A study of secondary moments and moment redistribution in continuous prestressed concrete beams

Abstract

Secondary or Parasitic internal bending moments in statically indeterminate continuous prestressed concrete beams are produced by the presence of the redundant reactions at the internal supports, assuming that the tendon profile does not coincide with the line of pressure produced in the concrete, i. e. that the tendon is not concordant. Whilst behaving in an elastic manner, these Secondary moments may be separated from the total internal bending moment (Secondary moment plus moment produced by applied loads) using various methods such as equivalent loads, together with a stiffness analysis. Beyond the Serviceability Limit State, the beam will begin to crack, altering the flexural stiffness as well as causing local increases in the tendon force, in turn altering the Secondary Moment. Therefore if the designer wishes to incorporate Moment Redistribution at the Ultimate Limit State, assuming that the critical sections have sufficient ductility, how to include Secondary Moments, if at all, is of much debate. Many different approaches have been adopted to shed light on the problem, the majority using nonlinear analyses of various forms. The advent of Finite Elements has seen an increase in their popularity for application to such nonlinear problems. This study begins with a Finite Element analysis of simply supported prestressed concrete beams, followed by an analysis of a two span example with a single curved tendon profile, fully bonded to the concrete, up to Ultimate Limit State. Although these analyses allowed an investigation of the overall nonlinear behaviour, the Secondary moment could not be separated from the Internal moment in the post cracking stage. As a result of the Finite Element Analyses, a method of applying equivalent loads past the Serviceability Limit State in an attempt to estimate the magnitude Secondary Moments up to the point where the beam is rendered statically determinate, was developed and utilised in a computer program. Two two-span beam examples and a three span beam, both with curved fully bonded parabolic tendon profiles were analysed to highlight the possible effects the secondary moment could have on the behaviour at Ultimate Limit State.

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