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R . & rVL No . 2652
( I 1 ,036 , 1 1 , 0 3 7 , 1 1 , 0 3 8 )
A . R . C . T e c h n i c a l R e p o r t
MINISTRY OF SUPPLY
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A E R O N A U T I C A L RESEARCH COUNCI[L
R E P O R T S A N D M E M O R A N D A
o o o o
Investigation of Skin Buckhng By
D. J. F , RRaR, M.A., of the Bristol Aeroplane Company, Limited
Crown Copyrigkt Reserved
L O N D O N : HER MAJESTY'S STATIONERY OFFICE
I953 PRxc~. i7s 6d NET
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Investigation of Skin Buckling By
D. J. FARRAR, M.A., of the Bristol Aeroplane Company, Limited
COMMUNICATED BY THE PRINCIPAL DIRECTOR OF SCIENTIFIC RESEARCH (AIR), MINISTRY OF SUPPLY
Reports Memoranda No. 2652* October, 1947
This report on an Investigation of Skin Buckling was originally prepared by the Bristol Aeroplane Co. Ltd., as Report No. C.R.434 in October, 1945.
With their permission it is now reproduced in condensed form. The test results are given in detail in S. & T. M. 12/47.
Summary.--(a) Purpose of Investigation.--The present tests were conducted on aluminium alloy plates in endwise compression, with varying conditions of edge support, to provide data on the buckling stress and post-buckling behaviour of aircraft skins.
(b) Range of Investigation.--All the plates tested were 35 in. long and nominally 0.064 in. thick. The plate width between the supports was varied between 35 and 120 times its thickness. Both clad (D.T.D. 546) and unclad (D.T.D. 646) material were tested. Three types of edge support were used: rows of steel balls in vee-grooved blocks, intended to imitate pin-edged conditions; rows of steel rollers in recessed blocks, intended to imitate clamp-edged conditions; and a single type of stringer used in previous panel tests.
Measurements were made of the plate load and mean strain, and of tile shape of the skin buckles. The test technique is discussed and the experimental results compared with theory.
(c) Conclusions. The ball edge supports did not accurately represent pin-edged conditions, neither did tile roller edge supports accurately represent clamped-edged conditions. The tests provided some data on the effect of plasticity in seriously reducing the load carried by the plate after buckling, and on the effect of cladding in reducing the buckling stress.
Tile buckling stresses measured for the panels with stringer edge supports were ill good agreement with theory. The load carried by the plate after buckling ill this case was further reduced by tile effect of plasticity in the stringers: a simplified theory is developed whose results are in agreement with the experimental observations.
(d) Further Devdopments.--The testing technique used is applicable to further investigations of tile buckling of plates as part of a panel.
The information obtained on the effect of plasticity has an important bearing on the load-carrying capacity of panels, and while the present results may form the basis of design data sheets, it is desirable that tile range of investigation be extended to cover other material specifications.
1. Introduct ion.--The present series of tests arose from some previous work (unpublished) which deals with tests on flat panels with Z-section stringers. The compressive stress at failure of these panels was lower than that predicted by theory, and one possible explanation was tha t the tangent stiffness of the skin was lower than expected. The main arguments developed in the previous report may be summarised as follows:--
(a) In the case of flexuraI instability, the tangent ftexural stiffness E1 is very dependent on the contribution of the skin to the moment of inertia.
* Bristol Aeroplane Report No. C.R.434, received 25th November, 1947. single report).
(Parts 1, 2 and 3 condensed into one
(b) The fa .... go vs. f~dge curves were deduced from the panel tests by finding the edge stress from the measured strain and material properties, and deducting the load carried by the stringers and edge members at this stress from the total load. The remaining load divided by the skin area yielded the average stress. It was found that the slope of the f , . . . . g e vs. foago curve fell off rapidly before failure. This reduction in af, .... ,o / af~dge would explain the premature failure in flexure. The observation is, however, open to some doub t . . If, because of local plasticity or large amplitudes in flexure, the edge stress was lower than that found from the mean strain, then the apparent f~w,a~o found as above would be fictitiously low, and there would be a reduction in the gradient of the apparent favor,~o VS. f~ago curve. To eliminate this' doubt, more exact knowledge of the edge stress is necessary.
(c) I t was, therefore, proposed that tests should be carried out on flat skins with simply supported and clamped edges and a range of b/t values. I t was decided t o imitate simply supported edge conditions by means of steel balls located in vee grooves in a test rig. In order to imitate clamped edge conditions, the edge support was by steel rollers located in slots in the test rig. The tests are supplemented by tests on panels with stringer edge supports, the stringers being identical with those of the panels previously tested. All the tests were done in the 50-ton Avery universal hydraulic machine at the Structural Research Laboratory, Filton.
2. Ball Edged Panels.--2.1 Description of Pands.--All the panels tested were 35 in. long, and nominally 0.064 in. thick. The panels were designed to cover the following range: - -
Clad material (D.T.D. 546)
Panel No. 1A 2A 3A 4A 5A 6A 7A 8A 19A* 20A*
bit 35 40 45 55 65 80 100 120 55 65
Unclad material (D.T.D. 646)
Panel No. 1B 2B 3B 4B 5B 6B 7B 8B
b/t 35 40 45 55 65 80 100 120
The panels were cut from the same sheet of material, in each case, as the further panels 9A to 18A and 913 to 18B. The panels marked * were made from the same batch of material, and were intended i o r a special investigation of wave shape along the length of the panel.
The panels were cut accurately to the 35 in. length, and the ends filed flat, but the overall width was about } in. greater than that corresponding to the specified bit and the nominal thickness.
The thickness of each plate was measured at a number of points (five down each side of the plate) and the mean thickness determined. The width between ball centres was then chosen to give the correct bit ratio.
The dimensions of the panels are summarised in Table 1, and the variation of thickness down the length in Table 2.
Before being set up in the testing machine, the panels were marked with grid lines symmetrical about the centre of the panel and extending over the length 3b. In the case of panels 19A and 20A the grid extended over the whole length of the panel.
2.2. Description of Test Rig.--2.2.1. Edge support.--The test rig is shown on Sheet (2). The hardened steel balls, ~ in. diameter, were located in 90 degvee grooves in steel blocks. These blocks were bolted to robust side supports of rolled steel joist section. In order to prevent
2
the buckled plate from forcing apart the lines of balls on opposite faces, the blocks were bolted together by 2 B.A. bolts perpendicular to the plane of the plate and the points of the at tachment to the side support reinforced with steel blocks.
