Civil Engineering Reference
In-Depth Information
properties are significant in the analysis. Therefore a point element is
assumed to have no physical dimensions (Ngo and Scordelis 1967). The
stiffness matrix of the linkage element is
(9.40)
For generality, the reference
x
Ó axis of the linkage element or bar element
may be oriented at any angle
with the horizontal axis of the beam. The
usual rotational transformation matrix
q
and its transpose [
T
T
]
should be applied to the displacement, force and stiffness matrices.
9.9
Discrete cracking model
Wherever relative movement such as slip or crack is anticipated, a linkage
element may be introduced at the nodal point at which a steel element is
connected to a concrete element or between the adjacent concrete elements
which are triangular or quadrilateral finite elements (Ngo and Scordelis,
1967). A discrete cracking model will then result (Figure 9.8).
The spring in the linkage element parallel to the longitudinal axis of the
bar represents the bonding between the steel and concrete elements. It will
Figure 9.8
Discrete cracking model
