The tower extends from the Earth to the geostationary orbit! The lower part of the tower may be damaged by wind, lightning, and icing. The minimum mass of a steel tower (for 1-ton cargo) is greater than the mass of the Earth! Buckling makes it even heavier than skyhook. A structural material of great specific strength and stiffness is needed to make this idea practicable. Plastic cannot be used because it is vulnerable to space radiation and thermal fatigue.
Space tower page at NASA.
Konstantin Edvardovich Tsiolkovsky, "Grezy o Zemle i Nebe (i) Na Veste" (in Russian, Speculations about Earth and Sky and on Vesta) Academy of Sciences, U.S.S.R., Moscow, 1959, p. 35 (first published in 1895).
Geoffrey A. Landis and Craig Cafarelli, "The Tsiolkovski Tower
Reexamined," IAF-95-V.4.07, 46th International Astronautical
Congress, October 2-6, 1995, Oslo, Norway.
(The inflated tower described in this article is impracticable because large amount of inner gas (helium or hydrogen) would leak through the very thin tower wall and through holes punched by space junk.)