The balls were intended to roll freely in a vertical direction, thus permitting unconstrained contraction of the plate. I t was also expected tha t there would be little lateral constraint in the plane of the plate. The reinforcements were thus intended only to provide the maximum possible constraint normal to the plane of the plate.
The balls were 5/16 ill. pitch, being separated by small rubber blocks. The choice of rubber for the blocks was governed by the fact that it was desirable to provide ball support as near the ends of the plate as possible, and if this were so and the panel contraction was considerable the top ball would come into contact with the headplate. In this case the additional load needed to compress the pile of rubber blocks would be negligible.
The method of adjustment was as follows: the side supports were placed some distance apart, and the balls and rubber blocks fed into the vee grooves with 16 S.W.G. Alclad strips in position to separate the two rows of balls. The panel was then inserted, pushing out the 16 s.W.G, strips, and the side supports moved laterally across the base plate until the desired value of b was obtained with the centroid of the panel on the axis of the loading machine. The side supports were then bolted down to the base plate.
The blocks with vee grooves were then adjusted. The bolts at taching them to the side supports were loosened, and the 2 B.A. bolts joining pairs of blocks gradually tightened until all the balls were in contact with the panel. The bolts on to the side supports were then also tightened.
2.2.2. Loading platens.--The lower end of the panel under test rested on the base plate of the testing machine. The upper end was loaded through a steel block bolted to the headplate of the machine. The lower side of the loading block was 0" 25 in. thick and was machine planed and set up parallel to the baseplate.
This block made it possible to extend the vee grooved blocks and bails to the upper end of the panel, and to allow for 0.3 in. contraction in this condition.
2.2.3. Measurement of skin buckles.--The amplitude of buckling was measured by means of a 0.001-in. dial indicator. The indicator was arranged to be free to slide laterally on a cross- frame, which was itself free to slide vertically on edge runners attached to the edge support rig. The weight of the cross-frame and indicator was balanced by lead weights and wires running over pulleys.
The dial indicator being constrained to move in a plane parallel to the plane of the plate, it was possible to measure amplitudes at all nodes of the marked grid.
2.2.4. Measurement of panel strain.--The mean panel strain was measured by a special type of averaging contractometer. The simple type of contractometer is unsuitable for this type of panel for two reasons. Firstly, it is designed to pick up on both sides of a stringer web, and owing to the large edge supports it would be impossible to arrange this type of at tachment in the present case. Secondly, the large deflections due to buckling would tend to tear out the a t tachment points of the contractometer if it were placed on the centre-line of the panel.
In tile averaging contractometer, the contractometer rod is at tached at the top to the mid- point of a lateral rod. This lateral rod has pick-up points at both ends, the distance apart of the pick-up points being adjustable to suit the width of the panel. The points are arranged to lie just inside the edge supports, where the amplitude of buckling is not large. A duplicate bar is arranged on the opposite side of the plate and the two bars are held together by means of a compression spring on a bar passing through a small hole in the plate. A similar lateral rod is attached to the lever at the bottom of the contractometer.
I t is seen that the strain measured is the mean of the strains near tile two edges of the panel.
3
2.2.5. End dials.--.In order to supplement the contractometer readings, which tend to become unreliable at large strains, the relative movement of the headplate and baseplate was measured by dial indicators at tached to the baseplate and picking up on the head plate. TWO indicators were used, in the plane of the panel, one close to each edge support.
2.3. Friction Tests.--2.3.1. Nature of friction present.--Two types of friction can occur in tests of this sort. One is friction in the edge supports, in which case the panel at the upper end cames the full indicated load. Down the length of the panel, the balls will exert a n upwards frictional force and the load in the panel will be reduced, the remainder of the load being carried by the side supports.
The other type involves friction between the loading ram and cylinder, and implies tha t tile indidated load (measured by the pressure difference inside the cylinder) is not equal to the load on the platen, the difference being the frictional force between the piston and the cylinder.
I t must be pointed out tha t this friction may be of either sign, depending on the nature of the loading (increasing or decreasing). Also, the friction may be expected to at tain some maximum value and then remain constant.
2.3.2. Standard test technique.--It has been standard practice in all tests to apply a settling load of about 0.2 tons to each panel, reduce the indicated load to zero, and set the dial indicators to zero reading, then loading i n increments. Accordingly any friction tests must provide a check on the conditions when this testing technique is used.
2.3.3. Friction tests.--A panel (Panel 10A) was set up with its lower surface about 0.1 in. clear of the baseplate. The vee blocks were arranged so tha t the ball supports were quite loose and free, the bolts joining tile blocks being slack. The blocks were then bolted firmly to the side supports.
The contractometer was set to zero, and the rams extended until the headplate was just in contact with the top of the panel. The end dials were then set to zero. The load was increased and readings taken of the contractometer and end dials. At a negligible indicated load the panel began to slip, until the lower surface came into contact with the baseplate. Small increments of load (0.025 tons) were then applied up to 0.7 tons. The indicated load was then reduced to zero, and a second set of readings taken with load increasing up to 0.7 tons. This second loading run was representative of standard panel test conditions.
The friction test was repeated with the bolts normally tightened. Once again, slip occurred at a negligible indicated load.
2.3.4. Discussion of results.--From the contractometer reading the mean load in the panel has been deduced, assuming E = 10.7 × 106.
I t is seen that on the initial loading the graph is very closely a straight line, of unit gradient, passing through the origin. I t is concluded therefore tha t no friction was present either in the edge supports or the rams. On reducing to zero indicated load, there was a mean load in the panel of 0- 23 tons in both sets of tests. As this load is independent of the edge support conditions, it follows tha t the load must be due to ram friction, which maintains the panel load even when the oil pressure difference has been reduced to zero. On increasing the pressure again, the mean load remained constant and there was no relative movement of the platens until an indicated load of 0 .2 tons. The graph then followed once more the straight line of unit slope, passing through the origin.
2.3.5. Conclusions.--The friction at the ball edge supports is negligible. When a settling load has been applied, there is a residual load in the panel due to ram friction.
(This might be expected, since the ram is designed only for the outgoing stroke and it is quite likely tha t seals might tend to jam on the return stroke). This results in the initial portion of
4
the load vs. strain curve being vertical; a phenomenon observed many times before in panels tested in this machine.
In order to obtain the corrected strain, the straight line on the load vs. strain diagram must be extrapolated backwards and the vertical portion neglected. The friction can then be neglected, no correction to the load being necessary.
Note: As a result of this investigation, it is proposed tha t in future tests the platen should be taken clear after the settling load, and readings started when the platen just comes into contact again with the panel.
