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Calculate the Mass and the Stiffness matrix for the shear frame below. The mass is lumped at each level. The supports at end A,B are fixed . The columns are considered to have no mass. (Modulus of elasticity E, Storey masses m1,m2, Column moment of inertia I1,I2. )
Solution
The shear frame has two degrees of freedom, the sideways horizontal displacements u1, u2.
In order to find the first column of the Stiffness Matrix we apply unit displacement u1=1 and u2=0.
In order to find the second column of the stiffness matrix we apply unit displacement u2=1 and u1=0.
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