Integrated Finite Element Model for Reinforced Concrete Slabs
Publication: Journal of Structural Engineering
Volume 117, Issue 4
Abstract
The first step of the nonlinear procedure consists in finding the solution of the elasticity problem for a doubly reinforced concrete slab. Ten different cracking patterns are assumed in this formulation. Use of each pattern implies the division of slab thickness into several layers (maximum three layers of concrete). This enables the replacing of the summation of constituent stiffnesses over the layers, as is the case in the layered method, by the appropriate analytical or simple numerical integration through the total thickness. This method allows for the nonlinear analysis of relatively low numerical effort in comparison with layered analysis, although the tips of the considered cracks need not lie on the interfaces of the layers. Results obtained in the proposed approach are compared with experimental evidence from tests performed on deep beams and slabs published by other researchers.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abdel Rahman, H. H. (1982). “Computational models for the nonlinear analysis of reinforced concrete flexural slab systems,” thesis presented to the University College of Swansea, at Swansea, Wales, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
2.
Absi, E., and Brandt, A. M. (1974). “Analiza i badania płyt zelbetowych w stanie zarysowania (Analysis and test of reinforced concrete cracked slabs).” PWN, Warsaw, Poland (in Polish).
3.
Ahmad, M., and Bangash, Y. (1987). “A three‐dimensional bond analysis using finite element.” Computers and Struct., 25(2), 281–296.
4.
Andermann, F. (1966). “Tarcze prostokatne. Obliczenia statyczne (Rectangular panels: Static calculations).” Arkady, Warsaw, Poland (in Polish).
5.
Bashur, F. K., and Darwin, D. (1978). “Nonlinear model for reinforced concrete slab.” J. Struct. Div., ASCE, 104(1), 157–170.
6.
Bažant, Z. P., and Oh, B. H. (1983). “Deformation of cracked net‐reinforced concrete walls.” J. Struct. Engrg., ASCE, 109(1), 93–108.
7.
Bell, J. C., and Elms, D. G. (1971). “A finite element approach to post elastic slab behavior.” Special Publication SP30‐15, American Concrete Institute 325–344.
8.
Berg, S., Bergan, P. G., and Holand, I. (1973). “Nonlinear finite element analysis of reinforced concrete plates.” 2nd Int. Conf. on Struct. Mech. in Reactor Tech., Berlin, Germany, Vol. M3/5.
9.
Borcz, A. (1962). “O obliczaniu płyt żelbetowych zbrojonych niesymetrycznie (faza I) [Computation of unsymmetrically reinforced concrete panels (phase I).” (in Polish)]. Archiwum Inzynierii Ldowej, VIII(3), 341–364.
10.
Buyukozturk, O. (1977). “Nonlinear analysis of reinforced concrete structures.” Comp. and Struct., 7(1), 149–156.
11.
Buyukozturk, O., and Shareef, S. S. (1985). “Constitutive modelling of concrete in finite element analysis.” Comp. and Struct., 21(3), 581–610.
12.
Cedolin, L., Crutzen, Y. R. J., and Dei Poli, S. (1977). “Triaxial stress‐strain relationship for concrete.” J. of Engrg. Mech. Div., 103(3), 423–439.
13.
Cevera, H., Abdel Rahman, H. H., and Hinton, E. (1984). “Material and geometric nonlinear analysis of reinforced concrete plate and shell systems.” Proc., Int. Conf. on Computer‐Aided Analysis and Design of Concrete Struct., Split, Yugoslavia, 547–563.
14.
Clark, L. A., and Speirs, D. M. (1978). “Tension stiffening in reinforced concrete beams and slabs under short‐term load.” Tech. Report No. 42.521, Cement and Concrete Association, Wexham Springs, Slough, England.
15.
Cope, R. J., and Rao, P. V. (1977). “Nonlinear finite element analysis of concrete slab structures.” Proc., Inst. Civ. Engrs., Part 2, 63, 159–179.
16.
Cope, R. J., and Rao, P. V. (1983). “A two‐stage procedure for the nonlinear analysis of slab bridges.” Proc., Inst. Civ., Engrs., Part 2, 75, 671–688.
17.
Cope, R. J. (1984). “Material modelling of real, reinforced concrete slabs.” Proc., Int. Conf. on Computer‐Aided Analysis and Design of Concrete Struct., Split, Yugoslavia, 85–117.
18.
Floegl, H., and Mang, H. A. (1982). “Tension stiffening concept based on bond slip.” J. of Struct. Div., ASCE, 108(12), 2681–2701.
19.
Franz, G. (1970). “Über die Beanspruchung der Bewehrung bei kreuzweise bewehrten, vierseitig frei drehbar gelagerten Rechteckplatten aus Stahlbeton.” University of Karlsruhe, Untersuchungsbericht zum Forschungsauftrag F.505. Karlsruhe, German (in German).
