Basic HTML Version
161
IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 1
T. E.T. BUTTIGNOL | L.C. ALMEIDA
2.3 Materials specifications
A non-linear elastic-plastic behavior was assumed for the concrete,
according to the characteristics shown in Table 2.
The concrete behavior, in the elastic regimen, follows Hook’s Law
which establishes linear relations in the stress-strain field. In the
post-cracking stress regimen, structure’s collapse plane is deter-
mined by Drucker-Prager (in compression) and Rankine criteria
(in tension).
The Specific Fracture Energy (
G
f
), determined by the Equation 1,
was originally proposed by Irwin [18] and corresponds to the tax
relief of the potential energy stored in the system. Nowadays, this
is an essential parameter of concrete structures numerical simula-
tions, allowing the development of more sophisticated modeling
forms. Its value corresponds to the internal area of the tension ver-
sus crack opening graphic shown in Figure 4a.
(1)
t
f
c
f
G
w
�
14,5
The software also considers the plastic strain effect in concrete, as
shown in Figure 4b, and the tension stiffening effect, which is the
concrete tension stress limit value that contributes to limit the crack
expansion, increasing the structural stiffness. Its value is deter-
mined by the tension stiffening factor (c
ts
), as shown in Figure 4c.
A perfect elastic-plastic behavior was assumed to the reinforce-
ment, with the properties shown in Table 3. The steel yielding crite-
rion was based on the von Mises definitions.
An elastic-isotropic material was assumed for the steel plates of
the piles supports and for the columns superior cross-section, as
specified in the Table 4.
The numerical analysis is divided in three main parts, the pre-pro-
cessing, the processing and the post-processing. In the pre-pro-
cessing, the geometric shape of the structure is defined, with the
reinforcement, the external load, the supports, the finite element
mesh, the monitoring points and the analysis method (Newton-
Rhapson or Arc-Length). In the processing, the numerical analysis
is executed and the loading (increments of force) and reactions
(stresses, strains and cracking) are monitored. In the post-pro-
cessing, the results are analyzed with auxiliary graphic elements
that show the structural behavior in different angles and situations.
Figure 2 – Piles reinforcement details
Figure 3 – Column's reinforcement detail
Table 2 – Concrete properties
Properties
Pile caps
Piles and
columns
Poisson’s
ratio (
)
0,2
0,2
Especific
fracture
energy (G )
f
2
70,18 J/m
2
120,5 J/m
Modulus of
elasticity (E )
c
34,03 GPa
43,69 GPa
Concrete
compressive
strength (f )
ck
30 MPa (Model 1)
35 MPa (Model 2)
40 MPa (Model 3)
76,50 MPa
Ultimate
concrete
tensile
strength(f )
tk
2,58 MPa (Model 1)
2,86 MPa (Model 2)
3,13 MPa (Model 3)
4,82 MPa