FEDERAL !.VIATION ADMINISTRATION

AbO 81996 ;·;:;

L-T-ECH-. N IC~AL-::CE:-:-::NTE~R L"7:1 BR--kRY-J ATLANTIC CITY INT'L AIRPORT, NJ 08~05

Strain Gage_ Instrumentation and Calibration of A Transport Aircraft Fuselage in _ Longitudinal Bending

W.F. Putman J.J:. Traybar

August 1985

DOT/FAA/CT-TN85/37

Document is on file at the Technical Center Library, Atlantic City Airport, N.J. 08405

AVAILABLE IN ELECTRONIC FORMAT

U.S. Department of Transportation

Federal Aviation Administration

Technical Center Atlantic City Airport, N.J. 08405

ililliilli 0001311:,8

NOTICE

This document is disseminated under the sponsorship of the Department of Transportation in the interest of information exchange. The United States Government assumes no liability for the contents or use thereof.

The United States Government does not endorse products or manufacturers. Trade or manufacturer's names appear herein solely because they are considered essential to the object of this report.

= -. '-

1. Report No. 2. Government Access i on No .

DOT/FAA/CT-TN85/37 4 . Title and Subtitle

STRAIN GAGE INSTRUMENTATION AND CALIBRATION OF A TRANSPORT AIRCRAFT FUSELAGE IN LONGITUDINAL BENDING

3. Rec ipient's Catalog No.

5. Report Date

August 1985 6 . Perform ing Organization Code

h:---:--:--:-;------------------------------j 8. Performing Organ i zation Report No. 7 . Author/ s )

William F. Putman and Joseph J. Traybar* 9. Performing Organization Name and Address

William F. Putman Company 3A Forrestal Campus Princeton, New Jersey 08540

10. Work Unit No . (TRAIS)

11 . Contract or Grant No.

13. Type of Report and Period Covered ~--------------~~----------------------~ 12. Sponsoring Agency Name and Address

U.S. Department of Transportation Federal Aviation Administration Technical Center Atlantic City Airport, New Jersey 08405

15. Supplementary Notes

*FAA Technical Center (ACT-330) Crashworthiness Branch Atlantic City Airport, New Jersey 08405

16. Abstract

Technical Note 14 . Sponsoring Agency Code

A strain gage instrumentation system was designed, fabricated, installed, tested, and calibrated for use on a full-scale transport type fuselage structure. Hydraulic jacks were used to apply loads to generate longitudinal bending moments on the transport aircraft fuselage structure. Strain gage data and load data were measured, recorded, and analyzed by means of a computer-supported data acquisition system. Results are presented as graphs of apparent strain at a given fuselage station, as a function of fuselage longitudinal bending moment.

17 . Key Words

Transport Aircraft Fuselage Structure

18. Distribution Statement

Strain Data Versus Longitudinal Bending Moment

Document 1s on file at the Technical Center Library, Atlantic City Airport, New Jersey 08405

19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of Pages 22. Price

Unclassified Unclassified Form DOT F 1700.7 (8-72l Reproduction of completed page authorized

,:!.

TABLE OF CONTENTS

Page

EXECUTIVE SUMMARY v

INTRODUCTION 1

TECHNICAL DISCUSSION 2

TEST RESULTS 4

APPENDIX

iii

Figure

l

2

3

4a

4b

5

6

7

8

9

10

11

12

l3

14

15

16

17

18

19

Table

l

2

LIST OF ILLUSTRATIONS

Comparison of Test Aircraft General Characteristics

Load Application Schematic

Fuselage Cross-Section (Rear View)

