Question 9.P.8: The water tower shown in Figure P9.8 has a mass of 24,000 kg...
The water tower shown in Figure P9.8 has a mass of 24,000 kg which can be assumed as being lumped at the center of the tank. The lateral stiffness of the supporting frame is 5,000 kN/m. The tank is subjected to a lateral load which varies as a half sine wave of amplitude 200 kN and period 1.0 s as shown in the figure. Using a frequency domain analysis and Fast convolution technique obtain the history of response for the first second of motion. Use a sampling interval of 0.05 s. Compare your results with a closed form solution. Neglect damping.
Closed form solution
\begin{array}{ll}u=0.0494(\sin 6.283 t-0.4353 \sin 14.43 t) \mathrm{m} & 0<t<\frac{1}{2} \mathrm{~s} \\u=-0.0173 \cos 14.43\left(t-\frac{1}{2}\right)-0.0343 \sin 14.43\left(t-\frac{1}{2}\right) \mathrm{m} & t>\frac{1}{2} \mathrm{~s}\end{array}
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