Environmental Engineering Reference
In-Depth Information
The bending moments according to second-order theory at the base of a concrete
chimney can be estimated with the following approximation [13]:
M
I
Ed
¼
M
I
Ed
9
a
2
1
þ
0
:
where
N
h
F
E
cm
I
c
a
2
¼
E
cm
mean value of the secant modulus of the concrete
I
c
mean value of the second moments of area of the shaft cross-sections
h
F
total height of deformed structure
N
vertical load at base of tower (chimney)
This approximation can generally be used as a guide for reinforced concrete towers as
well.
3.5 Design of cross-section for ultimate limit state
The member cross-sections have to be designed for the internal forces that were
determined according to second-order theory with the reduced mean values of the
material properties for short-term action effects (f
cR
¼
(f
ck
þ
8)/
g
C
;f
yR
¼
f
yk
), but
with the design values of the material properties for permanent action effects
(f
cd
¼a
f
ck
/
g
S
; see DIN 1045-1 [33] 8.6.1 (7)).
If this results in a reinforcement requirement that is larger than was used for the
deformation calculation, then this reinforcement is on the safe side and may be selected
for construction. Performing the deformation calculation again with more
reinforcement would lead to less deflections and hence to lower bending moments
in the deformed system, that is ultimately to less reinforcement being needed as well.
An iterative procedure enables the amount of steel reinforcement to be optimised.
g
C
;f
yd
¼
f
yk
/
3.5.1 Material resistance of concrete
The parabolic-rectangular stress diagram according to DIN 1045-1 [33] is used here,
but with the constraint shown in Figure 3.10 for the compressive strain in the concrete
in the centre-line of the shaft wall in compression. This corresponds to the stipulation
for the design of fully overcompressed flange plates in T-beam cross-sections and also
the provision according to [13] applied hitherto. The compressive strain in the concrete
e
c2m
was merely raised to the compressive yield strain
e
yd
, similarly to concentrically
compressed members, so that the reinforcement in compression can be fully utilised.
4)
However, it is quite acceptable to use this higher value as a limit value for compressive
strain in the centre-line of the shaft wall provided, on the one hand, small creep
deformations are taken into account and, on the other, we do not forget that stress
4)
Comparison of the approaches for the material resistances given in DIN 1056 [13] and
DIN 1045-1 [33], see Beton-Kalender 2006 [8].
