Fracture Mechanics Approach for Failure of Concrete Shear Key. I: Theory
Publication: Journal of Engineering Mechanics
Volume 119, Issue 4
Abstract
The objective of this paper is to develop a simple mechanical model for the analysis and design of plain or fiber‐reinforced concrete shear key joints. The method makes use of well‐known results of fracture mechanics and truss model theory, combined in a simple model. The analysis employs a single discrete crack model under wedging force and a smeared crack model under remote shear force. The proposed formulation identifies two main fracture mechanisms for shear‐off failure of key joints: single curvilinear cracking and development of multiple diagonal cracks. Furthermore, as a first step in developing design aids for the shear strength of shear keys, a simple design formula is obtained. The procedures developed in this study would be useful in designing shear key joints according to the precast concrete segmental method of construction, which is becoming increasingly popular.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ashby, M. F., and Hallam, S. D. (1986). “The failure of brittle solids containing small cracks under compressive stress states.” Acta Metall., 34(3), 497–510.
2.
Bakhoum, M. M. (1991). “Shear behavior and design of joints in precast concrete segmental bridges,” PhD thesis, Massachusetts Institute of Technology, Cambridge, Mass.
3.
Barr, B., and Derradj, M. (1990). “Numerical study of a shear (mode II) type test specimen geometry.” Eng. Fract. Mech., 35(1/2/3), 171–180.
4.
Bazant, Z. P., and Oh, B. H. (1983). “Crack band theory for fracture of concrete.” Mater. Struct., 16, 155–177.
5.
Bazant, Z. P., and Pfeiffer, P. A. (1986). “Shear fracture tests of concrete.” Mater. Struct., 19, 111–121.
6.
Beattie, S. M., Buyukozturk, O., and Bakhoum, M. M. (1989). “Structural behavior improvements in joints of PCSB through the use of steel fibers.” Res. Report No. R89‐03, Dept. of Civ. Engrg., Massachusetts Inst. of Tech., Cambridge, Mass.
7.
Bhide, S. B., and Collins, M. P. (1987). “Reinforced concrete elements in shear and tension.” Publication 87‐02, Dept. of Civ. Engrg., Univ. of Toronto, Toronto, Canada.
8.
“Building code requirements for reinforced concrete.” (1989). ACI 318‐89. American Concrete Institute, Detroit, Mich.
9.
Chen, W. F. (1982). Plasticity in reinforced concrete. McGraw‐Hill Book Company, New York, N.Y.
10.
Cholewicki, A. (1971). “Loadbearing capacity and deformability of vertical joints in structural walls of large panel buildings.” Building Sci., 6, 163–184.
11.
Davies, J. (1988). “Numerical study of punch‐through shear specimen in mode II testing for cementitious materials.” Int. J. Cem. Compos. Lightweight Concr., 10(1), 3–14.
12.
Einstein, H. H., and Dershowitz, W. S. (1990). “Tensile and shear fracturing in predominantly compressive stress fields—A review.” Eng. Geol., 29(2), 149–172.
13.
Erdogan, F., and Sih, G. C. (1963). “On the crack extension in plates under plane loading and transverse shear.” J. Basic Engrg., 85, 519–527.
14.
Freund, L. B. (1978). “Stress intensity factor calculations based on a conservation integral.” Int. J. Solids Struct., 14, 241–250.
15.
Hartranft, R. J., and Sih, G. C. (1973). “Alternating method applied to edge and surface crack problems.” Mechanics of Fracture, Noordhoff International Publishing, Netherlands, 179–238.
16.
Hillerborg, A. (1980). “Analysis of fracture by means of the fictitious crack model, particularly for fibre reinforced concrete.” Int. J. Cem. Compos. Lightweight Concr., 2(4), 177–184.
17.
Hillerborg, A. (1985a). “Determination and significance of the fracture toughness of steel fibre concrete.” Proc. Steel Fiber Concrete US‐Sweden Joint Seminar (NSF‐STU), S. P. Shah and A. Skarendahl, eds., Jun. 3–5.
18.
Hillerborg, A. (1985b). “Numerical methods to simulate softening and fracture of concrete.” Fracture mechanics of concrete: Structural application and numerical calculation. G. C. Sih and A. DiTimmaso, eds., Martinus Nijhoff Publishers, 141–170.
19.
Hognestad, E. (1951). “A study of combined bending and axial load in reinforced concrete members.” Bulletin Series No. 399, Univ. of Illinois Engrg. Experimental Station, Nov., Ill.
