Approximate Fundamental Frequencies for Chimneys

Chimneys are shell structures that are used for discharging gaseous effluents from factories or power plants. When designing a chimney, obtaining the fundamental frequency or period is necessary to be able to determine: (1) lateral forces due to earthquake; and (2) the critical wind velocity that would cause resonant vibrations, due to the shedding of the Karman Vortex. Determining the natural frequencies and performing the dynamic analysis of chimneys has become easier using computers. When performing the preliminary chimney design, engineers require a rapid means for obtaining a reasonably accurate fundamental frequency of a chimney to permit necessary modifications to develop the best design. For this reason, approximate formulas for fundamental frequencies are indispensable for practicing engineers. This note considers unguyed and unlined chimneys (or chimneys with self-supported independent lining). Several commonly used approximate formulas for computed fundamental frequencies are given. Frequencies for chimneys with practical ranges of dimension variables were obtained by computer using Newmark's method. Computer results were compared with those obtained by the existing formulas. From these studies, new approximate formulas that fit the computer results better than the existing formulas are proposed.