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Q] 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…
Dinesh Kumar
updated on 16 Jul 2023
Q] 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:
AIM:- To compute Ln , Mn and Γn for each of the five modes from the given equations.
To calculate the effective modal mass Mn* and the modal mass participating ratio for the 5 modes.
To obtain the base shear for each of the 5 modes of vibration and the combined base shear as per SRSS rule.
PROCEDURE:-
Step:-1
Step 2:
Step 3:
Step 4:
Step 5:
Step 6:
Now we need to obtain the base shear for each of the 5 modes of vibration, as shown below.
Step:-7
Combined base shear as per SRSS rule:-
Step:-8
RESULT:-
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