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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) and…
MAYUR KOKANI
updated on 27 Feb 2022
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:
RESULT:
• Calculated In , Mn and In for each of the five modes from the given equations.
• Calculated the effective modal mass Mn* and the modal mass participating ratio for the 5 modes.
• The base shear for each of the 5 modes of vibration are obtained.
• As per SRSS rule the combined base shear is obtained.
• The two modes are to be considered such that a modal mass participating ratio of 90% is obtained.
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