TECHNICAL PAPERS
Dec 1, 2001

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

Publication: Journal of Structural Engineering
Volume 127, Issue 12

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.

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References

1.
Aktan, A. E., Karlson, B. I., and Sozen, M. A. ( 1973). “Stress-strain relationship of reinforcing bars subjected to large strain reversals.” Struct. Res. Series No. 397, University of Illinois, Urbana, Ill.
2.
Belarbi, A., and Hsu, T. T. C. ( 1994). “Constitutive laws of concrete in tension and reinforcing bars stiffened by concrete.” ACI Struct. J., 91(4), 465–474.
3.
Belarbi, A., and Hsu, T. T. C. ( 1995). “Constitutive laws of softened concrete in biaxial tension-compression.” ACI Struct. J., 92(5), 562–573.
4.
Hsu, T. T. C., Belarbi, A., and Pang, X. B. ( 1991). “Stress-strain relationships for reinforced concrete membrane elements.” Concrete Shear in Earthquakes, Hsu and Mau, eds., Elsevier Applied Science, 43–54.
5.
Hsu, T. T. C., Belarbi, A., and Pang, X. B. ( 1995a). “A universal panel tester.” J. Testing and Evaluation, 23(1), 41–49.
6.
Hsu, T. T. C., and Zhang, L. X. ( 1997). “Nonlinear analysis of membrane elements by fixed-angle softened-truss model.” ACI Struct. J., 94(5), 483–492.
7.
Hsu, T. T. C., Zhang, L. X., and Gomez, T. ( 1995b). “A servo-control system for universal panel tester.” J Testing and Evaluation, 23(6), 424–430.
8.
Hsu, T. T. C., and Zhu, R. H. ( 2001). “Post-yield behavior of reinforced concrete membrane elements: The Hsu/Zhu ratios.” Post-peak behavior of reinforced concrete structures subjected to seismic load, ASCE, Reston, Va., 139–157.
9.
Kurihara, K., Ohmori, N., Takahashi, T., Tsubota, H., Inoue, N., and Watanabe, S. ( 1990). “Analytical hysteresis model for reinforced concrete panels subjected to cyclic in-plane shear.” J. Struct. and Constr. Engrg., Tokyo, 410, 93–105 (in Japanese).
10.
Menegotto, M., and Pinto, P. E. ( 1973). “Method of analysis for cyclically loaded reinforced concrete plane frames including changes in geometry and non-elastic behavior of elements under combined normal force and bending.” Proc., Symp. on Resistance and Ultimate Deformability of Struct. Acted on by Well-Defined Repeated Loads, International Association of Bridge and Structural Engineers, Zurich, 15–22.
11.
Ohmori, N., Takahashi, T., Tsubota, H., Inoue, N., Kurihara, K., and Watanable, S. ( 1989). “Experimental studies on nonlinear behaviors of reinforced concrete panels subjected to cyclic in-plane shear.” J. Struct. and Constr. Engrg., Tokyo, 402, 105–118 (in Japanese).
12.
Pang, X. B., and Hsu, T. T. C. ( 1995). “Behavior of reinforced concrete membrane elements in shear.” ACI Struct. J., 92(6), 665–679.
13.
Pang, X. B., and Hsu, T. T. C. ( 1996). “Fixed-angle softened-truss model for reinforced concrete.” ACI Struct. J., 93(2), 197–207.
14.
Robinson, J. R., and Demorieux, J. M. ( 1968). “Essais de traction-compression sur modeles d'ames de poutre en beton arme.” IRABA Rep., Part 1, Institute de Recherches Appliquees du Beton de l'Ame, France, 44.
15.
Robinson, J. R., and Demorieux, J. M. ( 1972). “Resistance ultimate du beton de l'ame de poutres en double te en beton arme.” IRABA Rep., Part 2, Institute de Recherches Appliquees du Beton de l'Ame, France, 53.
16.
Stevens, N. J., Uzumeri, S. M., and Collins, M. P. ( 1991). “Reinforced concrete subjected to reversed cyclic shear—experiments and constitutive model.” ACI Struct. J., 88(2), 135–146.
17.
Vecchio, F. J., and Collins, M. P. ( 1981). “Stress-strain characteristic of reinforced concrete in pure shear.” Proc., IABSE Colloquium, Advanced Mech. of Reinforced Concrete, International Association of Bridge and Structural Engineering, Zurich, 221–225.
18.
Yokoo, Y., and Nakamura, T. ( 1977). “Nonstationary hysteretic uniaxial stress-strain relations of a steel bar.” Trans. Arch. Inst. of Japan, Tokyo, 260, 71–80.
19.
Zhu, R. H., Hsu, T. T. C., and Lee, J. Y. ( 2001). “Rational shear modulus for smeared crack analysis of reinforced concrete.” ACI Struct. J., 98(4), 443–450.
20.
Zhang, L. X., and Hsu, T. T. C. (1998). “Behavior and analysis of 100 MPa concrete membrane elements.”J. Struct. Engrg., ASCE, 124(1), 24–34.

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Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 127Issue 12December 2001
Pages: 1402 - 1411

History

Received: Apr 26, 2000
Published online: Dec 1, 2001
Published in print: Dec 2001

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Authors

Affiliations

Asst. Prof., Dept. of Civ. and Const. Engrg., Bradley Univ., Peoria IL; formerly, Res. Asst., Dept. of Civ. and Envir. Engrg., Univ. of Houston, Houston, TX.
Lect., Dept. of Archit. Engrg., Sungkyunkwan Univ., Suwon, Korea; formerly, Res. Assoc., Dept. of Civ. and Envir. Engrg., Univ. of Houston, Houston, TX.
Moores Prof., Dept. of Civ. and Envir. Engrg., Univ. of Houston, Houston, TX.

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