K
FIGURE 27.12 Surface roughness and type of pressure distribution. Copyright 2005 by CRC Press the roughness parameter k/aR as shown in Figure 27.12, in which k is the height of the rib and aR is the mean distance between the ribs measured at about onethird of the height of the tower. Note that the coefficient along the windward meridian H(O) reflects the socalled stagnation pressure while the side suction is, remarkably, significantly affected by the surface roughness k/aR. As will be discussed in Section 27.6.2, the meridional forces in the shell wall and hence the required reinforcing steel are very sensitive to H(O). In turn, the costs of construction are affected. Thus, the design of the ribs, or of alternative roughness elements, is an important consideration. For quantitative purposes, the equations of the various curves are given in Table 27.1 and tabulated values at 5° intervals are available [4].
The circumferential distribution of the external wind pressure may be presented in another manner that accents the importance of the asymmetry. If the distribution H(d) is represented in a Fourier cosine series of the form n = 1
the Fourier coefficients An for a distribution most similar to the curve for K 1.4 are as follows [5]:
n An
1 0.2602
2 0.6024
3 0.5046
4 0.1064
Representative modes are shown in Figure 27.13. The n = 0 mode represents uniform expansion and contraction of the circumference, while n = 1 corresponds to beamlike bending about a diametrical axis resulting in translation of the crosssection. The higher modes n > 1 are peculiar to shells in that they produce undulating deformations around the crosssection with no net translation. The relatively large Fourier coefficients associated with n = 2, 3, 4, 5 indicate that a significant portion of the loading will cause shell deformations in these modes. In turn, the corresponding local forces are significantly higher than a beamlike response would produce.
To account for the internal conditions in the tower during operation, it is common practice to add an axisymmetric internal suction coefficient H = 0.5 to the external pressure coefficients H(d). In terms of the Fourier series representation, this would increase A0 to —0.8922.

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