State of Stress in RC Plates under Service Conditions
Publication: Journal of Structural Engineering
Volume 112, Issue 8
Abstract
A theory regarding the stresses of reinforced concrete shear walls and slabs under service loads is presented. Stresses are determined before and after cracking. The reinforcement provides forces and moments that compose tensors. These tensors, together with the corresponding concrete tensors, constitute the reinforced concrete tensors. After cracking, the force and moment tensors of reinforcement appear in their complete form, i.e., not only with the axial forces but also with the shear forces of steel bars. The existence of these shear forces is proved theoretically, and their magnitude is determined by the compatibility conditions of the strains at the crack. Equating the tensor of the internal forces or moments of plate with the tensor of reinforced concrete forces or moments, respectively, we obtain the angle of cracks, the steel stresses and the forces or moments of concrete between the cracks. Derived equations are applied to plates reinforced with an orthogonal reinforcing net or with reinforcing bars in one direction. Experimental and theoretical results show a very good agreement.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Baumann, T., “Tragwirkung orthogonaler Bewehrungsnetze beliebieger Richtung in Flächentragwerken aus Stahlbeton,” Deutscher Ausschuss für Stahlbeton, Heft 217, W. Ernst u. Sohn, Berlin, Germany, 1972, 53 pp.
2.
Baus, R., and Tolaccia, S., “Calcul á la rupture des dalles en béton armé et étude experimentale du critère de rupture en flexion pure,” Annates de l' Institut du Batiment et des Travaux Publics, Paris, France, Sept., 1963, pp. 869–894.
3.
Bazânt, Z., and Tsubaki, T., “Concrete Reinforcing Net: Optimum Slip‐Free Limit Design,” Journal of the Structural Division, ASCE, Vol. 105, No. ST2, Proc. Paper 14344, Feb., 1979, pp. 327–346.
4.
Bazânt, Z., and Tsubaki, T., and Belytschko, T., “Concrete Reinforcing Net: Safe Design,” Journal of the Structural Division, ASCE, Vol. 106, No. ST9, Proc. Paper, Sept., 1980, pp. 1899–1906.
5.
Borg, S., Matrix Methods of Continuum Mechanics, D. Van Nostrand Company, Inc., New York, N.Y., 1963, 313 pp.
6.
Duchon, N., “Analysis of Reinforced Concrete Membrane Subject to Tension and Shear,” American Concrete Institute Journal, Proceedings, Vol. 69, No. 9, Sept., 1972, pp. 578–583.
7.
Ebner, F., “Zur Bemessung von Stahlbetonplatten mit von der Richtung der Hauptzugspannung abweichender Bewehrungsrichtung,” Aus Theorie und Praxis des Stahlbetonbaus, W. Ernst u. Sohn, Berlin, Germany, 1969.
8.
Falconer, B. H., “Theory of Stresses Induced in Reinforced Concrete by Applied Two‐Dimensional Stress,” American Concrete Institute Journal, Proceedings, Vol. 53, No. 3, Sept., 1956, pp. 277–294.
9.
Fialkow, M. N., “Strength Design of Shell Membrane Reinforcement,” Journal of Structural Engineering, ASCE, Vol. 109, No. ST4, Apr., 1983, pp. 891–908.
10.
Gupta, A., and Sen, S., “Design of Flexural Reinforcement in Concrete Slabs,” Journal of the Structural Division, ASCE, Vol. 103, No. ST4, Proc. Paper 12888, Apr., 1977, pp. 793–804.
11.
Gupta, A., “Membrane Reinforcement in Shells,” Journal of the Structural Division, ASCE, Vol. 107, No. ST1, Jan., 1981, pp. 41–56.
12.
Kuyt, B., “Zur Frage der Netzbewehrung von Flächentragwerken,” Beton and Stahlbetonbau, Vol. 59, No. 7, 1964, pp. 158–163.
13.
Leitz, H., “Eisenbewehrte Platten bei allgemeinen Biegungszustand,” Die Bautechnik, Vols. 16 and 17, 1923.
14.
Lenschow, R., and Sozen, M., “A Yield Criterion for Reinforced Concrete Slabs,” American Concrete Institute Journal, Proceedings, Vol. 64, No. 5, May, 1967, pp. 266–273.
15.
Leonhardt, F., and Schelling, G., “Torsionsversuche am Stahlbetonbalken,” Deutscher Ausschuss für Stahlbeton, Heft 239, W. Ernst u. Sohn, Berlin, Germany, 1974.
16.
Peter, J., “Zur Bewehrung von Scheiben und Schalen für Hauptspannungen schiefwinklig zur Bewehrungsrichtung,” Die Bautechnik, Vol. 43, No. 5, 1966, pp. 149–154;
Vol. 43, No. 7, 1966, pp. 240–248.
17.
Rosenblueth, E., “Shell Reinforcement Not Parallel to Principal Stresses,” American Concrete Institute Journal, Proceedings, Vol. 52, No. 1, 1955, pp. 61–71.
18.
Sholz, G., “Zur Frage der Netzbewehrung von Flächentragwerken,” Beton und Stahlbetonbau, Vol. 53, No. 10, 1958, pp. 250–255.
19.
Vecchio, F., and Collins, M. P., “The Response of Reinforced Concrete to In‐Plane Shear and Normal Stresses,” Univ. of Toronto, Department of Civil Engineering, Publication No. 82‐03, Mar., 1982, 332 pp.
Information & Authors
Information
Published In
Copyright
Copyright © 1986 ASCE.
History
Published online: Aug 1, 1986
Published in print: Aug 1986
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.