Nonlinear Finite Element Analysis of Concrete Structures

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too
a(exp.)=10°0°20 CO 0 30°
0° 10° 20?30?40 o = a Itheo.)
100
Peter (196i)
theoretical
6 V [mm]
Fig. 5.1-5: Experimental and predicted (< = 0)
vertical displacements 6 .
predicted ones just after cracking. This is a consequence of the
so-called "tension stiffening effect" reflecting that in reality
discrete cracks develop and that the concrete between these
cracks is still bonded to the bar thereby contributing to the
stiffness. In general, however, the experimental data support
the prediction.
As discussed in section 4.6 the predicted failure loads are
determined as the loads where the force-vertical displacement
curve becomes horizontal. In the present case failure is determined
solely by the bars where infinite ductility was assumed.
However, as discussed in section 4.6 the analysis also includes
a slight stiffness contribution from the concrete as 0.5% of the
stiffness normal to the crack plane and present just before
cracking is always retained for numerical reasons. This is to
avoid a possible ill-conditioned equation system, but is in
principle not necessary here as the cracks are crossed by bars.
However, as the panels only posses a reinforcement percent equal
to 0.67% this small retained concrete stiffness results in
force-vertical displacement curves possessing a small slope even
when all reinforcement is at full yield. It is important to note