基于挠度的体外预应力梁应力增量统一算法

A unified algorithm for calculating stress increment of external tendons based on deflection

体外预应力筋应力增量的计算,是体外预应力结构在两种极限状态设计中的关键问题之一。由结构变形前后的几何关系,推导弹性阶段体外预应力筋应力增量的计算公式,并以此建立力筋应力增量与梁体跨中挠度的关系,进一步延伸到承载力极限状态力筋应力增量的计算,使体内、体外无黏结预应力筋在两种极限状态下应力增量的计算得到统一。公式考虑组合荷载作用的情况,并反映二次效应的影响。在以上推导的基础上,建立极限状态下应力增量计算的实用方法,方便工程应用;对美国学者Naaman所提出的黏结折减系数法进行改进,从理论上推导极限状态下的黏结折减系数;从减小二次效应的角度,对转向块的布置位置进行优化。最后,应用该方法与国内外3批试验进行对比,计算结果与试验结果吻合良好。

To determine the stress increment of external tendons is the key issue in designing externally prestressed structures under the service and ultimate limit states. Formulae for calculating the stress increment of external tendons are derived for externally prestressed beams under the service limit states. By establishing the relationship between the strain of tendons and the midspan deflection of the beams, the proposed formulae can be further extended to the ultimate limit states. A unified algorithm for calculating stress increment of external tendons is developed, which is suitable to both service and ultimate limit states, and also applicable to internal unbonded tendons. The proposed algorithm is shown to be capable of properly accounting for the second order effect and different types of loadings or their combinations. Additional studies are carried out based on the above analysis： 1） development of a practical method for computing the stress increment of tendons in ultimate limit states, 2） modification to Naaman＇s bond reduction coefficient, and 3） optimization to the arrangement of the deviators for minimization of the second-order effect. The accuracy of the proposed algorithm is verified through comparisons with experimental results in the literature.