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.

1ans)

now for mode1

now for mode2

now for mode3

mode4

mode5

1b)

• Finally, obtain the base shear for each of the 5 modes of vibration and the combined base shear as per SRSS rule. The pseudo acceleration design spectrum to obtain the base shear for each mode is provided below.
• 

ans)

the base shaer for each 5modes are following

1c)

• How many modes are to be considered such that a modal mass participating ratio of 90% is obtained?

ans)

to calculate mdal participating ratio as follows