Understanding the concepts on Degrees of Freedom

UNDERSTANDING THE CONCEPT OF DEGREE 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 Tn and thier corresponidng mode shape φn has been derived.

The fundamental period of vibration (T1=2 seconds) and its associated mode shape:

The second mode vibration (T2=0.6852 seconds) and its mode of shape:

The third mode vibration (T3=0.4346 seconds) and its mode of shape:

The fourth mode of shape (T4=0.3383 seconds) and its mode of shape:

The fifth mode of shape (T5=0.2966 seconds) and its mode of shape:

Ln, Mn, and Γn for each of the five modes are to be computed from the equation below.

Also, calculate the effective modal mass Mn* and the modal mass participating ratio for the 5 modes. The mass matrix will be required to evaluate these parameters.

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 desgin spectrum to obtain the base shear for each mode is provided below.

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

ANSWERS: