Nonlinear Finite Element Analysis of Concrete Structures

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where the same notation as in the previous section is applied
(i.e. the prime (') indicates that reference is made to the
local R'Z'-coordinate system, and index b indicates that reinforcement
bars are considered). Moreover, r* is the global radial
distance of the centre of the reinforcement element, t is the
thickness and d is the length, cf. fig. 2. In eq. (26) the matrix
1/ is given by eq. (5) while the initial stress vector a'
takes different forms depending on the reinforcement type.
For tangential reinforcement, cf. fig. 1 a), we have
ob
0
or (4.3-27)
where a is given by eq. (3-19). For RZ-reinforcement, cf. fig.
lb), we have
a ob
0
0
(4.3-28)
where a again is given by eq. (3-19). For membrane reinforcement,
cf. fig. 1 c), we have
'ob
'ol
'o2
(4.3-29)
where ø . and a _ are given by eq. (3-12) , i.e. the stress a ,
is directed in the R*-direction while a 2 is the tangential
stress«
Transformation of the force vector F' , from the local coordia
o
nate system to the global coordinate System and subsequent transformation
of these forces located at the nodal points A, B and C
of fig. 2 to the nodes of the involved triangular element follow