20.
Gilbert, R. I., and Warner, R. F. (1978). “Tension stiffening in reinforced concrete slabs.” J. Struct. Div., ASCE, 104(12), 1885–1900.
21.
Grünberg, J. (1978). “Spannungszustände und mitwirkende Plattenbreite eines Stahlbeton‐Plattenbalken‐Tragwerks im gerissenen Zusandt.” Beton‐ und Stahlbetonbau (in German), 73(7), 177–181.
22.
Hand, R. F., Pecknold, D. A., and Schnobrich, W. C. (1973). “Nonlinear layered analysis of R/C plates and shells.” J. Struct. Div., ASCE, 99(7), 1491–1505.
23.
Jofriet, J. C., and McNeice, G. M. (1971). “Finite element analysis of reinforced concrete slabs.” J. Struct. Div., ASCE, 97(3), 785–806.
24.
Karpenko, N. I. (1976). “Deformerovanya zhelezobetona s treshchunamy (Theory of deformation of reinforced concrete with cracks).” Stroyizdat, (in Russian), Moscow, U.S.S.R.
25.
Kupfer, H. H., and Gerstle, K. H. (1973). “Behavior of concrete under biaxial stresses.” J. Engrg. Mech. Div., ASCE, 99(4), 853–866.
26.
Leonhardt, F., and Walther, R. (1966). “Wandertige Träger.” Deutscher Ausschuss für Stahlbeton (in German), Verlag von Wilhelm Ernst und Sohn, Berlin, Germany, Vol. 178.
27.
Lin, C. S., and Scordelis, A. C. (1975). “Nonlinear analysis of RC shells of general form.” J. Struct. Div., ASCE, 101(3), 523–538.
28.
Link, J. (1976). “Eine Formulierung des zweiaxialen Verformungs und Bruchver‐haltens von Beton under deren Anwendung auf die wirklichkeitsnahe Berechnung von Stahlbetonplatten.” Deutscher Ausschuss für Stahlbeton (in German), Verlag von Wilhelm Ernst und Sohn, Berlin, Germany, Vol. 270.
29.
Maj, M., and Trochanowski, A. (1983). “Metoda obliczania zelbetowych płkyt z rysami (The method of calculation of reinforced concrete plates with cracks).” Konferencja: Mechanika konstrukcji betonowych (Conf., Mech. of Concrete Struct.) (in Polish), 207‐211, Wrocław, Poland.
30.
Müller, G., Kabir, A. F., and Scordelis, A. C. (1978). “Nonlinear analysis of reinforced concrete hyperbolic paraboloid shells.” Contr. IASS Symp., Darmstadt 1978, Werner Verlag, Düsseldorf, Germany, 191–203.
31.
Owen, D. R. J., Figueiras, J. A., and Damjanic, F. (1983). “Finite element analysis of reinforced and prestressed concrete structures including thermal loading.” Comp. Meth. in Appl. Mech. and Engrg., 41(3), 323–366.
32.
Ramm, E., and Kompfner, T. A. (1984). “Reinforced concrete shell analysis using an inelastic large deformation finite element formulation.” Proc., Int. Conf. Computer‐Aided Analysis and Design of Concrete Struct., Split, Yugoslavia, 591–597.
33.
Schäfer, H., Link, J., and Mehlhorn, G. (1975). “Zur wirklichkeitsnahen Berechung von Stahlbetonplatten mit der Finite‐Element‐Methode.” Beton‐ und Stahlbetonbau (in German), 70(11), 265–273.
34.
Srinivasa Rao, P., and Subrahmanyam, B. U. (1973). “Trisegmental moment‐curvature relations for reinforced concrete members.” J. of A.C.I., (70‐39), 346–351.
35.
Vebo, A., and Ghali, A. (1977). “Moment‐curvature relation of reinforced concrete slabs.” J. Struct. Div., ASCE, 103(3), 515–531.
36.
Wanchoo, M. K., and May, G. W. (1975). “Cracking analysis of reinforced concrete plates.” J. Struct. Div., ASCE, 101(1), 201–215.
37.
Zerna, W., Mungan, I., and Steffen, W. (1980). “Bestimmung der Beulsicherheit von Schalen aus Stahlbeton unter Berücksichtigung der physikalisch‐nichtlinearen Materialeigenschaften.” Deutscher Ausschus für Stahlbeton (in German), Verlag von Wilhelm Ernst und Sohn, Berlin, Germany, Vol. 315.
38.
Zienkiewicz, O. C. (1977). The finite element method, 3rd Ed., McGraw‐Hill Book Co., London, England.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 117 • Issue 4 • April 1991
Pages: 1017 - 1038
Copyright
Copyright © 1991 ASCE.
History
Published online: Apr 1, 1991
Published in print: Apr 1991
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.