Rapid Non-Contact Tension Force Measurements on Stay Cables

Rapid Non-Contact Tension Force Measurements on Stay Cables ∗

†

Marcus Schmieder, Alex Taylor-Noonan, Roland Heere

Abstract

‡

may exceed the replacement cost, especially when the repairs involve full or partial closure. Therefore,

Vibration to Tension Force calculations are known in

maintaining the structure and xing the issues when

the engineering community through the Taut String

they arise will be most cost ecient in the long run.

Theory. Precise calculations require accurate identication of the natural frequencies and incorporation

Periodic

of correction factors.

Additionally, the duration of

ten include a measurement of the cable tension

individual measurements must be optimized to allow

forces. Traditional methods to measure cable tension

for sucient data aquisition. The work presented in

forces in stay cables can be classied into 2 main

this paper describes a cost eective and optimized

categories:

approach to determine the tension force in stay ca-

Lift-o

bles. This optimization is necessary to accommodate

inspection

plans

for

these

bridges

of-

direct measurement by the lift-o method,

using hydraulic jacks.

any funding restrictions.

Frequency-based

1 Introduction

indirect

measurement

via

the

natural frequency of the cable. The natural frequency-based method centers on the

Cable Stay bridges gain more and more popularity

Taut String Theory, where the tension force

in the structural engineering world. The reasons for

cable of known length

T in a L and unit weight w can be cal-

the popularity of these structures include the cost ef-

culated from the

n-th

natural frequency of vibration

ciency of construction and the pleasing appearance

fn

by

of cable stay bridges. However, the main structural elements holding the deck in place are the stay cables

T =

which are in most cases not thoroughly inspected over the lifetime of the bridge.

The life span of

where

the structure may be shortened due to corrosion, slippage, settlement of the structure or part of the

An

structure, resulting in load imbalances in the cables.

Eng.

(1)

is the gravitational constant.

experimental

validation

of

the

determina-

tion of tension force through natural frequencies was

The costs of repairing signicant structural damages ∗ M. Ind.

g

4wL2 fn2 n2 g

published in Russell and Lardner [1998].

& Mgmt., NDT Specialist, Metro Test-

ing Laboratories Ltd, Burnaby, British Columbia.

As

Email:

[email protected]

the

size

of

bridges

presents

challenges

for

accelerometer installation, remote sensing methods

† B.A.Sc. E.I.T., Materials Engineer, Metro Testing Labo-

have been explored.

ratories Ltd. Email: [email protected]

A Laser Vibrometer is one

such device, in which a laser beam is directed at

‡ M.A.Sc. P.Eng., Senior Materials Engineer, Metro Testing

the

Laboratories Ltd. Email: [email protected]

1

location

of

interest

and

the

velocity

of

the

2

COMPARISON OF METHODS

1

vibration is measured .

2

Systems of this kind are

measured directly.

However, this method requires

capable of conducting measurements from distances

heavy jacking equipment which is costly to mobilize,

of up to 200 m. In 1999, Cunha and Caetano used

install and operate.

a

to

accessible and clear of lling materials. Furthermore,

those from cable-mounted accelerometers. Excellent

a suitable bearing location for the jacking mechanism

agreement was found.

is required.

laser

vibrometer

and

compared

the

results

A laser vibrometer was also

The anchorage points must be

used successfully by Miyashita and Nagai [2008] and Chen and Petro [2006] to determine the frequency of

Using

bridge cables.

measurements requires no access to the anchorage

accelerometers

to

conduct

frequency-based

points but does require access to the cable surface or This

paper

ca-

sleeve surface. A suciently sensitive accelerometer

laser-based

needs to be physically mounted onto the cable at

vibration measurements. First, the main methods of

a position where vibrations of multiple modes can

bridge cable tension assessment are compared. Next,

be

the authors present the results of original research

for instance).

