Experimental investigation of stability and post buckling behaviour of stiffened curved plates

VLIEG LJI\..yD~\J ___ Michiel de ~ltut""",,,.

14

feb. 1961

m :;:00 VlO m() C :;:03:

>m

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EXPERIMENTAL INVESTIGATION OF ST ABILITY AND POST BUCKLING BEHAVIOUR OF STIFFENED CURVED PLATES

hy

A. B. T. Soderquist

BUCKLING BEHAVIOUR OF STIFFENED CURVED PLATES by

A. B. T. Soderquist

..

_{A series of nineteen flat and curved plates having stiffeners}

of rectangular cross-section have been tested in compression.

Measure-ments made of initial buckling stress and effective widths subsequent to

buckling were consistent with previous work. The ultim ate strength of

the plates was found. to increase markedly with curvature, the rate of

The author is indebted to Dr. G. N. Patterson, Director of the Institute for providing the opportunity to work on this project and to

Professor E. D. Poppleton for his continuing interest in the progress of

the research, as weIl as for his direct assistance in carrying out some of the tests. The National Aeronautical Establishment, Ottawa, generously donated some of the testing equipment and lent some of it, Thanks are

also extended toward Professor C. F. Morrison of the Civil Engineering

Department, University of Toronto for permitting the experiments to be carried out in the laboratory of his department. The assistance of

Professors W. L. Sagar and C. E. Helwig, also of the above department,

is gratefully acknowledged.

The necessary financial support has been provided by the Defense Research Board of Canada. The author received a post graduate scholarship from the National Research Council of Canada for the duration

T ABLE OF CONTENTS

NOTATION

1. INTRODUCTION

Il. EXPERIMENTAL METHODS 2. 1 Description of Plates 2.2 Edge Supports

2.3 Preliminary Measurements 2. 4 Strain Measurem ent

2. 5 Testing Arrangement 2.6 Test Routine

lIl. DISCUSSION OF EXPERIMENTAL RESULTS 3. 1 Ultimate Strength

3.2 Effective Width Curves 3. 3 Initial Buckling Load CONCLUSIONS REFERENCES TABLES FIGURES ii 1 1 1 1 2 2 3 3 4 4 5 8 9 10 11

c

E L Pult R

u

c d h t w x Subscripts e cr yp NOTATION

compressive buckling factor for long cylinders Young's modulus in cornpression' (psi)

buckling instability coefficient

'2(I-y2)

(b)2.

Q"ër

T

7jl

E

total plate length (inches)

total applied ultimate load (lb. )

total mean radius of curvature (inches) uneveness factor

= b 2 IRt

stringer spacing (inches) end fixity coefficient stringer height (inches)

depth of Wood's metal (inches) length of sheet in panels (inches) sheet thickness (inches)

stringer width (inches) effective width (inches)

Horizontal distance measured from the centre of the plate (inches)

edge, or stringer value of the stress (psi) critical, or buckling values

Greek Symbols

E

Y

cr

strain in microinches per inch Poisson's Ratio

1. INTRODUCTION

A recent review (Ref. 3) of the strength of stiffened curved

plates and shells pointed out the lack of experimental data on the behaviour

of stiffened curved plates loaded in compression parallel to the generators

of fhe sheet. Some uncertainty seemed to exist regarding the effect of curvature on the ultimate strength of such plates. and a trend of decreasing

ultimate strength with increasing çurvature was seen in some cases.

con-trary to expectations . However when the results quoted in Ref. 3 were

re-examined it appeared th at for some b/t ratios there was a trend of

increasing ultimate strengths with increasing curvature. The present

testing programme was designed to investigate this trend. To eliminate

complications due to local instability of the stringers a rectangular

cross-section was chosen. stiff enough to prevent deflection of the sheet at the stringers.

