TECHNICAL PAPERS
Mar 1, 1999

Shear Design of Reinforced Concrete Deep Beams: A Numerical Approach

Publication: Journal of Structural Engineering
Volume 125, Issue 3

Abstract

A general framework aimed at dealing with the failure analysis of reinforced concrete beam-like structures is presented in this paper. It is based on the yield design theory combined with a “mixed modeling” of this kind of structure, according to which the concrete material is treated as a classical continuum, whereas the longitudinal reinforcements are regarded as elements working predominantly in tension. In addition, shear-reinforced web zones may be incorporated in the analysis through a homogenization procedure. Both lower- and upper-bound methods are then implemented numerically by means of a finite-element formulation, thus producing fairly accurate estimates for the load-carrying capacity of a shear loaded beam, taken as an illustrative application. In particular, it is shown that the shear-span-to-depth ratio, along with the amount of longitudinal reinforcement, play a crucial role in the transition from flexural to shear dominated failure modes of the beam. This conclusion is supported by numerous experimental observations reported in the literature. Numerical predictions even prove to be in good agreement with experimental results provided appropriate reduction factors be assigned to the concrete strength parameters, accounting for its brittleness under tensile loading conditions.

Get full access to this article

View all available purchase options and get full access to this article.

References

1.
Abdi, R. ( 1992). “Charges limites d'ouvrages en sol renforcé: Approches statique et cinématique.” PhD thesis, Université Joseph Fourier, Grenoble, France (in French).
2.
Abdi, R., de Buhan, P., and Pastor, J. ( 1994). “Calculation of the critical height of a homogenized reinforced soil wall: A numerical approach.” Int. J. Numer. and Analytical Methods in Geomech., 18, 485–505.
3.
Anthoine, A. ( 1989). “Mixed modelling or reinforced soils within the framework of the yield design theory.” Comp. and Geotechnics, 67–82.
4.
Ashour, A. F., and Morley, C. T. ( 1994). “The numerical determination of shear mechanisms in reinforced concrete beams.” The Struct. Engr., London, 72(23–24), 395–400.
5.
Ashour, A. F., and Morley, C. T. (1996). “Effectiveness factor of concrete in continuous deep beams.”J. Struct. Engrg., ASCE, 122(2), 169–178.
6.
Averbuch, D. ( 1996). “Approche du dimensionnement des structures en béton armé par le calcul à la rupture.” PhD thesis, École Nationale des Ponts et Chaussées, Paris (in French).
7.
“Building code requirements for reinforced concrete and commentary.” (1989). ACI 318-89, ACI Committee 318. American Concrete Institute, Detroit.
8.
Chen, W. F. ( 1982). Plasticity in reinforced concrete . McGraw-Hill, New York.
9.
de Buhan, P. ( 1985). “Critère de rupture macroscopique d'un matériau renforcé par armatures.” C. R. Acad. Sci. Paris, 301, Série II, 9, 557– 560 (in French).
10.
de Buhan, P. ( 1986). “Approche fondamentale du calcul à la rupture des ouvrages en sols renforcés.” PhD thesis, Université Pierre-et-Marie-Curie, Paris (in French).
11.
de Buhan, P. ( 1993). “Application of the yield design theory to the mechanics of reinforced soils.” Evaluation of global bearing capacities of structures, CISM Courses and Lectures N° 332, G. Sacchi Landriani and J. Salençon, Eds., Springer, Berlin, 46–90.
12.
de Buhan, P., and Salençon, J. ( 1993). “A comprehensive stability analysis of soil nailed structures.” Eur. J. Mech., A/Solids, 12(3), 325–345.
13.
de Buhan, P., and Taliercio, A. ( 1991). “A homogenization approach to the yield strength of composite materials.” Eur. J. Mech., A/Solids, 10(2), 129–154.
14.
Drucker, D. C. ( 1961). “On structural concrete and the theorems of limit analysis.” Int. Assoc. Bridge Struct. Engrg. Publ., 21.
15.
Johansen, K. W. ( 1943). Brudlinierteorier (Copenhagen) (Yield-line-theory). Cement and Concrete Association, London.
16.
Kani, G. N. J. ( 1964). “The riddle of shear failure and its solution.” ACI Proc., 61(4), 441–454.
17.
Kani, G. N. J. ( 1966). “Basic facts concerning shear failure.” ACI J., 63(6), 675–691.
18.
Kong, F. K., Robins, P., and Cole, D. ( 1970). “Web reinforcement effects on deep beams.” ACI J., 67(Dec.), 1010–1017.
19.
Kordina, K., and Blume, F. ( 1985). “Empirische Zusammenhänge zur Ermittlung der Schubtragfähigkeit stabförmiger Stahlbetonelemente.” Deutscher Ausschuss für Stahlbetonbau Heft 364. TU Braunschweig (in German).