on the importance of measurement duration. Three

lightweight (usually between 50 and 500 grams), this

methods for identifying the natural frequency from

task typically requires a boom lift for a technician.

the frequency plot are compared for varying mea-

Then, cabling must be run back to the frequency

surement durations.

analyzer.

ble

tension

describes

an

application

determination

through

of

stay

Then, a literature review on

detected

and

measured

(near

the

third-point

While the sensors themselves are

Trac control, or a bridge closure, may

the eects of sag-extensibility and bending stiness

be required if this equipment or cabling interferes

is conducted, and a system of correction factors is

with normal operation. Each stay cable may require

presented.

between 20 to 60 minutes for sensor installation and cabling.

2 Comparison of Methods As outlined previously, the primary methods to measure bridge stay cable tension are:

•

Lift-o method

•

Frequency-based method

 

By

using

non-contact

laser

based

sensors

like

a

Laser Vibrometer, no physical access to the cable is required.

This allows the location of the mea-

surement point to be at third or midpoint of the cable,

not limited by the reach of the available

boom lifts. per location.

Set-up time is only a few minutes At a rate of $100-150 per hour per

technician on site, reducing the set up time per caUsing accelerometers mounted on the cable Conducting remote measurements using a laser vibrometer.

ble will generate signicant cost savings for the client. A

full

investigation

of

a

cable

stay

structure

may include more than 100 cables. To evaluate these

The lift-o method has the advantage that each

cables a simultaneous or sequential measurement

strand can be jacked and its tension load may be

can be selected. The simultaneous approach usually

1 The

involves using many accelerometers at once. principle behind this device is that a laser beam re-

ected o a moving surface will experience a phase change

Given

that enough accelerometers and signal cables are

and will also have its frequency shifted through the Doppler

available, and the frequency analyzer has enough

eect.

A Laser Vibrometer is in eect an interferometer; in

input channels (these devices can often support 8,

which a single laser beam is split into a measurement beam

16 or 32 seperate channels), many measurements

and reference beam. After reecting o the vibrating surface, the measurement beam is recombined with the reference beam

can be conducted simultaneously.

However,

this

(which never left the instrument) and the interference pattern

requires the installation of many accelerometers and

is measured.

signal cables while ensuring that no cable confusion

3

IMPORTANCE OF MEASUREMENT DURATION

occurs.

Conversely,

a laser vibrometer can only

measure one point at a time,

and therefore the

3

As the duration of the measurement increases, the frequency resolution

fs

improves, and the natural

data collection phase becomes a large part of the

frequency can be determined to within a smaller

overall project.

interval.

Section 3 outlines the implications

of choosing an appropriate measurement duration Insucient

and an experimental verication is performed.

measurement

durations

will

result

in inadequate frequency resolution of the FFT analThe cost & time expenditures for each method

ysis. However, measurements beyond the minimum

are compared in Table 1. Because the time savings

required time will extend the time on site and may

during setup of each measurement location greatly

lead to higher costs for the client. The objective is to

outweigh the extra time spent during measurement,

minimize data acquisition time whilst still identifying

conducting

pro-

the natural frequency with adequate precision. This

gramme using a laser vibrometer is much quicker

section presents three analytical methods to increase

than with accelerometers.

the accuracy in identifying the natural frequency

a

cable

vibration

measurement

from

measurements

of

shorter

duration.

These

Overall, contactless laser vibrometer systems require

methods are then compared using experimental data

less equipment and less time and are therefore a cost

in order to determine an appropriate measurement

ecient

length.

based

alternative

and

lift-o

to

traditional

methods.

accelerometer-

Furthermore,

laser

vibrometers are generally quite transportable (an

The

entire system can be wheeled by one technician

Peak Method, where the rst natural frequency is

and checked as airline luggage) and provide similar

read from the FFT. Given a frequency resolution

measurement precision as accelerometer systems.

