No abstract

Analysis of externally prestressed beams involves particular difficulty related to slip between the external tendon and deviator. Slip without friction is usually assumed to simplify the problem. A concise friction element located at the angle bisector between external tendon and deviator is constructed, to simulate the slip with or without friction between the tendon and deviator. The non-linear stress–strain relationships of concrete, steel and external tendon are considered; a trilinear model of the bending moment–axial force–curvature of the beam section is adopted, so that the behaviour of the externally prestressed beam up to ultimate state can be investigated. Calculations regarding a simply supported beam and continuous beam for various factors are conducted, including different friction coefficients, different areas of external tendon and steel bar, different eccentricities, symmetric or asymmetric load patterns. Results indicate that, for the simply supported beam and continuous beam under symmetric load, the friction effect on load-carrying capacity is negligible; the friction effect on maximum prestress increment and deflection may not be negligible; the friction effect on minimum prestress increment is obvious. For a continuous beam under asymmetric load, the friction effect on load-carrying capacity, maximum and minimum prestress increments and deflection cannot be neglected.

Considering precisely the second-order deformation of external tendon, the analytical solution of natural frequencies of 2-span externally prestressed continuous beam was obtained by the energy method. The effect of external prestress compression softening is between the zero effect of unbonded prestress compression and the effect of axial outside compression and is determined by the influence coefficient ranging within 0∼1. The influence coefficient is mainly related to the number of deviators and slightly related to tendon layout. Without deviator, the influence coefficient is 1, and the effect of external prestress compression softening is the same as the effect of axial outside compression. As the number of deviators increases, the influence coefficient gradually decreases from 1 to near 0, and the effect of external prestress compression softening is close to zero effect of unbonded prestress compression. With one or more deviators, the effect of external prestress compression softening is negligible. As the eccentricity and area of tendon increase, only the first symmetric frequency increases obviously, and other frequencies almost remain unchanged. The influence of tendon layout linear transformation on the frequency is negligible.

In this paper, the M-N-ƒÓ relationship of a beam section and the calculation of deformation for the externally prestressed tendon with large eccentricities are studied. A general method for analyzing the stress increment of external tendon and beam flexural behavior is presented. In this method, the action of external tendon is expressed as the equivalent loads applying at the deviators and anchorage ends. The beam not including external tendon is subjected to bending moment and axial force caused by both applied loads and equivalent loads. By comparing the different positions of deviators and anchorage ends before and after loading, the force of external tendon is obtained, the deformation compatibility of the external tendon is met, and the loss of tendon's eccentricity can be considered automatically. The calculation results conform well to the experimental results in reference [1].