Tensile force estimation on tie beams by dynamic method

Tensile force control in tie beams of historic buildings can be assessed by non-destructive testing using the dynamic method. The general problem of determining the tension in a tie beam falls within the theory of cables subjected to their own weight and normal tensile force. If the ratio slenderness/inertia of the tie beam is relevant, the analysis is brought back to the equilibrium of cables, the flexural stiffness implicitly considered null. On the contrary the problem can be traced back to that of slender beams subjected to transverse loads and axial stress. The analysis methodologies generally provide two limit solutions which refer to the tie beams extremities considered as hinged or clamped. By considering the tie beam inertia and by analysing the frequencies and associated modal deformations it is possible to solve the problem in a general way by estimating with sufficient approximation the real constraint conditions, thus determining in a sufficiently precise manner the tension in the analysed tie beam.