of

simplest

fs ,

identication

method

is

the

First

identifying the natural frequency (f1 ) via the

First Peak Method only gives us the certainty that

fs fs < f1T rue < f1F P + 2 2

3 Importance of measurement duration

3.1

The number of samples collected during data acqui-

Methods that consider multiple use harmonics use

sition is critical for the precise determination of the

the relation of each

natural frequency.

quency

The natural frequency and har-

f1F P −

Considering multiple harmonics

frequency-domain representation of a time-domain function. For a discrete time series sampled at rate

fa

for duration

T,

tains a series of discrete frequency bins uniformly distributed between 0 Hz and

fa .

bins is the frequency resolution

n-th

harmonic, we have the certainty that

fnM easured −

fs fs < fnT rue < fnM easured + 2 2

(5)

The width of these

fs ,

which is indepen-

dent of the frequency setting of the analyzer, and is simply related to the measurement time

fs =

(4)

If we consider our certainty of identication of the

the FFT result is also a discrete

sequence of the same length (fa T ). This result con-

n-th harmonic to the natural frefn = nf1

monics are determined by nding the peaks of the Fast Fourier Transform (FFT), which provides the

(3)

fa 1 = fa T T

T

fnM easured −

by

(2)

fnM easured − n

fs fs < nf1T rue < fnM easured + 2 2 fs 2

< f1T rue
1 (in-plane)

(17)

for all n (out-of-plane)

[ Le = L 1 +

( wL cos θ )2 ] H

8

(18)

5

CONCLUSION

9

of the Royal Society of London. A. Mathematical

where

H

is the initial estimate of tension force along the

chord, determined by Equation 1. λ2 is as dened in Equation 12. For higher modes of vibration (n tion 13 becomes

and Physical Sciences, 341(1626):299, 1974. T. Miyashita and M. Nagai. Vibration-based Structural Health Monitoring for Bridges using Laser

> 1),

ωn = βn ωn s

Equa(19)

The bending stiness and sag-extensibility correction factors in this section should be calculated and applied to each measured peak before utilizing any of the three methods presented previously in Section 3.

Doppler Vibrometers and MEMS-based Technologies.

International Journal of Steel Structures, 8

(12):325331, 2008. YQ Ni, JM Ko, and G. Zheng. Dynamic analysis of large-diameter sagged cables taking into account exural rigidity. Journal of Sound and Vibration, 257(2):301319, 2002. J. C. Russell and T. J. Lardner.

5 Conclusion

Experimental de-

termination of frequencies and tension for elastic cables.

Stay bridge cable tension measurements are sometimes required to conrm the cables are indeed carrying the designed loads, calculated by the bridge de-

Journal of Engineering Mechanics, 124

(10):10671072, 1998. doi: 10.1061/(ASCE)07339399(1998)124:10(1067).

URL

http://link.aip.org/link/?QEM/124/1067/1.

signer. Laser-based vibration measurement systems

H. Tabatabai, A.B. Mehrabi, and P.Y. Wen-huei.

provide a fast and ecient solution to measure vi-

Bridge stay cable condition assessment using vi-

bration frequencies on stay cables without the need

bration measurement techniques.

for physical access to the cables. Identifying multiple

of SPIE, volume 3400, page 194, 1998.

harmonics allows the natural frequency to be identied to a greater precision by using methods such as a Variance-Weighted Average. Due to the non-contact approach and the long measurement range, these systems allow for fast set up and data acquisition. A fast set up and quick data acquisition results in signicant cost savings for the client.

References S.E. Chen and S. Petro. Nondestructive bridge cable tension assessment using laser vibrometry. Exper-

imental Techniques, 29(2):2932, 2006. A. Cunha and E. Caetano. Dynamic measurements on stay cables of cable-stayed bridges using an interferometry laser system.

Experimental Tech-

niques, 23(3):3843, 1999. H.M. Irvine. Cable Structures. MIT Press, 1981. H.M. Irvine and T.K. Caughey. The linear theory of free vibrations of a suspended cable.

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