Understanding the concepts on Degrees of Freedom
1)
Mass matrix (M)= [[m,0,0,0,0],[0,m,0,0,0],[0,0,m,0],[0,0,0,m]]
Modified mass matrix (M) = phi_n^t*m*phi_n
For the first mode (n=1) = [0.334,0.641,0.895,0.1078,1.173]*m*[[0.334],[0.641],[0.895],[0.1078],[1.173]]
M1= 3.861m
Similiarly for other modes,
M2= 3.861m
M3= 3.861m
M4= 3.861m
M5= 3.861m
Modal property (L) = phi_n^T*m*iota
iota= influence vector (Assuming 100% utilization of seismic force)= [[1],[1],[1],[1],[1]]
For the first mode (n=1) = [0.334,0.641,0.895,0.1078,1.173]*m*[[1],[1],[1],[1],[1]]
L1=4.121m
Similiarly for other modes,
L2= -1.297m
L3= 0.683m
L4= 0.381m
L5= 0.175m
Modal participation factor (Gamma)= L/M
For the first mode Gamma1= L1/M1
Gamma1= 4.121m/3.861m
Gamma1= 1.067
Similiarly,
Gamma2= -0.335
Gamma3= 0.177
Gamma4= -0.098
Gamma5= 0.045
Effective Modal mass (M^*) = L_n^2/M_n
For the first mode (n=1), M1^*=L1/M1
M1^*= (4.121m)^2/3.861m
M1^*= 4.398m
Similiarly,
M2^*= 0.436m
M3^*= 0.121m
M4^*= 0.038m
M5^*= 0.008m
Modal mass participation ratio = M_n*/m_j
Where m_j= Total mass of the building= m+m+m+m+m= 5m
Modal mass participation ratio of first mode (n=1) = 4.398m/5m= 0.88
Similiarly,
(n=2) = 0.09
(n=3) = 0.02
(n=4) = 0.01
(n=5) = 0.002
Adding first two modal mass participation ratios, we get 0.97, it is sufficient to achieve minimum 90% of Modal mass participation ratio
Base shear (V_B)= M_n^*.A_n
For the first mode (n=1 ),V_B1 = 4.398m*0.27g
V_B1 = 1.187mg
Similiarly,
V_B2 = 0.327mg
V_B3 = 1.126mg
V_B4 = 0.039mg
V_B5 = 0.008mg
Average base shear is calculated by the method of Square Root of Sum of square (SRSS)
Combined base shear = root of((V_b1^2)+(V_b2^2)+(V_b3^2)+(V_b4^2)+(V_b5^2))
V_b=1.15mg