Page 482 - Wind Energy Handbook

456 COMPONENT DESIGN

Assuming that a tower design with a uniform taper is to be adopted, the key
design parameters to establish are the diameter and wall thickness at the tower
base. The tower top diameter, on the other hand, is governed by the size of the yaw
bearing, and wall thicknesses at intermediate heights can generally be interpolated
between the tower base value and a sensible minimum at the top of about one
hundredth of the local radius.
The main considerations determining the tower dimensions at the base are
buckling of the shell wall in compression, strength under fatigue loading and
stiffness requirements for ‘tuning’ the natural frequency. These are dealt with in
separate sub-sections below.
As machines get larger, another important consideration is the maximum tower
base diameter that can be accommodated on the highway when tower sections are
transported overland. In the flat terrain of North Germany and Denmark, this limit
is generally 4.0–4.2 m, but elsewhere it will often be less.

Design against buckling

Given perfect geometry, the strength of a cylindrical steel tube in axial compression
is the lesser of the yield strength and the elastic critical buckling stress, given by
ó cr ¼ 0:605Et=r (7:68)

where r is the cylinder radius and t is the wall thickness. Yield strength governs for
r=t less than 0:605E=f y , which equates to 506 for mild steel, with f y ¼ 245 MPa.
However, the presence of imperfections, particularly those introduced by welding,
means that the tower-wall compression resistance is significantly reduced, even at
the relatively low tower-wall radius to thickness ratios normally adopted. There is
quite a wide disparity between the provisions of different national codes, with some
making an explicit link between compression resistance and tolerances on imperfec-
tions and others not. The recommendations produced by the European Convention
for Constructional Steelwork (ECCS, 1988) contain relatively straightforward em-
pirical rules for the design of thin-walled cylinders in compression, which are based
on sets of experimental results from several sources. These will eventually be
superseded by the provisions of Part 1–6 of Eurocode 3 ‘Supplementary rules for
shell structures’, but in the meantime the ECCS rules relating to cylinders subject to
bending loads are set out here.
The first step is to calculate a critical stress reduction coefficient for axial loading,
Æ 0 , from which a parallel coefficient for bending loading, Æ B , is derived:
0:83 0:70
Æ 0 ¼ p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi for r=t , 212, Æ 0 ¼ p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi for r=t . 212 (7:69)
1 þ 0:01r=t 0:1 þ 0:01r=t

and

Æ B ¼ 0:1887 þ 0:8113Æ 0 (7:70)