Displacement-based simulation of time-dependent behaviour of RC beams with prestressed FRP or steel tendons

Abstract

Predicting the time-dependent behaviour of prestressed concrete (PC) beams is crucial as time effects under serviceability loading can result in a critical loss of prestress. The conventional technique using moment–curvature (M/χ) to simulate the behaviour of PC beams is based on the Euler-Bernoulli corollary of a linear strain profile in which all deformations are accommodated through changes in the material strain, i.e. it is strain based. Consequently, the M/χ approach cannot directly accommodate discrete deformations associated with tension stiffening, such as the formation of individual cracks and reinforcement slip. Hence, the M/χ approach can simulate the behaviour prior to cracking purely through mechanics. However, for post-cracking behaviour it requires empirically derived correction factors, such as empirically derived flexural rigidities, to allow for the deformations associated with tension stiffening. This paper presents a displacement- based moment–rotation (M/Θ) approach for determining the behaviour of PC beams by applying the Euler-Bernoulli theorem of plane sections, as opposed to the conventional M/χ approach of a linear strain profile. Being based on plane sections, the M/Θ approach deals directly with displacements and, consequently, can simulate the mechanics of tension stiffening directly. The approach is shown to accommodate the time effects of concrete creep, shrinkage and reinforcement relaxation and can develop equivalent flexural rigidities directly from mechanics.