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DISPLACMENT-BASED NSF
In this paper, a nonlinear static procedure based on displacement is presented. The method is a
displacement-based analysis method that adds checking computation of displacement and deformation
of structures. It maintains the simplicity of pushover analysis, and extends pushover analysis to
investigate structural dynamic characteristic, and to account for development of displacement, and to
describe ductility capacity of members set plastic hinge on.
In this method, the acceleration of ground motion is monotonously increased step by step based on
different seismic hazard levels. The lateral displacement, instead of base shearing force, is calculated.
Moreover, the distribution of lateral displacement is selected by the mode shapes, which are
considered based on structural dynamic modification considering the residual displacement of inelastic
members, and post yield stiffness etc.
In this method, modal analysis is adopted, because the displacement or force distribution can be
expressed with the modal shapes, and the maximum displacement of each joint or floor of a structure
subjected to the ground motion acceleration can also be expressed with the maximum coordinate using
the displacement response spectrum. Furthermore, the higher modals are taken into consideration via
the SRSS/CQC method. When the displacement is increased to some extend, the structure enters
inelastic range, whose overall stif&iess is modified and whose dynamic characteristics is changed.
Then, the structure is anew done modal analysis in order to obtain dynamic characteristics of the
structure in inelastic range.
Modal Analysis
The structural motion differential equation is expressed as
(1)
Where M is the mass matrixes, C is the damping matrixes, K is the stiffness matrixes, X is the
displacement vector, x w is the ground acceleration history.
Calculate the eigenvalues and eigenvectors (natural frequencies and modal shapes) of the structure
under undamping free vibration. Assume that X satisfies
where O is the shape matrixes , q is the modal coordinate.
Substitute this expression for X in equation (1):
X=< (2)