Nonlinear Finite Element Analysis of Concrete Structures

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40 mild steel ribs with a thickness of 6 mm and uniformly distributed
along the periphery stiffen the flange. The ratio of
height to diameter is 0.35 indicating a massive structure and
even though the model scale is 1 : 11, it is apparent that the
model has quite large dimensions (outermost diameter = 720 mm).
During testing, the model was pressurized hydraulically by
water in a steel pressure vessel. The test duration was around
two hours.
The concrete had a w/c - weight ratio equal to 0.68 and the maximum
gravel size was 8 mm. Seven standard cylinders (300/150 mm)
were cast and cured together with the closure. These cylinders
were tested uniaxially in compression simultaneously with the
closure model testing that occurred 2 months after concreting.
The mean of the experimentally determined stress-strain curve
is shown in fig. 2a) together with the approximation employed
according to eq. 2.2-3. This approximation utilizes the parameters:
a = 45.0 MPa, e = 3.06 • 10~ 3 , E. = 2.84 -10 4 MPa and
c c i
D = 0.2.
The concrete parameters necessary for the constitutive model
were completely determined by assuming that o./a =0.08 and
v. = 0.15. The particular assumption of no-softening in the
post-failure region is also shown in fig. 2a).
The assumed stress-strain curve for the mild steel liner is
given in fig. 2b). The ribs and flange were assumed to behave
elastically. The values E = 2.05 • 10 MPa and v = 0.3 were
employed for all steel parts.
Fig. 3 shows the axisymmetric finite element mesh consisting of
298 triangula* elements. The liner is simulated as membrane reinforcement.
The triangular solid elements that represent the
flange appear from the figure. The strut forces are also indicated.
The ribs are simulated by RZ-reinforcement bars in the
horizontal and vertical direction. In each direction the volume
of the bars corresponds to that of the ribs.
The experimentally determined behaviour of the closure is charac-