The determination of effective column length from strain measurements

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Material Information

Title:
The determination of effective column length from strain measurements
Series Title:
NACA WR
Alternate Title:
NACA wartime reports
Physical Description:
6, 18 p. : ill. ; 28 cm.
Language:
English
Creator:
Schuette, Evan H
Roy, J. Albert
Langley Aeronautical Laboratory
United States -- National Advisory Committee for Aeronautics
Publisher:
Langley Memorial Aeronautical Laboratory
Place of Publication:
Langley Field, VA
Publication Date:

Subjects

Subjects / Keywords:
Airplanes, Tailless   ( lcsh )
Aerodynamics -- Research   ( lcsh )
Genre:
federal government publication   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )

Notes

Summary:
Summary: A method is presented for the experimental determination of the effective length of a column for which the end conditions are unknown by establishing the points of zero curvature from readings of strain gages distributed along the length of the column. Tests of four columns of different cross sections indicated that the proposed method gives satisfactory results even when there is considerable scatter in the strain-gage readings.
Statement of Responsibility:
by Evan H. Schuette and J. Albert Roy.
General Note:
"Originally issued June 1944 as Advance Restricted Report L4F24."
General Note:
"NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were previously held under a security status but are now unclassified. Some of these reports were not technically edited. All have been reproduced without change in order to expedite general distribution."

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003804669
oclc - 123894156
System ID:
AA00009424:00001


This item is only available as the following downloads:


Full Text

F cftL-N. 1
ARR No. L4F24


NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS






WARTIME REPORT
OMNALLY ISSUED
June 1944 as
Advance Restricted Report L4F24

THE DETERMINATION OF EFFECTIVE COLUMN LENGTH

FROM STRAIN MEASUREMENTS

By Even H. Schuette and J. Albert Roy

Langley Memorial Aeronautical Laboratory
Langley Field, Va.












3L. t*.: .' "'


WASHINGTON

NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of
advance research results to an authorized group requiring them for the war effort. They were pre-
viously held under a security status but are now unclassified. Some of these reports were not tech-
nically edited. All have been reproduced without change in order to expedite general distribution.

L 198







































Digitized by the Inlernel Archive
in 2011 wiIIh ILunding Irom
University oi Florida, George A. Smathers Libraries wilh support from LYRASIS and the Sloan Foundalion


http://www.archive.org details 'delerminaiioOlang








NACA ARR Mo. LF24

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS



ADV4i:CE RESTRICTED REPORT



THE DETERMINATION OF EFFECTIVE COLUMN LENGTH

FROM STRAIN MEASUREMENTS

By Evan H. Schuette and J. Albert Roy


SUMMARY


A method is presented for the experimental deter-
mination of the effective length of a column for which
the end conditions are unknown by establishing the points
of zero curvature from readings of strain gages dis-
tributed along the length of the column. Tests of four
columns of different cross sections indicated that the
proposed method gives satisfactory results even when
there is considerable scatter in the strain-gage readings.


INTROEUCT TOI


A suitable method is needed for experimentally
evaluating the effective length from column tests in
which the end conditions are unknown. One such method
consists in establishing the deflection curve from meas-
urements of lateral deflections and estimating from this
curve the locations of the inflection points. The prin-
cipal objection to this method is that the determination
of inflection points from an experimentally established
curve is an inherently inaccurate procedure. A more
accurate method of establishing the inflection points
consists in measuring the curvature rather than the
deflection and establishing from such measurements the
points of zero curvature, which define the inflection
points. The present report shows how strain measurements
can be used to indicate curvature and thus to establish
tie effective column length. Four columns of different
cross sections were tested to provide an experimental
check of the method.








