A 30m high steel chimney has the trefoil cross-section shown in Figure 2, consisting of three welded

A 30m high steel chimney has the trefoil cross-section shown in Figure 2, consisting of three welded tubes each 2m in diameter (median line dimension) and 36mm thick. The tubes are connected together so as to act a single section.

(a) In order to be able to calculate the magnitude of the possible wind-excited vibrations of the chimney, it is required to find the torsional characteristics of the section. Determine the torsion constant J for the box section of Figure 2.

(b) If the top of the chimney vibrates torsionally through an amplitude of + 0.6 degrees, find the corresponding maximum torsional shear stress that is induced. Assume that the angle of twist per unit length increases uniformly from the top to the bottom of the chimney, and that G for steel is 80 kN/mm2.

Show transcribed image text A 30m high steel chimney has the trefoil cross-section shown in Figure 2, consisting of three welded tubes each 2m in diameter (median line dimension) and 36mm thick. The tubes are connected together so as to act a single section. (a) In order to be able to calculate the magnitude of the possible wind-excited vibrations of the chimney, it is required to find the torsional characteristics of the section. Determine the torsion constant J for the box section of Figure 2. (b) If the top of the chimney vibrates torsionally through an amplitude of + 0.6 degrees, find the corresponding maximum torsional shear stress that is induced. Assume that the angle of twist per unit length increases uniformly from the top to the bottom of the chimney, and that G for steel is 80 kN/mm2.