2.4. Test Results.--2.4.1. Procedure.--A settling load of about 0.2 tons was applied to each panel, the load reduced and the contractometer set to zero. Measurements of panel strain were made at load increments of about 0-1 tons. Measurements of skin buckling were made at increments of deflection of about 0.01 in. Loading was continued until considerable plastic flow took place, at a strain of about 0.006.
2.4.2. Load vs. strain curves.--The load vs. strain curves were plotted for clad panels, and for unclad panels.
2.4.3. Buckle shape.--The buckled shape is plotted for clad panels and for unclad panels. The readings were generally of amplitude down the centre-line over a length 3b, 25 readings being taken over this length, and of amplitude across a section near a wave crest. In the case of Panels 19A and 20A the amplitudes clown the centre-line were measured along the entire length of the panel.
No readings were ta~ken of the initial shape of the panel, since this is modified by the supports at the edges. A reading of shape at low load is used instead.
Owing to the size of the edge supports it was not possible to take readings very near the edges of the panel.
2.5. Analysis of Results.--2.5.1. Predicted behaviour with pinned edges.--In R. & M. 1554, H. L. Cox has analysed the case of a fiat plate whose edges are constrained normal to the plate, but are free to move in the plane of the plate. This analysis gives K ~- 3.62, and ~fa .... ~e / afed~o z ½ initially, the wave form being a double sine curve. An approximate investigation of the post- buckled state is made, and it is found tha t ~favor~o/~f~d~o falls and the cross-section of the wave has a flatter top with increasing strain.
In R. &.M. 2178,* an investigation is made including higher order terms. For the case where the plate is free to move laterally at the edges, it is again found that K ~ 3.62, but the initial value of ~fawr~o/af~dgo is found to be 0-41, a value which is exact.
As the edge stress approaches the plastic region, there will tend to be plastic flow in some parts of the panel where the stress resultants are large, and this will involve a change of wave shape and a reduction of ~f~vor~go/af~dg~. The onset of this effect can be predicted fairly accurately, but its nature and magnitude have not been determined theoretically.
In both analyses the initial buckling mode has a half wavelength equal to the panel width.
2.5.2. Predicted behaviour of ball edged panel.--It was evident from the inception of the tests, tha t ideal pinned or clamped edges could not be obtained in practice. The ball edges might be expected to offer negligible constraint in the plane of the plate, and their angular constraint at the edges must be small at any rate during the earlier stages of buckling. (During the late stages of buckling, owing to the slope of the plate at the edge, the points of contact with the balls tend to deviate from a straight line and the reaction between the balls and the plate cause a clamping effect.)
* Theory of Flat Plates Buckled in Compression, by W. S. Hemp.
5
Even assuming no constraint from the ball supports, the panel can still not be treated as pin edged at these supports. The perturbation is due to the strips of plate which must be present outside the ball supports. These strips, which for practical reasons are about 0" 1 of the panel width, act as elastic angular constraints at the edges, and also provide some lateral constraint. The former affects the buckling stress while both affect the post-buckled behaviour.
In order to estimate the effect of the former on the buckling stress, an energy calculation has been made (see Appendix I). The results of this calculation give theoretical values of K which are plotted against the ratio c/b.
The effect of the constraints on the post-buckled behaviour of the plate has not been analysed theoretically.
Two other forms of constraint are present. One is that the panel is of finite length, and the half wavelength can not, in general, be equal to the panel width, but should be some fraction of the total length. This also implies that any tendency tot the ends of the panel to be clamped, as would be the case for small amplitudes of a panel whose ends are accurately plane and parallel, will cause perturbation of the buckling stress and wave shape.
The ends of the panel, being i n contact with the platens, are constrained against lateral expansion. There will therefore be a further perturbation extending from the panel ends, due to this lateral constraint.
2.5.3. Experimental buckling stress coefficients.~The buckling strain has been determined by two methods. One value of the strain is found from the load vs. strain diagram, being defined as the strain at which a sudden reduction in slope occurs. The other value of the buckling strain has been determined from the post-buckled amplitude. The square of the mean amplitude was plotted against the strain, and the graphs were substantially linear, the intercept on the strain axis being the buckling strain.
We know fb = KEr(t/b) ~
i.e., E,eb = KEr(t/b) ~.
E, Hence , K = eb(b/t) ~ F.T"
The values of K are summarised in Table 3, and are plotted against the theoretical values, defined by the ratio e/b. I t is at once apparent that the experimental scatter is severe. The clad panels exhibit values of K about 15 per cent lower than the unclad panels, with the exception of those which buckled below 10,000 lb/sq in. in which there is agreement between the two sets of results. This is consistent with a reduction in buckling stress due to yielding of the cladding at stresses above 10,000 lb/sq in. Apart from this effect, there is fair agreement between the values of K observed and those found theoretically in section 2.5.2 and Appendix I.
2.5.4. Amplitudes after buckling.--In N.A.C.A., T.N. 752 a theoretical value is given for the amplitude after buckling
4~ fe --fb a 2
~2 E
i.e., a" = (e - eb).
7~ 2
This theoretical slope of the a 2 vs. e diagram is compared with the experimental values in Table 4: the values of t chosen are the mean values observed.
2.5.5. Wavelengths after buckling.--The mean wavelength was plotted against the edge strain, and it was apparent that 2]b did not generally assume the value closest to 1.0
6
2.5.6. f , . . . . g e vs. f~ag~ curves.--The ~¢alue of 'foago has been deduced h:om the strain, using the panel E in the elastic region. In the plast ic region the curves have not been plotted out fully. I t has been assumed tha t the strips outside the supports carry the full stress fedgo, and hence fave~go is deduced.
The theoretical value plotted for initial 0favor,go/0foage
is 0" 82 1- + .(X/b)" 3 +
which represents the results of R. & M. 2178 corrected for changes in wavelength.
NOte: i n order to allow for the variation in the stress at which the second modulus for D.T.D'. 546 occurs, the following procedure has been adopted for clad panels between this stress and 45,000 lb/sq in. : if the initial panel modulus is El, and the transition stress fz, then at a strain e we write for the stress
f = O. 9Ele + O" lfl.
2.5.7. Change in buckled shape.--The cross-sectional shape near a wavecrest is plotted for various values of e/eb. I t is seen that the top of the wave becomes flattened with increasing e/e~, and the form approximates to
w = a sin ay 3~y. -b- + B sin b
3. Roller Edged PamIs.--3.i. Description of Panels.--The panels were 35 in. long and nomin- ally 0.064 in. thick. They were designed to cover the following range: - -
Clad material (D.T.D. 546).
