# Info

to the stabilizing effect of the interaction of compression and tension forces of the two main parabolas. (Gioncu 1992, Graf 2002).

The subsequent load cases/combinations were examined, in which the wind was applied perpendicular to the direction of the transmission lines, in the following called x-direction (fig. 7). For the analyses, the load factors 1.35 for dead load, and 1.5 for live loads were applied.

The self weight of the tower was determined as 1090 KN. The resultant wind forces in x-direction for the tower structure itself are

1.5 x 1002 KN = 1503 KN for the 50 year wind, compared to 1239 KN as calculated by Suchov. Although the base shears are quite similar, the overturning moments are significantly higher if the modern code is applied, due to the vertical distribution of wind pressures. The forces in the members of the first hyperboloid section under different load cases are summarized in table 3.

LC 1: self weight of the tower

LC 2: self weight of the tower including the transmission line, factored LC 3: like LC 2 plus 50-year wind load in x-direction, factored LC 4: like LC 2 plus 24% of the 50-year wind in x-direction, factored LC 5: Self weight including transmission line plus wind load in x-direction according to the original calculations of Suchov. LC 6: Current condition without transmission lines. Self weight of the tower plus 5-year wind in x-direction, factored.

Figure 7. Deformed shape of the tower under self weight and wind load in x-direction, displaying larger deformations at the transition between the different hyperboloid sections.

4.5 Structural behaviour

4.5.1 Under self weight

Under self weight, all verticals are subjected evenly to compression forces, whereas the lattice girders are

Figure 8. Transition between first and second hyperboloid section. From top to bottom: Structure, followed by qualitative contours of deformation, normal force distribution, and bending moments of the lattice girder.

subjected to tension forces. This is caused by the differently inclined verticals above and below each lattice girder. The outward thrust is thus balanced by the lattice girder.

The ring elements are not subject to any forces. They simply act as bracing elements for the verticals.

4.5.2 Under self weight and horizontal wind load in x-direction The tower displays a remarkably high bending stiffness. The horizontal deformation of the structure under unfactored wind load is 340 mm, resulting in a deflection ratio of l/388.

Under self weight and wind load, the structure displays a tube-like load bearing behaviour. All verticals are subjected to normal forces. Predictably, the verticals at the front face are under tension and the ones at the rear face under compression. At the "sides", verticals are alternating under tension or compression, depending on their twisting angle. This imposes a vertical distortion of the lattice girder at the end of each section.

The discontinuity of the verticals between the different hyperboloid sections results in a decrease of the shear stiffness, causing large deformations in these areas. The lattice girders are subject to linearly increasing compression forces on the front face and tension forces on the opposite side, thus balancing the normal forces of the inclined verticals below.

The bending action of the tower causes the lattice girder to ovalize, thereby inducing bending moments around the strong axis of the member. (fig. 8) In addition, the girders are even more affected by the push-pull action of the sidewise verticals, acting around their weak axis. The ring elements adjacent to the lattice girders get affected by the distortion in this area as well, causing overstress due to bending.

Based on the current analysis and load assumptions, the structure would not be adequate to sustain the 50-year wind, due to buckling of the verticals in the first section. The structure including transmission lines would only satisfy code requirements if the factored wind loads are reduced by 76%. Even the current condition without the transmission lines would not be sufficient to sustain the 5-year wind.

Despite of some minor local overstressing, almost all other members of the structure are suitable (load case 3).