ORIGINAL ARTICLE Behaviour of concrete beams under torsion: NSC plain and hollow beams Luı ´s F. A. Bernardo Æ Se ´rgio M. R. Lopes Received: 24 May 2007 / Accepted: 20 September 2007 / Published online: 19 October 2007 Ó RILEM 2007 Abstract A simple computation procedure is devel- oped to predict the general behaviour of reinforced concrete beams under torsion. Both plain and hollow normal strength concrete beams are considered. Different theoretical models are used to reflect the actual behaviour of the beams in the various phases of loading. To pass from a phase to the following one, transition criteria need to be taken into consideration. Such criteria are explained. The theoretical predic- tions are compared with result from reported tests. Conclusions are presented. The main conclusion is that the calculation procedure described in this paper gives good predictions when compared with the actual behaviour of the plain and hollow beams. Keywords Reinforced concrete Beams Torsion Theoretical behaviour 1 Introduction The first studies on torsion of reinforced concrete beams were published in the beginning of the past century. Theoretical models were developed. These models can be divided into two main theories: the Skew–Bending Theory which was the base of the Amer- ican code between 1971 and 1995; and the Space Truss Analogy which is currently the base of the American code (since 1995) and of the European model code (since 1978). The newest theory is the Variable Angle Truss-Model which firstly aimed to unify the torsion design of small and large sections (for instance, small sections in buildings structures and large sections in bridges) and of reinforced and prestressed concrete. The first version of the model was presented by Rausch [29]. Other authors have contributed for new updated versions of the Model, such as: Andersen [3], Cowan [11], Lampert and Thurlimann [19], Elfgren [12], Collins and Mitchell [10]. The first versions of the model were complemented with the influence of the diagonal cracking on the compressive strength of the concrete struts (Softening Effect), as presented by Hsu and Mo [17, 18]. In 1973, Collins [9] has developed the Variable Angle Truss-Model using a different path, which was based on the compatibility of deformations, instead of the theory of plasticity. The next develop- ments of the model by Mitchell and Collins [10, 23, 24] and Vecchio and Collins [32, 33] led to the so called Modified Compression Field Theory (MCFT). In 1995 and in 1996, Rahal and Collins [25, 27] have reported L. F. A. Bernardo (&) Departamento de Engenharia Civil, University of Beira Interior, Edifı ´cio II das Engenharias, Calc ¸ada Fonte do Lameiro, 6201-001 Covilha, Portugal e-mail: [email protected] S. M. R. Lopes Departamento de Engenharia Civil, University of Coimbra, Polo II da Universidade, Pinhal de Marrocos, 3030, Coimbra, Portugal e-mail: [email protected] Materials and Structures (2008) 41:1143–1167 DOI 10.1617/s11527-007-9315-0
Behaviour of concrete beams under torsion: NSC plain and hollow beams
Jun 18, 2023
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