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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

TECHNICAL NOTE

No. 1564

METHODS OF CONSTRUCTING CHARTS FOR ADJUSTING TEST . RESULTS FOR THE COMPRESSIVE STRENGTH OF PLATES

FOR DIFFERENCES IN MATERIAL PROPERTIES

By George J. Heimerl

Langley Memorial Aeronautical Laboratory Langley Field, Va.

Washington

April 1948

TECHNICAL LIBRARY ~IRESEARCH MANUFACTURING CO.

9051·9951 SEPULVEDA BLVD. INGLEVIOOD, CAL I FOP. r~ I A

I

https://ntrs.nasa.gov/search.jsp?R=19930082370 2020-07-26T20:05:04+00:00Z

NATIONAL ADVISORY COMMITTEE FOR AERONAUI'ICS

TECHNICAL NOTE NO. 1564

METHOffi OF CONSTRUCTING CHARI'S FOR ADJUSTIID TEST

RESULTS FOR TEE COMPRESSIVE STRENGTH OF PLATES

FOR Dll,]'ERENCES IN MATERIAL PROPERTIES

By George J. Heimerl

SUMMARY

Methods are presented for constructing charts suitable for ad justing to standard values plate test results for the critical compressive stress and the average stress at maximum load. The methods take into account the difference between the compressive properties of the material used for the tests and those upon which the design is to be based. Illustrative charts are included for extruded 24s-T and 75S-T aluminum alloys.

INTRODUCTION

The results of tests to determine plate compressive strength~ as i n the case of columns , cannot be used directly for design purposes) because the compressive properties of the material used for the tests ordinarily differ from the standard values to which the design is to be made. Methods are consequently necessary for ad justing plate test results for differences in compressive properties.

Extensive tests were made recently to evaluate the plate compressive strength of various aircraft s tructural materials (see summary paper, reference 1) and to show how the compress ive strength of plates could be determined from the compr essive stress-et rain curve for the material. The conclusion was reached that the critical compress i ve stress for the extruded plate assemblies could be obtained approximately by the use of the secant modulus of elasticity . (See also r eferences 2 and 3.) On the basis of these tests, methods have been devised for adjusting for differences in material properties plate test results for the critical compress ive stress and the average compressive stress at maximum load .

For convenience in adjusting plate test results , charts providing adjustment factors are useful for des ign purposes . This paper therefore presents methods for constructing such charts and includes illustrative charts for extruded 24s- T and 75S-T aluminum alloys.

l

2

€cr

Eteat

O'test

O'crstd

NACA TN No. 1564

SYMBOlS

calculated elastic critical compres.sive strain

compressive strain taken from compressive stress-etrain curve for material tested

compressive stress corresponding to Etest

compressive stress taken from standard stress-etrain curve

test result for critical compressive stress

value of adjusted to standard value

°' test result for average compressive stress at maximum load nl8.X.test

O'cYstd

c

value of C1mev adjusted to standard value ~est

compressive yield stress (O.? percent offset)

compressive yield stress taken from stress-etrain curve for material tested (0.2 percent offset)

com~ressive yield stress taken from standard stress-etrain curve (0.2 percent offset)

adjustment factor by which

°' Grstd

adjustment factor by which

obtain

constant

°' crtest

a maxtest

CHARI'S

is to be multiplied to obtain

is to be multiplied to

Charts for adjusting to standard values plate test results for the critical compress ive stress and the average stress at maximum load are shown in figures 1 to 3 for extruded 24s-T and 75S-T aluminum alloys. In the following sections ~ the principles upon which the c,harts are based are presented and the accuracy and range of applications of the charts are briefly discussed .

NACA TN No. 1564 3

Charts for the critical compressive stress.- The results of the tests of the H-, Z-, and C(channel)-eection plate assemblies for extruded aluminum and magnesium alloys showed that the basic relationship between the test results for the critical compressive stress crcrtest and the calculated

elastic critical compressive strain Ecr is given approximately by the

secant modulus of elasticity taken from the compressive stress-etrain curve for the material (see reference 1). Hence for a given value of Ecr' the adjustment factor Kcr by which cr is to be ·multiplied in order crtest to obtain the standard value crcrstd is determined by the ratio of the

compressive stress crstd taken from the standard stress-strain curve to

the compressive stress crtest taken from the stress-strain curve for the material tested. Thus,

where

crstd K = ---cr crtest

When values of crcrtest and Ecr and the stress-etrain curve for the material tested and that for the standard design are given, values of crcrstd ~ be readily determined from e~uation (1). Such a procedure,

(1)

however, is not as convenient as the use of adjustment charts of the nondimensional form given in the ANG-5 bulletin (reference 4) in which only the ratios crCYtest/crCYstd and crcrtest/crCYtest are re~uired. Methods

for constructing such charts , based upon e~uation (1), are therefore included and, because of the detail involved, are given in the appendix.

