fatigue testing and analysis theory and practice

The concept of strain e, as itrelates to the mechanical behavior of loaded components, is the change inlength DL the component experiences divided by the original componentlength L, as s

+08'00'

(Theory and Practice)

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Printed in the United States of America

To my wife Barbara.

- Richard B Hathaway

To my wife, Tammy, and our daughters Lauren and Anna.

- Mark E Barkey

Over the past 20 years there has been a heightened interest in improvingquality, productivity, and reliability of manufactured products in the groundvehicle industry due to global competition and higher customer demands forsafety, durability and reliability of the products As a result, these productsmust be designed and tested for sufficient fatigue resistance over a large range

of product populations so that the scatters of the product strength andloading have to be quantified for any reliability analysis

There have been continuing efforts in developing the analysis techniques forthose who are responsible for product reliability and product design Thepurpose of this book is to present the latest, proven techniques for fatiguedata acquisition, data analysis, test planning and practice More specifically,

it covers the most comprehensive methods to capture the component load, tocharacterize the scatter of product fatigue resistance and loading, to performthe fatigue damage assessment of a product, and to develop an acceleratedlife test plan for reliability target demonstration

The authors have designed this book to be a useful guideline and reference tothe practicing professional engineers as well as to students in universities whoare working in fatigue testing and design projects We have placed a primaryfocus on an extensive coverage of statistical data analyses, concepts,methods, practices, and interpretation

The material in this book is based on our interaction with engineers andstatisticians in the industry as well as based on the courses on fatigue testing

and analysis that were taught at Oakland University, University of Michigan,Western Michigan University and University of Alabama Five major con-tributors from several companies and universities were also invited to help usenhance the completeness of this book The name and affiliation of theauthors are identified at the beginning of each chapter.

There are ten chapters in this book A brief description of these chapters isgiven in the following

Chapter 1 (Transducers and Data Acquisition) is first presented to addressthe importance of sufficient knowledge of service loads/stresses and how tomeasure these loads/stresses The service loads have significant effects on theresults of fatigue analyses and therefore accurate measurements of the actualservice loads are necessary A large portion of the chapter is focused on thestrain gage as a transducer of the accurate measurement of the strain/stress,which is the most significant predictor of fatigue life analyses A variety ofmethods to identify the high stress areas and hence the strain gage placement

in the test part are also presented Measurement for temperature, number oftemperature cycles per unit time, and rate of temperature rise is included Theinclusion is to draw the attention to the fact that fatigue life prediction isbased on both the number of cycles at a given stress level during the servicelife and the service environments The basic data acquisition and analysistechniques are also presented

In Chapter 2 (Fatigue Damage Theories), we describe physical fatigue anisms of products under cyclic mechanical loading conditions, models todescribe the mechanical fatigue damages, and postulations and practicalimplementations of these commonly used damage rules The relations ofcrack initiation and crack propagation to final fracture are discussed in thischapter

mech-In Chapter 3 (Cycle Counting Techniques), we cover various cycle countingmethods used to reduce a complicated loading time history into a series ofsimple constant amplitude loads that can be associated with fatiguedamage Moreover the technique to reconstruct a load time history withthe equivalent damage from a given cycle counting matrix is introduced inthis chapter

In Chapter 4 (Stress-Based Fatigue Analysis and Design), we review methods

of determining statistical fatigue properties and methods of estimating thefatigue resistance curve based on the definition of nominal stress amplitude.These methods have been widely used in the high cycle fatigue regime fordecades and have shown their applicability in predicting fatigue life ofnotched shafts and tubular components The emphasis of this chapter is on

Design & Evaluation Committee for the last two decades for its applicability

in the low and high cycle fatigue regimes It appears of great value in theapplication of notched plate components

In Chapter 6 (Fracture Mechanics and Fatigue Crack Propagation), thetext is written in a manner to emphasize the basic concepts of stress concen-tration factor, stress intensity factor and asymptotic crack-tip field for linearelastic materials Stress intensity factor solutions for practical crackedgeometries under simple loading conditions are given Plastic zones andrequirements of linear elastic fracture mechanics are then discussed Finally,fatigue crack propagation laws based on linear elastic fracture mechanics arepresented

In Chapter 7 (Fatigue of Spot Welds), we address sources of variability in thefatigue life of spot welded structures and to describe techniques for calculat-ing the fatigue life of spot-welded structures The load-life approach, struc-tural stress approach, and fracture mechanics approach are discussed indetails