Panel No. 9A~ 10A 11A 12A 13A 14A 15A 16A 17A 18A t 21A*
b/t 0 35 40 45 55 65 80 100 120 0 45
Unclad material (D.T.D. 646). :
Panel No. 9B~ 10B l l B 12B 13B 14B 15B 16B 17B 18B~
bit 0 35 40 45 55 65 80 100 120 0
Panels marked * were designed for a special investigation of wave shape down the length of the panel.
Panels marked ,t were designed to provide a direct comparison with compression control tests, and no measurements of buckled shape were made.
The construction of the panels was similar to those with ball edge supports, and the dimensions are summarised in Tables 5 and 6.
3.2. Description of Test Rig.--The test rig was identical with that already described with the exception of the edge supports. In this case the hardened steel rollers, } in. diameter, were located in slots cut vertically in steel blocks, the blocks being bolted, as before, to the side supports. The rollers were at ~ in. pitch, being separated by small rubber blocks. The axes of tile rollers were horizontal, so that one face rolled on the plate and the other on the steel block, thus permitting panel contraction. The edges of the grooves in the steel blocks located the rollers laterally, with a small clearance.
The clamping action of the rollers on the plate involved forces tending to separate the steel blocks on opposite faces of the plate. In trial tests it was discovered that the blocks did in fact
7
separate suddenly, precipitating failure of the panel by wrinkling at the edges. The blocks were, therefore, tied together by 2 B.A. bolts and the increase in stiffness was sufficient to prevent serious separation of the blocks.
3.3. Friction Tests.--Friction tests were performed on a panel, in the same manner as previously. The results are plotted for bolts loose, bolts tight, and for lubricated edge supports.
In the first loading, the panel sustained an appreciable load before slipping occurred. (0.08 tons with bolts loose, 0.35 tons with bolts tight). This load increase involved relative movement of the platens, and was due to friction between the plate and the rollers. As loading proceeded after the bottom end of the panel had come into contact with the baseplate, the load indicated by the machine increased at a greater rate than tha t deduced from the mean panel strain. This did not occur in the case of ball edge supporfs, and it was, therefore, concluded to be due to increasing friction between the panel and the rollers.
On reloading, the mean load carried by the panel remained constant at 0.15 tons while the indicated load was increased from zero to 0.15 tons. The curve then tended to follow the same course as before, with indicated load increasing at a greater rate than mean load. This phenom- enon on reloading may be associated with jamming of the rams on the return stroke, and this is par t ly confirmed by the fact that the mean load carried at zero indicated load is the same in all cases.
I t is known, from an examination of the other test results, tha t the rate of increase of indicated load becomes equal to that of the mean load after a load of about 1 ton. This shows that the friction at the rollers reaches a limiting value.
3.4. Interpretation of Load vs. Strain Curves*.--It is clear from t4he foregoing that the i n d i c a t e d load is not equal to the mean load carried by the panel, owing to friction with the rig; and the strain measured from zero indicated load, is not equal to the panel strain, owing to jamming of the rams on the return stroke.
Consider a typical load vs. strain curve as under : - -
P,
. J
E j l
i j I / " ¸
k t__
G
A
[::) 0 MEA%URED 5 T R A I N
In the portion OA the indicated load is increasing, the load carried by the panel being constant. In the portion AB the friction between the panel and the rollers is increasing, and in the portion 13C tile friction has reached a limiting value.
I t is not known how much of the load AO is carried by friction, but it seems reasonable to assume tha t the rate of growth is similar to that along AB. This is confirmed by the first loading in the friction tests.
Referring to the diagram above, the corrected strain, must therefore be measured from the point D and the corrected load (giving the mean load in the panel) from the point E for all loads past the point B.
* A fuller development of these arguments is made in t3.A.C. Ltd. Technical Office Report No. 25 (unpublished).
8
OD represents the initial mean strain in the panel at zero indicated load. ED represents half the limiting friction between the panel and the rollers (assuming constant friction down the edges), and its deduction gives the mean load in the panel. For the load at the bottom end of the panel, twice the above deduction would then have to be made.
a: o _1
b
. v 0 ~ ' ~ / / '
M E A N 5 T R A L N
3.5. Test Results.--The test procedure and readings taken were the same as for ball supports with the exception that no readings of buckled shape were taken in Panels 9A, 18A, 9B, 18B since these were fully supported. The load vs. strain curves and the buckled shapes were plotted.
3.6. Analysis of Results.--3.6.1. Predicted behaviour with clamped edges.--The case of clamped edges has been treated in R. & M. 1554, in which it is assumed that the edges are unconstrained laterally. I t is found that K = 6.32, and ~f~verago/~fod~o = 0"548 initially, the value of ~/b at btickling being 0.66. The value of ~f~vor~o/~fed~o falls with increasing strain.
In R. & M. 2178, which includes higher order terms, it is found that K = 632 as before, and the initial value of af~v~ra~o/~fod~o is 0" 50, for a value of ~/b chosen equal to 0.7.
3.6.2. Effects present in roller edged panel.--These may be summarised as follows:-- (a) Incomplete clamping owing to the deformability of the rollers, flexibility of the side
blocks and initial lack of fit. (b) Lateral constraint from the strips of metal clamped between the rollers, and also possibly
from lateral frictional forces at the rollers. (c) Lateral constraint at the ends of the panel due t o friction with the loading platens. (d) The panel is of finite length, and the half wavelength should therefore be equal to some
fract ion of the length, a n d not to that which gives the minimum K for any infinitely : long panel. (e) The ends of the panel may tend to be clamped at the platens if they are machined
accurately plane and the amplitudes are not large.
Theoretical analysis has not been applied to any of these effects.
3.6.3. Experimental buckling stress coefficients.--These have beeh determined as before in two ways; from the load vs. strain curves and from plots of the square of the mean amplitude against strain. ~ ,
: 9
• The values of K are summarised in Table 3, taking b as t h e distance between inside faces of the rollers, and are plotted against b/t. Once again the scatter is severe, but the clad panels exhibit values of K lower than the unclad ones. It is apparent tha t the clamping at the edges of the panels was by no means complete, being sufficient to increase K by only 50 per cent of the amount required for full clamping. The amount of clamping appears to increase with increasing b/t.
3.6.4. Amplitudes after buckling.raThe slopes of the a ~ vs. e diagrams are summarised in Table 8.
3.6.8. Wavelengths after buckling.--!t is apparent that l/b is generally greater than 0.7 and does not assume the value closest to~0" 7.
