PSI - Issue 64

Cevdet Enes Cukaci et al. / Procedia Structural Integrity 64 (2024) 531–538 Cukaci and Soyoz / Structural Integrity Procedia 00 (2024) 000 – 000

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cable tensions are estimated using the vibration method from the displacement response of cables with the vision based modal identification and compared with the first two methods. 2.1. Lift-off testing Lift-off testing is one of the most used direct measurement methods. The tension of the strand inside the cable is measured using a load cell, a displacement sensor, and a hydraulic jack, usually placed during the construction phase, as shown in Fig. 1(a). While the free end of this strand is pulled with a hydraulic jack, up to a certain point. When the pulling force of the hydraulic jack exceeds the strand tension, the wedge is lifted from the anchor block at the strand end. Since the material property of the strand is elasto-plastic, the tensile force of each strand is calculated by multiplying the displacement with the Modulus of Elasticity (E) or directly from force sensor. When lift occurs, the tension remains constant at the point where the displacement slope changes. As shown in Fig. 1(b), this point is considered as the strand tension and plastic displacement begins after this point. Using the tension of each strand, the cable tension is calculated as = ∑ = 1 (1) In this method, tension is assessed only for a subset of the strands in the cable. The term n s in the relevant formula denotes the number of strands for which tension is directly measured. T i represents the measured tension value for each of these strands. By using these values, the average tension per strand can be calculated. The term n refers to the total number of strands within the cable. To estimate the overall cable tension, this average strand tension is multiplied by the total strand number (Cho et al., 2013; Zarbaf et al., 2018).

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Fig. 1 (a) lift-off testing working principle; (b) force-displacement graph during measurements.

2.2. Vibration method In stay-cable bridges, the natural frequency of cable changes with the cable tension. When the applied tension is known, the natural frequency can be calculated with the cable characteristics. The vibration method aims to calculate the cable tension inversely by calculating the natural frequency from the cable response and using the cable characteristics. Using acceleration sensors, laser displacement sensors and vision-based monitoring systems, the cable response is obtained in terms of acceleration, velocity or displacement and their natural frequencies can be calculated. The vibration method was initially based on a simplistic theory without considering the bending stiffness and cable sag. Subsequent studies were carried out to enhance its practicality and precision with these factors. The most widely used technique for tension estimation is the least squares method. The cable is considered as a beam to assess bending stiffness as shown in Fig. 2(a). According to this assumption, the equation of motion of the cable can be defined as 2 ( , ) 2 = 2 ( , ) 2 + 4 ( , ) 4 (2) In this equation, T represents the longitudinal cable tension. The term ν(x,t) refers to the cable's vertical displacement response, where x is the position along the cable's length, and t is time. w stands for the cable's unit weight. EI denotes the bending stiffness of the cable with respect to the gravity. Theoretically, the bending stiffness of an actual cable is influenced by factors such as the cable's length, tension, and degree of bending. Nonetheless,