In Chapter 8 (Development of Accelerated Life Test Criteria), we providemethods to account for the scatter of loading spectra for fatigue designand testing Obtaining the actual long term loading histories via real timemeasurements appears difficult due to technical and economical reasons

As a consequence, it is important that the field data contain all possibleloading events and the results of measurement be properly extrapolated.Rainflow cycle counting matrices have been recently, predominately usedfor assessing loading variability and cycle extrapolation The followingthree main features are covered: (1) cycle extrapolation from short termmeasurement to longer time spans, (2) quantile cycle extrapolation frommedian loading spectra to extreme loading, and (3) applications of theextrapolation techniques to accelerated life test criteria

In Chapter 9 (Reliability Demonstration Testing), we present various tical-based test plans for meeting reliability target requirements in the accel-erated life test laboratories A few fatigue tests under the test load spectrashould be carried out to ensure that the product would pass life test criteria

statis-The statistical procedures for the choice of a test plan including sample sizeand life test target are the subject of our discussion.

In Chapter 10 (Fatigue Analysis in the Frequency Domain), we introduce thefundamentals of random vibrations and existing methods for predictingfatigue damage from a power spectral density (PSD) plot of stress response.This type of fatigue analysis in the frequency domain is particularly useful forthe use of the PSD technique in structural dynamics analyses

The authors greatly thank to our colleagues who cheerfully undertook thetask of checking portions or all of the manuscripts They are Thomas Cordes(John Deere), Benda Yan (ISPAT Inland), Steve Tipton (University ofTulsa), Justin Wu (Applied Research Associates), Gary Halford (NASA-Glenn Research Center), Zissimos Mourelatos (Oakland University), Keyu

Li (Oakland University), Daqing Zhang (Breed Tech.), Cliff Chen (Boeing),Philip Kittredge (ArvinMeritor), Yue Chen (Defiance), Hongtae Kang (Uni-versity of Michigan-Dearborn), Yen-Kai Wang (ArvinMeritor), PaulLubinski (ArvinMeritor), and Tana Tjhung (DaimlerChrysler)

Finally, we would like to thank our wives and children for their love,patience, and understanding during the past years when we worked most ofevenings and weekends to complete this project

Yung-Li Lee, DaimlerChrysler

Jwo Pan, University of Michigan

Richard B Hathaway, Western Michigan University

Mark E Barkey, University of Alabama

1 Transducers and Data Acquisition 1Richard B Hathaway, Western Michigan University

Kah Wah Long, DaimlerChrysler

Yung-Li Lee, DaimlerChrysler

Yung-Li Lee, DaimlerChrysler

Darryl Taylor, DaimlerChyrysler

Yung-Li Lee, DaimlerChrysler

Darryl Taylor, DaimlerChyrysler

Yung-Li Lee, DaimlerChrysler

Darryl Taylor, DaimlerChyrysler

6 Fracture Mechanics and Fatigue Crack

Jwo Pan, University of Michigan

Shih-Huang Lin, University of Michigan

Mark E Barkey, University of Alabama

Shicheng Zhang, DaimlerChrysler AG

Yung-Li Lee, DaimlerChrysler

Mark E Barkey, University of Alabama

Ming-Wei Lu, DaimlerChrysler

Yung-Li Lee, DaimlerChrysler

Dr Yung-Li Lee is a senior member of the technical staff of the Stress Lab &Durability Development at DaimlerChrysler, where he has conducted re-search in multiaxial fatigue, plasticity theories, durability testing for automo-tive components, fatigue of spot welds, and probabilistic fatigue and fracturedesign He is also an adjunct faculty in Department of Mechanical Engineer-ing at Oakland University, Rochester, Michigan.

Dr Jwo Pan is a Professor in Department of Mechanical Engineering ofUniversity of Michigan, Ann Arbor, Michigan He has worked in the area ofyielding and fracture of plastics and rubber, sheet metal forming, weldresidual stress and failure, fracture, fatigue, plasticity theories and materialmodeling for crash simulations He has served as Director of Center forAutomotive Structural Durability Simulation funded by Ford Motor Com-pany and Director for Center for Advanced Polymer Engineering Research

at University of Michigan He is a Fellow of American Society of MechanicalEngineers (ASME) He is on the editorial boards of International Journal ofFatigue and International Journal of Damage Mechanics

Dr Richard B Hathaway is a professor of Mechanical and Aeronauticalengineering and Director of the Applied Optics Laboratory at WesternMichigan University His research involves applications of optical measure-ment techniques to engineering problems including automotive structuresand powertrains His teaching involves Automotive structures, vehicle sus-pension, and instrumentation He is a 30-year member of the Society of

Automotive Engineers (SAE) and a member of the Society of mentation Engineers (SPIE).