3.6.6. fa .... ~o vs. rodeo curves.--The f~vo~ago v s . f,d~o curves have been deduced and were plotted. In the case of panels 9A, 18A, 9B, 18B the result yields a stress vs. strain curve. In all cases, both the measured load and the measured strain have been corrected for friction as in section 3.4.
The variation in the stress at which the second modulus occurs has been allowed for as follows: if this stress is f l and the first panel modulus is El we write for elastic strain e above f ,
f = 0.9E~e + O" lfl. i
3.6.7. Change in buckled shape.--The cross-sectional shape near a wave crest is plotted for various values of e/eb and compared with the theoretical mode of buckling f o r a panel with damped edges.
4. Stringer Edged Panels.--4.1. Introduction.--The foregoing tests Were intended to define the behaviour of a buckled plate under ideal conditions of edge support. These results, though of fundamental importance, do not necessarily apply to a plate supported b y stringers, since a number of new variables are introduced. For example, the angular restraint at the edge of the .plate depends on the stiffness of the stringer, and this st i,ffness may be modified b y plasticity in the stringer analogous to the plasticity in the plate which caused failure i n these tes ts . Analysis of these effects is postponed until the end of the report.
I n order to provide some experimental data on the behaviour of panels with stringer edge supports, the present series of tests was undertaken. The stringers used were identical (except that they were in D.T.D. 646 not D.T.D. 546), with those of the compression box panels previously tested* and were intended to give a check on the results of that report; however, in the current tests there are two stringers per pitch of skin and the conditions are not, therefore, strictly comparable.
Tile conclusions from all the tests with ball, roller and stringer edge supports are given at the end of this section, together with a summary of the control test results.
4.2. Description of Panels.--All the panels tested were 35 in. long. The stringers were 16 s.w.G. D.T.D. 646, of Z section 1.65 × 0.75 in. with 5t inside-bend radius. The stringers were riveted -18 in. diameter D.T.D. 303 rivets at } in. pitch to the edges of the plate, with the free flanges facing outwards.
The plate was 8 in. wide, and two panels were made for each plate gauge, viz.: 18, 16, 14 and 12 s.W.G.
The panel dimensions are summarised in Table 9. The ends of the panels were cast in Wood's metal and machined plane and parallel before setting up for test.
4.3. Test Rig.--The measurements made on test were fundamental ly the same as previously, but the portion of the rig for edge support of the panel was omitted, as was also the special loading head. The panel was set up with its centroid on tile vertical axis of the testing machine.
* Reported in B.A.C. Report C.R.404 (unpublished).
10
The skin buckle shape was measured by a universal apparatus Similar to tha t used previously. In order to permit readings of skin buckles near the ends of the panel, a pair of dial indicators was carried on the cross tubes. Of these indicators the upper one gave the buckled shape at the top of the panel, and the lower one the shape at the bottom. The two indicators were set so tha t they gave identical readings for a point at the centre of the panel.
The panel strain was measured by contractometer of the Mark I type attached to the stringer webs, and the relative movement of the platens was measured by means of two dial indicators attached to the baseplate and regigtering on the headplate.
4.4. Test Results.--4.4.1. Procedure.--A settling load of 0.2 tons was appl iedto each panel, the headplate was then lifted clear of the panel and brought into contact again. The dial indicators were then set to zero and contractometer measurements made at load increments of about 0.1 tons. Measurements were made of skin buckles at increments of 0.01 in. amplitude, the readings giving an amplitude plot down the centre-line of the panel and cross-sections at two or three troughs or crests near the middle of the panel.
Loading was continued until panel failure took place.
4.4.2. Load vs. strain curves.--The load vs. strain curves were plotted, as before.
4.4.3. Buckle shape.--The buckled shape was plotted; the amplitude readings were carried to the edges of the panel, in order to determine the effective width of the plate for buckling (see section 4.5.2).
4.5. Analysis of Results.--4.5.1. Apparent favera~e VS. fodgo curves.--In order to determine the apparent skin fawra~o VS. lodge curves, the method of analysis used in previous panel tests was applied. For a given edge strain, the edge stress was calculated using the measured panel E. (In these tests the edge stress was sufficiently low for there to be no drop in tangent modulus.) I t was assumed that the stringers carried the stress fod~ and hence their load was calculated. This load was deducted from the total load to give the load carried by the skin, which divided by the skin area gave favo,~g~.
The assumption that the stringers carry a uniform stress rodeo is open to some question. The buckling involves distortion of both the skin and stringers, and it is possible tha t the stringer amplitudes may be large enough to cause an appreciable local reduction of stress. Also, the
local transverse stresses in the stringer may cause plasticity and a consequent reduction in the compressive stress carried.
4.5.2. Analysis of buckle readings taken on test.--The skin contour was measured by two 1/1000-in. dial indicators mounted on a carriage, sliding on two horizontal bars. The horizontal bars were then free to slide in a vertical plane guided by two steel bars which were set perpendicular to the machine baseplate.
On setting up, the panel was placed in position with its centroid on the centre-line of t h e machine and was then rotated till the skin at its lower end was parallel with the plane of the buckle measuring gear. A very light load (0.05 tons) was then applied to the panel and the dials set to zero at the lower end on the panel, the top end was then moved till the skin there was parallel to the reference plane and the same distance from it as the lower end.
Movement of the panel relative to the reference plane may occur through any of the following effects:--
(a) Headplate lateral movement, causing the top end of the panel to move towards or away from the reference plane.
(b) Flexure of the stringers. The stringers usually move in opposite directions but not by the same distance, giving flexure and twist of the panel.
(c) Curvature of the skin due to fixing moments applied by the stringers.
11
The objects for which buckle contours were measured a r e : ~ (a) To find from cross-sectional plots, the value b, the effective distance between skin
nodal lines down the length of the panel. (b) To find buckling strain from plots of the square of the amplitude against strain. (c) To plot ~/b against strain. (d) To obtain plots of the shape of buckle cross-section eliminating the influence of flexure
and skin curvature. The mean line of the skin at panel centre-line was plotted by taking the observed readings
for the amplitude of buckles at each crest and trough, finding the algebraic mean of each pMr of adjacent readings then finding the average of each pair of adjacent means. The curve obtained by joining these plots was regarded as the mean flexure of the two stringers, unless curvature of the skin had occurred.
I t has been assumed tha t the difference in mean stringer flexure at two sections is the same as the difference shown by the skin mean line.