20.
Horii, H., and Hemat‐Nasser, S. (1986). “Brittle failure in compression: Splitting, faulting and brittle‐ductile transition.” Philosophical Trans. of the Royal Society of London, 319, 337–374.
21.
Hsu, T. T. C., Mau, S. T., and Chen, B. (1987). “Theory of shear transfer strength of reinforced concrete.” ACI Struct. J., 84(2), 149–160.
22.
Ingraffea, A. R., and Panthaki, M. J. (1985). “Analysis of shear fracture tests of concrete beams.” U.S.‐Japan seminar on finite element analysis of reinforced concrete structures, Tokyo, May 21–24, 71–91.
23.
Kaneko, Y. (1992). “Modelling of shear‐off failure of concrete: Fracture mechanics approach,” PhD thesis, Massachusetts Institute of Technology, Cambridge, Mass.
24.
Kaneko, Y., Connor, J. J., Triantafillou, T. C., and Leung, C. K. (1993). “Fracture mechanics approach for failure of concrete shear key. II: Verification.” J. Engrg. Mech., ASCE.
25.
Kaneko, Y., and Li, V. C. (1993). “Fracture behavior of shear key structures with a softening process zone.” Int. J. of Fract.
26.
Kollegger, J., and Mehlhorn, G. (1987). “Material model for cracked reinforced concrete.” IABSE Reports 54, Coll. Comp. Mech. of Reinforced Concrete, Delft Univ. Press, 63–74.
27.
Koseki, K., and Breen, J. E. (1983). “Exploratory study of shear strength of joints for precast segmental bridges.” Res. Report. No. 248‐1, Ctr. for Transp. Res., Bureau of Engrg. Res., Univ. of Texas at Austin, Austin, Tex.
28.
Lim, T. Y., Paramasivam, P., and Lee, S. L. (1987a). “Analytical model for tensile behavior of steel‐fiber concrete.” ACI Mater. J., 84(4), 286–298.
29.
Lim, T. Y., Paramasivam, P., and Lee, S. L. (1987b). “Bending behavior of steel‐fiber concrete beams.” ACI Struct. J., 84(6), 524–536.
30.
Mansur, M. A., and Ong, K. C. G. (1991). “Behavior of reinforced fiber concrete deep beams in shear.” ACI Struct. J., 88(1), 98–105.
31.
Mattock, A. H. (1974). “Effect of aggregate type on single direction shear transfer strength in monolithic concrete.” Report No. SM74‐2, Dept. of Civ. Engrg., Univ. of Washington, Seattle, Wash.
32.
Mattock, A. H., and Hawkins, N. M. (1972). “Shear transfer in reinforced concrete‐recent research.” PCI J., 17(2), 55–75.
33.
Mattock, A. H., Li, W. K., and Wang, T. C. (1976). “Shear transfer in lightweight reinforced concrete.” PCI J., 21(1), 20–39.
34.
Petit, J.‐P. (1988). “Normal stress dependent rupture morphology in direct shear tests on sandstone with applications to some natural fault surface features.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 25(6), 411–419.
35.
Petit, J.‐P., and Barquins, M. (1988). “Can natural faults propagate under mode II conditions?” Tectonics, 7(6), 1243–1256.
36.
Rots, J. G. (1988). “Computational modelling of concrete fracture,” PhD thesis, Delft University of Technology, Delft, Netherlands.
37.
Rots, J. G., and Blaauwendraad, J. (1989). “Crack models for concrete: Discrete or smeared? Fixed, multi‐directional or rotating?” Heron, 34(1).
38.
Soroushian, P., Choi, K., and Alhamad, A. (1986). “Dynamic constitutive behavior of concrete.” ACI J., 83(2), 251–259.
39.
Vecchio, F. J., and Collins, M. P. (1986). “The modified compression‐field theory for reinforced concrete elements subjected to shear.” ACI J., 83(2), 219–231.
40.
Watkins, J., and Liu, K. L. W. (1985). “A finite element study of the short beam test specimen under mode II loading.” Int. J. Cem. Compos. Lightweight Concr., 7(1), 39–47.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 119 • Issue 4 • April 1993
Pages: 681 - 700
Copyright
Copyright © 1993 American Society of Civil Engineers.
History
Received: Aug 17, 1991
Published online: Apr 1, 1993
Published in print: Apr 1993
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.