Prediction of Distributed Discrete Concrete Cracking in RC Analysis
Publication: Journal of Structural Engineering
Volume 119, Issue 10
Abstract
The approach presented in this paper is considered a viable alternative for the prediction of distributed discrete concrete cracking. Cracks are confined to the edges of elements of the mesh. Different crack‐initiation criteria are used for concrete and concrete‐steel interfaces. A discontinuous linear relation between crack width and tensile stress is proposed. Link elements are installed to connect the faces of a crack. The tensile stress associated with the crack is integrated along crack faces to obtain equivalent nodal forces. These nodal forces are then used to evaluate the stiffness of the link elements. The procedure is automated for iterative analysis. Crack‐width control and fracture‐energy control are proposed as auxiliary solution constraints to deal with convergence problems. Identification and treatment of mechanisms is proposed to avoid mechanism singularities in the solution process. An example application demonstrates the capability of the approach to predict the pattern of progression of dominant cracks, the interface behavior, and the correlation between these and specimen behavior.
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References
1.
Bathe, K. J., and Dvorkin, E. N. (1983). “On the automatic solution of nonlinear finite element equations.” Comp. & Struct., 17(5–6), 871–879.
2.
Batoz, J. L., and Dhatt, G. (1979). “Incremental displacement algorithm for nonlinear problems.” Int. J. Numer. Meth. Engrg., 14(8), 1262–1267.
3.
Bazant, Z. P. (1985). Mechanics of fracture and progressive cracking in concrete structures, fracture mechanics of concrete: structure application and numerical culation. G. C. Sih and A. Ditommaso, eds., Martinus Nijhoff Publishers, Dordrecht, The Netherlands, 25, 28.
4.
Bellini, P. X., and Chulya, A. (1987). “An improved automatic incremental algorithm for the efficient solution of nonlinear finite element equations.” Comp. & Struct., 26(1–2), 99–110.
5.
Broms, B. B. (1965). “Technique for investigation of internal cracks in reinforced concrete members.” ACI J., 62(1), 35–44.
6.
Broek, D. (1986). Elementary engineering fracture mechanics. 4th ed. (revised ed.), Martinus Nijhoff Publishers, Boston, Mass., 18, 103.
7.
Cedolin, L., Darwin, D., Ingraffea, A. R., Pecknold, E. A., and Schnobrich, W. C. (1982). “Chapter 4: Concrete Cracking.” Finite element analysis of reinforced concrete, ASCE, New York, N.Y., 204.
8.
Crisfield, M. A. (1981). “A fast incremental/iterative solution procedure that handles snap‐through.” Comput. Struct., 13(1), 55–62.
9.
Gerstle, W., Ingraffea, A. R., and Gergely, P. (1982). “The fracture mechanics of bond in reinforced concrete.” Department of structural engineering report 82‐7, School of Civ. and Envir. Engrg., Cornell Univ., Ithaca, N.Y., 144.
10.
Gopalaratnam, V. S., and Shah, S. P. (1985). “Softening response of plain concrete in direct tension.” J. Am. Concrete Inst., 82(3), 310–323.
11.
Goto, Y. (1971). “Cracks formed in concrete around deformed tension bars.” ACI J., 68(4), 244–251.
12.
Hillerborg, A. (1985). “Numerical method to simulate softening and fracture of concrete.” Fracture mechanics of concrete: structural application and numerical calculation, G. C. Sih and A. Ditommaso, eds., Martinus Nijhoff Publishers, Dordrecht, The Netherlands, 144.
13.
Ingraffea, A. R., and Saouma, V. (1985). “Numerical modeling of discrete crack propagation in reinforced and plain concrete.” Fracture mechanics of concrete: structural application and numerical calculation, G. C. Sih and A. Ditommaso, eds., Martinus Nijhoff Publishers, Dordrecht, The Netherlands, 171–225.
14.
Mirza, M. S., and Houde, J. (1979). “Study of bond stress‐slip relationships in reinforced concrete.” ACI J., 76(1), 19–46.
15.
Ngo, D., and Scordelis, A. C. (1967). “Finite element analysis of reinforced concrete beams.” J. Am. Concrete Inst., 64(14), 152–163.
16.
Ngo, D. (1975). “A network‐topological approach for the finite element analysis of progressive crack growth in concrete members,” PhD. dissertation, Univ. of California, Berkeley, Calif.
17.
Nilson, A. H. (1972). “Internal measurement of bond slip.” ACI J., 69(7), 439–441.
18.
Schweizerhof, K. H., and Wrigger, P. (1986). “Consistent linearization for path following methods in nonlinear FE analysis.” Comp. Methods in Appl. Mech. and Engrg., 59(1), 261–279.
19.
Watstein, P., and Mathey, R. G. (1959). “Width of cracks in concrete at the surface of reinforcing steel evaluated by means of tensile bond specimens.” ACI J., 56(1), 47–56.
20.
Yao, B., and Murray, D. W. (1992). “Finite element analysis of distributed discrete concrete cracking.” Structural rep. no. 179, Dept. of Civil Engineering, University of Alberta, Edmonton, Alberta, Canada.
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Copyright © 1993 American Society of Civil Engineers.
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Received: Sep 2, 1993
Published online: Oct 1, 1993
Published in print: Oct 1993
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