Wavelength, ~, has been taken as the intersection of the skin contour lines with the mean line.
To find b, plots of skin contour were taken in horizontal planes acrossan adjacent crest and trough at several load stations for each panel (except panel B. 4 A). The contour of each peak was plotted as obtained on test, but readings for the troughs were corrected for the difference of flexure at the two sections, by plotting on the buckle centre-line, the difference in ' mean flexure ' of the two sections, given by the skin mean line. Then the base line for each trough was drawn through its respective point and inclined in such a way that the difference between the ordinates of trough and crest was equal at the first and last station.
The value of b has been taken as the distance between intersections of the troughs and crests. To plot the buckle shape, the difference of corrected crest and trough was founda t each station
and expressed as a percentage of its maximum value. Thus, the effect of bending in the skin due to stringer twist over a larger wavelength was eliminated. The mean mode on which the buckling was superimposed was found by taking the mean of crest and trough amplitudes. This mean mode is also plotted.
4.5.3. Experimental buckling stress coefficients.--The buckling strain has been determined by two methods, from the change of slope of the load vs. strain curve and from the post-buckled amplitude. In this second method the square of the amplitude is, plotted against the strain, and the intercept on the strain axis is the buckling strain.
The mean value of b has been determined and K evaluated from the relation
K : eb(b/t) ~.
The values of K are summarised in Table 10.
4.5.4. Wavelengths after buckling.--The wavelengths were determined and were plotted against the strain. The mean value of a/b is close to 0.8 for most panels.
4.5.5. Slope of a 2 vs. e curve.--The mean slopes o f the (amplitude) ~ vs. strain curves are summarised in Table 11.
4.5.6. Variation of b with strain.--The values of b are plotted against the ratio e/eb. I t is seen tha t with increasing edge strain, the value of b increases slowly at first, and then suddenly up to the full panel width of 5 in. This sudden increase may be due to plasticity in the stringer web and flange. The location of the skin nodal line on the stringer flange is shown, where the location is plotted against e/eb. I t is seen tha t with increasing skin thickness the nodal line tends to be nearer to the stringer web.
12
4.5.7. Variation of wave shape.~The wave cross-sectional shape has been determined as described in section 4.5.2, and is plotted non-dimensionally for values of the strain equal to 1-0, 1.25, 1" 5 and 2.0 times tile buckling strain. Little change of shape with e/eb is observable, but considerable clamping is seen to be afforded by the stringers.
4.6. Comparison with Theoretical Results.--4.6.1. Statement of the problem.--The theory of buckling of panels is not so well-developed as that for plates. This is inevitable, because the addition of (say) a Z-section stringer to a plate adds three new geometrical variables to the problem. Two aspects of the problem require analysisl
(a) The value of the buckling stress coefficient K. (b) The distribution Of stress in the skin and stringers for values of the edge strain greater
than the buckling strain.
Some progress has been made with (a), but analysis of (b) is still lacking.
4.6.2. Buckling stress coefficient.--In the Royal Aeronautical Society Data Sheet* 02.01.18, the initial buckling stress of a flat panel with Z-section stringers is determined. The panel is assumed to have a large number of stringers which are rigidly attached to the skin.
In the present tests the support from the stringers is greater, since there are two stringers to one skin panel. In order to allow for this a fictitious ' effective s tr inger ' is found and the results of Data Sheet 02.01.18 applied.
This effective stringer has the same h/t, ratio as tile actual stringer, but the stiffness of its web for rotations about one flange is doubled, i.e., t~/h is doubled. This gives a stringer having twice the dimensions of the actual stringer. (The error due to this assumption is in the wave- length of initial buckling).
The results obtained from Data Sheet 02.01.18 for this effective stringer are plotted and are in good agreement with the experimental points.
4.6.3. Effect of stringer amplitude whose deflection is w,
1C~(Ow~ ~ e = f + ~ d o \ ~ / dx
where x is measured along the half-wavelength.
on post-buckled behaviour.--For any longitudinal fibre,
Assuming a wave form
we have
o r
~zX w = w0 sin T
f gr2W° l
e=- + 4~ ~
f = E(e
Thus the reduction in fibre stress is proportional to the square of the maximum amplitude.
The observed mode of distortion has been considered, and by integration across tile stringer tile reduction in stringer average stress has been calculated to be about 2 per cent of the reduction in skin average stress. We conclude, therefore, that the apparent skin faver,,o VS. fod,o curves are not more than about 2 per cent in error due to this cause.
-* See Note which appears later.
13
4.6.4. Plasticity in stringer web.--The fixing moment between the skin and stringer causes local stresses which will induce local plasticity in the stringer web and flange. This means that the stiffness at the flange, for providing angular constraint at the edges of the sheet, is reduced.
The maximum stress difference in the stringer (or in the skin where this is thinner than the stringer) has been calculated by an approximate method and is plotted. It is seen that the skin nodal line moves outwards at the same time as the theoretical plastic stress difference is reached.
The sudden decrease of slope of the f~e~ag~ VS. foago curve appears to be due to the plasticity mentioned above. Consider a panel which buckles at a value of K greater than 3-62. The panel will follow the f , .... ~ vs. fod,o curve appropriate to this value of K. When plasticity in the stringer is fully developed, the skin will become effectively pinned at the edges and will behave as if it had buckled at K = 3.62.
Further analysis of this effect is developed in B.A.C. Technical Office Report No. 26 (unpublished).
5. Summary and Conclusions.--The values of 2/b were plotted against the values of K realised by the panels, and compared with the theoretical curve of N.A.C.A.T.N. 752. I t is seen that the experimental Values of K corresponding to a given X/b are less than the theoretical values, and that this is more marked in the case of D.T.D. 546 than in the case of D.T.D. 646.
The experimental points for Ofavora~o/Ofoago are plotted against fb and ledge for clad and unclad panels with the various conditions of edge suppor t . .Mean contours of Of, vora~,/0f~a~e are drawn through the experimental points, and hence by cross-plotting 0f, vora~o/0foago is plotted against. fedge/fb for various values of fb. In this form the information is suitable for design office use.
It is seen tha t the value of fi has a marked effect on Of~vo~go/Of~a~o the reduction being more marked when f~ is large. This reduction for large buckling stresses is associated with plastic flow in the portion of the plate where the local stresses due to buckling are large. As a comparison with the experimental results, the theoretical results of Data Sheet 02.01.i are plotted; the theoretical reduction of 0f, v~=~o/0foa~o is in quite good agreement with experiment during the earlier stages of buckling, but the reduction is less than tha t found experimentally in the later stages. This is as would be expected, since the theory of Data Sheet 02.01.i takes no account of changes of mode due to plasticity. (The results of Data Sheet 02.01.02 are also plotted for comparison.)
