Tower Design and Manufacture - Small Wind Turbines: Analysis, Design, and Application - page 212

and the results for the maximum of the cyclic load are included in Fig. 10.3 . The
maximum stress is 70 MPa which is well below the endurance limit for most steels.
However, as in Chap. 9 , it is necessary to see the effect of the non-zero mean stress
which will reduce the fatigue life of structural steel. As in Chap. 9 the effect can be
assessed using Gerber's relation and assuming an endurance limit of 200 MPa.
Gerber's relation for the allowable maximum stress, r n , can be written as

2

r n
200 ¼ 1

0 : 1442 350
350

¼ 0 : 98 ð 10 : 23 Þ

with the yield stress again used as the ultimate stress. The reduction in the
allowable stress is very small. Since 70 MPa \ 0.98 9 200 MPa, the tower will
not fatigue.
To complete the design load cases, Fig. 10.3 shows the maximum stress dis-
tribution for Load Case B with the gyroscopic moment of 3097 Nm as determined
by Eq. 9.11 :

Once the overall tower geometry has been set, it is necessary to consider the
details such as the access door if there is one, the tower-turbine connection, and
base. As would be expected, the base and access door, especially if in the bottom
part of the tower, are the most critical. Figure 10.4 shows the detailed FE modeling
of the base of the 18 m tower in Fig. 10.2 with the elements indicated along with
the von Mises stress distribution. Notice that the high stress levels on the down-
wind face are mitigated by the baseplate and gussets.

10.3 Optimisation of Monopole Towers

The analysis of the previous section can be extended to determine optimal tower
shapes, with the first aim of minimising the tower mass which is closely associated
with the cost of manufacture, transport, and foundations. Simple optimisation is
only possible for a constant diameter, d, constant thickness, t, tower for which
t d. With M 0 neglected, ( 10.5 ) becomes

qU 2 C d h 2
3 : 50336 þ

0 : 87584td 2 þ 1

T max h m tt g

1 : 6568

r 0 max ¼ r max q t gh ð 10 : 24 Þ

td

on the reasonable supposition that the maximum compressive stress occurs at the
base. Any possible problem of matching d to the turbine yaw assembly will be