Civil Engineering Reference
In-Depth Information
value and the same delineated model with the node numbers can be
retained throughout the entire non-linear analysis.
9.11
Modelling of constitutive relationships of concrete
In non-linear finite element analysis of reinforced concrete structures, the
stress-strain relationships of concrete under various conditions are required.
A great deal of research work has been done in this field in recent years and
there are several proposals commonly used in the finite element analysis of
reinforced concrete structures.
Liu, Nilson and Slate (1972) assumed concrete to be orthotropic with two
tangential moduli of elasticity which vary according to the state of stress and
strain in each principal direction. They proposed the following incremental
constitutive relations in the form of an elasticity matrix:
(9.42)
in which EÓ
1b
and EÓ
2b
the two tangential moduli, are given by
(9.43)
and
(9.44)
Tasuji, Slate and Nilson (1978) suggested the following expression for
the biaxial stress-strain relationship for plain concrete:
(9.45)
is principal strain,
E
is the uniaxial elastic
modulus, v is PoissonÓs ratio,
k
is the ratio of principal stresses,
where
s
is principal stress,
e
s
p
is the
