Structural Concrete - Hassoun

17.8 Analysis of Two-Way Slabs by the Direct Design Method 639
where x is the shorter dimension of each component rectangle and y is the longer dimension of
each component rectangle. In calculating C, the component rectangles of the cross section must be
taken in such a way as to produce the largest value of C.
The preceding expressions are introduced here and will also be used in Section 17.12, Equivalent
Frame Method.
If a panel contains a beam parallel to the direction in which moments are being determined,
the torsional stiffness, K t , given in Eq. 17.19 must be replaced by a greater value, K ta , computed as
follows:
K ta = K t × I sb
I s
where
I s = l 2 h 3 /12 = moment of inertia of a slab that has a width equal to full width between panel centerlines
(excluding that portion of beam stem extending above or below slab)
I sb = I s , including portion of beam stem extending above or below slab
Cross sections of some attached torsional members are shown in Fig. 17.17. Once K ec is calculated,
the stiffness ratio, α ec , is obtained as follows:
α ec =
K ec
∑ (Ks + K b )
(17.21)
where
K s = 4E cs I s
l 1
K b = 4E cb I b
l 1
= flexural stiffness of slab
= flexural stiffness of beam
I b = gross moment of inertia of longitudinal beam section
The distribution of the total static moment, M 0 , in an exterior panel is given as a function of α ec as
follows:
(
)
0.1
Interior negative factored moment = 0.75 − ( ) M 0
1 + 1∕αec
Positive factored moment =
(
0.63 −
(
)
0.65
Exterior negative factored moment = ( )
1 + 1∕αec
)
0.28
( ) M 0
1 + 1∕αec
These values are shown for a typical exterior panel in Fig. 17.18. These factors take into consideration
the effect of the stiffness of the exterior column as well as the slab end beam giving adequate
distribution of moments.
17.8.8 Summary of the Direct Design Method (DDM)
Case 1. Slabs without beams (flat slabs and flat plates).
1. Check the limitation requirements explained in Section 17.8.1. If limitations are not met,
DDM cannot be used.
M 0