与有粘结相协调的无粘结预应力混凝土梁刚度及裂缝宽度计算方法

由于无粘结筋相对于其周围混凝土可发生纵向相对滑动,因此受弯构件中的无粘结筋对构件抗弯刚度的贡献及其对裂缝开展的抑制作用小于有粘结预应力筋。为了实现无粘结与有粘结预应力混凝土受弯构件刚度及裂缝宽度计算方法的协调和统一,提出了受弯构件中无粘结筋等效折减系数的概念,通过对无粘结预应力混凝土受弯构件的变形试验数据和按已有公式对设计试件的变形试算数据进行分析,得出了无粘结筋等效折减系数的建议取值(α=0.23)。用等效纵向受拉钢筋配筋率代替有粘结预应力混凝土受弯构件刚度计算公式中纵向受拉钢筋配筋率,用等效纵向受拉钢筋面积代替用于计算有粘结预应力混凝土受弯构件裂缝宽度的纵向受拉钢筋等效应力计算公式中的纵向受拉钢筋面积,就可分别得到与有粘结相协调的无粘结预应力混凝土受弯构件刚度及裂缝宽度计算公式,两公式计算结果与试验结果均吻合良好,可用于工程设计。

Calculation methods of stiffness and crack width of UPC beam in accordance with bonded PC beam

Because unbonded tendons can slip along the surrounding concrete, their contributions to flexural stiffness and restraint to growth of crack are smaller than those of bonded tendons in flexural member. To unify the calculation methods of stiffness and crack width of unbonded prestressed concrete (UPC) flexural member with those of bonded prestressed concrete (PC) flexural member, the conception of the equivalent reduced coefficient of unbonded tendons is presented, moreover, the recommended value (α=0.23) is proposed by analyzing the deformation data of model tests and simulated tests according to the existing formulas. The stiffness formula and crack width formula of UPC flexural member in accordance with bonded PC flexural member can be developed if the ratio of longitudinal tension reinforcement in the stiffness formula of bonded flexural member is replaced by the ratio of the equivalent longitudinal tension reinforcement, and the area of total longitudinal tension reinforcement in equivalent stress formula in calculating crack width formula of bonded flexural member is replaced by the equivalent area of longitudinal tension reinforcement. The calculated results by using these two formulas are in good agreement with test results and therefore they can be used in the design of civil engineering.