Understanding the concepts on Degrees of Freedom

Aim -

1) To calculate L_n, M_nand Γ_n for each of the five modes.

2) To calculate the effective modal mass M_n* and the modal mass participating ratio for the 5 modes.

3) To find the base shear for each of the 5 modes of vibration and the combined base shear as per SRSS rule.

1

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

From above results we can say that

Only 2 modes of Modal participation is required to obtained above 90%

Modal Participation of node 1 + Modal Participation of node 2 = 88% + 8.72% = 96.72%

Results -

i) The combined Base Shear is calculated by using SRSS method is = 1.22mg

ii) Two modes are to be considered such that a modal mass participating ratio of 90% is obtained .

iii)

Parameters	Mode 1	Mode 2	Mode 3	Mode 4	Mode 5
(Mn) = ϕnT m ϕn	3.861	3.861	3.85	3.861	3.861
Ln=ϕTn m i	4.121	-1.297	0.687	-0.381	0.175
Γn=Ln/Mn	1.067	-0.336	0.178	-0.098	0.045
Mn∗=Ln^2/Mn	4.397	0.436	0.122	0.030	0.007
Modal mass participating ratio	88%	8.72%	2.44%	0.6%	0.14%
Vb=Mn*⋅An	1.187	0.33	0.126	0.031	0.0072