Nonlinear Finite Element Analysis of Concrete Structures

- 86 -
at point A, B and C are given by
U A
V A
a b
U B
V B
(4.3-1)
u c
where index b in general indicates that a reinforcement bar is
considered. The points A, B and C are the nodal points of the
reinforcement element and the vector eL" contains therefore the
nodal displacements. In accordance with the triangular element
concept, we work with a linear displacement field i.e.
u' = a, + a 2 r' + a- z'
V
= a 4 + a 5 r' + a g z'
To determine the constants a, a 6 the displacement values
at point A(r' = z' -= 0), B(r' = d, z' = 0) and C(r' = 0, z' = d) ,
i.e., the nodal points, are applied. I-- follows that
u' =
V =
U A +
V Å +
* < U B
* < V B
u^)r' + ^(uv£)r'
+ Js(v^
u A )z'
"A>« 1 (4.3-2)
The corresponding reinforcement strains of interest are
£ R
3u'
e ' =
u
—(u'cosa - v'sino)
(4.3-3)
RZ
3u' . 3v'
3z' 3r»