Find the natural frequencies of the water tank considered in Problem 12.22 (Fig. 12.28) using a one-beam element idealization.

Data From Problem 12.22:-

A water tank of mass \(W\) is supported by a hollow circular steel column of inner diameter \(d\), wall thickness \(t\), and height \(l\). The wind pressure acting on the column can be assumed to vary linearly from 0 to \(p_{\max }\) as shown in Fig. 12.28. Find the bending stress induced in the column under the loads using a one-beam element idealization. Data: \(W=5000 \mathrm{~kg}, l=12 \mathrm{~m}, d=0.6 \mathrm{~m}, t=0.02 \mathrm{~m}\), and \(p_{\max }=700 \mathrm{kPa}\).

Transcribed Image Text:

W Water tank Pmax Column FIGURE 12.28 Water tank.