Understanding the concepts on Degrees of Freedom

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 T_n and their corresponding mode shapes, φ_n has been derived.

ANSWER :

RESULTS:-

• L_n , M_n and Γ_n for each of the five modes calculated from the given equations.
• the effective modal mass M_n* and the modal mass participating ratios are Calculated for the 5 modes.
• The base shear for each of the 5 modes of vibration are found.
• 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.