PROBLEM An SDOF portal frame fixed at its base has a mass of 1,000 kg at roof level. The system is supported by two columns each with stiffness of 12,000 N/m. The viscous damping coefficient is 500 N s/m. Under free vibrations, find the natural period of oscillations and cyclic as well as circular natural frequencies for both damped and undamped conditions. For the damped condition, if the initial displacement and velocity are 10 mm and 15 mm/s, respectively, compute frame side sway after 1.5 s.

Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
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PROBLEM
An SDOF portal frame fixed at its base has a mass
of 1,000 kg at roof level. The system is supported
by two columns each with stiffness of 12,000
N/m. The viscous damping coefficient is 500 N
s/m. Under free vibrations, find the natural period
of oscillations and cyclic as well as circular natural
frequencies for both damped and undamped
conditions.
For the damped condition, if the initial
displacement and velocity are 10 mm and 15
mm/s, respectively, compute frame side sway after
1.5 s.
Show your complete solution. Round your answers
to four decimal places.
Transcribed Image Text:PROBLEM An SDOF portal frame fixed at its base has a mass of 1,000 kg at roof level. The system is supported by two columns each with stiffness of 12,000 N/m. The viscous damping coefficient is 500 N s/m. Under free vibrations, find the natural period of oscillations and cyclic as well as circular natural frequencies for both damped and undamped conditions. For the damped condition, if the initial displacement and velocity are 10 mm and 15 mm/s, respectively, compute frame side sway after 1.5 s. Show your complete solution. Round your answers to four decimal places.
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