Strain Gage Instrumentation Layout

Strain Gage Layout and Load Cell Versus Channel Number

Boeing 707-131 Fuselage

Main Gear Bogie Jacks

Aft Body Station Attachment Rig

Tail Loading Structure and Aft Fuselage

Tail Upload at Aft Pressure Bulkhead

Tail Download at Aft Pressure Bulkhead

Calibrated Load Cell

Data Acquisition System and Support Computer

On-Site Data Monitoring, Conditioning and Printing Setup

Comparison of Load Cell and Hydraulic Gage Measurements

Primary Strain Channel 1 Versus Applied Bending Moment

Secondary (Redundant) Strain Channel 2 Versus Applied Bending Moment

Primary Strain Channel 3 Versus Applied Bending Moment

Secondary (Redundant) Strain Channel 4 Versus Applied Bending Moment

Tail Yoke Deflection Versus Hydraulic Gage Up and Down Load

LIST OF TABLES

Test Aircraft General Data

Loading Data

1V

Page

6

7

8

9

10

11

11

12

12

13

13

14

14

15

16

17

18

19

20

21

Page

2

5

EXECUTIVE SUMMARY

A strain gage instrumentation system was designed, fabricated, installed, tested and calibrated for use on a full-scale transport type fuselage structure. Hydraulic jacks were used to apply loads to generate longitudinal bending moments on the transport aircraft fuselage structure. Strain gage data and load data were measured, recorded , and analyzed by means of a computer-supported data acqu1s1t1on system. Results are presented as graphs of apparent strain at a given fuselage

• station, as a function of fuselage longitudinal bending moments.

~- · .. ~

v

INTRODUCTION

A full-scale transport airplane "Controlled Impact Demonstration" (CID) program was conducted by the Federal Aviation Administration (FAA) and NASA-Dryden on December 1, 1984 at Edwards Air Force Base/NASA-Ames/Dryden Flight Research Facility, Edwards, California. The major goal of the the CID experiments was to demonstrate and validate technology that can improve transport aircraft occupant crash survivability through reduced postcrash fire hazard and improved crash impact protection. One of the objectives related to improved crash impact protection focused on the acquisition of airplane structural data that would provide baseline impact and structural information that enhances the fundamental knowledge and understanding of transport crash structural behavior.

Selected CID aircraft fuselage and wing structure stations were instrumented with full strain gage bridges and associated wiring and equipment. Also, two data conditionin~/acquisition systems were installed onboard the CID aircraft.

Prior to the crash impact demonstration of the CID aircraft, the Crashworthiness Branch at the FAA Technical Center conducted a parallel experiment at their Atlantic City test site for the purpose of providing initial strain gage calibra­tion data and information directly related to the projected strain gage calibra­tions and test data acquisition on the CID airplane. The FAA Technical Center tests complimented the projected NASA/FAA strain gage calibrations and provided preliminary data values and data conditioning information pertinent to these particular CID efforts.

A portion of the instrumentation package onboard the Boeing 720-027 CID aircraft consists of fuselage mounted strain gage installations to measure the strain in the aft part of the fuselage structure. In order to provide some initial in·sight and to obtain a preliminary calibration of the candidate instrumentation system without dedicating or compromising the actual flight aircraft, a Boeing 707-131B fuselage located at the FAA Technical Center, Atlantic City Airport, New Jersey was instrumented and loaded in such a manner that the relationship between applied load and structural element strain on the Boeing 720, CID test aircraft could be inferred from the relationships observed on the FAA Technical Center test specimen aircraft, the Boeing 707-131B. Specifically, since the two fuse­lages of the two Boeing aircraft appear to be similar and are dimensionally identical at fuselage Body Station locations aft of BS-1020, comparable bending moments induced in their structures would produce comparable strains in either structure, up to the point of similarity (and structural fabrication identity) (figure 1) Thus, it was possible to determine and show the feasibility of performing a large-range loading calibration of the non-flight article (the Technical Center Boeing 707-131B) and apply the resulting calibration data to the flight art Jcle (CID, Boeing 720) with only an intermediate range proof loading of the latter J By this approach, considerable efficiencies of effort and cost were realized, as well as some initial insight into the strain/bending moment behavior for these types of aircraft fuselage structure. Moreover, when the CID strain gage calibrations are available in dimensional form, meaningfu~ comparisons between the Boeing 720 and Boeing 707 fuselage data can be made.

