Nonlinear Finite Element Analysis of Concrete Structures

- 98 -
exactly the same lines as the transformations of the feme vector
F* . caused by temperature stresses and dealt with in the
previous section. Therefore an expression similar to eq. (22)
holds, i.e..
i» _ni '-'T* ^"T —V ~•
or
o
A B C o_r>
o
(4.3-30)
where F
is the equivalent nodal force vector due to reinforcement
at the nodes of the involved triangular element. The index
r indicates that reinforcement is considered. As given previously
the matrix S
is described by eq. (4.2-4) where the coordinates
of point A are applied. The matrices N and IL, are
_ B t.
given similarly. The matrix L is given by eq. (14) and F" ,
by eq. (26). °
To reduce computer time it is convenient to give a closed form
_m _
expression for the term L
trivial matri>. multiplications we obtain:
Tangential reinforcement:
F' . present in eq. (30). After
I T
F'
ø b
. = -irdt cr
o
o
1
0
1
0
0
0
where o is expressed by eq. (3-19).
RZ-reinforcement:
-cosa
-sina
rV T F
51
°o
b = -2iTr*t a
cosa
sina
0
0