Photo-Instru-Dr Mark E Barkey is an Associate Professor in the Aerospace Engineeringand Mechanics Department at the University of Alabama He has conductedresearch in the areas of spot weld fatigue testing and analysis, multiaxialfatigue and cyclic plasticity of metals, and multiaxial notch analysis Prior tohis current position, he was a Senior Engineering in the Fatigue Synthesis andAnalysis group at General Motors Mid-Size Car Division

A c q u i s i t i o n Richard Hathaway Western Michigan University

Kah Wah Long DaimlerChrysler

This chapter addresses the sensors, sensing methods, measurementsystems, data acquisition, and data interpretation used in the experimentalwork that leads to fatigue life prediction A large portion of the chapter isfocused on the strain gage as a transducer Accurate measurement of strain,from which the stress can be determined, is one of the most significantpredictors of fatigue life Prediction of fatigue life often requires the experi-mental measurement of localized loads, the frequency of the load occurrence,the statistical variability of the load, and the number of cycles a part willexperience at any given load A variety of methods may be used to predict thefatigue life by applying either a linear or weighted response to the measuredparameters

Experimental measurements are made to determine the minimum andmaximum values of the load over a time period adequate to establish therepetition rate If the part is of complex shape, such that the strain levelscannot be easily or accurately predicted from the loads, strain gages will need

to be applied to the component in critical areas Measurements for ture, number of temperature cycles per unit time, and rate of temperature risemay be included Fatigue life prediction is based on knowledge of both thenumber of cycles the part will experience at any given stress level during that

tempera-life cycle and other influential environmental and use factors Section 1.2begins with a review of surface strain measurement, which can be used topredict stresses and ultimately lead to accurate fatigue life prediction One ofthe most commonly accepted methods of measuring strain is the resistivestrain gage.

Modern strain gages are resistive devices that experimentally evaluate theload or the strain an object experiences In any resistance transducer,the resistance (R) measured in ohms is material and geometry dependent

with cross-sectional area (A) along the length of the material (L) making upthe geometry Resistance increases with length and decreases with cross-sectional area for a material of constant resistivity Some sample resistivities

1C



If the wire experiences a mechanical load (P) along its length, as shown

in Figure 1.2, all three parameters (L, r, A) change, and, as a result, the to-end resistance of the wire changes:

DR¼ rL
pLL

2 L

0B

1C

2

0B

1

The resistance change that occurs in a wire under mechanical load makes itpossible to use a wire to measure small dimensional changes that occurbecause of a change in component loading The concept of strain (e), as itrelates to the mechanical behavior of loaded components, is the change inlength (DL) the component experiences divided by the original componentlength (L), as shown in Figure 1.3:

It is possible, with proper bonding of a wire to a structure, to accuratelymeasure the change in length that occurs in the bonded length of the wire.This is the underlying principle of the strain gage In a strain gage, as shown

in Figure 1.4, the gage grid physically changes length when the material towhich it is bonded changes length In a strain gage, the change in resistanceoccurs when the conductor is stretched or compressed The change in resist-ance (DR) is due to the change in length of the conductor, the change in cross-sectional area of the conductor, and the change in resistivity (Dr) due to

DL/2 DL/2

L

e = DL/L

Where

e = strain; L = original length;

A simple wire as a strain sensor.

be produced at lower cost

The product of gage width and length defines the active gage area, as shown

in Figure 1.6 The active gage area characterizes the measurement surface andthe power dissipation of the gage The backing length and width define therequired mounting space The gage backing material is designed such that high

Backing Material

Strain Wire Lead Wires

Etched resistance foil

Resistance wire and etched resistance foil gages.

transfer efficiency is obtained between the test material and the gage, allowingthe gage to accurately indicate the component loading conditions.

