Abstract
Concrete structures are cracked in tension at working loads. The opening and closing of the existing cracks during load variations renders these structures nonlinear elastic. Under proportional load variations and for single loads, these structures exhibit bilinear mechanical response in the form of discontinuity at origin in their load displacement relations. The typical values of bilinearity ratio, i. e., the ratio of the two values of stiffness, of common reinforced concrete beams range up to 10. In this paper, the dynamic response of concrete structures under working loads has been studied by modeling them as damped single-degree-of-freedom bilinear systems under the action of sinusoidal forcing function. Using the available techniques of bilinear dynamic analysis of moored buoys developed by Thompson and coworkers, concrete structures has been shown to exhibit sub-harmonic resonance response and extreme sensitivity to initial conditions leading to chaos. The limitations of the current practice of dynamic analysis have been exposed and the practical relevance of the work done has been discussed.