Evaluation of Tension Force Using Vibration Technique Related to String and Beam Theory to Ratio of Moment of Inertia to Span

Tie rods are structural elements that transfer axial tensile loads and are typically used on walls, vaults, arches, and buttresses in historical buildings. To verify their load-bearing capacity and identify possible structural damage risks, the forces transferred by tie rods and the corresponding stresses must be determined. However, this is often a challenging task due to the lack of project documentation for historical buildings. Uncertainties like complex boundary conditions or unknown material and geometrical properties make it hard to assess the tie rods’ load level. This paper presents a methodology for the determination of axial forces in tie rods that combines on-site experimental research and a numerical model-updating technique. Along with the common approach based on a determination of the natural frequency of tie rods, this paper presents an approach based on tie rods’ mode shapes. Special emphasis is placed on the boundary conditions coefficient, which is a crucial parameter in the analytical solution for axial forces determination based on the conducted on-site experiments. The method is applied in a historical building case study.

show abstract

“…Ultimately, a natural frequency for the nth mode shape in tie rods can be determined according to [19,20] as…”

Section: Analytical Solution For Lateral Tie Rod Vibrationmentioning

confidence: 99%

“…Value of boundary condition parameter κ for the first two[19] and nth[20] natural frequencies having various boundary conditions.…”

mentioning

confidence: 99%

Determination of Axial Force in Tie Rods of Historical Buildings Using the Model-Updating Technique

et al. 2020

View full text Add to dashboard Cite

show abstract

“…By solving equation 3 for the tension yields, the cable force (T) can be written as (Nugroho et al, 2014), (Fang, and Wang, 2012), (Kim and Park, 2007):…”

Section: Analytical Theory 21 the String Theorymentioning

confidence: 99%

Natural Frequency of Tension Cable Based on Moment Inertia to Span Ratio: Determination Using Analytical, Numerical and Experimental Study

Nugroho

2020

IJSCET

Self Cite

View full text Add to dashboard Cite

Health monitoring using vibration technique is usually conducted on cable structure. The hanger cable on the suspension bridge has a difference of span. To predict axial force of cable, the beam-string theory includes a parameter of bending stiffness. However, string theory has neglected the effect of bending stiffness. The shorter the span of the cable the greater the effect of the bending stiffness would be. This paper raises parameter moment of inertia to span ratio (I/L) to determine the apropriate analytical formula between string and beam-string. Experimental research was conducted using a vibration technique. The specimens use solid cylindrical steel beam, having length specimens of 2 m, hinge-hinge of boundary condition, and difference variations I/L of 0.024, 0.08, 0.58, 1.53 and 10.22. Numerical analysis was simulated by using Abaqus software v 6.13. The result shows that the ratio of I/L equally lowers than 0.082 has close to the analytical string theory. The ratio of I/L greather than 0.082 has close to the beam string theory.

show abstract

“…is is achieved by taking the Laplace transform of both equations and rearranging (11) to substitute it into the Laplace transform of (12). Finally, the ratio of Laplace output, Y r (s), to the Laplace input, U r (s), represents the transfer function, TF or H r (ω), of the system.…”

Section: Analytical Dynamic Modelmentioning

confidence: 99%

“…Determining the mean tensile force in cables through vibration methods has been widely studied [10][11][12]. Frequencybased vibration methods may be simply, quickly, and accurately used to measure cable forces.…”

Section: Introductionmentioning

confidence: 99%

Determining Time Variation of Cable Tension Forces in Suspended Bridges Using Time‐Frequency Analysis

Stromquist-LeVoir

McMullen

Zaghi

et al. 2018

Advances in Civil Engineering

View full text Add to dashboard Cite

A feasibility study was conducted to develop a novel method to determine the temporal changes of tensile forces in bridge suspender cables using time-frequency analysis of ambient vibration measurements. An analytical model of the suspender cables was developed to evaluate the power spectral density (PSD) function of a cable with consideration of cable flexural stiffness. Discrete-time, short-time Fourier transform (STFT) was utilized to analyze the recorded acceleration histories in both time and frequency domains. A mathematical convolution of the analytical PSD function and time-frequency data was completed to evaluate changes in cable tension force over time. e method was implemented using acceleration measurements collected from an in-service steel arch bridge with a suspended deck to calculate the temporal variation in cable forces from the vibration measurements. e observations served as proof of concept that the proposed method may be used for cable fatigue life calculations and bridge weigh-in-motion studies.

show abstract

Evaluation of Tension Force Using Vibration Technique Related to String and Beam Theory to Ratio of Moment of Inertia to Span

Cited by 18 publications

References 2 publications

Determination of Axial Force in Tie Rods of Historical Buildings Using the Model-Updating Technique

Determination of Axial Force in Tie Rods of Historical Buildings Using the Model-Updating Technique

Natural Frequency of Tension Cable Based on Moment Inertia to Span Ratio: Determination Using Analytical, Numerical and Experimental Study

Determining Time Variation of Cable Tension Forces in Suspended Bridges Using Time‐Frequency Analysis

Contact Info

Product

Resources

About