Conclusions.--1. Tests with ball edge supports have not imitated pin edged conditions owing to the torsional stiffness of the plate material outside the supports.
2. Tests with roller edge supports have not imitated clamped edge conditions owing to the flexibility of the rollers.
3. The tests are, however, representative of slight edge fixation and heavy edge fixation, corresponding to K = 4 and K = 5 (approx.) respectively.
4. The tests with stringer edge supports show good agreement with the values of K determined from Data Sheet 02.01.18.
5. The scatter in the observed wavelength is severe, but mean values of X/b for ball, roller and stringer support are 0.95, 0.7 and 0.8 respectively.
6. The values of Of ..... =o/afedge are dependent on the value of the buckling stress as well as on fed,Jfb. Data Sheets of the type 02.01.02 are therefore inadequate, since account must be taken of plasticity in the plate. Data Sheet 02.01.i represents a better approximation over a limited range.
7. Plastic strain in the stringer modifies the conditions of edge support for the panel when a certain edge stress is reached. This modification is discussed in B.A.C. Technical Office Report No. 26 (unpublished).
14
8. In tests of the ball and roller support type, the test results must be corrected for initial errors due to friction and contact deformation. These effects are discussed in B.A.C. Technical Office Report No. 25 (unpublished).
A cknowledgement.--The laboratory work, on which this report is based, was undertaken by Mr. C. j . Wilson, Mr. C. H. Jones, Mr. E. E. Fenn and Mr. P. R. V. Walmsley of the Bristol Aeroplane Company.
Note: Since this report was first published by the Bristol Aeroplane Company, the numbering of the Royal AeronauticaI Society's Data Sheets on stressed skin structures has been revised.
The data sheets are referred to in this report by their 1947 numbering. The current (April, 1953) changes are given below for those who wish to refer to the Data Sheets.
02.01.18. has now been reissued, with amendments, as 02.01.25. In the new issue the corrected portions of the curves refer to a lower buckling stress than in the original issue, associated with a torsional-cum-local buckling mode of the stringers. The comparisons made in this report are with the npper parts of the curves, which are unaltered, since the geometry of the panels tested here was such that the other type of mode was not critical.
02.01.02. was reissued under the same number in December, 1947, to include the effects of lateral constraint which had previously been neglected. The new issue is appropriate only to conditions immediately after buckling. The well- buckled state is covered by 02.01.03.
02.01.i. was a draft data sheet on the effect of plasticity in buckled plates. This draft was discussed by the Structures Committee of the Royal Aeronautical Society, but was not issued. The only information issued on plasticity is therefore that contained in 02.01.03.
NOTATION
b
g2)
t
Er
Es
fb K
ledge faverage
g
eb
B.A.C.
Panel width between ball centres or inside ends of rollers
Overall panel width
Panel thickness
Tangent modulus
Secant modulus
Half wavelength of buckles
Buckling stress
Buckling stress coefficient, defined by fb = KE(t/b) ~
Longitudinal stress at edges of panel
Average stress across width b
Mean panel strain
Buckling strain
Amplitude of,buckling
Bristol Aeroplane Company, Ltd.
15
APPENDIX I
Energy Calculation for Panel with Edge Strips
A
W
E~ ""
Assume • ~x ~Y between A and B. w = a sm -b- sin
W m y sin ~- to the left of A, etc.
Then total energy of contract ion
fro ( = ½ \-g-x/ f l dx dy
0 --C
a2g~ 2 ~4C3 8 f t+-g-g3a~f t"
Strain energy of plate
fb fb Et 8 [{ O~w,~2 @ O~ w O~ w ( Oe~w~ I = ½ o o 12(1 -- ~) t\Txx ~) 2 0 x ~ ~y~ + \--~y~) j dxdy
_ Et% 2 ( ~ ) 12(1 -- ~) ~ "
Stra in energy of strips
t 3 ~ 4 a 2 C = 0 .385E - 1
6 b~ ~"
E q u a t i n g strain energy to potent ia l energy at buckling,
K = 3 .62 + 5.06c/b 1 + 13"33d/Y "
16
T A B L E 1
Dimension of Panels. Ball Edge Su~borts
0 o
w
Clad Panels D.T.D. 546
7
Panel
W
b
c/b
t
wt
1A
2.922
2.160
0.176
0.0618
0.1806
2A
3.280
2.550
O. 136
O. 0637
O. 2070
3A
3.581
2.910
0.115
0.0647
.0-2316
4A
4.425
3-600
0.090
0-0656
0- 2782
5A
4.951
4. 290
0" 077
0.0660
0" 3267
6A
5.887
5.270
0"058
0.0659
0" 3878
7A
7.190
6-520
0.051
0"0652
0.4689
8A
8-250
7-900
0" 039
0" 0634
0" 5400
19A
4"359
3"730
0"084
0'0677
0"2954
20A
4"733
4.460
0.031
0"0687
0-3248
Unclad Panels D.T.D. 646
Panel '
b
c/b
t
wt
1B
2.905
2 ~ 240
0.148
0.0641
0.1861
2B
3" 230
2" 630
0"114
0" 0658
0"2124
3]3
3" 575
2"880
0" 120
0" 0639
0"2285
4B
4.244
3.630
0.085
0.0660
0"2802
5B
4"900
4"350
0-063
0" 0669
0" 3276
6B
5" 890
5"550
0"031
0" 0693
0" 4084
7B
7"210
6- 870
0.024
0.0687
0.4954
8B
8"525
8-010
0.031
0.0668
0" 5693
17 (25590)
TABLE 2
Variationin ThicknessdowutheLe~th. Panelswith BallE~eSupports
Panel 1A 2A 3A 4A ' 5 A
Top 0-0622 0.0612 0.0662 I
Bottom
0-0622 0.0622 0.0624 0.0622
0.0612 0.0613 0.0613 0.0612
0.0632 0.0640 0 . 0 6 3 3 0.0640 0.0632 0-0640 0.0632 0-0639 0.0633 0.0647
0-0644 0.0644 0.0644 0.0644 0.0642
0.0652 0.0651 0.0650 0.0651 0.0645
0.0658 0.0654 0.0657 0,0649 0.0657 0.0655 0.0658 0.0654 0.0659 0.0652
0.0660 0.0662 0-0663 0.0662 0.0662 0.0660 0.0657 0.0657 0.0655
Panel 6A 7Jk 8A 19A 20A
Top 0,0654 0.0656 0.0654 0.0654 0.0654 Bottom
0.0645 0.0645 0.0643 0-0642 0-0645
0.0654 0-0657 0-0657 0.0660 0.0662
0-0627 0-0625 0-0622 0.0622 0.0622
0.0657 0.0660 0.0660 0.0660 0.0660
0.0680 0-0679 0-0677 0.0680 0.0678 0.0678 0.0679 0.0671 0.0680 0.0672
0.0652 0.0650 0.0652 0.0650 0.0645
0.0683 0.0685 0.0694 0.0683 0.0688 0.0684 0.0683 0.0686 0.0690 0.0688
Panel 1B 2B 3B 4B 5B
Top 0-0663 0-0661 0.0652 0-0646 0.0645
7B
0.0702 0.0696 0.0692 0.0683 0.0690
0.0643 0.0643 0.0632 0.0631 0.0630
0.0670 0.0670 0.0660 0.0655 0.0655
0,0693 0.0685 0.0682 0.0675 0.0673
6B
0.0705 0-0700 0.0692 0,0688 0.0687
0.0632 0,0633 0.0634 0.0636 0.0638
8B
0.0690 0.0682 0.0685 0.0670 0.0666
Bottom
Panel
0.0640 0.0645 0,0642 0.0644 0,0648
0.0665 0.0660 0.0660 0.0652 0.0648
0.0652 0.0649 0.0645 0.0642 0.0640
0.0704 0-0697 0-0692 0-0685 0-0684
0.0675 0.0668 0.0669 0.0660 0.0665 0.0651 0.0656 0.0651 0.0655 0 .0653
Top
Bottom
0-0662 0-0659 0-0665 0.0660 0-0670 0-0668 0.0675 0-0670 0.0683 0-0675
18
Value of K.
