Nonlinear response of plain concrete shear walls with damage

During earthquakes, the natural frequencies of concrete structures are often signifi- cantly lower than those predicted by conventional linear elasticity. This can cause severe motion of piping systems because the design of support structures utilizes val- ues of predicted natural frequencies. In an experimental program to investigate the problem, a further decrease in stiffness was noted for model concrete structures. In this study continuum damage mechanics is proposed as a constitutive model for de- scribing both the changes in natural frequencies, and the reduction in initial stiffness of small concrete structures. Structural members made with brittle materials such as concrete experience damage under seismic excitation, which is reflected through al- tered natural frequencies for the structure. With regard to scale models, it is suggest- ed that microcracking as a result of shrinkage may be the source of the loss in initial stiffness. Shrinkage cracks are easily reflected in the constitutive equation as initial isotropic damage. Finite element predictions based on anisotropic damage mechan- ics indicate that the proposed approach may be practicable for routine engineering analyses.