I!. EXPERIMENT AL METHODS

2. 1 Description of Plates

The plates were formed in conformity with general standards

prevailing in the aircraft industry from hare aluminum aHoy sheet of

specification QQ-A-355 (24ST). The stringers were cut from extruded

aluminum alloy rod stock of specification QQ-A-267 (24ST) or machined

from such stock to the required dimensions. AttachmenL of the stringers

to the sheet was by means of nuts and round head machine screws with a

pitch of . 75". Stringers which were attached to curved plates were

radiused to match the plate curvature. To prevent local deformation of

the sheet and "to ensure a uniform distribution of compressive end load.

the ends of the plates were provided with a series of holes approximately

. 40" in diameter and set in Wood's metal to a depth of approxirnately 1". The ends of the plate were then machined flat and normal to the length of the" stringers. (Refer to Fig. 1 for details of construction).

2. 2 Edge Supports

To simulate simple support at the unloaded sheet edge, two

stiff angle sections were fitted around it as shown in Fig. 1. The angle sections were separated by a strip of sheet of the sam e thickness as the

plate being tested. A number of equally spaced screws joined the angles.

The screws were only tightened enough to allow the edge support assembly

to stay c1amped onto the free edge. but the supports could be easily slid

up or down along the sheet edge. Initially before the testing was begun.

a clearance of approximately 1/8" existed between the ends of the supports

2. 3 Prelim inary Measurem ents

On completion of the machining of the ends of the plate, the edge supports were installed and the plate assembly was placed on a sur-face table, stringer side down and supported on two parallel steel blocks located underneath the stringers. A dial gauge pointer was moved

parallel to the stringers along the sheet surface at a position midway

between the stringer screw rows, and midway between a screw row and the edge of the sheet at both sides. A typical set of readings is given in

Table 4.

The radius of curvature of the formed plates was measured using a dial gauge fitted centrally in the "U" formed by two steel prongs mounted in a steel block. An orthogonal grid was drawn on the convex face of the sheet and measurements were obtained at nine vertical stations spaced two inches apart. The number of transverse readings varied from 11 to 15. From these readings mean radii of curvature were found.

To illustrate the typical distribution of radii over the sheet surface a contour map has been drawn for constant radii for plate 9 in Fig. 2. It can be seen that the plates were far from perfect, but it is considered that their quality was typical of those used in practice. The mean radii in the vicinity of the stringers are given in Table 5.

2. 4 Strain Measurement

Seventeen plates were equipped with strain gauges to investigate the transverse distribution of the mean longitudinal strain at the plate mid height. The gauges were cemented to the plates using the Eastman 910 adhesive. To obtain a reading proportional to the mean compressive strain in the sheet the gauges were connected in a four-arm bridge circuit, which yields a strain reading proportional to the com-pressive strain and also provides compensation for temperature induced strains. Dummy gauges were cemented to aluminum plates and located in the immediate vicinity of the testing machine. The strain gauge circuit was completed by a type PSBA 20 Model 3, 20 channel switching and balancing unit and a SR-4 strain indicator type N. No attempt was made to correct the strain readings for lead wire resistance. As a rough approximation however it may be said that the maximum error irt

the recorded strains due to lead wire resistance would be less than 10/0. A built-up structure of Dexion angles supported four dial gauges. Two of these recorded the total vertical decrement between the slotted platen and the lower face of the I beam (see Fig. 3). They were located at the front and rear extremities of the width of,the I beam where "rear" refers to the stringer side of the plate. Two gauges positioned at the midheight of the stringers measured their horizontal

movement in a direction normal to the tangent plane rnidway between the stringers . However, due to deformations of the support structure at high loads the strain as com puted from vertical dial gauge readings did not correlate weIl with the strain obtained from strain gauges. The dial gauge readings were however useful in determining the ultimate load capacity of the plates (see Sec. 3. 1).

2. 5 Testing Arrangement

The tests were conducted in a 120, 000# capacity Baldwin compression testing machine with hydraulic loading (see Fig. 3). The panel was placed on a steel bar 2" thick and 5" wide, the faces of which had been machined flat and parallel to each other. The steel bar in turn rested on ten load cells positioned in a metal retaining cage. The retain-ing cage was placed on a flat steel sheet and securely bolted to the slotted lower platen of the testing machine. On the top adjustable head of the machine was mounted a 5" de ep wide-flanged steel I beam the faces of which had been machined flat and parallel to each other. Three reinforc-ing webs were welded between the flanges to stiffen the beam.

