Continuous deep beams - Reinforced Concrete Deep Beams - page 104

All finite element programs are different. It is, however, essential that the
model incorporate non-linear constitutive relationships for the steel and
concrete. In the case of the concrete, the model should account for strain
softening. The accuracy will be best for under-reinforced members with at
least modest web reinforcement (to ensure some ductility).
Currently non-linear finite element analysis is still not used for routine
design, but for special critical problems it offers an alternative to physical
testing.
4.3.3 ACI 318
The recommendations of ACI 318 (1977) were used to assess the strength of
Rogowsky et al. 's test specimens. For the continuous beams, the ratios of test to
calculated strengths ranged from 1.38 to 0.48. Over half of the tests had
measured strengths less than the strength predicted by the ACI code. The
discrepancy arises because the empirical design method given in ACI is based
on simple span test data. Had ACI chosen to use the ratio of shear span to depth
ratio as the prime parameter rather than the ratio of shear to moment at the
critical section, better agreement may have been achieved. The ACI code is not
based on a clear mechanical model of behaviour and is not recommended.
4.3.4 Kong, Robins and Sharp
The method of Kong, Robins and Sharp (1975) was used to analyse the data
of Rogowsky et al. The ratio of test to calculated strength ranged from 0.53
to 1.31. Their method was found to be safe for beams with heavy stirrup
reinforcement (vertical web reinforcement ratio approximately 0.006) where
the average test to predicted ratio was 1.17. For the remainder of the tests,
the ratio of test to predicted values was highly variable and generally quite
unsafe. The method was originally developed for simple span deep beams
deeper than those analysed.
4.3.5 Truss models
In a truss model analysis one idealises the beam as a truss consisting of
concrete compression struts and steel tension ties. These models are based
on the theory of plasticity and in various forms have been proposed by a
number of authors including Grob and Thurlimann (1976), Nielsen et al.
(1978), Marti (1985a, b) and Schliach (1987). Truss models specifically for
deep beams have been presented by Rogowsky and MacGregor (1986).
Truss models have gained increasing acceptance as they have grown less
rigorous. The Canadian concrete design code (CSA A23.3-M84) contains
rules for use of truss models in design.
Truss models were used to analyse the two span data of Rogowsky et al.
Some of the predictions were excellent. For the beams with heavy stirrups
(assuming the effective concrete strength equal to the specified strength) the