This report considers the design and installation of the instrumentation and calibration testing performed on the FAA Technical Center Boeing 707-131B fuselage on June 5, · 1984. This information was forwarded to NASA-Dryden for their projected B-720 calibrations. (ADFRF-FLRF-8401, October 1, 1984). The results of the FAA Technical Center experiments are shown in a series of dimensional calibration graphs.

1

TECHNICAL DISCUSSION

The two test aircraft utilized for this strain gage instrumentation and calibration of a transport aircraft fuselage in longitudinal bending were the Boeing 707-131B and the Boeing 720-027. Longitudinal bending is defined in this report as the bending induced along the fuselage length (and about the nose and main landing gear fulcrum points) as caused by vertical up and down loads applied at the tail . Figures 1 and 2, and table 1, depict and compare some of the aircraft's general characteristics and dimensions for the two test vehicles. The load reaction and jacking points are shown as well as the aft fuselage strain gaged stations at BS 1030. The FAA Technical Center test specimen was the Boeing 707-131B and the test specimen for the corresponding FAA/NASA experiment at Dryden (Edwards Air Force Base (AFB), California) was the Boeing 720-027, the candidate aircraft for the Controlled Impact Demonstration (CID).

TABLE 1 . TEST AIRCRAFT GENERAL DATA

Aircraft Version

FAA Type Certificate Data Sheet

Aircraft Serial Number

Maximum Ramp Weight

Maximum Landing Weight

Fuselage Length

Fuselage Length (Aft of BS 1030)

Moment Arm Between Load Application Station and Instrumented Station

Boeing 720-027

No. 4A28

18066

230,000 (pounds)

175,000 (pounds)

1,566 inches

646 inches

532 inches

Boeing 707-131

No. 4A21

17668

248,000 (pounds)

190,000 (pounds)

1,666 inches

646 inches

411 inches

As depicted ~n figures 1 and 2, it can be reasoned that, for geometrically and elastically identical structures of the aft section of the fuselage (i.e., aft of BS-1020), a moment distribution induced in the aft structure by a vertical ·load applied near the tail and reacted by the nose and main gear support points will be similar in both aircraft and proportional to the product of the applied load and the application distance (i.e., the moment arm). Although it is assumed, for the purpose of this experiment, that the two fuselage structures aft of BS-1020 are essentially geometrically and elastically identical structures, no detailed con­struction parts number and "parts-count" comparison was made of the two test air­craft fuselages. It is recognized that, depending on the buyer/customer, each air­craft could have different structural versions, but it is presumed that structural changes in the very aft sections of these two aircraft are not vast. Further, for

2

..

identically-placed strain sensors (strain gages) on the identical structures, the observed strains due to identical bending loads will be identical. In actuality, since the fuselage beam is composed of many elements joined together and the placement of gages on the stringers is subject to some variation, the observed strains will not be exactly identical. Proof loading of the flight aircraft should be a necessary but sufficient experiment to correlate the two structure/instrumen­tation systems.

Figure 3 presents a cross section of Body Station 1030 (BS-1030) on the Boeing 720/CID aircraft and indicates the strain gages instrumentation locations (A, B, C, and D) at this body station. This body station is identical to Body Station 1030 on the FAA Technical Center Boeing 707-131B aircraft which was instrumented as documented in figure 4. Note that the individual gages were combined into four element bridges, as indicated in figure 4, in such manner as to make them sensitive to longitud inal bending loads but insensitive to lateral bending, shear and axial loads and that bridge output in millivolts depends upon excitation voltage and gage factor (appendix). Referring to the expressions developed in the appendix, the br idge outputs can be expressed as follows:

For channels 1 and 2:

EA - EB Apparent microstrain = ~~-~~--Y-~ 1 + f:A + EB

For channels 3 and 4:

EA - EC Apparent microstrain = ~·-~~~-~~

1 + ~A + f:c

where E i is the strain in the micro inches per inch ( p. in/ in) at location i.

