Challenge

Understanding the concepts on Degrees of Freedom

GIVEN DATA : 5 Storey structure, 5 transational degree of freedom, each mass 'm' ,
T1 = 2 s
T2 = .6852 s
T3 = 0.4346 s
T4 = 0.3383 s
T5 = 0.2966 s

DETAILED CALCULATION PDF ID ATTACHED BELOW

The following calculations can be derived from the above data:
MODAL PROPERTY
L1= 4.121m
L2 = -1.327m
L3 = 0.683m
L4 = -0.381m
L5 = 0.175m

MODIFIED MASS MATRIX
M1= 3.861m
M2 = 3.79m
M3= 3.86m
M4 = 3.86m
M5 = 3.86m

MODAL PARTICIPATION FACTOR
Γ1 = 1.067
Γ2 = 0.335
Γ3 = 0.177
Γ4= -0.098
Γ5 = 0.045

EFFECTIVE MODAL MASS
M1*= 4.398m
M2* = 0.436m
M3* = 0.121m
M4* = 0.038m
M5* = 0.008m

Modal mass participation ratio = MMPR = 0.88, 0.09, 0.02, 0.01, 0.002
First two modes are enough for getting 90% of mass participation ratio

BASE SHEAR
Vb1 = 1.187mg
Vb2 = 0.327mg
Vb3= 0.126mg
Vb4 = 0.039mg
Vb5 = 0.0048mg
COMBINED BASE SHEAR = 1.15mg

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