# Inelastic Seismic Response of Structures

## Inelastic Seismic Response of Structures

• Under relatively  strong  earthquakes, structures undergo inelastic  deformation  due to  current seismic design philosophy.
• Therefore, structures should have sufficient ductility  to deform beyond the yield limit.
•  For understanding the ductility demand imposed by the  earthquake,  a  study  of  an  SDOF system  in inelastic range is of great help.
• The  inelastic  excursion  takes  place  when   the restoring force in the spring exceeds or equal to the yield limit of the spring. or this, nonlinear time history analysis of SDOF system under earthquake is required; similarly, nonlinear analysis of MDOF system is useful for   understanding non-linear behaviour of MDOF system under earthquakes.
• Nonlinear analysis is required for other reasons   as well such as determination of collapse state, seismic risk analysis and so on.
• Finally, for complete understanding of the inelastic behaviour of structures, concepts of ductility and inelastic response spectrum are required.
• The above topics are discussed here.

## Non linear dynamic analysis

If structure have nonlinear terms either in inertia or in damping or in stiffness or in any form of combination of them, then the equation of motion becomes nonlinear. More common nonlinearities are stiffness and damping nonlinearities. In stiffness non linearity, two types of non linearity are encountered :

•   Geometric
•   Material (hysteretic type)

Equation of motion for non linear analysis takes the  form

## Bidirectional Interaction

Bidirectional interaction assumes importance under:

•    Analysis for two component earthquake
•    Torsionally Coupled System

For such cases, elements undergo yielding depending upon the yield criterion used. When bidirectional interaction of forces on yielding is considered, yielding of a cross section depends on two forces. None of them individually reaches yield value; but the section may yield.