Noniterative formulae for torsional precracking responses and torsional strengths in prestressed concrete members

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.