An interpretation of the bridge output information is to regard the entire fuselage as a beam instrumented to read longitudinal bending with two independent sets of instrumentation. Thus, by means of the calibration data presented herein and the bridge outputs, the bending moment at Body Station 1030 can be evaluated (redun­dantly). Reduction of the data presented later in this report gives the following relationships:

For channels 1 and 2 : I

Moment (pey unit microstrain) at Body Station 1030

MBS1030

= 34,400 i:~lb [Floor Orientation] 1 ,2 '

For channels 3 and 4:

Moment (per unit microstrain) at Body Station 1030

MBS1030 = 25,000 in-lb J!.E

3,4 [Lower Orientation]

3

Test Arrangement and Approaches

Figures 5 through 13 present photographs of the calibration test arrangement and the various items of test apparatus, identified as follows:

Figure Figure Figure Figure Figure Figure Figure Figure Figure

5 - Boeing 707-131 Fuselage 6 - Main Gear Bogie Jacks 7 - Aft Body Station Attachment Rig 8 - Tail Loading Structure and Aft Fuselage 9 - Tail Upload at Aft Pressure Bulkhead

10 - Tail Download at Aft Pressure Bulkhead 11 - Calibrated Load Cell 12 13

Data Acquisition System and Support Computer - On-Site Data Monitoring, Conditioning and Printing Setup

Two items of test apparatus are of particular interest; the tail load cell pictured in figure 11 allowed direct measurement of the vertical, up and dowri loads applied to the fuselage and greatly increased the confidence level in the data (figure 14). Also, the portable computer-supported data acquisition system (housed in the van) allowed reduced (dimensional) data plots to be available virtually online (figures 12 and 13). These facilities permitted the tests to be conducted and data reduced in one afternoon of testing.

The vertical load application apparatus, consisting of loading fixtures, a wide nylon bridle strap around the forward part of the fuselage and anchored to the ground (to inhibit nose lift-off for large tail downloads) and calibrated hydraulic jacks (figures 5 through 11), allowed precise vertical loading and positioning of the fuselage with backup transduction in the form of calibrated hydraulic pressure gages. These gages, calibrated in pounds-of-force at the jacks, were hand recorded and the data are presented in table 2. It should be noted that the bending moment data of figures 15 thru 18 were plotted using only the more accurate load cell readings shown in table 2. The hydraulic gage gear location readings also shown in the table are listed for the record only.

The loading apparatus and tail yoke were qualified for operation at loads up to 13,500 pounds at the tail jacking point and as limited by yeild stress (no factor of safety) in the loading fixture yoke.

TEST RESULTS

The test results are presented in figures 15 through 18; figures 15 and 17 are graphs of primary channels for upward and downward loadings. Figures 16 and 18 are plots of the secondary (or redundant) channel data. Comparison of primary and secondary plots demonstrates that both channels are in good agreement for all loadings.

The data presented in figures 15 through 18 serve to calibrate the instrumentation for measuring fuselage longitudinal bending moment -at BS 1030 (as induced by a vertical load applied at a moment arm of 411 inches from BS 1030). For downloads these data are quite linear and give slopes of 34,400 in-lb~E for channels ! ·and 2, and 25,000 in-lb~E for channels 3 and 4. The upload data are quite nonlinear, due possibly to the uploading of the riveted structure by removal of the dead weight gravity loading. The slopes as drawn reflect the apparent zero shift.

The tail movement and fuselage deflection data presented in figure 19 serve to indicate - further the nonlinear nature of the structure around the zero absolute load.

4

I DATA NO.

