Practical cable force formulas for short suspender of arch bridge considering end effect

ObjectiveThis study proposes practical cable force formulas considering end effect to address the challenges in accurately measuring short suspender cable force of arch bridges by using vibration frequency method. The aim is to reduce measurement errors and improve the precision of cable force assessment for short suspenders.MethodFirst, the basic principles and formulas of vibration frequency method were outlined. An idealized homogeneous finite element model of suspender was developed with ANSYS. The fundamental frequencies in various conditions were computed and validated against analytical solutions from existing formulas. Second, a three-segment model incorporating end effect was established. The influences of three parameters (i.e., density ratio between end and middle segment, section to diameter ratio, and end length) on the fundamental frequency were analyzed. Third, the statistical relations between fundamental frequency incremental percentage and suspender length were derived in different boundary conditions. An end effect correction factor was calculated to adjust the measured fundamental frequency, which was then substituted into the theoretical beam-cable formula to obtain the modified cable force formulas. Finally, the proposed formulas were verified by using field data from anchor-load cells on a two-span continuous thrust-free spatial variable-section steel-box arch bridge under construction.ResultThe proposed correction formulas demonstrate high accuracy and strong applicability, particularly for short suspenders with lengths less than 10 m. For such suspenders, the cable force measurement error is reduced from 25.90% to 4.01%.ConclusionThe proposed formulas effectively mitigate measurement errors and significantly improve the accuracy of cable force evaluation for short suspenders. It is of guiding significance for the safety assessment of suspenders of half-through and through arch bridge.