Stresses in Freely Falling Chimneys and Columns

Abstract

A chimney or column is considered as a rigid rod, initially in a vertical position, and hinged at its base. The internal forces and stresses which are developed as the rod falls freely from the vertical position are calculated. It is shown that the inertial reaction forces produce a bending moment which results in a tension on the leading side and a compression in the trailing side of the rod. This tension in the leading side has its maximum value at roughly 0.3 to 0.5 the height of the rod, depending upon its shape and the angle of inclination from the vertical. This tension usually produces a transverse rupture in large falling chimneys or columns, though not always. These transverse ruptures should occur at the point of maximum tension. It is shown that in very tall columns or chimneys the vertical shear stress near the base is sufficient to produce a tension rupture there—and usually does. The positions of these latter ruptures cannot be predicted accurately in actual cases because of the greatly variable conditions which may exist at the point of support after dynamiting. Calculations are given for the cases of solid columns of uniform cross section, solid columns of uniformly tapered cross section, and uniformly tapered chimneys of constant wall thickness. Photographs of actual falling chimneys are presented to check the theory.