20.
Kordina, K., and Hegger, J. ( 1987). “Zur Schubtragfähigkeit von Stahlbeton- und Spannbetonbalken.” Beton- und Stahlbetonbau, 1, 5–9 (in German).
21.
Marti, P. ( 1985a). “Basic tools of reinforced concrete beam design.” ACI J., 82(1), 46–56.
22.
Marti, P. ( 1985b). “Truss models in detailing.” Concrete Int., Dec., 66–73.
23.
Michalowski, R. L., and Zhao, A. (1996). “Failure of unidirectionally reinforced composites with frictional matrix.”J. Engrg. Mech., ASCE, 122(11), 1086–1092.
24.
Morrow, J., and Viest, I. M. ( 1957). “Shear strength of reinforced concrete frame members without web reinforcement.” ACI J., 53(9), 833–849.
25.
Mörsch, E. ( 1909). Der Eisenbetonbau, seine Anwendung und Theorie, 3rd Ed. McGraw-Hill, New York.
26.
Nielsen, M. P., Bræstrup, M. W., Jensen, B. C., and Bach, F. ( 1978). Concrete plasticity . Danish Society for Structural Science and Engineering, Lingby, Denmark.
27.
Nielsen, M. P. ( 1984). Limit analysis and concrete plasticity . Prentice-Hall, Englewood Cliffs, NJ.
28.
Pastor, J. ( 1978). “Analyse limite: Détermination numérique de solutions statiques complètes. Application au talus vertical.” J. de mécanique appliquée, 2(2), 176–196 (in French).
29.
Pastor, J. ( 1983). “Application de la théorie de l'analyse limite aux milieux isotropes et orthotropes de révolution. Formulation numérique de l'approche statique par la méthode des éléments finis.” Thèse de Doctorat d'Etat, U.S.M.G.-I.N.P.G., Grenoble (in French).
30.
Ritter, W. ( 1899). “Die Bauweise Hennebique. Schweizerische Bauzeitung.” (Zürich) 33(7), 59–61 (in German).
31.
Rogowsky, D., MacGregor, J., and Ong, S. ( 1986). “Tests of reinforced concrete deep beams.” ACI J., 83(4), 614–623.
32.
Salençon, J. ( 1990). “An introduction to the yield design theory and its application to soil mechanics.” Eur. J. Mech., A/Solids, 9, 477–500.
33.
Schlaich, J., Schäfer, K., and Jennewein, M. ( 1987). “Toward a consistent design of structural concrete.” PCI J., 32(3), 74–150.
34.
Siao, W. B. ( 1993). “Strut-and-tie model for shear behavior in deep beams and pike caps failing in diagonal splitting.” ACI Struct. J., 90(4), 356–363.
35.
Siao, W. B. ( 1994). “Shear strength of short reinforced concrete walls, corbels and deep beams.” ACI Struct. J., 91(2), 123–132.
36.
Siao, W. B. ( 1995). “Deep beams revisited.” ACI Struct. J., 92(1), 95–102.
37.
Sloan, S. W. ( 1988). “Lower bound limit analysis using finite elements and linear programming.” Int. J. Num. Anal. Methods in Geomechanics, 12, 61–77.
38.
Sloan, S. W. ( 1989). “Upper bound limit analysis using finite elements and linear programming.” Int. J. Numer. Analytical Methods in Geomech., 13, 263–282.
39.
Smith, K. N., and Vantsiotis ( 1982). “Shear strength of deep beams.” ACI J., 79(3), 201–213.
40.
Suquet, P. ( 1985). “Elements of homogenization for inelastic solid mechanics.” Homogenization techniques for composite media. C.I.S.M., Springer, Udine, Italy, 193–278.
41.
Turgeman, S. ( 1983). “Contribution au calcul des charges limites en milieux isotropes et orthotropes de révolution par une approche cinématique numérique.” Thèse de Doctorat d'Etat, U.S.M.G.-I.N.P.G., Grenoble, France (in French).
42.
XPRESS-MP reference manual . (1984–1995). Dash Associates, Blisworth, U.K.
43.
Zienkiewicz, O. C. ( 1994). The finite element method, 4th Ed., McGraw-Hill, London.

Information & Authors

Information

Published In

Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 125Issue 3March 1999
Pages: 309 - 318

History

Received: Jul 22, 1997
Published online: Mar 1, 1999
Published in print: Mar 1999

Permissions

Request permissions for this article.

Authors

Affiliations

Res. Engr., Institut Français du Pétrole, 1 et 4 avenue de Bois-Préau, 92852 Rueil-Malmaison Cédex, France; formerly, Laboratoire de Mécanique des Solides, (URA 317 Centre National de la Recherche Scientifique), Ecole Nationale des Ponts et Chaussées–Centre d'Enseignement et de Recherche en Calcul des Structures et des Ouvrages, 6 et 8 avenue B. Pascal, Cité Descartes Champs-sur-Marne, 77455 Marne-la-Vallée Cedex 2, France.
Prof. in Struct. Des., École Nationale des Ponts et Chaussées, Head of Centre d'Enseignement et de Recherche en Calcul des Structures et des Ouvrages (Res. Ctr. for Struct. Des.), Ecole Nationale des Ponts et Chaussées, 6 et 8 avenue B. Pascal, Cité Descartes Champs sur Marne, 77455 Marne-la-Vallée Cedex 2, France.

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.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share