Experimental and theoretical evaluation of axial forces in short steel ropes

Assessing rope force in bridge structural health monitoring, particularly for shorter lengths, poses challenges. The vibration method, commonly utilized for taut strings, yields inaccurate results for short ropes due to neglecting bending stiffness. To address this, the differential equation of lateral vibration of a prismatic beam possessing bending stiffness EI, evenly distributed mass m under the tension force N is solved approximately and numerically using FEM for greater accuracy. Nonlinear fitting via the Gauss-Newton aids in refining results. Laboratory experiments, varying axial forces and rope characteristics, validated these methods, offering recommendations for improved accuracy.