An orthogonal grid of fine steel wires was positioned in front of the plate assembly. A point source of light was positioned a few feet away from the grid so that the wires cast a weIl defined shadow onto the sheet. The wires and their shadow we re photographed by a camera located a few feet from the plate. This arrangement was used in Ref. 4 and is a very useful means of detecting the onset of buckling. Photos we re taken whenever a significant change in the buckle patern was detected (see Fig. 11).

2. 6 Test Routine

The plate assembly was positioned on the machine steel bar so that the centres of pressure of the plate and the load cells coincided. The top adjustable head was lowered until the lower face of the I beam almost touched the top face of the plate. While employing feeier gauges the length of the load cells were adjusted until the top face of the plate was parallel to the under face of the I beam. Using a spirit level a vertical position of the plate was obtained.

A small cornpression load was next applied, well below the estimated lower buckling load of the plate. The load cell strain indications were noted and by a process of repeated adjustments of the load cell lengths (and hence the load locally) a nearly uniform end load distribution over the width of the plate was achieved.

The tot al applied load was increased in small steps and the strain gauge and load cell indications we re noted together with the dial gauge readings . . It was noticed that with increasing load the end load as

found by the load cells ten.ded to peak in the vicinity o,f the stringers . Frequent visual inspections were made to ensure that the edge supports were properly positioned, When the buckling 'load was approached the lamp was switched on and a close watch was maintained on the develop-ment of the buckled form, visible by a transition of the shadows cast by the vertical wires from a straight line to a curved one. The

displace-ment of the sheet away from or towards the centre of curvature could be

differentiated. Photos were taken whenever new buckles appeared or there was a change in the buckle pattern. The load was increased until

the horizontal displacement of the stringers became very large and the

total load dropped with increasing straining.

lIL DISCUSSION OF EXPERIMENTAL RESULTS

3. 1 Ultimate Strength

During testing, the plates we re subjected to an increasing

load up to that point where an additional strain did not produce a load

increment. However the behaviour of the plates during loading differed

greatly. In some cases the vertical dial recorded a steady linear length

decrement for increasing load up to the point of maximum load, in other

cases large stringer horizontal deflections at a given critical total load

produced a discontinuity in the vertical dial gauge decrement curve. The

sudden large deflection of the stringers was usually accompanied by aloud

"popping" noise. Due to the momentary drop in the registered load, the

load needIe follower on the testing machine dial would indicate the load at this point. This sequence of events is shown in Fig. 4, which illustrates

the behaviour of Plate 14, the failing load of which was indicated by the

dial to be 16, 520 lb, To obtain a uniform criterion of failure of the plate,

applicable to all plates, failure was said to occur at that load at which

large horizontal stringer deflections accompanied by a discontinuity in the

plot of vertical total length decrement vs. total load occurred. In those

cases where no noise or drop in total load accompanied the failure load

point, failure was taken to occur at the mean of the loads prior and

subse-quent to the symptoms defining failure. Values appear in TabIe. 2.

The ratios of ultimate loads of curved plates to those of flat plates defined as above are shown plotted vs. Zb for discrete values

of bit in Fig. 5. It can be seen that for increasing Zb values the ultimate

load capacity of a given bit series of plates increases appreciably. With

bit increasing the curves seem to approach the horizontal axis. The

, series with bit = 189 is an apparent deviation from the general behaviour

but it is thought that perhaps the flat com parison plate for th is series

failed prematurely and this is to be investigated further. It may be

observed from the graphs in Fig. 5 that the plots for bit = 70. 6 and

bit

=

142 would coalesce fairly well into a single curve if the Zb values

were divided by bit to yield b/R as the abscissa. It is noted that the

The empirical approach to the calculation of ultimate plate strength suggested by Sechier and Dunn (Ref. 2) is to find first the ultimate

load capacity of an equivalent flat plate. The increment in load capacity

for an equivalent curved plate is,found as (b - ._{2we ) t}

cr

cr where (J cr is the theoretical critical buckling s.tress of a curved plate with the

appropriate edge restraintS. Sechler and Dunn suggest the use of the formula of Kanemitsu and Noji~a for

cr

cr which applies in the range

500

-<

Rit

<.