2 NACA ARR No. L4F24


SYMBOLS


L actual length of column, inches

Le effective length of column, inches

El, 2 strains at two points in cross section

d distance between points in cross section for
which strains E1 and E2 are taken, meas-
ured perpendicular to neutral axis, inches

r radius of curvature, inches


METHOD OF TITAS'i I;*' CHUVATURE AEID DETERMINING

EFFECTIVE CC.LUrMI1 LENGTH


If it is assumed that sections remain plane after
bending, the curvature 1/r of a column at a given cross
section is related to the difference in strain at two
points on the particular cross section according to the
e iuation

1 El '2
r d

This equation indicates a convenient experimental method
for determining curvature from strain measurements taken
along the length of the column. The method consists in
attaching a number of strain gages on opposite sides
of the column along its lenQth and recording the dif-
ferences in strain on the two sides. It is then necessary
only to plot the curvature or, if d is constant, the
strain difference 1 2 against distance along the
length of the column and to determine the points of zero
curvature.


SPECIETENS AND TEST EQUIPMENT


In order to check experimentally the practicability
of the strain-measurement method for determining effective








NACA ARR No. LLF24 5


length, colu-r.ns of four different types of cross section
were tested. A rectan.-'.,lar car xvas tested vwith strain
gigEes placed copprite cacv h c.,.her n-. the wider sides. The
cross sections and th? locat.' ns of th- resistance-type
wlre strain ages for tihe Z--.cti..n ccluinn, the skin-and-
stiffeicr ccl.Jrn, ar.d the i nc-st. -er; -1 penel column are
shown in figures 1, 2, and 3, resuectively.

The wire strain gages were attached along'the length
of each column at small intervals. The.j approximate
distance d between strain gags at a particular cross
section, measured perpendicular to the neutral axis, was:


Column I d



i ffe. i er i
C- .- -
--i : ... .



The over-all &c"urac,, of the strain measureanents was
within 2 percent.

Th, sp ,l;imens were tested filt-ended in hydraulic
testing machir.es having accuracies within three-quarters
of 1 recent for the range of load used. Figure 4 shows
the Z-sr-ction column under load.


RESULTS AIJD DISCUSSION


The results of the tests are presented in two sets
of figures. The first set (figs. 5 to 8) shows the
curvatiure of the ;ol'.un-s, as given by the di'L'frerces in
stiusin for the g ges aL each cros3 section, plotted
against ,'istance iaonx the Icrlgtr, of the colt-r ."or
several lo.d? ne.r the- r.i nitmum. load. The ht~ i:- tal
lines r'ep-r' sent zerio t.3-in d] fference. I"' '.-:- C nd set
(I'i.s. rQ t,_' 12) 3'.C". o .s c ratio i' effEctive D, .h to
actual le .., obtained fron the first set of' i -siures,
plotted against Load.

Except for the Z-scction column, the values plotted
in figures 5 to 3 represent the increase of curvature







4 NACA ARR No. LLF2


caused by loads in excess of a particular initial load
near the maximum. The use of a fairly high initial load
in the calculation of strain differences had the effect
of eliminating a large part of the scatter in the test
data. It was believed that this procedure would not
affect the accuracy of the results, because the strain
differences at the particular initial load were quite
small in comparison with the differences that were
recorded at leads near the maximum. For the Z-section
(fig. .), however, a somewhat more satisfactory plot was
obtained wh.n the strain increments were taken from zero
load, because large strain differences were recorded as
soon as loading was started.

A part of the scatter in the plot for the skin-and-
stiffener column (fig. 7) results from the fact that
slightly different curvatures were measured on the right
and left sides of the cnlumn. Near the bottom of the
column, especially on the left side, some of the scatter
is thought to be due also to local buckling of the skin.
All strain gages were placed on the stiffener, but it is
probable that the effect of the buckles in the skin
carried over to some extent into the stiffener and influ-
enced the strain readings.

In the plot for the hat-stiffened panel (fig. 8)
the effects of any possible differences in curvature
between the two stiffeners to which strain gages were
attached were eliminated by using averages of the corre-
sponding gage readings-on the two stiffeners.

