A Smeared — Fixed Crack Model for FE Analysis of RC Membranes Incorporating Aggregate Interlock

Abstract

This paper reports the development of the cracked membrane model using a fixed-crack approach for the finite element modelling of orthogonally reinforced structural elements under plane stress. The model falls into the broad category of “compression field models” combining elemental components from the modified compression field theory with those of the tension chord model. The tension stiffening effect is developed using a steel-concrete bond relationship with its basis in limit analysis. With this approach the tension stiffening and tension softening components of the concrete tension resistance mechanism are decoupled allowing for rational models for each component. With adoption of a fixed crack formulation aggregate interlock along the cracks is explicitly modelled allowing for modelling of reinforced concrete members containing no or low quantities of steel reinforcement where slip along cracks significantly affects the results. For example, the modelling of shear critical beams containing low shear reinforcement volumes. The model has been incorporated into the finite element program for the analysis of reinforced concrete structures with verification of the finite element model presented.

Keywords

finite element reinforced concrete cracked membrane aggregate interlock

Get full access to this article

View all access options for this article.

References

Bresler

and Scordelis

A.C.

(1963). “Shear strength of reinforced concrete beams”, American Concrete Institute Journal, Vol. 60, No. 1, pp. 51–74.

Collins

M.P.

, and Porasz

(1989). “Shear strength for high strength concrete”, Bulletin No. 193, Design Aspects of High Strength Concrete, Comite Euro International du Beton (CEB), pp. 75–83.

Darwin

and Pecknold

D.A.

(1977). “Non-linear stress-strain law for concrete”, Journal of the Engineering Mechanics Division, ASCE, Vol. 103, No. 2, pp. 229–241.

Foster

S.J.

(1992). “An application of the arc length method involving concrete cracking”, International Journal for Numerical Methods in Engineering, Vol. 33. No. 2, pp. 269–285.

Foster

S.J.

and Gilbert

R.I.

(1990). “Non-linear finite element model for reinforced concrete deep beams and panels”, UNICIV Report No.R-275, School of Civil Engineering, University of New South Wales, Kensington, December, pp. 113.

Foster

S.J.

and Marti

(2002). “FE modelling of RC membranes using the CMM formulation”, Proceedings of the Fifth World Congress on Computational Mechanics, July, Vienna, Austria, Mang

H.A.

Rammerstorfer

F.G.

and Eberhardsteiner

, ed., Vienna University of Technology, Austria.

Foster

S.J.

and Marti

(2003). “Cracked membrane model: FE implementation”, Journal of Structural Engineering, ASCE, Vol. 129, No. 9, pp. 1155–1163.

Kaufmann

and Marti

(1998). “Structural concrete: Cracked membrane model”, Journal of Structural Engineering, ASCE, Vol. 124, No. 12, pp. 1467–1475.

Leonhardt

and Walther

(1966). Wandartige Träger, Bulletin No. 178, Wilhelm Ernst and Sohn, Berlin, pp. 159.

10.

Marti

Alvarez

Kaufmann

and Sigrist

(1998). “Tension chord model for structural concrete”, Structural Engineering International, International Association for Bridge and Structural Engineering, Vol. 4, No. 98, pp. 287–298.

11.

Petersson

P.E.

(1981). “Crack growth and development of fracture zone in plain concrete and similar materials”, Report no. TVBM-1006, Division of Building Materials, Lund Institute of Techonology, Lund, Sweden, pp. 174.

12.

Thorenfeldt

Tomaszewicz

and Jensen

J.J.

(1987). “Mechanical properties of high strength concrete and application in design”, International Symposium on Utilization of High Strength Concrete, Stavanger, Norway, pp. 149–159.

13.

Vecchio

F.J.

(2000). “Analysis of shear critical reinforced concrete beams”, American Concrete Institute Structural Journal, Vol. 97, No. 1, pp. 102–110.

14.

Vecchio

F.J.

and Collins

M.P.

(1982). “The response of reinforced concrete to in-plane shear and normal stresses”, Publication No. 82–03, Department of Civil Engineering, University of Toronto, Canada, March, pp. 332.

15.

Vecchio

F.J.

and Collins

M.P.

(1986). “The modified compression field theory for reinforced concrete elements subjected to shear”, American Concrete Institute Journal Proceedings, Vol. 83, No. 2, pp. 219–231.

16.

Walraven

J.C.

(1980). Aggregate Interlock: A Theoretical and Experimental Analysis, Delft University, Netherlands, pp. 200.