Understanding the concepts on Degrees of Freedom

Aim:

To compute L_n , M_n and Γ_n for each of the five modes from the given equations.

To calculate the effective modal mass M_n* 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:-

Results

• Ln, Mn, Tn values are calculated for each of the 5 modes
• The base shear force for each of the 5 modes is obtained.
• Effective modal mass and the modal mass participating ratio for 5 modes 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.