Page 41 - vol5_n3

318 IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 3
Contribution to assessing the stiffness reduction of structural elements in the global stability analysis of
precast concrete multi-storey buildings
(13)
cd c
yd tot s
f A
f A , = w
and
fcd is thedesign valueof the compressive strengthof concrete(MPa);
λ is the slenderness ratio;
j is the creep coefficient;
tot s A , is the total longitudinal area of steel in the section.
d) Brazilian standard for precast concrete - NBR 9062:1985
[12]
Because the current Brazilian standard for structures of precast
concrete (NBR 9062:2006 [13]) does not mention the reduction co-
efficient for obtaining secant stiffness in columns, it was utilized the
previous version of NBR 9062:1985 [12]. The reduction of stiffness
in columns on frames with symmetrical reinforcement is, therefore,
determined by the following expression:
(14) α = 0.2 + 15ρ
where
(15)
bd
A tot s , =r
e) Committee of the American Institute of precast/prestressed
Concrete [14]
The Committee on Prestressed Concrete Columns from the Pre-
cast/prestressed Concrete Institute provides the following equation
to calculate reduced stiffness in the columns:
(16)
d
m gc IE
EI b
l
+
=
1
/
sec
where:
(17) 0 . 3 ³ = qh lm
(18) 70 6 6.15.20 ££Þ + = h h
P
P
b) Committee 318 of the American Concrete Institute - ACI
318-08 [10]
The ACI 318-08 (Building Requirements for Structural Concrete
and Commentary) contains two expressions. The first (Eq. 7) is
designed for situations with high axial load and small eccentricity
values, wherein the effect of slenderness is large. The second (Eq.
8) is a simplified version of the first.
(7)
d
s s gc IE IE
EI b+
+
=
1
2.0
sec
(8)
d
g c IE
EI b+
=
1
4.0
sec
where
c E is the modulus of elasticity of the concrete. According to ACI,
its value is Ec = 4700 f c ', where f´c is the specified compressive
strength of concrete;
s E is the modulus of elasticity of steel;
g I is the moment of inertia of concrete in relation to the section’s
center of gravity without considering reinforcement;
s I is the moment of inertia of the reinforcement in relation to the
section’s center of gravity;
d b is the coefficient related to the creep of concrete and express-
es the relationship between the dead axial load and the total axial
load. In the case where creep is not considered, bd = 0.
c) Bulletin 16 of the Beton International Federation [11]
In Bulletin 16 (Design examples for FIP recommendations ‘practi-
cal design of structural concrete’), the Beton International Federa-
tion (FIB, Federation Internacional du Beton) presents the follow-
ing expression for stiffness evaluating:
(9)
s s gc e IE IE EI + = aaj sec
where
(10) αφ = 1 - 0.8φ(1 - λ/200)ω0.25
(11) αe = 0.08ν0(0.85fcd )0.6 e(λ/100- 2ω)
(12) ν0 = Nd A c0.85fcd –