1.2.1 GAGE RESISTANCE AND EXCITATION VOLTAGE

Nominal gage resistance is most commonly either 120 or 350 ohms.Higher-resistance gages are available if the application requires either ahigher excitation voltage or the material to which it is attached has lowheat conductivity Increasing the gage resistance (R) allows increased excita-tion levels (V) with an equivalent power dissipation (P) requirement as shown

in Equation 1.2.5

Testing in high electrical noise environments necessitates the need forhigher excitation voltages (V) With analog-to-digital (A–D) conversion forprocessing in computers, a commonly used excitation voltage is 10 volts At

10 volts of excitation, each gage of the bridge would have a voltage drop

of approximately 5 V The power to be dissipated in a 350-ohm gage is therebyapproximately 71 mW and that in a 120-ohm gage is approximately 208 mW:

At a 15-volt excitation with the 350-ohm gage, the power to be dissipated

in each arm goes up to 161 mW High excitation voltage leads to highersignal-to-noise ratios and increases the power dissipation requirement Ex-cessively high excitation voltages, especially on smaller grid sizes, can lead todrift due to grid heating

1.2.2 GAGE LENGTH

The gage averages the strain field over the length (L) of the grid If the gage

is mounted on a nonuniform stress field the average strain to which the active

backing width gage lead

gird length

gage area is exposed is proportional to the resistance change If a strain field

is known to be nonuniform, proper location of the smallest gage is frequentlythe best option as shown in Figure 1.7

1.2.3 GAGE MATERIAL

Gage material from which the grid is made is usually constantan Thematerial used depends on the application, the material to which it is bonded,and the control required If the gage material is perfectly matched to themechanical characteristics of the material to which it is bonded, the gage canhave pseudo temperature compensation with the gage dimensional changesoffsetting the temperature-related component changes The gage itself will betemperature compensated if the gage material selected has a thermal coeffi-cient of resistivity of zero over the temperature range anticipated If the gagehas both mechanical and thermal compensation, the system will not produceapparent strain as a result of ambient temperature variations in the testingenvironment Selection of the proper gage material that has minimal tem-perature-dependant resistivity and some temperature-dependent mechanicalcharacteristics can result in a gage system with minimum sensitivity totemperature changes in the test environment Strain gage manufacturersbroadly group their foil gages based on their application to either aluminum

or steel, which then provides acceptable temperature compensation forambient temperature variations

The major function of the strain gage is to produce a resistance changeproportional to the mechanical strain (e) the object to which it is mountedexperiences The gage proportionality factor, commonly called the gagefactor (GF), which makes the two equations of 1.2.6 equivalent, is defined

A gage length that is one-tenth of the corresponding dimension of any

stress raiser where the measurement is made is usually acceptable.

Peak Strain Indicated Strain

Position X

LThe gage factor results from the mechanical deformation of the gage gridand the change in resistivity of the material (r) due to the mechanical strain.Deformation is the change in length of the gage material and the change incross-sectional area due to Poisson’s ratio The change in the resistivity, calledpiezoresistance, occurs at a molecular level and is dependent on gage material.

In fatigue life prediction, cyclic loads may only be a fraction of the loadsrequired to cause yielding The measured output from the instrumentationwill depend on the gage resistance change, which is proportional to the strain

If the loads are relatively low, Equation 1.2.7 indicates the highest output andthe highest signal-to-noise ratio is obtained with high-resistance gages and ahigh gage factor

Example 1.1 A 350-ohm gage is to be used in measuring the strain tude of an automotive component under load The strain gage has a gagefactor of 2 If the component is subjected to a strain field of 200 microstrain,what is the change in resistance in the gage? If a high gage factor 120-ohmstrain gage is used instead of the 350-ohm gage, what is the gage factor if thechange in resistance is 0.096 ohms?

magni-Solution By using Equation 1.2.7, the change in resistance that occurs withthe 350-ohm gage is calculated as

By using Equation 1.2.7, the gage factor of the 120-ohms gage is

DRR

0:096120

1.2.4 STRAIN GAGE ARRANGEMENTS

Strain gages may be purchased in a variety of arrangements to makeapplication easier, measurement more precise, and the information gainedmore comprehensive A common arrangement is the 908 rosette, as shown

in Figure 1.8 This arrangement is popular if the direction of loading isunknown or varies This gage arrangement provides all the informationrequired for a Mohr’s circle strain analysis for identification of principlestrains Determination of the principle strains is straightforward when athree-element 908 rosette is used, as shown in Figure 1.9.

