Recent studies have revealed the complex characteristics of cracking torques, T_cr, in prestressed concrete (PC). The distribution pattern of the longitudinal prestressing tendons in the cross-section is an important factor, but it is not considered in any methods. Recent studies have also shown that a PC-T_cr can be expressed in terms of the prestress ratio and a T_cr value calculated using an existing rational formula for reinforced concrete (RC). Therefore, this study collects data on multiple PC experiments from the literature and compares their results with the corresponding values calculated using two existing rational formulae for RC, and develops a series of noniterative formulae that facilitate the direct calculation of T_cr, the cracking angle of twist and the initial torsional stiffness for solid and hollow PC members. The developed formulae are verified to calculate the torsional precracking responses of 55 collected PC specimens reasonably well. This study also proposes a simple exponential formula for the inclination angle α of the compression diagonals in concrete for calculating the ACI-318 torsional strengths, T_n. The proposed α-formula is verified to calculate the values of ACI-318 T_n for 59 collected PC specimens very well, and is considerably more accurate than the latest ACI 318-19 α-criterion.

中文翻译：

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预应力混凝土构件扭转预裂响应和扭转强度的非迭代公式

最近的研究揭示了预应力混凝土 (PC)中开裂扭矩T _{cr的复杂特性。}截面中纵向预应力筋的分布模式是一个重要因素，但在任何方法中都没有考虑。最近的研究还表明，PC- T _cr可以用预应力比和T _cr表示。使用现有的钢筋混凝土 (RC) 有理公式计算的值。因此，本研究从文献中收集了多个 PC 实验的数据，并将其结果与使用两个现有的 RC 有理公式计算的相应值进行比较，并开发了一系列便于直接计算T _cr的非迭代公式，即开裂角实心和空心 PC 构件的扭转和初始扭转刚度。对所开发的公式进行了验证，可以较好地计算收集到的 55 个 PC 试件的扭转预裂响应。本研究还提出了一个简单的指数公式，用于计算混凝土中受压对角线的倾角α ，用于计算 ACI-318 抗扭强度，吨。_{_} 所提出的α公式经过验证，可以很好地计算 59 个收集的 PC 标本的 ACI-318 T _n值，并且比最新的 ACI 318-19 α标准要准确得多。