3000 and . 1 4:

kiR

~ 2.5, i. e.,

~"=

9ÎRye

+

o.16(~r3

(1)

The ultirn ate strength of the plates was calculated using Sechler and Dunn's approach. The end fixity coefficient c for the stringers was estimated trom measurements of the inflexion points on

the failed stringers and these values of care given in Table 6. Bas~d

on c and a proportional limit stress of 20, 000 psi a Johhson parqbolic

curve was construced in the usual fashion. The value of

q-

cr was

found using equation (1) even when the plate fell outside the recommended ranges. The resulting curves are shown on Fig. 5 and it is seen that the method consistently underestimates the failure load.

The calculations were repeated using the measured values of

<r-

cr and it will be seen from Fig. 5 that whereas excellent agreement

with measurements was found for

bit

= 70. 6, the agreement was poor for the case of

bit

=

142. In th is latter case the calculated values showed a

trend which differed qualitatively from the experirnental values. The

difference in ultimate strength between plates otherwise identical but with different stringer strengths, predicted in both calculations, was not

notieed.

Experirnental values of the ultimate load capacity of the plates tested in Ref. 1 are plotted in Fig. 6 for comparison. These show a similar dependence of the ultimate load on

bit

as in the present tests,

but here, rough estimates of the ultimate load using the method of Sechler and Dunn gave results which were sometimes unconservative.

3. 2 Effective Width Curves

Since the strain at the centre of the stringer was not mea-sured directly, it had to be estimated from strain gauge data at positions adjacent to the stringer. Initially it was attempted to measure the

stringer strains directly by attaching gauges to the stringer and the sheet between the screw holes. However, due to the strain concentration in the vicinity of the holes the measured strain was far less than the ave rage

strain. An attempt to place strain gauges onto the "d" faces of the stringers (see Fig. 1. Stringer Detail) was not successful as the strains found were much lower than the ave rage strain. Moreover, the dial gauge readings of the platen movement could not be used due to the deflections of the support structure mentioned previously.

A survey of the information given by the strain gauges revealed four different types of strain distribution in the vicinity of the stringer, the nonuniformity being attributed to local irregularities (Fig. 2)

and to the fact that buckling of the outer panels always occured before buckling of the centre panel. These distributions have been depicted schematically below:

X

1

X

l

X

2

A

c

X

3

X

4

X

1

X

1

X

2

X

2.

8

X.

3

D

X

3

X

4

X

4

The difference in readings (2) and (3) in Case B might typically amount to approximately 10"/0.

To find a reasonable extrapolated stringer strain the follow-ing procedure was adopted:

Case A

(Ref. 2, p.

(J=

Using the strain distribution suggested by Sechler and Dunn

202) i.e.,

I

S(

)

)

2ïTX

l

and applicable to flat plates, a value of the stringer strain was obtained based on the experimental strains at positions (2) and (3). The stringer strain was put equal to the greater of the extrapolated strain and the strain at (1).

Case B The stringer strain was chosen to be the greater of the

strains (1) and (3); strain reading (2) was ignored.

Case C The stringer strain was found by extrapolation using the

method of Sechler and Dunn and the strains at (2) and (3).

Case D The stringer strain was put equal to the strain at (2). The validity of using the flat plate strain distribution for curved plates was verified by predicting the edge strain for a few of the plates tested in Ref. 4. Excellent agreement with theory was noted.

The effective widths were then computed assuming no

diffusion of load into the outer panels and using simple trapezoidal rule integration. Due to irregularities (Fig. 2) and nonuniform distribution of the applied load, the strain distribution was not symmetrical and

application of the above method lead to values of we which differed from b

/2

at buckling. To account for this fact the effective widths were

normalized by dividing by the effective widths at the time of buckling of the

sheet. These values of we/we have been plotted vs. the critical strain

€

cr

ratio

I

EC.f in Figs. 8 and 9.

