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Computers and Concrete Volume 3, Number 4, August 2006 , pages 213-233 DOI: https://doi.org/10.12989/cac.2006.3.4.213 |
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Saw-tooth softening/stiffening - a stable computational procedure for RC structures |
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Jan G. Rots, Stefano Invernizzi and Beatrice Belletti
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| Abstract | ||
| (Received December 21, 2005, Accepted May 3, 2006)rnAbstract. Over the past years techniques for non-linear analysis have been enhanced significantly via improved solution procedures, extended finite element techniques and increased robustness of constitutive models. Nevertheless, problems remain, especially for real world structures of softening materials like concrete. The softening gives negative stiffness and risk of bifurcations due to multiple cracks that compete to survive. Incremental-iterative techniques have difficulties in selecting and handling the local peaks and snap-backs. In this contribution, an alternative method is proposed. The softening diagram of negative slope is replaced by a saw-tooth diagram of positive slopes. The incremental-iterative Newton method is replaced by a series of linear analyses using a special scaling technique with subsequent stiffness/strength reduction per critical element. It is shown that this event-by-event strategy is robust and reliable. First, the model is shown to be objective with respect to mesh refinement. Next, the example of a large-scale dog-bone specimen in direct tension is analyzed using an isotropic version of the saw-tooth model. The model is capable of automatically providing the snap-back response. Subsequently, the saw-tooth model is extended to include anisotropy for fixed crack directions to accommodate both tensile cracking and compression strut action for reinforced concrete. Three different reinforced concrete structures are analyzed, a tension-pull specimen, a slender beam and a slab. In all cases, the model naturally provides the local peaks and snap-backs associated with the subsequent development of primary cracks starting from the rebar. The secant saw-tooth stiffness is always positive and the analysis always | ||
| Key Words | ||
| softening; saw-tooth softening; snap-back; sequentially linear analysis; cracking; fracture; reinforced concrete. | ||
| Address | ||
| Jan G. Rots; Faculty of Architecture and Faculty of Civil Engineering & Geosciences, Delft University of Technology, P.O.Box 5043, 2600 GA - Delft, The NetherlandsrnStefano Invernizzi; Department of Structural Engineering and Geotechnics, Politecnico di Torino, rnCorso Duca degli Abruzzi 24, 10129 - Torino, Italy. Also research fellow at TUDelft.rn Beatrice Belletti; Department of Civil and Environmental Engineering and Architecture, University of Parma, Parco Area delle Scienze 181/a, 43100 - Parma, Italy. Also research fellow at TUDelft. | ||