Loadbearing structures and detailed design - Concrete Structures for Wind Turbines - page 177

Fig. 4.40 Modi cation factor l c3 (N, r) for compression meridian stresss and effective minimum
stress S 33 , cd,min ¼0

l c3 (N, r) therefore depends on the number of fatigue cycles N and is determined as a
reciprocal value of s

fat

c33 ; max (N, r)/f c1 :

fat
c33

r Þ¼ s

max ð N

; r ¼ 0 Þ

f c1 ð N ; a ¼ r ¼ 0 Þ

;

l c3 ð N ; ¼ (4.38)

fat
c33

fat
c33

s

max ð N

; r Þ s

max ð N

; r Þ

; ;

The courses of the modification factor l c3 (N, r) are presented in [74] for practical
applications depending on the loading ratio r and the actual number of fatigue cycles N
for different effective minimum stresses S c33,min . The modification factor l c3 (N, r) can
be read off from these charts and used in Equation 4.33. As an example, Figure 4.40
shows the curves for S c33,min ¼ 0.

4.9.5.3 Derivation of modi cation factors ) for biaxial fatigue loads

Modification factors can also be determined for biaxial fatigue loads for use in
Equation 4.29. According to Equation 4.39, these can be obtained directly from
failure curves for biaxial fatigue loads. The loading ratio here is described by a¼
s 11 / s 22 . The stress in the transverse direction is denoted by s 11 and the stress in the
principal loading direction by

l c2 (N, a

s 22 .

fat

; aÞ¼ s

c22 ; max ð N

; a ¼ 0 Þ

f c ; 1 ð N ; a ¼ r ¼ 0 Þ

l c2 ð N ¼ (4.39)

fat

S fat

s

c22 ; max ð N

; aÞ

c22 ; max ð N

; aÞ

For practical applications, Figures 4.41 to 4.45 show the diagrams for l c2 (N, a )
depending on the loading ratio a and the actual number of fatigue cycles N for various
effective minimum stresses S c22,min .