

7.13.4 Waffle Slabs

For very heavy floor loads or very long spans, waffle slab floor systems become viable (see Figure 7.2o). A waffle slab can be visualized as being a very thick flat plate but with coffers to reduce weight and gain efficiency. The design procedure is therefore the same as for flat plates as presented in Section 7.13.2.

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