The accuracy of the charts depends first upon whether the buckling stress-strain curve (Ocrtest plotted against Ecr) and the compressive

stress-strain curve for the material are affinely related and second upon whether the families of compressive stress-strain curves for a given material are themselves affinely related. For the first condition, the curves are affinely related if one curve can be obtained from another by the trans­formation · 0crtest = COtest and Ecr = CEtest' where C is a constant

and Etest is the strain corresponding to 0test from the compressive stress-strain curve for the material tested . Reference 1 showed that the secant-IDodulus relationship is an approximate one which varies somewhat for different materials and types of plate assemblies. The test r esults (reference 1) together with unpublished data, however, indicate that an affine relationship between buckling stress-etrain curves and compressive stress-strain curves may be expected for a given material and type of plate assembly. Conse~uently, the value of C is approximately a constant

-----.----~ ---

L

4 NACA TN No. 1564

for a given material and type of plate. With regard to the second condition -whether stress-etrain curves for a given material are affinely related -observation has shown that such a relationship often actually holds to a good degree of approximation (see reference 5). If affine relationships hold for both conditions, e~uation (1) is valid and the charts will provide an accurate method for adjusting 0crtest. Furthermore, if both these conditions are met,the method is general and may be applied to other than extruded materials and H-, Z-, and C-sections.

The marked differences between the charts for extruded 24s-T and 75S-T aluminum alloys (see figs . 1 and 2) emphasize the fact that a chart suitable for one material cannot generally be used for another.

Charts for the average stress at maximum load.- For stresses greater than three-fourths the compressive yield stress 0cy' adjustment charts such as shown in figures 1 and 2 for 0crtest can also be used to adjust

test results for the average stress at maxiIDum load amax t' because tes

0maxtest is approximately e~ual to 0crtest in this high-stress region

(see reference 1). The same principles and methods for constructing adjustment charts for Ocrtest' conse~uentlYJapply to correction charts for

0maxtest. This method of adjusting 0maxtest can be said to be about as

general with regard to application to different as is the method when used to adjust 0crtest.

materials and types ~f plates For stresses below 4 0cy'

however , this method is no longer valid because values of Omaxtest become

much greater than 0crtest as 0crtest is reduced (see reference 1).

A method for approximately adjusting 0maxtest over the entire stress

range was obtained from an analysis of the data of reference 1 from which the following empirical relationship was found

Omaxstd == Kmaxamaxtest ( 2)

where

Kmax oCYstd

==

° cYtest

An adjustment chart based upon e~uation (2) is shown in figure 3. This chart evidently can be applied to H-, Z-, and C-eection plate assemblies of extruded 24s-T, 75S-T, and R30}-T aluminum alloys. Application of the chart to the test results for extruded ZK60A magnesium alloy in the high­stress region (reference 1), however, did not give satisfactory results, and

NACA TN No. 1564 5

there is no reason to believe that this method and the r elationship upon which it is based are necessarily suitable for materials or types of plate assemblies other than those previously mentioned. As a matter of fact~ for stresses greater than r crcy where the method for adjusting crcrtest also

applies to cr ~ is a function of cr /cr as well as maXtest~ ~ crtest cYtest

crcYstd!crcYtest (see equation (2)) so that a single adj~tment curve (see

fig . 3) is not theoretically adequate for accurately adjusting crmaxtest in

the hi~tress region.

VERIFICATION OF CHARI'S

In order to provide a verification of the charts for ad justing plate compressive strengths~ values of acrtest and crIDBXtest from reference 1 for H-section plate assemblies are adjusted and compared with similar test data having different values of crcy. Because the principles of the methods apply equally well to H-~ Z-~ and C-eection plate assemblies ~ only H-eections are dealt with. Values of crcy that apply in each case take into account

the variation of crcy over the cross section of the H-sections and were

obtained by calculating a weighted average of the values of crcy f or the

flange and web based upon the areas of these elements (see reference 1).

The critical compressive stress.- In figure 4~ values of cr for - crtest extr uded 24s-T aluminum-alloy H-eections (crcy = 46.8 ksi~ reference 1)

were adjusted by means of the chart (fig. 1) for comparison with similar unpublished test results for which crcy = 40.0 ksi. Good agreement is

indicated between adjusted and comparative test results for the extruded 24s-T aluminum-alloy H-eections.