8 9

10 11 12 13 14 15 16 17 18 19 20 21 22

\JI 23 24 25 26 27 28 29 30 31 32 33 34 35 36

,, ~

•J

_. , J

~

TABLE 2. LOAD IN:; Jll.\TA, HYDRAULIC GAGES AND f.D..Zill CELL (LB. )

MAIN GEAR BOOIE NOOE I MAIN GEAR BOOIE I LOAD

LEFT I LEFT RIGHT I RIGHT TAIL APPLICATIOO FRONI' I REAR GEAR FRONI' REAR LOAD DIRECTIOO

13050 13000 13500 13250 15250 12600 0 UP 11800 12400 15600 14500 12500 2500 UP 10600 11000 17900 13400 12450 5000 UP 10800 11250 16400 13500 12500 2500 UP 11300 12000 13500 13500 12450 0 UP 11500 12000 13400 13500 12450 0 UP 12800 13400 10600 13500 13450 2500 OOWN 13550 14100 9000 13500 14100 4750 OOWN 13600 14400 10000 13500 14000 2500 OOWN 13400 13700 12700 13500 13800 0 OOWN 13400 13900 12900 14000 14000 100 OOWN 13900 14500 8400 14000 14500 5000 OOWN 14000 14850 9950 14000 14200 0 OOWN 14200 14900 8490 14000 14450 4975 OOWN 15050 15500 6200 14500 16000 7500 OOWN 15200 15750 5750 14500 16050 7750 OOWN 15400 15700 5500 14900 16000 7500 OOWN 16000 16550 4000 15400 17000 9750 OOWN 16100 16850 5500 15100 16900 5750 OOWN 13400 13500 12800 15000 15000 0 UP 10900 11000 17500 13500 12500 5000 UP 10800 11000 17500 13500 12500 5000 UP 10600 9800 19800 12200 11500 7500 UP

8700 8500 21500 11400 10500 9450 UP 8500 8300 22000 11000 10200 10000 UP 7400 7500 24000 10000 9500 12200 UP 8900 9400 19000 10000 9500 5000 UP

11500 11950 13500 11500 11000 0 UP

~I

2610 4860 2830 +50

2690 4340 2700 +50 100 4950 100 4900 7030 7440 7300 8990 5680 + 50 4790 4810 7130 8780 9380 11400 5250

0\ '

BOEING 707·131 B

BOEING 720

(CID AIRCRAFT)

'~ I 0 ., ~

II) ID

0 ., ~

II) ID

,, '(,

TRUE LENGTH =1 ,666"

~ 646" -------~

0 ., ., Ul ID

&

0 co ., ~ •

0 0 ... ... ., co Ul II)

ID ID

0 ., 01 II) ID

WHEEL WELL

· TRUE LENGTH =1 ,566

goo ... ., ooo ~~~

wl"4 Cl c( Cl z : In~

oog ., s 0 .,_ .... II) Ul II) 1D ID 1D ..

~ ~ ~I ... In"

0 II).,

ID~

646"

UP LOAD

f

0 .., .., ~

II) ID

TN-85/37-1

NOTE: SHADED AREAS REPRESENT TYPICAL ADDED SECTIONS FOR DIFFERENT VERSIONS.

FIGURE 1. COMPARISON OF TEST AIRCRAFT GENERAL CHARACTERISTICS

l ~

., ., ., iii ID

., ., 10

II) ID

'-J

•• ., ... , )

8·707·131 8

- 52'4"

837"

8·720

---·-

0 10 01 en m

1i ~ fi!IJ

~ g UPAND : ~ DOWN LOADS

~ . . ~ ~g: ::-to ~ ol\o411" ~ ~~OMENTARM g:

0 .., 0 .. ., en m

HYDRAULIC JACK & LOAD CELL

I 646"

1 ,020" .-.::.1 DOWNLOAD WEIGHTS PLACED ON STABILIZER

~

-~ en m

• 50'8'' ~ ~ MOMENT ARM ~ I: 817"•103" : IV 532" ..... 920" ,. 646"

TN-!35/37-2

FIGURE 2. LOAD APPLICATION SCHEMATIC

FUSELAGE BODY STATION 1030

60

0 0

STRAIN GAUGE LOCATION 8

40 20

STRAIN GAUGE LOCATION C

I

I 0 20

0 0

STRAIN GAUGE LOCATION D --~ _,,

40 60

STRAIN GAUGE LOCATIONS: A, 8, C, D.

