Nonlinear analysis of concrete shells including effects of normal and transverse shear stresses

Abstract

The previously developed numerical model of the authors for the analysis of conventional reinforced and prestressed concrete shells under short-term and long-term loading was improved by including the effects of transverse shear stresses on the shell failure. The 9-node degenerated shell element with the layered material model through the thickness of the shell was used. The reinforcement was modelled as a separate layer. To include the effect of transverse shear stresses on the shell failure, the failure criterion for concrete and longitudinal reinforcement was defined by a relation of transverse shear stresses and normal stresses in two mutually perpendicular vertical planes. The total transverse shear bearing capacity of the shell crosssection is obtained by summing up the concrete and reinforcement contributions. The developed numerical model and appropriate software were verified based on experimental tests. Das von denAutoren kürzlich entwickelte numerische Modell zur Analyse von konventionell verstärkten und vorgespannten Betonschalen unter Kurzzeit-und Langzeitbelastung wurde durch Berücksichtigung der Effekte in Folge der Querschubspannungen verbessert. Das degenerierte Schalenelement mit 9 Knoten mit einem schichtweisen Materialmodell über die Dicke wurde verwendet. Die Verstärkung wurde als eine eigene Schicht modelliert. Um die Effekte der Querschubschubspannungen auf das Schalenversagen zu berücksichtigen, wurde ein Versagenskriterium für Beton und die Längsverstärkung definiert, die die Querschubschubspannungen und die Normalspannungen in zwei zueinander senkrechten Ebenen beinhaltet. Die gesamte Lasttragfähigkeit auf Grund des Querschubs wird durch Summation der Beiträge von Beton und Verstärkung erhalten. Das entwickelte numerische Modell und das entsprechende Programm wurden mittels experimenteller Versuche verifiziert. Schlüsselwörter: Betonschale / Querschub / Schubfestigkeit / Experiment / numerisches Modell

Numerički model za analizu prednapetih provješenih mostovaSažetak

“…The model is a compilation and upgrade of the previously developed numerical models for the static and dynamic analysis of structures and for the analysis of structures under a long-term load [9][10][11][12][13][14][15][16][17]. The model upgrade consists in its capability to model stages construction of structures, in a more accurate modelling of shear failure of concrete, and in more efficient calculation procedures.…”

“…In the scope of an iterative time algorithm, an increase in shrinkage strain between two neighbouring times t n and t n+1 can be determined as follows: (16) where the coefficients correspond to times t n and t n+1 . In the context of the shell problem under consideration, it is assumed that the concrete shrinkage takes place in defined orthogonal directions x, y in the shell plane and, at that, shrinkage strain increments are calculated for particular directions as shown for the one-dimensional problem.…”

“…to include the lowest possible number of parameters. Assumptions adopted in the structural material models, and assumptions regarding the geometry of the structure, its construction stages, loads and actions, and design algorithms, are such that the presented numerical model still ensures a very good correspondence with numerous experimental results and results of other numerical models, even for the cases of deep nonlinear behaviours (see references [9][10][11][12][13][14][15][16][17]). Nevertheless, an additional verification of this model is considered necessary.…”

Development of CSMM-based shell element for reinforced concrete structures

“…Since the 1970's, many researchers have proposed an analytical model to predict the behavior of RC shell structures using the finite element method. The main approach used by most researchers is to develop a reinforced concrete shell element by combining a rational constitutive model of reinforced concrete material into finite element formulations of a general shell element with layer approaches (Hand, Pecknold [2]; Cervera, Hinton [3]; Scordelis and Chan [4]; Hu and Schnobrich [5]; Polak and Vecchio [6]; Kim, Lee [7]; Zhang, Bradford [8]; Lee [9]; Xiang, Mo [10]; Gopinath, Iyer [11], Matešan, Radnić [12], Hrynyk and Vecchio [13], and Lu, Xie [14]). The main problem faced by most researchers in the analysis of RC shell structures using the finite element method was that it often required expensive computational time due to the complicated material models and the difficulties encountered in the stability and accuracy of the solutions.…”