When you conduct pushover analysis with fiber elements, the calculation
for the concrete may not be converged because the load on the concrete
may not increase gradually. Various factors like the length of fiber elements,
the size of mesh, and the loading way contribute to the coverage problem.
As to the stress-strain curve of type 2 described in the specifications
for highway bridges Part‡X Seismic design, ultimate displacement of concrete
become bigger than the displacement reached at the maximum compressive
stress, because of the lateral constraint of lateral tie. In other words,
the stress- strain curve is minus curve until the concrete reach at the
ultimate displacement from the maximum compressive stress.
When the case a post-peak region have to be considered, the loading by
not a force A but forced displacement needed to imposed.
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Fig1. Concrete hysteresis |
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Fig2. Analysis model |
Here, the crown of the single pole (shown Fig.2) is loaded by force and
displacement and the results are compared.
Fig.3 shows that the load-displacement curve of the crown of the pole,
loaded by the two ways: force and displacement.
In the case loaded by force, it doesn't converge at the point of the 40mm
displacement. On the other side, in the case loaded by displacement, it
converges at all steps. It is thought that un-equilibrium force become
bigger and divergence, for the strength degradation of the resistible concrete,
although the stress-displacement curve of concrete become the minus curve
at the point over 40mm and increase gradually.
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Fig3. load-displacement curve |
Here introduced that when there are the minus curve in the hysteresis of
fiber elements, the load way increasing lateral force gradually doesn't
converge. The way of giving the forced displacement is useful. Remember
that this way is also useful when there are the minus curve in the M-ƒÓ
characteristic of M-ƒÓ elements, not limited to the fiber elements. |