---,-WL300

--+-WL210

--....J-WL 140 ~,..,

GAUGE ORIENTATIONS: A, B, D--. CHANNELS 1 & 2.

:A & C _,..CHANNELS 3 & 4. TN-85/31-3

FIGURE 3. FUSELAGE CROSS-SECTION (REAR VIEW)

8

LEG NO. 1

------S(+)

......_.-----E(-) a....---------S(·)

CHANNEL NUMBER 1 : Primary Bridge at Upper and Floor

Legs 1 and 3 at top, upper fuselage Leg 2 near floor on portside Leg 4 near floor on starboard side

CHANNEL NllJMBER 2: Secondary (Redundant) Bridge at Upper and Floor

Legs 1 and 3 at top, upper fuselage Leg 2 near floor on portside Leg 4 near floor on starboard side

CHANNEL NUMBER 3: Primary Bridge at Upper and Lower

Legs 1 and 3 at top, upper fuselage Leg 2 at bottom (port) lower fuselage Leg 4 at bottom (stbd) lower fuselage

CHANNEL NUMBER 4: Secondary (Redundant) Bridge at Upper and Lower

Legs 1 and 3 at top, upper fuselage ~ ~ Leg 2 at bottom (port) lower fuselage

Leg 4 at bottom (stbd) lower fuselage

~. CHANNNEL NUMBER 5: Load Cell Readout

Calibx·ated in pounds. · Load times 411-inch moment arm equals applie:d moment ( in-lbs).

FIGURE 4a. STRAIN GAGE INSTRUMENTATION LAYOUT

9

..... 0

NOTE: INSTRUMENTED BODY STATION VIEWED FROM REAR

CHANNEL1 CHANNEL2 CHANNEL3 CHANNEL4

PRIMARY . .

REDUNDANT .PRIMARY REDUNDANT (SECONDARY) (SECONDARY)

LOCATION A . LOCATION A LOCATION A LOCATION A

~ ·~ ~ /.(Jl LEG

NUMBERS

2 4

(CATION ) (' /1 \ (LOWER)

B LOCATION

D

. BRIDGE ORIENTATION

UPPER (A) AND

FLOOR (B,D)

lo ... ~

LOCATION LOCATION LOCATION LOCATION B D c c

BRIDGE BRIDGE BRIDGE ORIENTATION ORIENTATION ORIENTATION

UPPER (A) UPPER (A) UPPER (A) AND AND AND

FLOOR (B,D) LOWER (C) LOWER (C)

FIGURE 4b. STRAIN GAGE LAYOUT AND LOAD CELL VERSUS CHANNEL NUMBER

" ( o ,, fl ,

CHANNELS

APPLIED MOMENT MEASURE

AFT FUSELAGE LOAD CELL

X MOM. ARM EQUALS

APPLIED MOM. (IN-LBS) TN-85/37-4(b)

r

FIGURE 5. BOEING 707-131 FUSELAGE

FIGURE 6. MAIN GEAR BOGIE JACKS

11

•

FIGURE 7. AFT BODY STATION ATTACHMENT "RIG

- . ~ ·

FIGURE 8. TAIL LOADING STRUCTURE AND AFT FUSELAGE

12

FIGURE 9. TAIL UPLOAD AT AFT PRESSURE BULKHEAD

FIGURE 10. TAIL DOWNLOAD AT AFT PRESSURE BULKHEAD

13

FIGURE 11. CALIBRATED LOAD CELL

FIGURE 12. DATA ACQUISITION SYSTEM AND SUPPORT COMPUTER

14

e

~ <&

itt

... FIGURE 13. ON-SITE DATA MONITORING, CONDITIONING AND PRINTING SET-UP

15

PLOAD CELL

10

8

6

4

10001b

2 PLOAD CELL =0. 93P HYD. GAGE

0~------~------~----~.------.-------.--0 2 4 6 8 10

PGAGE, 1 000 lb

FIGURE 14. COMPARISON OF LOAD CELL AND HYDRAULIC GAGE MEASUREMENTS

16

~ I

.... '-J

160

120

80

c ,._ I~ 40

,-~ 0 0 L u ~

E -40

1 -~ ! tO -80

L

+> (J)

-120

-160

.. . .. \ J ' ..

