Distributive relationship of anchorage force relative to reinforcement and headed bars

When using headed bars, the distributive relationship of anchorage force between reinforcement and headed bars is crucial. This study conducted pull-out tests on 120 specimens, categorized into 24 groups, with a cross-sectional area of 150 × 150 mm, and the parameters considered were diameter (d), yield strength of reinforcement (f_y), embedment length (l_ah), and strength grades of concrete (f_cg). The corresponding programs were proposed and verified based on test results. The concept of a stable development length (l_as) was proposed as the critical length to determined whether the headed bars entered a working state. An analysis indicated that the ratio of l_as to d increased linearly with the ratio of f_y to the tensile strength of concrete (f_t,m), and decreased nonlinearly with the ratio of the protective thickness (c) to d. A formula was established for l_as using two independent variables. l_as and the critical development length (l_ac) were determined to be 1.28 times and 0.66 times the general development length (l_a), respectively. A further analysis demonstrated that the ratio of the pressure of headed bars (F_p) to f_y and the ratio of l_ah to l_as were only related to the ratio of c to d. Thus, the distributive relationship of the anchorage force between the reinforcement and the headed bars was obtained.