Understanding the concepts on Degrees of Freedom

Aim:

• To compute L_n , M_n and T_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 modes of vibration and combined base shear as per SRSS rule.

Procedure:

Step 1:

Similarly,

M2 = 3.861 m

M3 = 3.851 m

M4 = 3.861 m

M5 = 3.861 m

Step 2:

Similarly,

L2 = -1.297

L3 = 0.687

L4 = -0.381

L5 = 0.175

Step 3 : Finding Tn

Tn = Ln/Mn

T1 = 1.067

T2 = -0.33

T3 = 0.178

T4 = -0.09

T5 = 0.04

Step 4 : Finding effective modal mass

M2* = 0.43

M3* = 0.122

M4* = 0.03

M5* = 0.008

Step 5: Finding Modal mass participating ratio

Modal mass participating ratio = Mn*/Mj

Mj = M+M+M+M+M = 5M

Modal mass participating ratio for mode 1 = 0.88

Modal mass participating ratio for mode 2 = 0.086

Modal mass participating ratio for mode 3 = 0.024

Modal mass participating ratio for mode 4 = 0.006

Modal mass participating ratio for mode 5 = 0.001

Step 6: To obtain the Base shear

Step 7: Using SRSS rule