Question

A 5-story frame building has the following properties: m= 0.93 kip-s2/in, for all floors K1= 170 kip/in, for first floor K2= 150 kip/in, for second floor K3= 100 kip/in, for third floor K4= 50 kip/in, for fourth floor K5= 20 kip/in, for fifth floor Find the natural periods of vibration for the given building.

Answer 1

Natural frequency of building = square root (Ke/m)

All the floors are in series,

So, for equivalent stiffness,

(1/Ke) = (1/K1)+(1/K2)+(1/K3)+(1/K4)+(1/K5)

= (1/170)+(1/150)+(1/100)+(1/50)+(1/20)

Therefore, Ke = 10.805 kip/in

So, Natural frequency = square root (10.805/0.93)

= 3.41 rad/s

= 0.54 Hz