In the absence of test data on two sets of 75S-T aluminum-alloy H-eections of widely difrerent properties, values of cr from reference 1

crtest for extruded 75S-T aluminum alloy (crcy = 78.1 ksi) were adjusted for comparison with similar test results for R30}-T aluminum alloy for which crcy = 71 .8 ksi. (See fig. 4.) The less satisfactory agree~nt i n this case

is believed to result primarily because the correlation of the test results with the compress ive stress-etrain curves was not quite the same for the two materials (see reference 1). This lack of agreement again emphasizes the point that the same chart cannot ordinarily be used indiscriminately for different materials if accuracy i s desired .

The average stress at maximum load.- In figure 5~ values of crmaxtest

from reference 1 for extruded 75S-T and 24s-T aluminum-alloy H-sections are adjusted by means of the chart (fig . 3) for comparison)respectively;with

6 NACA TN No. 1564

similar data for extruded R303-T (from reference 1) and 24s-T (unpublished data) alumInum alloys. The fairly good agreement in each case between the adjusted and comparative values of ama~ for the H-eections indicates

-vest that the chart (fig . 3) can apparently be applied to a number of extruded aluminum alloys. This conclusion, however, is in some respects misleading. As previously mentioned, a single curve (fig . 3) cannot be expected to provide an accurate adjustment for aIDaXtest for stresses greater than

f. cr • The UI'.expectedly good agreement between comparative results for Lt cy cr x~ for extruded 75S-T and R303-T aluminum alloys (fig . 5) is not ma_-vest consistent either with this analysis or with the less favorable agreement for the comparative results for crcrtest ( see fig. 4). Likewise , the

relatively poor agreement betweeu comparative results for crmaxtest for

extruded 24s-T aluminum alloy (fig. 5) does not correspond t o the very good agreement for comparative results for cr for these materials (see crtest fig. 4). These contrasting results therefore indicate that the use of an adjustment chart for crmaxtest' employing a single curve and single

parameter such as shown in figure 3, does not basically provide an accurate method for adjusting aIDaXtest' The method may suffi ce , however, as a rough,

convenient way for adjusting crmax~ for some materials and types of --vest plate assemblies .

Langley Memorial Aeronautical Laboratory National Advisory Committee for Aeronautics

Langley Field, Va., February 3, 1948

NACA TN No. 1564 7

APPENDIX

CONSTRUCTION OF CHARI'S FOR AD.ru3TING TEST RESULTS FOR

THE CRITICAL COMPRESSIVE STRESS

The charts for adjusting test results for the critical compressive stress acrtest for differences in material properties have the same convenient

form as that given in the ANC-5 bulletin (reference 4). Details of the procedure for constructing the charts are outlined as follows:

1. Select a value of aCYstd in accordance with the design specificatjons.

In order to illustrate the procedure, aCYstd = 41 ksi is chosen for extruded

24s-T aluminum alloy (ltbasis B, It table 5-5 of reference 4). The use of the chart, however, is not restricted to this particular value of aCYstd'

2. Construct a compressive stress-etrain curve having the selected value of aCYstd from a representative compressive stress-etrain curve for the material, assuming the two curves to be affinely related. (See fig. 6.)

3. Construct a family of compressive stress-etrain curves by like methods for assumed ratios of ~cy Jacy of 0.90, 0·95, 1.00, •

tes std 1.20, and 1.25. (See fig. 6.)

4. The determination of the adjustment factor Kcr for given values of a Ja and acy JaCY is illustrated by the following example: crtes cYtest tes std

aCYt t acrt t (a) Assume that es = 1.25 and es = 0.90. Then,

aCYstd aCYtest aCYtest = 1.25 x 41 = 51.3 ksi (point A, fig. 6), and

acrtest = 0·90 x 51.3 = 46.2 ksi (point B, fig. 6).

(b) Establish point C (39.7 ksi, fig. 6) on the standard curve directly below point B. The adjustment factor is then (see equation (1))

astd 39.7 Kcr = d = ----46 = 0.860 (point D, fig. 1).

test .2

---- - - -- -

8 NACA TN No . 1564

REFERENCES

1. Heimerl, George J.: Determination of Plate Compressive Strengths . NACA TN No . 1480, 1947.

2. Gerard, George : Secant Modulus Method for Deterrrdning Plate Instability above the Propor tional Limit. J our . Aero . Sci ., vol . 13, no. 1, Jan . 1946 l pp . 38-44 and 48 .

3. Stowell, Elbridge Z.: A Unified Theory of Plasti c Buckling of Columns and Plates . NACA TN No . -1556 , 1948.

4. Anon . : Strength of Metal Aircraft Elements . ANC- 5, Arroy-Navy-C i vil Committee on Aircraft Design Criteria . Revi sed ed ., Dec . 1942 ; Amendment 2, Aug . 8, 1946 .

5. Osgood, W. R.: A Rational Definition of Yiel d Strength . J our . Appl . Mech., vol . 7 , no. 2, June 1940, pp. A-61 - A-62 .