Mohr’s circle for strain would indicate that with two gages at 908 to eachother and the third bisecting the angle at 458, the principle strains can

be identified as given in Equation 1.2.8 The orientation angle (f) of principle

The principle strains are then given by Equations 1.2.11 and 1.2.12:

tan 2f¼ 45 x y

ex ey

(1:2:13)With principle strains and principle angles known, principle stresses can beobtained from stress–strain relationships Linear stress–strain relationshipsare given in Equations 1.2.14–1.2.25 In high-strain environments, theselinear equations may not hold true

The linear stress–strain relationships in a three-dimensional state of stressare shown in Equations 1.2.14–1.2.16 for the normal stresses The stresses andstrains are related through the elastic modulus (E) and Poisson’s ratio (m):

Equations 1.2.22 and 1.2.23 can be used to obtain principle stresses fromprinciple strains:

The change in resistance that occurs in a typical strain gage is quite small,

as indicated in Example 1.1 Because resistance change is not easily measured,voltage change as a result of resistance change is always preferred A Wheat-stone bridge is used to provide the voltage output due to a resistance change

at the gage The strain gage bridge is simply a Wheatstone bridge with theadded requirement that either gages of equal resistance or precision resistors

be in each arm of the bridge, as shown in Figure 1.10

1.3.1 THE BALANCED BRIDGE

The bridge circuit can be viewed as a voltage divider circuit, as shown inFigure 1.11 As a voltage divider, each leg of the circuit is exposed to the same

excitation voltage (Eex) The current that flows through each leg of the circuit

is the excitation voltage divided by the sum of the resistances in the leg, asshown in Equation 1.3.1 If the resistance value of all resistors is equal

As a voltage divider circuit, the voltages measured between points

A and D and between C and D, at the midpoint, are as shown in Equation1.3.3:

If the bridge is initially balanced, points A and C are of equal potential,

With the bridge output zero, eA eC¼ 0, Equation 1.3.6 results for abalanced bridge Note that the bridge can be balanced without all resistances

1.3.2 CONSTANT-CURRENT WHEATSTONE BRIDGE

The constant-current Wheatstone bridge (Figure 1.13) employs a currentsource for excitation of the bridge The nonlinearity of this circuit is less thanthat of the constant-voltage Wheatstone bridge (Dally and Riley, 1991) Theconstant-current bridge circuit is mainly used with semiconductor straingages The voltage drop across each arm of the bridge and the output voltageare as shown in Equations 1.3.7 and 1.3.8:

is then as shown in Equation 1.3.9:

Bridge Out/Excitation (mV/V)

Bridge Output at 5(mV)

eo¼ VAD VDC¼ I1R1 I2R2¼ 0 (1:3:9)Because the bridge is representative of a parallel circuit, the voltage drop

on each leg is equivalent and equal to the circuit voltage drop, as shown inEquation 1.3.10:

(I) can then be obtained by applying Equations 1.3.12 and 1.3.13:

R4 are multiples of R(R3¼ R4 ¼ kR, where k is any constant multiplier),

a balanced, more flexible output circuit can be designed as shown in Figure1.14

By substituting the resistance values in the circuit of Figure 1.14, Equation1.3.15 is obtained:

264

375

k

(1:3:16)

1.3.3 CONSTANT-VOLTAGE WHEATSTONE BRIDGE

The constant-voltage Wheatstone bridge employs a voltage source forexcitation of the bridge The output voltage is as shown in Equation 1.3.17:

multiples of R(R3¼ R4¼ kR), a balanced, more flexible output circuit can bedesigned, as shown in Figure 1.15.

By substituting the resistance values of Figure 1.15 into Equation 1.3.18,the sensitivity and linearity of the constant voltage Wheatstone bridge can becalculated:

375

in the bridge are replaced with active strain gages

With strain gages installed in the bridge arms, the bridge output is easilydetermined Figure 1.16 shows the previously examined bridge with a strain

quarter bridge as only one arm has been equipped with a strain-sensingdevice The anticipated bridge output is important, because most output is

B

kR

digitized through an A–D conversion process and then analyzed by

the strain and the bridge output if the component is expected to be loaded toapproximately 70% of its yield strength and the single gage has a gage factor

In the analysis, let the initial values of the bridge be as follows, with

Rgage1¼ R2¼ R3¼ Rgage2¼ R

For the half bridge shown in Figure 1.17, the output, with two active gages

is approximately 1.0 mV/V at 1000 microstrain If the bridge excitation is

10 V, the bridge output with the material loaded to about 70% of the yield is10.0 mV, or approximately 1.0 mV per 100 microstrain

