Help me please, I will upvote. Thankyou :) Under free vibrations and damped conditions, a SDOF portalframe fixed at its base has a mass of 1,500 kg at roof level.Lateral stiffness of frame columns 1 and 2 are: k1 = 12,500N/m, and k2 = 13,500 N/m. Viscous damping coefficient is435 N s/m. Find:1.) the natural period of oscillations2.) cyclic natural frequencies3.) circular natural frequencies4.) If the initial displacement and velocity are 20 mm and 23mm/s, compute frame side sway after 1.5 s.

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Answered: Under free vibrations and damped…

Under free vibrations and damped conditions, a SDOF portal frame fixed at its base has a mass of 1,500 kg at roof level.

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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Help me please, I will upvote. Thankyou :)

Under free vibrations and damped conditions, a SDOF portal
frame fixed at its base has a mass of 1,500 kg at roof level.
Lateral stiffness of frame columns 1 and 2 are: k1 = 12,500
N/m, and k2 = 13,500 N/m. Viscous damping coefficient is
435 N s/m. Find:
1.) the natural period of oscillations
2.) cyclic natural frequencies
3.) circular natural frequencies
4.) If the initial displacement and velocity are 20 mm and 23
mm/s, compute frame side sway after 1.5 s.

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Step 1 Given Data

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Step 2 Calculating Lateral stiffness of Column

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Step 3 Applying equation of motion

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Step 4 Calculation of Cyclic Frequency (f) and Natural time period

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