Cyclic Stress-Strain Curves of Concrete and Steel Bars in Membrane Elements

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Abstract
The shear behavior of reinforced concrete membrane elements (panels) can be predicted by rational models that satisfy the three principles of mechanics of materials: stress equilibrium, strain compatibility, and constitutive relationships of concrete and steel bars. At present, these models can only be applied to the monotonic shear behavior, because only the monotonic constitutive relationships of materials are available. This paper reports the reversed cyclic tests of six panels to generate the cyclic constitutive relationships of concrete and steel bars. These fundamental stress-strain curves allow us to extend the rational models to predict the cyclic shear behavior of reinforced concrete structures. The cyclic stress-strain curves of steel bars embedded in concrete were found to have two characteristics: (1) the backbone envelope curve of steel in tension can be expressed by the monotonic stress-strain curve proposed by Belarbi and Hsu; and (2) the unloading and reloading curves can be expressed analytically in the form of a Ramberg-Osgood equation to simulate the Bauschinger effect. The three characteristics of the cyclic stress-strain curves of concrete are (1) the backbone envelope curve of concrete in compression can be expressed by the monotonic stress-strain curve for compression proposed by Belarbi and Hsu; (2) the backbone envelope curve of concrete in tension can be expressed by the monotonic stress-strain curves for tension proposed by Belarbi and Hsu; and (3) the unloading and reloading stress-strain curves of concrete are expressed analytically by a set of points connected by straight lines.