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Question 1: A five storey structure with 5 translational DOF is shown here. Each storey has mass ‘m’. The eigenvalue problem has been solved and the 5 periods of vibration Tn and their corresponding mode shapes, φn has been derived. The fundamental period of vibration (T1 = 2 seconds)…
Karthiga Devi
updated on 19 May 2021
Question 1:
A five storey structure with 5 translational DOF is shown here. Each storey has mass ‘m’. The eigenvalue problem has been solved and the 5 periods of vibration Tn and their corresponding mode shapes, φn has been derived.
The fundamental period of vibration (T1 = 2 seconds) and its associated mode shape:
The second mode of vibration (T2 = 0.6852 seconds) and its associated mode shape:
The third mode of vibration (T3 = 0.4346 seconds) and its associated mode shape:
The fourth mode of vibration (T4 = 0.3383 seconds) and its associated mode shape:
The fifth mode of vibration (T4 = 0.2966 seconds) and its associated mode shape:
(ANSWER):
AIM:
To calculate Ln, Mnand Γn for each of the five modes from the given equations.
To calculate the effective modal mass m∗nand the modal mass participating ratio for the 5 modes.
To obtain the base shear for each of the five modes of vibration and the combined base shear as per SSRS rule.
PROCEDURE:
STEP 1:
RESULT:
Finally, calculate Ln, Mnand Γn for each of the five modes from the given equations.
Calculate the effective modal mass m∗nand the modal mass participating ratio for the 5 modes.
Obtain the base shear for each of the five modes of vibration and the combined base shear as per SSRS rule.
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