Nonlinear Finite Element Analysis of Concrete Structures

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routine developed by Tingleff (1969) determines the intersection
points with all involved triangular elements. Two such intersection
points for a particular triangular element are shown as
point A and B in fig. 2. The distance between A and B is termed
Z
Fig. 4.3-2: Reinforcement bar intersecting a triangular element
d. The figure also indicates a local coordinate system R'Z'
located at point A and with the R'-axis in the bar direction.
The displacements of point A and B determine the in-plane forces
in the reinforcement element. To determine the shear strain and
thereby ti.e shear stress an additional point is necessary. Point
C located on the Z'-axis at a distance d from point A is used
for this purpose. First, the reinforcement element is treated in
the local R'Z'-coordinate system. Then a transformation to the
global RZ-coordinate system is performed and finally the response
of the reinforcement element is described by the nodal displacements
of the involved triangular element. Let us first treat the
reinforcement element in the local R'Z'-plane.
The displacements in the R'-direction and in the Z'-direction are
given by
L v'
where the prime(') in general indicates that reference is made
to the local R'Z'-coordinate system. Similarly, the displacements