In the precast prestressed concrete frame assembled by post-tensioning unbonded tendons with ungrouted sheaths, called an unbonded PCaPC frame, the beam rotates against the column face as a rigid body, causing remarkable opening at a connecting interface between a precast concrete column and a beam with scarce residual deformation. This can be achieved by the post-tensioning unbonded tendon, since its tensile strain is kept constant over the whole length. The unbonded PCaPC frame is designed as a strong column-weak beam system, so an accurate and simplified evaluation method for the ultimate flexural strength and deformation of the beam is necessary to mitigate earthquake damage. Attempts to estimate these values were carried out in previous studies. However, most studies dealt with an isolated beam removed from a moment-resisting frame, which cannot well reflect the precise seismic behavior of actual frames. In addition, they also requires a complicated mathematical calculation.
In this study, therefore, a macro-model, which can reproduce the flexural behavior of the cruciform unbonded PCaPC subassemblage, is proposed to evaluate the ultimate flexural strength and deflection of the beam, whose unbonded tendons are placed symmetrically at the top and the bottom. An accurate and simplified estimation method for the ultimate flexural strength and deflection is then proposed based on the macro-model. These values predicted by the method are finally compared with previous experimental results to verify its validity. The proposed macro-model and general findings taken from this study can be summarized as follows.
(1) In the macro-model, after an opening occurs at the beam-column interface due to bending moment, the beam rotates as a rigid body. Beam axial deformation resulting from compressive strain, which develops at the extreme compression fiber along the entire length of the beam, is supposed to concentrate on the beam end. Concrete on the compressive side of a beam is shortened at a tendon position, and the opening at the beam-column interface contributes primarily to elongation of the beam at a tendon position on the tensile side.
(2) The evaluation formula for the ultimate flexural strength and deflection of a beam was proposed based on the plane section assumption at the beam end and the following conditions; the sum of axial deformation attributed to both the concrete shortening and the opening distance at the beam-column interface at the tendon position in a cruciform subassemblage is equal to the total elongation of the tendon, and the tensile and compressive resultant force in a beam section is the same.
(3) In the evaluation formula, the distance from extreme compression fiber to neutral axis in a beam section at the beam flexural strength, defined as xn, is a crucial factor to calculate the beam strength and deflection. To obtain xn, therefore, both an iterative method and a simplified manner were introduced.
(4) Predicted ultimate flexural strength and deflection of a beam by the proposed method showed a good agreement with the previous experimental results. The discrepancy between the calculated and observed ultimate flexural strength remained in a range of ±10%, and that of the ultimate beam deflection remained within ±15%.
(5) Since the distance xn, obtained from the simplified manner aforementioned, tended to be slightly greater than that from the iterative method, the ultimate flexural strength and deflection of a beam by the simplified manner were found to be somewhat smaller than those by the iterative method. However, their discrepancy remained in a range of ±5% for both the ultimate flexural strength and deflection when the prestressing ratio of a tendon to its yield strength is greater than 0.6, which is generally accepted in an actual construction.
