The water tank shown in Fig. 14.33 is supported by a hollow circular steel column. The tank, made of steel, is in the form of a thin-walled pressure vessel and has a capacity of 40,000 litres. Design the column to satisfy the following specifications:

(a) The undamped natural frequency of vibration of the tank, either empty or full, must exceed a value of \(1 \mathrm{~Hz}\).

(b) The mean square value of the displacement of the tank, either empty or full, must not exceed a value of \(0.01 \mathrm{~m}^{2}\) when subjected to an earthquake ground acceleration whose power spectral density is given by

\[S(\omega)=0.0002 \frac{\mathrm{m}^{2} / \mathrm{s}^{4}}{\mathrm{rad} / \mathrm{s}}\]
Assume damping to be 10 percent of the critical value.

Transcribed Image Text:

Cylindrical tank Column 12 m FIGURE 14.33 Water tank subjected to ground acceleration.