The unloading stiffness of reinforced concrete members

Student: Viviana Iris Novelli
Supervisors: Dr. T.J. Sullivan, Dr. R. Pinho, Prof. Calvi G. M.


Concrete structures present a reduction in stiffness as a function of the ductility and one of the best hysteretic rules introduced to represent the non-linear behaviour is the Takeda hysteresis model.

After a literature review on the hysteresis cycle defined by the Takeda model, the research focuses on the unloading stiffness behavior as a function of the ductility and other characteristics of the structure.

First of all, analyses are carried out using the experimental results available from the Kawashima Laboratory of the Tokyo Institute of Technology.

Afterwards, a numerical model with a single-degree- of-freedom (SDOF) oscillator is developed in SeismoStruct and parameters are calibrated to obtain the hysteretic behavior observed through experimental analyses. After testing its efficiency, such a model is used to study the unloading stiffness behavior as a function of the displacement ductility, varying the following parameters of the SDOF: section ratio, aspect ratio and axial load ratio.

The next step introduces the lumped-plasticity modeling, which follows the unloading rules defined by Takeda for hysteresis cycles. In such a way it is possible to analyze the SDOF stiffness in function of the curvature ductility varying the same structure parameters mentioned previously.

Finally in Ruaumoko 2D, non linear time history analyses are run with a series of accelerograms on a cantilever column having a hysteretic moment-curvature plastic hinge and an equivalent SDOF spring system having the same initial stiffness and strength as the column but with hysteretic behaviour defined in terms of force and displacement.

From the results of these analyses it is concluded that the unloading stiffness depends on the displacement ductility and the axial load ratio.

You may download a digital version of this MSc dissertation here.