Nonlinear Finite Element Analysis of Concrete Structures

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evident contrast to the finding of Cedolir. and Dei Poli (1977)
who also investigated beams failing in sheer. As here they analysed
beams tested by Bresler and Scordelis (1963), but their
beams had a shear span ratio = 4 whereas the beams considered
here have a shear span ratio = 5. In their important investigation,
Cedolin and Dei Poli (1977) found an extreme influence
of the n-value as n = 0.25 resulted in a failure load twice as
large as that determined when n = 0.025 was utilized. However,
the failure loads as determined by Cedolin and Dei Poli (1977)
were not clearly related to physical phenomena and large differences
between their approach and the present one exist. In
particular, the strain softening in the post-failure region was
not considered? dilatation and secondary cracking of the concrete
was ignored. As here Cedolin and Dei Poli (1977) used constant
strain elements, but no diagonal cracking was determined
at failure. Cedolin and Dei Poli (1977) suggest this to be a
consequence of the smeared crack representation. If true this
finding has important consequences, but the present study gives
no support to it as diagonal cracking indeed is determined. As
previously discussed, diagonal cracking follows as a result of
a strain localization in the region adjacent to the load point
and this strain localization is a consequence of strain softening.
Therefore, modelling of strain softening is considered as
decisive.
The behaviour of beams failing in shear is obviously very dependent
on the existence of small tensile stresses. However, as
demonstrated by case no. 2 and 4 the choice of different realistic
tensile strength values has only a minor influence for a
20% decrease of the o.-value results in a decrease in failure
load of only J%.
To investigate the importance of modelling of secondary cracks,
case no. 5 is compared with case no. 2. In case no. 5 the calculations
were terminated before failure was reached. It appears
that modelling of secondary cracks is in fact essential. This
conclusion is in accordance with the findings of Arnesen et al.
(1979) who also analysed beams failing in shear. Considering
plane stress states Arnesen et al. (1979) also demonstrated that