Loadbearing structures and detailed design - Concrete Structures for Wind Turbines - page 118

Fig. 4.8 Stress-strain curve for concrete for use in deformation calculations

4.4 Prestressing
Prestressing forces applied by tendons can be considered as actions due to the anchorage
and change-of-direction forces, or as active internal forces. The resulting internal forces in
the composite cross-section disappear in loadbearing structures with statically determi-
nate supports. A residual stress state is established between the prestressing force in the
steel tendons and the reaction internal forces in the concrete cross-section (Figure 4.9).
The prestressing introduces an eccentric compressive force N ð 0 Þ

cp , with the following

associated bending moment M ð 0 Þ

cp :

N ð 0 Þ

cp ¼ P ð 0 Þ

M ð 0 Þ

cp ¼ P ð 0 Þ

z ip

Fig. 4.9 Residual stress state for prestressing

ð 0 Þ p with

Alternatively, the prestressing can be regarded as a strain state (prestrain e

ð 0 p is then taken into account in the resistance
of the cross-section and is related to the prestressing bed condition. The prestressing bed
condition is the stress and strain state in the prestressing steel corresponding to the stress-free
concrete cross-section, and indeed for anypoint in time t taking into account time-dependent
deformations of the prestressing steel and the concrete, see DIN 1045-1 [33] 8.7.1 (3):

(0) ). The prestrain e

corresponding precamber k

0 ¼

M ð 0 Þ
cp
E c I i

P ð 0 Þ
E p A p

1
r

e ð 0 Þ
p

k ð 0 Þ ¼

¼