1.20

1.10

1.00

Ker

.90

.80

.70

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I I~tmillti:~ iLt~ ~H:i

3 .4 .5 .6 .7 .8 .9 Lo 1.1 1~2

(Tertest

(TeYtest ~

Figure I. - Factors for adjusting plate test results for the critical compressive stress for extruded 24S-T aluminum alloy.

-----,

z· ~ o ~

f--3 Z Z o . I-' CJl ()';) ~

c:o

Kcr

[.

1m

1.10 L ~

1.00 ---"±

.90 -'--

1=

-+

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II .. "Illi+lrr

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t..c

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.70 L .3 .4 .5

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1- lj [D:; T~MJW=[:jjiftJ~lr¥ ., 4- r$/ _1.. 1-'-

.6 .7 CTcr test

CTcy test

.8 .9 1.0

~ 1.1

Figure 2:- Factors for adjusting plate test results for the critica 1 compressive stress for extruded 75S-T aluminum alloy.

-ni" ~IBI

......... o

~ o !:P ~ Z Z o

......... CJ1 OJ fP.

Kmax

1.20n !:rllTTrrltllJf :-:f" 1r! ~

~ I I -, -1.10

f;J.t · t~# NI~~~ r .

t-;

~ _Ci~

Loot 1111 1~l ·· t ~.J lAI~ -

- --·l 'l F~ T ' I \r- I '- ):tr --- ! I~ 1-~f~ ~I- l - +-

.90 I I j I I 11-1 A ~ ··~l I '1l f~~ - _" t t , ~ _ ~ I I f I '-Cl ++r J

.80 I I II f1, S ~d t 1mH~~Xts~ ~i I I I 1 I i

I .70 I , I I i I I Itt k~ t I "-J! I \ I I - I i

.SO .90 1.00 1.10 1.20 1.30

G"cy fest

G"CYsfd ~

Figure 3. - Factors for adjusting plate fest results for the average stress at maximum load for H-, Z-, and C-section plate assemblies of extruded a luminum alloys.

~ (1

~

f-3 Z Z o . ~ ()l

OJ ,p..

f--' f--'

l_

12

<Tcrtest , ksi

so

70

60

50

40

30

20

10

o o

NACA TN No. 1564

~ c))

75S-T (<Tcy= 7S.1 kSi)~ B

Q] P> Of

~ E;5S-T(<TCY = 7S.1 ksi)

R303-T(<Tcy = 71.S kSi\ ,~ adjusted to <T~y:: 71. 8 ksi

'U

I OJ f:s

Q> r24S-T (OCy = 46. 8 ksi) , I;:

8. ~ t!

(> ~ (>

& ~ ~ (>

~ v

"'-

\ 24S-T (OCy =40.0 ks

~ $ is

j)

0' "-24S-T(<Tcy =46.S ksi)

b adjusted to <Tcy =40.0ksi

.002 .004 .006 .008 .010 .012

Ecr ~

Figure 4.- Comparison of adjusted values of <Tcrtest for extruded 75S-T and 24S-T H-sections with similar data for extruded R303-T and 24S-T.

NACA TN NJ. 1564 13

BO ~

75S-T (OCy=7B.1 ksj) \ b BI(5-

I IG ~ \ <r.,

. .

70 R303-T (<Tcy=7I.B ksi) ~ e 75S-T(OCy= 7B.1 ksi)

o~ adjusted to <Tcy = 71.B ksi

60 n

etl A

C B e: ~

~

6 d~ t ~

l qJ ~. 1 ~ -~

~'h 6

8 24S-T(OCy=46.6 :'r,

'-& l's

24S-T(OCy = 40.0 ksi} 0-

50

ksi)

40

(J"maXtest , ~ ~ -r

(> 24S-T(<Tcy =46.B ksi) ksi

30

20

10

o o

&> fl. fJ ~ ;§~

.002

adjusted to <Tcy =40.0 ksi

.004 .006 .OOB .010 .012

Ecr ~

Figure 5.- Comparison of adjusted values of cTmaxtest for extruded 75S-T and 24S-T H-sections with similar data for extruded R303-T and 24S-T.

14

0",

ksi

NACA TN No. 1564

60 O"cYtest

O"CYstd

1.25 1.20 1.15

50 1.12-(representative) 1.10 1.05 1.00- (std )

0.95

40 0.90

30r-----~~~~~------~-------4------~

20 r------H-------+------~------4-----~

10 r-~~--r_----~r_----~-------4--------

O ~------~----~~----~------~------~

o .002 .004 .006 .008 .010 Strain ~

Figure 6.- Compressive stress-strain curves for extruded 24S-T aluminum alloy used in constructing the chart (fig. I).

J