Finite Element Modeling and Analytical Study on the Behavior of Beams Prestressed with Unbonded Tendon

Abstract

There are two types of unbonded prestressed concrete beams according to tendon layout: unbonded internally prestressed concrete beam and externally prestressed concrete beams. Because of the advantages of simple construction, structural safety and economy, the unbonded prestressing technique has been widely used in the new construction of large civil engineering structures. Also, Many engineering structures at service especially bridges are suffering from fatigue or structural harm due to structure aging, corrosion of reinforcement bar and overweight. It is very effective to strengthen these harmed or fatigue structures using the externally prestressing technique. Analysis of beams prestressed with unbonded tendon is much more complicated than that of bonded concrete beams. As to bonded concrete beams, complete bond between steel and concrete is always assumed, so analysis can be performed based on plane section hypothesis. However, the strain compatibility between tendon and its adjacent concrete is no longer valid when unbonded internally or externally unbonded concrete beams are analyzed. The precise analysis of unbonded beams performed should be based on structural compatibility condition using iterative method. In this dissertation, analysis model for beams prestressed with internal unbonded or external tendon based on large deformation finite element theory is developed, and material and geometrical nonlinearities are involved. By replacing the effect of internal unbonded or external tendon with equivalent nodal loads of beam element, analysis can be performed with ordinary bonded reinforced concrete beams, whose internal forces are caused by externally applied loads and equivalent nodal loads from unbonded tendon together. Fibre integration method is initially proposed to cope with arbitrary concrete section of beam element and to derive the section tangent stiffness matrix. Computational efficiency is remarkably improved. Conventional strip method is also utilized in this dissertation. Based on these, standard finite element formulae are established by utilizing nonlinear plane beam element. Two numerical examples are analyzed to verify the validity of the proposed model. It is difficult to analyze unbonded prestressed beams by commercial finite element programs with conventional methods. To solve this problem, a commercial finite element program, ABAQUS, was used to develop an analysis model for concrete beams prestressed with internal unbonded or external tendon. The finite element model included two types of main element: beam element for concrete and truss element for internal unbonded or external tendon. The end nodes of main elements were connected with internal constraints named MPC in ABAQUS. Spring elements with very large stiffness were set up at the place of the deviators of externally prestressed beams, or along the span with relatively little space of unbonded internally prestressed beams. The modified Riks method is utilized to trace the entire structural response of beams prestressed with unbonded tendon from zero to ultimate loads. The reliability of the analysis model is verified by analytical results of typical test beams in comparison with experimental ones. Eight series 76 beams prestressed with internal unbonded tendon and two series 21 beams prestressed with external tendon and 3 comparative beams prestressed with internal unbonded tendon are designed to conduct parametric study. The designed beams are analyzed using the finite element model proposed in this dissertation. Influence of various parameters including ratio of nonprestressed reinforcement, ratio of unbonded prestressing tendon, span-depth ratio, effective prestress, cylindrically compressive strength of concrete, ultimate tensive strength of prestressing tendon, yield strength of nonprestressed reinforcement and loading pattern on the behavior of unbonded prestressed concrete beams and the ultimate stress in tendon, fps, are investigated in detail. Parameters having important influence on second-order effects of externally prestressed concrete beams as deviators, tendon configuration and load type are evaluated. The study makes an in-depth understanding and recognition on the working behavior and structural mechanism of beams prestressed with internal unbonded or external tendon. Therefore, a sound basis is offered for optimal design of unbonded prestressed beams and for future modification in new code equation for fps.