K.K.Pathak, Department of Civil and Environmental Engineering, NITTTR, Bhopal
Saleem Akhtar, Department of Civil Engineering UIT (RGPV), Bhopal
IntroductionApplications of prestressed concrete are many, especially in recent times, it has been widely used in bridges, buildings, rail sleepers, nuclear vessels, water and other liquid retaining structures etc. Prestressed concrete is a particular form of reinforced concrete in which external prestressing force is applied on the concrete to reduce or eliminate the tensile stresses and thereby control or eliminate cracking. Prestressed concrete is a typical set up of cable and concrete which makes a prestressed concrete section considerably stiffer than reinforced concrete section. In prestressed concrete, cable layout plays an important role in reducing tension from the concrete. Due to curvature, cable exerts forces on the concrete to counterbalance the forces causing tension. In curved tendons, upward force is imposed on the concrete which may reduce or eliminate the downward deflection as well; which is almost always the governing factor in structural design.
Akhtar et.al (2008) carried FEA analysis of prestressed concrete beams using B-spine cable profile for non friction conditions. Pathak et.al (2004) presented analysis of prestress concrete beam considering different cable models. Bapat et.al (2010 found cost effe ctiveness of HDPE sheathing for post tensioned prestressed concrete structures over galvanized metallic ducts. Lorenc et al.(2006) experimented the failure mechanisms and behavior of composite steel–concrete beams prestressed with external tendons subjected to positive bending. Özcan et al.(2009) carried out experimental and finite element analyses of the steel fiber-reinforced concrete (SFRC) beams. The results obtained from the finite element and experimental analyses were compared and found in good match. Chung et al.(2006) worked on the deflection estimation of a full scale prestressed concrete girder using long-gauge fiber optic sensors. It was demonstrated that long-gauge fiber optic sensors could provide the same accuracy with conventional sensors. Frederick et al.(2000) carried out experimental study on CFRP-prestressed high-strength concrete bridge beams. Fiber-reinforced polymer (FRP) tendons and reinforcing bars (rebar) were developed for use with concrete. FRP products are non-corrosive and lightweight when compared to traditional steel members. Zhanga et al (2009) attempted experimental and theoretical studies on composite steel concrete box beams with external tendons. Sung et al.(2009) established stress–strain and deflection relationships of RC beam bonded with FRPs under sustained load Fiber-reinforced polymer (FRP) systems that had a strong resistance against long-term deformation. Padmarajaiah et al. (2002) attempted finite element assessment of flexural strength of prestressed concrete beams with fiber reinforcement. Influence of fibers on the concrete failure surface and stress–strain response of high strength concrete and the nonlinear stress–strain curves of prestressing wire and deformed bar were considered. Padmarajaiah et al.(2004) carried out flexural strength predictions of steel fiber reinforced high-strength concrete in fully and partially prestressed beam specimens. These studies mainly attempted to determine the influence of trough-shaped steel fibers in altering the flexural strength at first crack and check the load–deflection and moment–curvature characteristics, ductility and energy absorption capacity of the beams. Cattaneo et al.(2012) investigated the flexural behavior of reinforced, prestressed and composite self-consolidating concrete beams. The flexural behavior at service stage and at ultimate limit state was experimentally studied by means of four-point bending tests on six beams. Eythor et al.(2011) tested prestressed concrete beams with BFRP (basalt fibred reinforced polymer) tendons. The main findings were that the stiffness and bearing capacity of the beam increased relative to un-prestressed beams.
In this paper the displacement behaviors of a double span indeterminate prestressed concrete beam have been studied numerically with analytical and numerical methods. A prestress concrete beam with parabolic cable profile for constant amount of prestressing force was analyzed by Macaulay's method, matrix method (STAAD.Pro) and finite element method (FEM) for constant amount of prestressing forces. For finite element method (FEM), cable is modeled as B-spline. The B-spline model represents the realistic cable profile. The results of these three methods were computed and results are critically analyzed and compared.
|Figure 1: Parabolic profile and Actual profile at juncture||Figure 2: B - spline Cable profile|
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