Unified rational formula for pre-cracking torsional stiffness of solid and hollow reinforced concrete members

• A rational formula for calculating the torsional stiffness of solid and hollow RC members is proposed.
• The formula predicts the stiffness of nine hollow RC beam specimens almost perfectly.
• Formula-calculated stiffness values for 147 RC beam specimens are presented and compared.
• Elastic stiffness values of the 147 specimens are examined using the proposed formula.
• The proposed bi-linear simplification can be used in performance-based engineering.

It is generally assumed that the elastic torsional stiffness of structural reinforced concrete (RC) members that are subjected to a torsional moment less than the cracking torque can be accurately estimated, despite a lack of adequate experimental or theoretical examination. The softened membrane model for torsion (SMMT), which has been validated experimentally, provides accurate estimates of pre-cracking torsional stiffness for solid and hollow RC members. However, the SMMT requires an iterative solution algorithm, and is thus inconvenient for design purposes. This paper presents a simplification of the SMMT and proposes a unified rational formula for the direct calculation of the initial torsional stiffness of solid and hollow RC members. The proposed formula predicts the initial torsional stiffness of nine hollow RC beam specimens almost perfectly. When used to calculate the stiffness of 147 solid and hollow RC beam specimens, the proposed formula is found to be an almost perfect simplification of the SMMT in terms of initial torsional stiffness. However, the elastic stiffness values of the 147 specimens deviate from the formula-calculated values by −40% to +50%, suggesting the values may not be as accurate as commonly presumed. It is also shown that the proposed formula can combine with an existing Tcr-θcrTcr-θcr formula to provide a precise bi-linear simplification of the nonlinear pre-cracking torque-twist curves for solid and hollow RC members; this can then be conveniently used in the nonlinear finite element analyses needed in performance-based engineering.