Nonlinear Finite Element Analysis of Concrete Structures

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evdn though some features of dowel action are indeed reflected,
the approach is in general not preferable.
As concrete and reinforcement is assumed _o follow each other,
the full shear capacity of the bars is to be considered. While
this assumption is fair for uncracked regions, it is obvious that
as a result of cracking relative deformations parallel to the
crack plane will be localized to the vicinity of the crack where
local bending of the reinforcement is initiated and where local
crushing of the concrete may be present. As a result, the stiffness
of the bar parallel to the crack plane is considerably
lower than that given by the original shear stiffness. This effect
can be accounted for in the program by using the term KG
where 0 < K < 1 instead of the original shear modulus G of the
reinforcement material. Due to simplicity we employ a constant
K-value and as the shear capacity of reinforcement bars is insignificant
when no cracking is present a realistic K-value
might be determined by means of calibration calculations on a
structure where cracking and dowel action dominate the response.
Such calculations are performed in section 5.1 and, as previously
mentioned, it is found there that neglect of dowel shear, i.e.,
K = 0, constitutes in fact the most preferable value. This finding
is supported by the calculations in section 5.3. Consequently,
except for certain sensitivity studies the value K = 0
is always employed in the program.
The objective of the following considerations is to determine
the stiffness contributions of reinforcement eleme^s to the involved
triangular elements. In section 4.3.1 only linear material
response is considered. Section 4.3.2 then treats the necessary
modifications when plastic strains develop. Moreover, when temperature
stresses are present the contribution from the reinforcement
to the nodal forces of the involved triangular elements
are also determined in section 4.3.1.
4.3.1. Elastic deformation of reinforcement
Every reinforcement bar is located along an arbitrary straight
line. From the start and end point of each bar a special search