The critical strain, or the stringer strain at the time of buckling of the centre panel, was determined in two different ways. In most of the tests on the strongly curved plates buckling was accompanied by a sharp noise and a sudden drop in the central strain gauge reading

(refer to Fig. 7). In other cases, mostly applicabie to flat and slightly curved plates, buckling occurred gradually and was said to take place either when the strain registered by the central strain gauge showed a peak value, or when the edge strain was markedly greater than the

average indicated strain. The whole process was less c1early defined in

this case.

The experimentally found effective width curves were com-pared with those given by the empirical formulae of Wenzek in Ref. 1

and Sechler and Dunn in Ref. 2. Wenzek's effective width formula which

applies for a condition of restraint intermediate between simple and

clamped support at the edges may be· written

We

(3) l~

\Ne

cr

~

( \ _

Ec..~)

R

E

The formula of Sechler and Dunn may be written

(

E:.

r)(f-

)0.37

0.50

1+; ;f

,

€c.y

Eyp

(4)

It can be seen that, by and large, the theoretically predicted effective widths are conservative, and that they do correctlypredict the general trend of effective widths with increasing Zb values.

The fact that some effective width ratios are greater than unity prior to buckling is ascribed to a somewhat nonuniform transverse strain distribution in some cases. Another factor is the imposed

con-straint that all effective width ratio plots go through the point (1, 1).

The summary plot of effective width ratios for flat and nearly flat plates shows a fairly well defined grouping of the experimental points. The empirical formula of Sechier and Dunn of Ref. 2 gives reasonable fit for large values of bIt. The plots show that the effective width ratio depends only upon the critical strain ratio, whereas Sechier and Dunn pre-dict a dependence up on the critical strain as wen. It should be emphasized that the effecti ve widths shown in these figures can only be regarded as qualitatively correct due to the rather indirect evaluation.

3. 3 Initial Buckling Load

The buckling instability coefficient Kc is plotted vs. Zb in Fig. 10. lndividual points are identified with respect to their RIt value in an attempt to verify the expected trend predicted in Ref. 5. The equation (30) therein gives

which may be written

t

crc-r

:=:

C E

-R

(5)

(5a)

where C is a function of the initial plate imperfections and RIt. A curve of C is given in Ref. 5 and this was used together with an uneveness factor U of . 00025. This is the value which is shown to give a good fit to the data of Batdorf, Schildcrout and Stein in Ref. 5. The theoretical curves of Kc vs. Zb were drawn for RIt

=

O. 250_ and 500. No attempt was made to define the low and transition regions of Zb because of insufficient number of experi-mental points.

The theoretically predicted dependence of Kc upon RIt for large Zb values cannot be observed here because the Zb values are not large enough .

CONCL USIONS

1. The ultimate load capacity of thecurved stiffened plate"s shows astrong dependence up on the curvature parameter Zb and

bit.

For example, for Zb

=

27.8,

bIt

=

70.6 the curved plate ultimate strength was 154% of th at of the corresponding flat plate.

2. For a constant Zb value the ultimate load ratio decreases with increasing bIt ratio so that at Zb = 30 the ratio is approximately 1. 57 for bIt = 70.6 and 1. 18 for bIt • 142.

3. The empirical method of Ref. 2 does not predict the

ultirnate load capacity of the curved stiffened plates of this report satisfac-torily if the buckling stress is calculated by the formula of Kanemitsu and Nojima. The calculations were qualitatively correct, however, and seem to yield a consistently conservative estimate. If the measured buckling stress is used then the m ethod of Sechler and Dunn gave good agreement with the case when bIt'" 70. 6 but the agreement was poor in other cases. In the case of the data of Ref. 1 the estimates were at times unconservative.

4. The effective width plots show. astrong dependence on the

I

parameter Zb' The theoretically predicted effective width curves are consistently conservative. No dependence on the critical stram was noted in contrast to the predictions by Ref. 2.

5. The buckling instability coefficients show no consistent trend with

RIt.

However, the general run of the plots seems to indicate a trend toward "long cylinder" behaviour at lar~e

ztl

values.

1. Ramberg, Walter Levy, Samuel

Fienup, Kenneth, L. 2. Sechler, Ernest, E.,

Dunn, Louis, G. 3. Becker, Herbert 4. Jackson, K. B., Hall, A. H. 5. Gerard, George Becker, Herbert REFERENCES

Effect of Curvature on Strength ofAxially

Loaded Sheet-Stringer Panels.