Figures 5 to 8 establish the effective lengths for
several loads below the msaimum. In order to extrapolate
from these values to the maximum load, the ratio of
effective length to actual length is plotted against load
in figures 9 to 12. In the extrapolation, greater weight
was given to the values obtained at the higher loads.
This procedure seemed justified because the absolute
scatter in the curvature plots was approximately the
same for all loads and thus relatively less important
in comparison with the greater curvatures that existed
at higher locds. Theoretical considerations, moreover,
lead to the conclusion that the shape of the elastic
curve for maximum load is more and more accurately
ajproximated as the maximum load is approached, and the
effective length thus approaches a definite value.








iiACA ARR No. L'4F214 5


It will be noted that, for all except the Z-section
column, a reasonable extrapolation to maximum load was
accomplished by drawing a horizontal line through the
test points. This fact is of particular interest in the
case of the skin-and-stiffener column (figs. 7 and 11),
for which quite consistent results were obtained even
though considerable scatter was evident in the curvature
plot. For the Z-section column (fig. 10), the extra-
polation was accomplished by drawing a curve through
the points for high loads in such a manner that the
tangent to the curve was horizontal at the maximum load.

Because of the presence of ineffective widths of
skin, it was impossible to check the loads obtained from
the skin-and-stiffener column and the hat-stiffened panel
against the values given by the Euler column formula.
Such a check was made for the other two columns, however,
and the results are given in the following table:


Experimental Euler load
maximiun load based on experi-
Conn (Ib) mental Le
(lb)
Bar 50,000 147,800
Z-section 2,800 2,950


The calculated values of Ruler load, based on the experi-
mentally determined effective length, are within 5 percent
of the test values.


LIMITATIONS OF' THE METHOD


The method presented for the determination of effec-
tive column length from strain measurements is not
applicable in all cases. If there is local buckling of
the column, the strain measurements will be adversely
affected. Whether the results are completely invalidated
will depend on the extent to which the local buckling
takes place at the points where the strain gages are
located. In the tests of the skin-and-stiffener column
reported herein the local buclkling did not carry over
into the sides of the stiffener, where the strain gages
were located, in a sufficient degree to invalidate








NACA ARR No. L4F24


completely the results obtained but the effects of the
buckling were evident in the strain measurements.

Another limitation is imposed by the size of the
column being tested. It is evident that the accuracy of
the results depends to some extent on the distance d
between strain gages. If the column cross section is
such that this distance must be small, the accuracy of
the results will be impaired, especially if there is a
variation in strain across the width of the strain gages.


CONCLUDING REMARKS


The test data presented indicate that the proposed
strain-measurement method for the experimental deter-
mination of the effective length of a column for which
the end conditions are unknown gives satisfactory results
even when there is considerable scatter in the strain-
gage readings.


Langley Memorial Aeronautical Laboratory
National Advisory Committee for Aeronautics
Langley Field, Va.






NACA ARR No. L4F24


Strain gage


NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS


Figure 1.-


Cross Sec ton of
column.


Z- section


Fig. 1









%






NACA ARR No. L4F24


Strain gage


NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS


Figure 2. -


Cross section of skin-and- stiffener
column.


Fig. 2



























i





NACA ARR No. L4F24


Figure 3.-


NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS

Cross section, of hat- tiffened panel
column.


Fig. 3


Ft- nf,














NT






NACA ARR No. L4F24


Figure 4.- Z-section
column under load.


Fig. 4



















,N -






NACA ARR No. L4F24


Top Bo/tom


tNA TONAL ADVISORY
COMMinEE FOR AEROLWTIICS

S.002 Curvature,
1/in.
2
Lst/ance along column, in.


figuree 5.- Curvalure of rectonular
bar.


Fig. 5a


















SY
-






NACA ARR No. L4F24 Fig. 5b


Top Bottom


Load= 485


Distance long column, in.


Figure 5.- Continued.


S NATlONhA ADVISORY
CC MMiTniE FTR ALRONAUIICS


Toooz Curvature,
O/in.












N,, -






NACA ARR No. L4F24


Top Bottom


Lood= 49.5 kips


Distance along column, in.



Figure 5.- Concluded.


