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Define the displacement of the i-th joint X,, using SRSS of N modes:
(11)
where 4> g is the z-f/z joint corresponding to j-th mode shape, &>j is the natural frequency
corresponding to j-th mode, £j is the damping ratio corresponding to j-th mode, YJ is the mode
participant parameter corresponding loj-th mode.
When the maximum of acceleration of ground motion is increased step-by-step, formation of a desired
earthquake-resistant mechanism comes into effect, and various modal parameters are modified.
Therefore, the modal parameters and X,- are calculated anew. The dynamic performance of the
structure in inelastic range is expressed via modal parameters and X, modified.
Modify
stiffness
When formation of a desired earthquake-resistant mechanism comes into effect, one or some structural
members enter inelastic range, whose stiffness is or are substituted post yield stiffness for. In this paper,
the hysteretic model is bilinear one, no stiffness degradation. Furthermore, both residual displacement
and P-Delta effect is taken into account as geometric nonlinearity. The i-th inter-storey drift, A I|9 is
equal to sum both inter-storey lateral drift at yield, A y, and inter-storey lateral drift after yield, A p.
ApA^ + A, (13)
Determine the inter-storey yield
For each structural member, its nonlinear stiffness model is a bilinear stiffness model. For each storey,
its nonlinear storey shearing stiffness is also simplified to a bilinear stifmess model, that is, the
nonlinear storey lateral force versus inter-storey lateral drift response of the prototype structure is
represented by a bilinear approximation. The bilinear approximation has three defining characteristic:
(a) The initial stiffness, Kj , (b) the maximum storey force and inter-storey drift, F u and A a ,
respectively and (c) the second (post yield) stifmess, £•
The initial elastic stiffness is calculated from a linear-elastic analysis where the linear stiffness of the
members. The maximum load and deformation at the limit state, F u and A u , respectively, in the
bilinear approximation are equal to those of the nonlinear curve. The second stiffness, £2, is calculated
by equating the strain energy in the nonlinear curve to that in the bilinear approximation, where the
strain energy can be calculated by means of integrating the piece-wise-linear inter-storey force-drift
curve.
Meanwhile, The storey lateral force, F y , and niter-storey lateral drift, A 7 , at yield are defined by the