NACA TN 944, August, 1944.

Airplane Structural Analysis and Design. John Wiley & Sons, New York, 1942.

Hand book of Structural Stability Part VI -Strength of Stiffened Curved Plates and Shells. NACA TN 3786, July, 1958.

Curved Plates in Compression.

National Research Council of Canada Aeronautical Report AR-I,

NRC 1495 MM-180, 1947.

Hand book of Structural Stability Part 111 -Buckling of Curved Plates and Shells, NACA TN 3783, August, 1957.

TABLE 2

Summary of Plate Parameters and UItimate Loads

Experimental Ca1culated Ca1culated

Plate Z Puit (LB.) Puit (LB) PuIt (LB)

No bIt RIt =

b~

IRt

cr

_{cr from}

_Ü

cr mea-Eqn. (1) sured 1 70.6

_aJ

0 53800 54500 54500 2 70.6 2250 2.22 39000 2) 56000 3 70.6 284 17.5 68000 64700 70900 4 70.6 174 28.6 81100 75800 82800 5 70.6 179 27.8 82700 74800 6 142

₀₀

0 21320 23800 23800 7 142 4510 4.48 21300 24100 25900 8 142 1300 15. 5 23000 24500 26700 9 142 564 35.8 26300 25800 28900 10 142 352 57.5 32500 27800 30500 11 142

_<Xl

0 13540 14000 14000 12 142 5960 3.39 13700 14300 13 142 1320 15.3 14000 14600 14 142 576 35. 1 16520 15700 17800 15 142 379 53.3 19020 17000 19800 16 142 CD 0 6460 -' 17 189 00 0 4125 5370 5370 18 189 1850 19.3 6430 5680 6740 19 189 714 50.0 7500 6060 7590

Notes 1 Puit determ ined from criterion of large stringer horizontal deflection coupled with a change in slope of load vs. vertical decrement curve.

2. Plate 2 failed prematurely when the Wood's metal broke off from the sheet.

3. Loads ca1culated from Ref. 2 using a measured value of E = 10 7 psL

TABLE 3

Summary of Plate Parameters and Ultimate Average Stresses (Data of Ref. 1)

Plate No. 1 2 3 4 ,7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Notes bit 162 154 159 156 78.1 75.9 76.5 77.1 76.6 40. 1 40.5 40.3 40.4 40.5 21. 4 21. 4 21. 4 21. 4 21. 2 1

Average Compressive Stress at Failure (Klps)

z

=

b2>/Rt Experiment

CJ

_{cr Calc.}

G'

~r Meas.

8.47 31. 0 31. 2 32.3 16.1 29.7 31. 4 33.1 25.0 30.0 31. 5 33.5 32.6 29.8 31. 9 34.2 0 29.2 29. 2 29.2 3.97 28.9 29.8 31. 7 8.01 29.0 30.0 33.2 12.1 28.2 30.8 33.7 16.0 29. 1 31. 6 0 32.8 32.8 32.8 2.19 32. 9 33.4 35.8 4.16 33. 1 33. 9 36. 1 6.33 34.7 34.5 36.2 8.26 36.1 35.3 36.6 0 37.2 Note 2. 1. 12 36.4 2.23 39.2 3.34 40.7 4.41 42.5

The ca1culated ultimate average stress was

found by calculating the ultimate plate strength based on the measured ultimate stringer stress using

the approach of Ref. 2.

2. Calculation indicated that the flat plate would fail prior to buckling.

TABLE 4

Initial Deviations of the Sheet from a Cylindrical Surface Form (Plate 5) Vertical Position

Counted Positive Up From a Plate Midheight (inches)

Deflection of Sheet Away From Centre of Curvature in 1/1000"

A B C

Left Panel Centre Panel Right Panel

Notes: 8 .7 _6 5 4 3 2 1

o

-1 -2 -3 -4 -5 -6 -7 -8 (50300) 0 3. 1* 4.8 7.3 8.7 10 9.2 8.9 7.6* 6.5 5.3 (77400) 4.2 4. 1 2.4 2.3 . 9 0 0 0 .5 1.2 1.0 2.5 1.8 4.0 .7 4.0 .6 (50700) 4.8* -.6 5.7 .9 7.3 1.8 8.9 1.9 8.8 2.3* 8.6 1.6 8.4 2.0 7. 9 .4 6.4 -.8 4.8 -. 9 2.5 0 0

Measurements were taken along vertical reference lines A, Band C. A was located 6" to the left of the plate centre, B at the centre and C 6" to the right of the plate centre.