707 Strain Te s t Data {Channel :JI:l vs. Channel 91=5 * 411 in)

--- ······-,----··-----

l~-~ --~- F-~ -- ------~:+~--~:~--r-t ~-~~--~---d ----­--- i-----~-- - t---- ------ -~----· -------~---- -------- ~- --------- + ---- -----_i ______ _J__ _ ____ J_

J-+-- t-t - I~ _____ j

-~ --1----------

' ------___ i ___ - ·------~-' ~ -- -:- ------ --+---------- -- -~- ---·------~---- - I -- - -1 ---------r------ --r- 1 -- ----- --+-- .J- --------- ~-----· ---- - _____ I ___ -:1-- I I ! - - I I I ---------

-240 - SL I 1 ___ 1--r--1 ----- ~----~-- - --~ --t·-1 _ __ L I i ---]

- 200

-5 - 4 -3 - 2 -1 0 1 2 3 4 5

Up l o ad at t a i l 6 Download at tail . Bending Moment * 10 , in - lb s

L ______________________________ ___ __ ___________________________ ·-------·-----------···--····--- ---------- --- -···- --------------------

FIGURE 15. PRIMARY STRAIN CHANNEL 1 VERSUS APPLIED BENDING MOMENT

,_. 00

- ---· - - ---- - ----· ---· ---·-- -- ---- ~--------- -- --·- - --~------ --- - --· ·· ------- ---- ------- -r·-- ------1

?07 Strain Test Data {Channel #2 vs. Channel :JI:5 * 411 in }

I 160

I 12

-T ~ -- I T---r--- I I ! , . I I . .

0 r - ----1--------~ - ---r- -- ~-- ----1 I s0

I ~ 40 ~---l ----t-_ - --~ --- -t- +-----+- ---!-- ---- ~ - -- i--~---l o i I ; I I r 1 ~ 0 ---- -- - ----- - ----- .. ·------ ---,---- --- --------J-- ---- - , --.. ·---.. ---_- _ .. ___ -------r----- ------·-------1 ·~ I j I I I . I E I I I -40 ___ ____ .. ___ ___ ·------------ .... ,...-... -... ... ...... ... ·t---------- --- --------..

i ~ -80 1- ----- --~ 1 -- -- L. -- I ____ l ___ j _ --- ~- - -+ --·-+------i---·--·-··------~ I I I I I I I

-120 1- ------- -- ~,~ -- +- l -------r --_ - ~~· - ---:------ t--- t --- ~ -----1 , r . , ! ____j__ I -160 1- - -- ---- - ---t - ----- - ·1··--- - --·- ---- ----·l- -- --- -~---- - --- ·- - ---· ___ l ______ 1 ____ l _____ --- _ I I ! 1 ! I I I I I

-200 L- n t --t ---r--+ ---t ------ ---~- ----t-- --j-- - ~ - 2 4 0 ____ _j _ _ _ __j_____ _l __ ___ L _______ ~__ __ j _______ ..L ____ L ______ _L _ _ _

- 6 - 5 - 4 -3 -2 - 1 0 2 3 4

I Up 1 o ad at t a i 1 Down 1 o ad at t •a i 1

L ... .. . .

s Bending Moment * 10, in-lb s

---- ---------··· --· -- ··-··-·-·· ... ·· ··· - - · --·--· ---···-·- -·--· -·-. ·· ··----- ·- ___ " ___ ·-· --- ----- _ ...... ..... --- .. . ·------------·-·

