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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.

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
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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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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