Environmental Engineering Reference
In-Depth Information
In both cases the actual deformations remain smaller than those of the yield
condition.
A non-linear calculation of the internal forces according to second-order theory is
therefore unavoidable if we are to achieve a realistic and hence also economic design of
the tower shaft. Bending moment-curvature relationships can be used as a basis for this
(see Section 3.3).
3.2 Material laws for reinforced and prestressed concrete
Deformation calculations according to second-order theory (see Section 3.1) may be
based on short-term action effects when the wind loads govern. The following stress-
strain curves may be assumed in this situation.
3.2.1 Non-linear stress-strain curve for concrete
We generally use the mean values of the cylinder compressive strength of the concrete
(f
cm
¼
f
ck
þ
8 [MPa]) when calculating the deformations (Figure 3.1). Deformation
calculations according to second-order theory require the theoretical mean values of
the material strengths according to DIN 1045-1 [33] 8.5.1 (4) when using non-linear
methods to determine the internal forces (Table 3.1), that is:
1
=
3
1
Þ
f
c
¼
f
cR
¼
0
:
85
a
f
ck
and E
cR
¼
E
c0m
¼
9500
ð
f
ck
þ
8
Þ
A uniform partial safety factor (
g
R
¼
1.30 or
g
RA
¼
1.10) should be used for the design
value of the ultimate resistance. Alternatively, DIN 1045-1 [33] 8.6.1 (7) does permit
Fig. 3.1 Stress-strain curve for concrete for use in deformation calculations
1)
Other values for the elastic modulus of concrete were specified in [36]. The following
applies for the secant moduli: E
cm
[MPa]
¼
22 000
(f
cm
/10)
0.3
. The following applies for
the tangent moduli: E
c0m
¼
1.05
E
cm
.