FIGURE 16. SECONDARY (REDUNDANT) STRAIN CHANNEL 2 VERSUS APPLIED BENDING MOMENT

b ,, ,. ~ to (I

•• \•

~

5

I i

I

I - .. .J

.._ 1.0

ti .. • J

·'!<

" ,. .. ~-- --- - - -- ------- --- -·-. -·--- -- - - - - - -----------··- ------------ ------------------- -------- ------- . -- ·- --------,

1

707 Strain Test Data (Channel *3 vs . Channel *5 * 411 in) · . j

I· ::: IT~=[·~~-~~L]~ _L: ___ j ___ ~--~L-~_] I . I I I i i II \ 1 ,, , 1 I I I 8 0 - - ---·+------_____ l __ ··-------1------ ---- --- -·- --·-·- --·-- --· ---------+--______ ,

1_________ --------···

1·- -----t---- -

c I I I I I I I

I , r j . r- j------- _______ _j~--- ---- - ··------ ·----·--·· 0 -·-·l ··-- -·--'-·-··---- -- ' I

L 0 ~ i [ . I . -----·-··t-· -----·-···-··! ·--·--·-_--·--· u ' l I I ' ~ ········-· --·- o.···----- -----i-···---·------· .E - -··-·-·-· ····. ··-- ·--- -- ··-·- ·-·---- --I~ --- - - - ----- ........ 1. I ., I I . ~ -40 -------. I . . : I .0 -80 L

! .p (J)

-120 I

I -160 I ~-- -- - --+ I I I I l I ----\-----v r ·--- - - ~ --- t ---.---- -t -r --·-, -----·t· -·---~- - -· - ~--- --T--- ·· · ·+ -- ·=t· -- ---- ---1--------t-------·- ___ j_ _________ lt __ --· ·----200 ~ - - -- · ·---1- --

1 j ! I i i I l _______ j____ I [__ _j _ ____ _L__j ' __ _j

1

. -240 L I --6 --5 -4

l Up l o ad at t a i 1

. ·- ·· ·· ···--·- -~-- ·· ·---------·"- .__. __ ____ , .. _____ __ - - -- ·-··-··- ··

-3 -2 -1 0

6 Bending Moment * 10,

2 3

Download i n-lb s

FIGURE 17. PRIMARY STRAIN CHANNEL 3 VERSUS APPLIED BENDING MOMENT

4 5

at ta i 1

I I I

I l

......... J

N 0

?0? Strain Te s t Data

---··-------·--·-------------------·-----------·-------·------·l {Channel 4!:4 v s . Channel #5 * 411 in ) 1

160

120

80

c

I ~ 40 i c I ~ -~

i 0 0 L 0

j ·~

-- -1--=r-------- -F---~- +---~------t--~~- -~1--- ---zt--___ L ___ __ r_ -1--j----r----1---- ! -- -;- ~--- -r- -

~--+ ---l · - -+ - --~ ~---~- ----~ _____ t __________ l ~-t-----r--·--- ---- -------1---- r- --+--- . -- -----~

IE -40 I ~ l c !-~ I IU -80

L

+-'

I 1 . '- I I

- -- -- --~- -----r-=~~t:=-~- -~ = --- --~=-: r ~=--l••~•~] - ---- - -~-- l -1 I I l I I I ! ; , (f)

I

I - 120 I

1 -160

I I l -200

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APPENDIX

E el = E - Rl

ez = E - Rz

il E =

Rl + R4

0

For longitudlinal (vertical) bending: R1 = R3 and Rz = R4

Therefore i1 = iz = i = E R1 + Rz

e out = e = ez - e1 = i (Rl Rz)

e E

= Rl - R2 R1 + R2

= R+ .. ~R-R- ~Rz

2R+ ~R1 + ~R2 =

where G = E (~in/1n) and at G = 2

e E =

il

iz

lz = E ' Rz + R3

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