Nonlinear Finite Element Analysis of Concrete Structures

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where the angle g denotes the inclination of the local R'Z'-
coordinate system with the global RZ-coordinate system, cf. fig.
2. The term r denotes the radial distance of the particular
point of interest in the global RZ-coordinate system. Moreover,
as reinforcement is assumed to have small dimensions in the
direction of the Z'-axis, the variation of eA = E„ due to different
z'-values can be ignored. Use of eqs. (1), (2) and (3)
then results in
e b = B b a b
(4.3-4)
where
1
"d
1
d
B i
-cosg -
1-^
d
sing
—jcosg
r'
rd
r'
-^sing 0
rd
1
"d
1
d
1
d
1
d
As expected, all strains except the tangential strain are constant
within the reinforcement bar. Similarly to the treatment
of the triangular element in section 4.2 the variation along the
bar of the tangential strain is ignored and as an approximation
the value at the center of the bar element is used. At this
center r' = d/2 applies ana 'enoting the global radial distance
of the center by r* the above expression for the matrix B, simplifies
to
1
d
0
1
d
0
0
5i
_
"b "
cosg
2r*
sing
2r*
cosg
2r*
sing
2r*
0
(4.3-5)
1
d
1
~d
0
1
d
1
d
Corresponding to the reinforcement strains of interest the
stresses in a bar are given by