Structural Concrete - Hassoun

426 Chapter 12 Slender Columns
2. For reinforced concrete members, the moment of inertia I varies along the member, depending
on the degree of cracking and the percentage of reinforcement in the section considered.
To evaluate the factor ψ, EI must be calculated for beams and columns. For this purpose,
I can be estimated as follows (ACI Code, Section 6.6.3.1.1):
a. Compression members:
Columns I = 0.70I g
Walls − Uncracked I = 0.70I g
b. Flexural members:
−Cracked I = 0.35I g
Beams I = 0.35I g
Flat plates and flat slabs I = 0.25I g
Alternatively, the moments of inertia of compression and flexural members, I shall be
permitted to be computed as follows:
c. Compression members:
(
I = 0.80 + 25 A )(
st
1 − M )
u
A g P u h − 0.5P u
I
P g ≤ 0.875I g (12.2)
0
where P u and M u shall be determined from the particular load combination under consideration,
or the combination of P u and M u determined in the smallest value of I, I need not
be taken less than 0.35I g .
d. Flexural members:
(
I =(0.10 + 25ρ) 1.2 − 0.2 b )
w
I
d g ≤ 0.5I g (12.3)
where I g is the moment of inertia of the gross concrete section about the centroidal axis,
neglecting reinforcement.
ρ = ratio of A s
in cross section
bd
The moment of inertia of T-beams should be based on the effective flange width defined
in Section 8.12. It is generally sufficiently accurate to take I g of a T-beam as two times the
I g of the web, 2(b w h 3 /12).
If the factored moments and shears from an analysis based on the moment of inertia of a
wall, taken equal to 0.70I g , indicate that the wall will crack in flexure, based on the modulus
of rupture, the analysis should be repeated with I = 0.35I g in those stories where cracking is
predicted using factored loads.
The values of the moments of inertia were derived for non-prestressed members. For prestressed
members, the moments of inertia may differ depending on the amount, location, and
type of the reinforcement and the degree of cracking prior to ultimate. The stiffness value
for prestressed concrete members should include an allowance for the variabilty of the stiffnesses.
For continuous flexural members, I shall be permitted to be taken as the average of values
obtained from Eq.12.3 for the critical positive and negative moment sections. Moment of
inertia I need not be taken less than 0.25I g .