Bending Moment–Shear Force Interaction Domains for Prestressed Concrete Beams Antonino Recupero 1 ; Antonino D’Aveni 2 ; and Aurelio Ghersi 3 Abstract: The performance of a prestressed concrete beam, subjected to bending moment M together with shear force V, has been the object of many studies and is an important aspect to take into account in the design. Some models, proposed by researchers and international codes, evaluate the shear strength of prestressed beams by modifying the truss model by Morsch, so as to account for the different slope of stress fields in the web due to the prestressing action. More recent approaches add a strut-and-tie model to the traditional truss model. This paper generalizes a model that was previously proposed for box and I-shaped reinforced concrete cross sections of structural elements. The model, that now includes the effect of prestressing tendons, considers variable-depth stress fields applied to the cross section, subdivided into layers, and allows evaluation of normalized m–v design domains depending both on the web and flange reinforcement and on the slope of the prestressing steel tendons. The reliability of the method has been validated by comparing its numerical results to the strength provided by tests on reinforced concrete beams and on thin-webbed prestressed concrete beams, referred to in the literature. Finally, it has been used in the design of a pretensioned bridge beam to evaluate the additional reinforcement necessary in the flanges, as a function of the reinforcement provided to the web. DOI: 10.1061/ASCE0733-94452005131:91413 CE Database subject headings: Concrete beams; Concrete, prestressed; Design; Models; Trusses. Introduction The large majority of codes propose different models for rein- forced concrete structures and for prestressed elements ACI Committee 318 1983; EC2 1996. In the case of reinforced con- crete elements, the shear strength in the presence of axial force has been discussed by many authors, both referring to rectangular cross sections Mattock 1969; Haddadin et al. 1971 Puleri et al. 1991; Fanti and Mancini 1995 Puleri and Russo 1997; Mancini and Recupero 2000; ;  and to T- or I-shaped cross sections Re- cupero et al. 2003. Some of them proposed design formulations based on experimental results. Other researchers, starting from the stress fields approach by Bach et al. 1978, tried to obtain a more general model able to account for the simultaneous presence of different internal actions. Different models have been proposed to evaluate shear- prestressing interaction Schlaich et al. 1987; CEB-FIP 1993; Fanti and Mancini 1994; Fanti et al. 1995; Collins et al. 1996, once again obtaining design formulations by experimental results, or accounting for the prestressing tendons by adding a strut-and- tie model to the traditional truss model by Ritter and Morsch. The analytical model here proposed is the generalization of a previously proposed model for the the axial force-bending moment-shear force N–M–V interaction, based on the stress fields approach, which now includes the effect of prestressing tendons, thus providing a unified approach for reinforced concrete and prestressed concrete elements. The reliability of the model has been validated by comparing its numerical results both to experimental results already analyzed for reinforced concrete beams and to the strength values obtained by means of failure tests performed on thin-webbed prestressed concrete beams, re- ported by Tan and Ng 1998. Finally, it has been used in the design of a pretensioned bridge beam, so as to show how it allows the evaluation of the additional reinforcement necessary in top and bottom flanges, in function of the longitudinal reinforcement provided to the web. Analytical Model The actual distribution of axial and shear stress in a beam, close to collapse, cannot be easily foreseen, because of the strong cor- relation between flexural and shear failure. Nevertheless, the physical evidence given by deformations and cracks suggests the use of a simplified layered model, in which the flanges and the outmost portion of the web resist only to axial stresses, while the central portion of the web is subjected also to shear stresses Figs. 1 and 2. The ultimate resistance of a prestressed beam may thus be evaluated using a five-layer model, in which concrete and steel contributions are evaluated assuming that: • The concrete flanges and the top and bottom portions of the web having z 1 and z 2 depth, respectively are subjected to 1 Research Assistant, Dept. di Costruzioni e Tecnologie Avanzate, Univ. of Messina, Via Salita Sperone 31, 98166, Messina, Italy. E-mail: ninocosimo@tiscalinet.it 2 Associate Professor, Dept. di Ingegneria Civile ed Ambientale, Univ. of Catania, Viale Andrea Doria 6, 95100, Catania, Italy. E-mail: adaveni@tiscalinet.it 3 Professor, Dept. di Ingegneria Civile ed Ambientale, Univ. of Catania, Viale Andrea Doria 6, 95100, Catania, Italy corresponding author. E-mail: aghersi@dica.unict.it Note. Associate Editor: Dat Duthinh. Discussion open until February 1, 2006. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and possible publication on September 26, 2003; approved on November 1, 2004. This paper is part of the Journal of Structural En- gineering, Vol. 131, No. 9, September 1, 2005. ©ASCE, ISSN 0733- 9445/2005/9-1413–1421/$25.00. JOURNAL OF STRUCTURAL ENGINEERING © ASCE / SEPTEMBER 2005 / 1413