Environmental Engineering Reference
In-Depth Information
According to [49], the conditions for both a repeated compressive load and a repeated
tensile load should be satisfied for reversed loads.
Here, the minimum stress for a repeated tensile load is
s
ct
;
min
¼
0
(4.16)
and that for a repeated compressive load is
s
cd
;
min
¼
0 (4.17)
The reader is referred to the information given in [33] and Model Code 90 [66] for the
analysis of the fatigue capacity in connection with cyclic shear forces. Commentaries
can be found in, for example, [49,72].
4.9.3 Multi-stage fatigue loads
Support structures for wind turbines are subjected to high numbers of load cycles with
different stress ranges and maximum stresses. Up until now the influence of such multi-
stage fatigue loads on the fatigue behaviour of concrete could only be determined
indirectly by exploiting the numbers of fatigue cycles to failure on the basis of a linear
accumulation hypothesis. It is therefore not possible to obtain details about the ongoing
development of stiffness, or rather damage, during the predicted design working life of
a loadbearing structure. However, in order to be able to ascertain the true fatigue
process with more accuracy, such information is critical for designs, for example
prestressed concrete towers, in which changing stiffness relationships lead to redis-
tributions of stress. In particular, knowledge about the actual distribution of stiffness as
a result of fatigue is indispensable for numerical analyses of the structural behaviour of
a design if we are to obtain realistic calculations.
Based on an energy approach to the fatigue process, Pfanner [73] devised a mechanical
damage model for fatigue loads with a constant stress range.
Further studies can be found in [74], which deals with to what extent Pfanner's energy-
based damage model [73] can be extended to multi-stage fatigue loads. The reader is
referred to [74] for the damage development in concrete subjected to multi-stage
fatigue loads and the evaluation of the linear accumulation hypothesis.
4.9.4
Numbers of fatigue cycles to failure for multi-axial fatigue loads
4.9.4.1 Procedure
The regulations currentlyapplicabledonot containdetails of howtocalculate thenumbersof
fatigue cycles to failure formulti-axial fatigue loads. Some tests for determining the number
of fatigue cycles to failure for selected loading relationships can be found in the literature.
Ref. [74] introduces a new approach for ascertaining the numbers of fatigue cycles to
failure for multi-axial fatigue loads; this is summarised below. It is based on a change in
the failure envelopes of the concrete when subjected to multi-axial fatigue loads.
According to the method, the volume enclosed by the failure envelope decreases as the
number of fatigue cycles increases.
This phenomenon can be illustrated using the example of the uniaxial fatigue strength. As
the number of fatigue cycles increases, so the uniaxial fatigue strengthdecreases.What this
