Understanding the concepts on Degrees of Freedom

GIVEN:

Modified mass matrix(m)

m=ϕ^T_nm ϕ_n

_m1=3.861m

_m2=7.56m

_m3=3.861m

_m4=3.86m

_m5=3.861m

_{Modal Property(L)}

_L=ϕ^T_nml

l=influence factor

L1=4.123m

L2=-1.3m

L3=0.683m

L4=-0.381m

L5=0.175m

Modal Participation factor (Г)

Г=L/M

Г1=1.067

Г2=-0.172

Г3=0.177

Г4=-0.099

Г5=0.045

Effective Modal mass(M*)

M*=L²/M

M*1=4.4m

M*2=0.2235m

M*3=0.121m

M*4=0.038m

M*5=0.008m

Modal mass ratio participation

n=Mn*/Mj

Mj=Total mass of building =m+m+m+m+m=5m

n1=0.88

n2=0.05

n3=0.0242

n4=0.0076

n5=0.0016

By adding the first two modal participation ratio to acheive more than 90% @(0.88+0.05)=0.93

Base shear(VB) =Mn*xAn

An obtained for pseudo acceleration graph bu using the 'n'

An1=0.27g

An2=1.2g

An3=1.04g

An4=1.03g

An5=1g

Base shear=Mn*An

VB1=1.188mg

VB2=0.2682mg

VB3=0.126mg

VB4=0.03914mg

VB5=0.008mg

Average base shear is calculated by method of SRSS(Square root of sum square) combination

VB=1.22mg