Keywords: dynamics, seismic analysis, reinforced concrete structure, frame structure, nonlinear behaviour, pushover analysis, strong ground motion, nonlinear response history analysis.

The response of reinforced concrete structures subject to strong ground motion is associated with nonlinear behaviour. Pushover analysis has always been understood as a nonlinear capacity estimation tool and generally called capacity analysis. On the other hand, the standard concept of pushover method does not often provide solution which can be reliably compared with the rigorous procedure of nonlinear response history analysis.

The most used and convenient methods for seismic calculation are based on response spectrum. The response spectrum gives an envelope of maximum load effects for given dynamic properties of the structure. Methods based on response spectrum are very appropriate for linear calculations. They give results comparable with time history analysis. Response spectrum methods cannot be used for non-linear calculations. This is because they are based on a linear combination of natural modes of vibration, which is not applicable for non-linear calculations.

The pushover method uses non-linear material relations, but loads are based on linear assumptions. This is not appropriate for investigating the real behaviour of a structure under seismic loading. However, this method is appropriate for assessment of total load resisting capacity and for determination of dissipation properties. This can be used to estimate the coefficient of ductility.

The new modified pushover method (NMPM) has been developed [1] and the algorithm can be summarised as follows:

1. The first step is the non-linear analysis of the structure under static loading, such as a dead load or live loads. Static analysis shall be done prior to the seismic analysis as the resulting overall stresses and strains are not linear and cannot be simply combined together.
2. The second step is the calculation of dynamic properties of the loaded structure, determining secant stiffness matrix. Calculation can be linearized by determining the modal matrix and spectral matrix. The spectral method can be used. Seismic forces will be determined for given modal characteristics.
3. Seismic loads obtained from step 2 will be used in the non-linear static analysis, in which structure will be loaded by load increments and the increments of deformation will be calculated. There will be a new secant stiffness matrix determined for the deformed structure. This matrix differs from the matrix obtained in the step 2 as a result of the non-linearity of the system.
4. In the fourth step the dynamic characteristics of the system will be newly determined from the modified secant stiffness matrix obtained from step 2.
5. The structure will be loaded by increment of seismic forces. Steps 3 and 4 will be repeated until the sum of seismic increments is equal to overall seismic force.

The results obtained by this method are in appropriate accordance with the results obtained using nonlinear response history analysis. Seismic forces obtained from the modified method take into account both changes in modal characteristics of the structure and energy dissipation. Load effects were investigated in the stress and strain range both under the limit of design resistance and over this limit, where plastic behaviour is significant. Results are within 10% difference compared to direct integration.

1

K. Pohl, "Seismic response of reinforced concrete frame structures", PhD. thesis, CTU Prague, 2010.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £130 +P&P)