If the bridge is configured with additional strain gages, the output of thebridge can be enhanced, provided the gages are properly positioned in thebridge If a component under test experiences a bending or torsional load,

it may be advantageous to mount the gages such that two gages experience

a tensile strain while the other two gages experience a compressive strain The

four gages, when wired into the bridge, complete what is referred to as a fullbridge, as shown in Figure 1.18.

compression This arrangement will provide maximum bridge output:

the bridge excitation:

Lead wires and lead-wire temperature changes affect the balance and thesensitivity of the bridge If temperature changes occur during measurement,drift will occur Dummy gages are used to compensate for componenttemperature variations that occur during the test

Length

A two-lead-wire gage system.

If all lead wires are of equal length, subject to the same temperature, and

of the same material, then Equation 1.5.4 is the governing equation A lead system compensates for lead-wire resistance and resistance change due to

1.5.3 LEAD-WIRE SIGNAL ATTENUATION

If long leads are used, the resistance in the leads will tend to reducethe gage factor of the system, reducing sensitivity, and, potentially, introdu-cing error The gage factor is based on gage resistance and gage resist-

1.5.4 DUMMY GAGES

Dummy gages can be used as temperature compensation devices, as shown

in Figure 1.21 The dummy gage and its lead wires provide compensation fortemperature changes of the test specimen, lead wires, and lead-wire resistancechanges if properly designed The dummy gage is ideally mounted on thesame type of material with the same mass as the test component or mounted

on the test component itself in an unstressed area The dummy gage must beexposed to identical conditions, excluding the load, as the test component

System calibration is a very important part of any measuring system(Figure 1.22) Calibration is performed by shunting a high-calibration resis-tor across one arm of the bridge circuit When possible, the shunt is placedacross one of the active arms With the calibration resistor in position, thebridge is unbalanced and a known output is produced The output voltage as

a function of the excitation voltage for this bridge is given quite accurately byEquation 1.6.1 and exactly by Equations 1.3.17 and 1.4.4:

Determine the equivalent resistance of the shunted arm and determine thebridge output.

If 120-ohm gages with a gage factor (GF) of 2 are used, determine theindicated strain

equations for a parallel resistance circuit as follows:

For a previously balanced bridge, with a 60-kohm shunt resistor in one arm,

a GF of 2, using a 120-ohm gage, the indicated strain is then given aspreviously shown in Equation 1.4.4

Switch

the data analysis stage The interdependency of the desired quantity andany unintended load-related quantities produces a cross-talk between themeasured data.

1.7.1 CANTILEVER BEAM IN BENDING

One of the simplest types of strain gage sensors is a cantilever beam inbending, as shown in Figure 1.23 For a cantilever beam, with the loadapplied between the end of the beam and the gage, the flexural outer fiberstresses and the strain on the top surface of the beam at the gage location are

1.7.2 CANTILEVER BEAM IN BENDING WITH AXIAL

LOAD COMPENSATION

The cantilever beam shown in Figure 1.24 has gages on both surfaces.Because of the configuration of the bridge, the gages compensate for anyapplied axial load and compensate for uniform temperature changes whilehaving increased sensitivity over the system shown in Figure 1.24 For thecantilever beam, Equation 1.7.2 is used, which is derived from Equation 1.4.4:

1.7.3 TENSION LOAD CELL WITH BENDING COMPENSATION

The bridge shown in Figure 1.25 has two gages in the axial loaded tion and two gages in the Poisson orientation This cell has both bending andtorsion compensation and is therefore sensitive to tensile and compressiveloads only The resulting bridge output is as given in Equation 1.7.3:

direc-DE

1.7.4 SHEAR FORCE LOAD CELL

The shear force load cell is designed with high sensitivity to shear forcewhile canceling the bending and torsion load output The bridge output of

A

B

D C P

1.7.5 TORSION LOAD CELL

The torsion cell shown in Figure 1.27 is highly sensitive to torsionalloading and insensitive to bending loads It is common to build this cellwith a pair of 908 gages located exactly 1808 around the shaft from eachother

1.7.6 COMMERCIAL S-TYPE LOAD CELL

A typical commercial-type load cell is shown in Figure 1.28 The cially available S-type load cell is a high-output load-measuring device thatoffers temperature compensation and inherent damage protection for thestrain gages These units are available in a range of load capacities

commer-BLACK WHITE

D C

(E −) (S−)

WHITE BLACK

A

B

D C