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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 1
Steel fibre reinforced concrete pipes. Part 2: Numerical model to simulate the crushing test
3.2.2 Basic hypotheses about sectional behavior
The following classical hypotheses have been adopted for the modeling
the sectional behavior: (1) the sections have a symmetry axis and are sub-
jected to straight flexo - compression; (2) perfect bond between themateri-
als in the section; (3) sections initially planes remain planes after applying
the forces; (4) shear strains arenegligibleand thereforearenot considered;
and (5) the pipe curvature does not affect on stress-strain distribution.
3.2.3 Idealization of the section
The positive signs are for: (1) the bending moments which com-
press the upper fibre; (2) the axial forces which compress the sec-
tion; (3) compressive stresses and (4) the shortenings.
3.2.4 Equilibrium and compatibility equations
The stress-strain state (see Figure [3a]) resulting from a com-
bination of internal efforts (normal force
N
and bending mo-
ment
M
) is defined by the stress distribution of the materials
and the plane formed by the strain in the most bottom layer
of the concrete section (taken as the reference layer) and the
sectional curvature (
ε
c,inf
, χ
). This state is obtained by applying
the internal balance equations (Eqs. 3 and 4) and establish-
Figure 5 – Schema adopted to simulate the crushing test
N
θ
M
θ
S
C
R
m
R
m
o
F
F
M
c
M
s
θ
S
N
θ
M
θ
F
M
c
M
s
θ
R
m
R
m
C
o
F
F
N
θ
M
θ
F
M
c
M
s
θ
R
m
R
m
S
C
S
C
R
m
R
m
o
v
c
u
s
a)
b)
c)
d)
o