NAIialaL ADVISORY
COMMiiIEE FOR AERONAUTICS



S0002 Curvature,
I/in.


Fig. 5c

























a.






NACA ARR No. L4F24


Top Bottom



o Load =2.40 Aips









o 2.45









2.50






0002 Curvaoure,

Distance long column, in.
NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS
Figure 6.- Curvature of Z-section
column.


Fig. 6a









NACA ARR No. L4F24


Top


Bottom


Load: 2.55 kit


2.65


NATIONAL ADVISORY
COMMITTEE FOR AEPOINAuIICS


I.oo2 Curvalure,
I/in .


Distance among column, in.


Figure 6.- Continued.


Fat


Fig. 6b










N'






NACA ARR No. L4F24


Top Bottom






0
SLoad= 2.70 has













2.75








NATIONAL ADVISORY
COMMuITEE FOrR AERONAUTICS


0ooo2 Curvature,

Distance along column, in.


Concluded.


Fig. 6c


i


Figure 6. -









N







NACA ARR No. L4F24


Top

:-8


Bottom
ro^0-
^c-,~


Load= 270 kips


Qt0%Q -,


- 0


o -



20.5


N'
-~


"10
10'


Distance along column, in.


/ C
ooo00005 Curvature.
I/in.


SRight side
o Left side


Figure 7 Curvature of skin- ond- stiffener column.


__- Wa


Fig. 7














Top Bottom

0
o o


\



0 Load= 30.5 kips o

II



S\ /










31.0


0 0

o\ 1

~\ NAIIONAL AO1ISORf
S/ COMMinEE FOR AERiEAUTICS


S000oo05 Curvatui
/0 0/ i n.
Distance o/ony column, in.
o eightt side
o Left side


Niure Concluded.


NACA ARR No. L4F24


Fig. 7b


"e.









NACA ARR No. L4F24


Top Bottom



\ Load =113 kips

/
\ ,


1//6
/16^


1/9


\ NATIONAL ADVISORY
\ COMMIfEE FOR AERONAUIICS

.0002 Curvature,
1/in.
5
LDstance along column, in.


Figured.- Curvoaure of hat-stiffened
panel column.


Fig. 8a













NT






NACA ARR No. L4F24


Top Botlom


Load = 22 kios


/
/
/
/
N. -


125


NATIONAL ADVISORY
COMMI[n[[ FOR AERONAUTICS


5
distance along


\/
\ i


I
r0a2 Curvature
1/in.


column, in.


Figure d-Concluded.


Fig. 8b



















-a'.
1t






NACA ARR No. L4F24


.6




.5




.4




.3

Le
L

.2









0


46


49


Load, kips


Figure 9. -


Ratio of effective length to actual
length for rectangular bar.


Maximum load









L Le

I -




NATIONAL ADVISORY
COMMITTEE FOF AERONAUTICS


45


50


Fig. 9









K






NACA ARR No. L4F24


.5



.4



S.3

Le
L
.2


2.T


2.6


2.7


2.8


2.9


Load, kips


F/iure /0. -


Rotio of effective length to actual
length for Z-section column.


N/aximum load-








--
L Le






NATIONAL AD ISORY
C MMITTEE FOR A RONAUTICS


Fig. 10









,






NACA ARR No. L4F24


.6



.5



.4



.3

Le
L
.2






.

0


?8 29
Load, kibs


30


Fiure ll.-Rafio ao effective lengthh to actual
lengthh for akin on tiffener column.


l7



Maximum load--f






r-
L Le




NATIONAL AD ISORY
__ _MMITEE FOR A iONAUTICS


Fig. 11


















K






NACA ARR No. L4F24


e6-


maximum /load







L Le

'




NATIONAL A VISORY
COMMITTEE FOR AERONAUTICS


/22


/26


Load, kips


Figure 12.-


Paf17 of eYffective length to acfuo/
lengthh for hot stiffened panel
column.


.4



.3

Le

.2


O10


/10


Fig. 12








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