Simplified Design for Two-Way Slabs - Simplified Design of Reinforced Concrete Buildings - page 110

The moment coefficients of Table 4-3 (flat plate with spandrel beams) are valid for β t ≥ 2.5, the coefficients of

α f1 ˜ 2 / ˜ 1 ≥ Table 4-6 (two-way beam-supported slabs), are applicable when α f1 are

stiffness parameters defined below). Many practical beam sizes will provide beam-to-slab stiffness ratios such
that

1.0 and β t ≥ 2.5 ( β t , and

α f1 ˜ 2 / ˜ 1 and β t would be greater than these limits, allowing moment coefficients to be taken directly from
the tables. However, if beams are present, the two stiffness parameters α f1 and β t will need to be evaluated.

For two-way slabs, the stiffness parameter α f1 is simply the ratio of the moments of inertia of the effective beam

and slab sections in the direction of analysis, α f1 = I b /I s , as illustrated in Fig. 4-6. Figures 4-7 and 4-8 can be

used to determine α f .

Relative stiffness provided by a spandrel beam is reflected by the parameter β t = C/2I s , where I s is the moment

of inertia of the effective slab spanning in the direction of ˜ 1 and having a width equal to ˜ 2 , i.e., I s = ˜ 2 h 3 /12.
The constant C pertains to the torsional stiffness of the effective spandrel beam cross section. It is found
by dividing the beam section into its component rectangles, each having smaller dimension x and larger
dimension y, and summing the contribution of all the parts by means of the equation.

⎛
⎜

0.63 x
y

⎞
⎟

x 3 y
3

∑

C = 1 −

The subdivision can be done in such a way as to maximize C. Figure 4-9 can be used to determine the torsional
constant C.

L L

˜ 2

Slab, I s

Beam,
I b

b

b + 2 (a - h) ≤ b + 8h

C L

˜ 2 /2 + c 1 /2

b + (a - h) ≤ b + 4h

Slab, I s

Beam , I b

b

c 1

Figure 4-6 Effective Beam and Slab Sections for Stiffness Ratio α f (ACI 13.2.4)