Environmental Engineering Reference
In-Depth Information
The tensile stresses in the vertical reinforcing steel should be calculated for the cracked
state for the critical design load case, that is quasi-permanent or frequent, in order to
determine either the maximum diameter of the reinforcing bars d
s
or their maximum
spacing according to [33]. A minimum amount of reinforcement for controlling crack
widths is unnecessary because the tower shaft is a statically determinate component
without restraint stresses.
Similarly to DIN 1045-1 [33] 13.1.1 (1), the following minimum reinforcement
is required to guarantee ductile behaviour of the member (see Section 3.2 and
Tabl e 3 . 2) :
f
ctm
f
yk
a
Ed
f
ctm
r
s
>
where
f
ctm
mean value of concrete tensile strength according to [33] Tables 9
or 10
f
yk
characteristic value of yield point of reinforcing steel
a
Ed
¼g
C
E
s
/E
c0m
see Section 3.2
Table 4.9 replaces Tables 18 and 19 of DIN 1045-1 [33].
4.8.2 Restraint stresses acting on shaft wall
The temperature gradient between the exterior air and the inside of the tower give rise to
a bending restraint in both the vertical and circumferential directions.
According to DIN 1045-1 [33] 11.2.2, we get the following minimum percentage of
reinforcement for guaranteeing limited crack widths under bending restraint stresses:
2
s
c
;D
T
f
ctm
s
s
r
s
¼
0
:
s
s
0
:
2
related to the total wall thickness
where
s
c
;D
T
¼ a
T
;
c
E
c0m
D
T
=
2 and
D
T
¼
15 K according to [9].
Here,
s
s
is the permissible steel stress in the minimum reinforcement immediately
following the appearance of the first crack, depending on the theoretical crack width w
k
(see Section 4.8.1) and the limiting diameter d
s
(see DIN 1045-1, Table 20 [33]).
From this we get, for example, for C 20/25 concrete:
s
c
;D
T
¼
10
5
28 800
15
=
2
¼
2
:
16 MPa
<
f
ctm
¼
2
:
21 MPa
According to this, the minimum reinforcement for limiting the crack widths according
to DIN 1045-1 [33] 11.2.2 already governs for concrete grades C 20/25 and higher.
Further, assuming w
k
¼
0.20mm and d
s
¼
12mm, then
:
f
ct0
f
ctm
¼
12
3
0
d
s
¼
d
s
21
¼
16
:
3mm
2
:
s
s
¼
214 MPa