*

Denote the approximate vertical positions of the centres of the buckles which appeared in the panels during test. All buckle dis-placements were toward the centre of curvature. The totalload

TABLE 5

Tabulation of Mean Radii of Curvature (Inches)

Left Stringers _{Right Stringers}

No. of _{No. of}

Plate No. Mean Readings Mean Readings

1 2 180 approx. _{180 approx.} 3 23.45 36 23.58 36 4 14. 12 36 13. 93 36 5 14.65 36 14.15 36 6 00 ₀₀ 7 180 approx. _{180 approx.} 8 56.38 36 52-.51 36 9 22.79 36 23. 01 36 10 14. 16 42 14.07 42 11 00 36 00 36 12 209.6 36 237.6 36 13 60.48 36 53.19 36 14 22. 94 36 23.12 36 15 15.21 36 14.49 36 16 17 18 54.04 36 60.43 36 19 24.85 36 22.56 36

TABLE 6

Tabulation of Measured End Fixity Coefficients c

Plate No. 1 to 5 inc!. 6 to 10 incl 11 to 15 inc!. 17 to 19 inc!. Length of Stringer Between Inflexion Points

11. 48" 10.40" 8.18" Not Measured Ca1culated Value of c _Based on Length L 3.2 3. 9 greater than 4.0 use 4.0

..

;

.

""

l

•

•

f

I I

~

h8

I

I

MIN I/S" i CLEARAN!cE

J.

~ 2" b SECTION 8 B

~

~-h

n

~~

'375

/$~~r~

DIA.-40"APPROX., WOOD'S METAL A STR!N~ER QETAIL

~.ATfRIAL: SHEET BARE ALUMINUM, SPEC. QQ-A-355 (24ST)

STRINGER EXTRUDED ROD, SPEC. QQ-A-267 (24ST4)

DETAIL "A"

_

..

---TABLE 1.

Summary of Plate Dimensions.

Total Nominal Mean R t b L 1 d W Plate No. IN IN IN IN IN IN IN 1 00 .0800 5.65 20.5 18.3 .750 .750 2 180 appr.

"

_"

20.5 18.2

_"

_"

3 22.76

"

_"

20.4 18.3

_"

" 4 13.92

_"

_"

20.5 18.2

_"

_"

5 14.32

"

"

20.5 18.3

_"

_"

6 00 .0399 5.65 20.5 18. 6 .500 .750 7 180 appr.

"

_"

20.5 18.5

"

_"

8 51. 76

"

"

20.5 18.5

"

_"

9 22.46

_"

_"

20.3 18.3

_"

_"

10 14.05

_"

_"

20.5 18.5

_"

_"

11 00 .0399 5.65 20.4 18.4 .375 .750 12 238

_"

_"

20.4 18.2

_"

_"

13 52.86

_"

_"

20.5 18.3

_"

_"

14 22.99

_"

" 20.4 18.4

"

_"

IS' 15.11

_"

_"

20.4 18.6

_"

_"

16 ()() _{.0399 5.65 20.4 18.4 .250 .750} 17 00 .0323 6.10 19.9 18.2 .250 .750 18 59.82

.

"

" 20.0 18. 1

"

_"

19 23.07

"

_"

19.9 18. 1

"

_"

NOTE: t IS AN AVE RAGE VALUE FOUND FROM MEASUREMENTS OF A NUMBER OF THE PLATES IN EACH SERIES.

APpRQX

16" Radii in inches. APPROX. I 11 ---~

I

, i : _--- STR INGEf< ~ __ _

22

.

- . .

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LOCATION OF DI AL GAU MEASURING LENGTH DECREMENT G

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