Tension determination of stay cable or external tendon with complicated constraints using multiple vibration measurements

• A new method using mode shape ratios was lately developed for tension determination.
• A crucial restriction of symmetric boundary constraints was imposed in that method.
• A shifting parameter is added in this study for generalization to unsymmetrical BC’s.
• Numerical difficulty associated with this new formulation is discussed and solved.
• Numerical investigations, practical validations and applications are also conducted.

A novel concept of combining the mode shape ratios with the modal frequencies was recently introduced to develop an accurate method for the determination of stay cable force. A crucial restriction of symmetric boundary constraints at both ends was imposed in this method for the optimization of effective vibration length. However, there certainly exist a number of cases with apparent unsymmetrical boundary constraints such as the case of stay cables with supplementary dampers and that of external tendons affected by intermediate diaphragms. To deal with such difficulties, this method is further generalized in the current study by introducing a shifting parameter in the shape function to effectively consider the unsymmetrical boundary constraints. The numerical difficulty of the more complicated nonlinear optimization process associated with this new formulation is first discussed, followed by extensive numerical investigations, practical verifications, and real applications.