TABLE 3
Panels with Ball Edge Supports
Panel
KI
Ks
Panel
K1
K2
1A
3 "80
3.68
1B
4.03
3.97
2A
3.26
3.28
2B
3-95
3.77
3A
3"35
3.56
3B
3.95
4.40
4A
3.48
3.48
4B
3.96
4.06
5A
3.47
3.22
5B
4-66
4.23
6A
3-53
3"21
6B
4"10
3"97
7A
4"00
3"30
7B
3.20
3"00
8A
3.89
4.33
8B
4.18
4.18
19A
3.47
4.07
20A
3.77
4.18
NOTE :
/£1 found from load Vs. strain curve.
K2 found from post-buckled amplitude.
1 Values of KoJn,Fig. 8 have been corrected for wavelength by mult iplying 'by (a/b)2 + (b/a)3"
19 (25590) B#
T A B L E 4
Slope of (amplitude) ~ vs . strain curves. Panels with Ball Edge Supports
Panel 1A 2A 3A 4A 5A 6A 7A 8A
Theoretical 2.50 2.71 3.53 5.09 6.03 14.50 18.0 21.7
Measured 2.50 3.00 4.20 6-00 6.40 14.50 18.0 23.3
Panel 1B 2B 3B 4B 5B 6B 7B 8B •
Theoretical 1.76 2.82 3.10 4.55 7.12 9.65 25.0 i 5 .0
Measured 2.30 2.90 4.30 4;60 7.90 10.80 21.5 17.5
Panel 19A
Wave 1 2 3 4 5 6 7 8 9
Theoretical 4.08 4.58 4.58 5.1 5.1 5.1 5.65 5.65 4.58
Measured 5.6 5.9 6.1 6-0 6 .7 5.8 6.0 5.2 6.0
Panel 20A
Wave 1 2 3 4 5 6 7 8 9
Theoretical 3.51 5.54 5.54 6.81 7- 28 7.28 7.28 7.28 7.3
Measured 4.6 5.3 7 .5 7.4 9.1 9-6 9 .0 9 .6 6.9
I 10
5.1o
3.6
20
T A B L E 5
Dimensions of Panels. Roller Edge Supports.
t w 4 Clad Panels D.T,D. 546
Panel
W
b
t
wt
" 9A
2.505
0
0.0661
0-1655
10A
4.314
2.18
0.0624
0.2695
l lA
4'642
2.57
0.0643
0-2980
12A
4-980
2.94
0.0654
0.3260
13A
5.648
3.645
0.0663
0.3740
14A
6-320
4-335
0-0667
0-4215
15A
7.280
5.265
0.0659
0.4800
16A
8.610
6.388
0.0639
0-5500
17A
9.925
7"600
0"0633
0"6300
18A
2.510
0
0.0665
0-1670 L
2 1 A
5 " 0 0 0
3 "086
0" 0687
0"3435
Unclad Pands D.T.D. 646
12B 15B Panel
W
b
t
wt
9B
2.517
0
0.0696
0.1752
10B
4-370
2.207
0.0631
0.2755
l lB
4.730
2.627
0-0657 i
0-3107
4.995
3-062
0.0674
0.3364
13B
5.640
3.590
0.0653
0.3685
14B
6.300
4-260
0-0656
0-4133
7.280
5.180
0.0647
0.4713
16B
8.610
6.300
0.0630
0-5427
17B
9-925
7 . 3 2 0
0.0610
0.6054
18B
2.508
0
0.0655
0.1643
21
T A B L E 6
Variation in Thickness down Length. Panels with Roller Edge Supports
Panel
Top
Bottom
9A
0.0662 0.0664 0.0664 0.0662 0.0662 0.0662 0 . 0 6 6 2 0 . 0 6 5 5 0.0656 0.0657
10A
'0"0632 0"0615 ]0.0630 0.0615 :0.0630 0.0620 0.0628 0.0625 0.0628 0.0615
l l A
0.0650 0.0638 0.0650 0.0638 0.0648 0.0640 0-0645 0.0638 0.0645 0.0639
12A
0.0662 0"0650 0.0659 0.0650 0"06600 .0652 0"0657 0.0652 0"06540 .0648
13A '
i0[0668 0-0661 !0.0668 0-0661 0.0668 0.0663 0.0665 0.0660 0"0660 0.0660
14A
0.0670 0.0670 0"0669:0.0669 0.0669 0.0670 0"0665 0.0666 0.0665 0.0665
Panel
Top
Bottom
Panel
Top
Bottom
15A
0.0659 0.0660 0.0655 0.0665 0.0650
'gB
0.0685 0.0688 0.0693 0-0698 0-0705
0.0662 0.0661 0.0660 0.0660 0.0660
0.0691 0.0695 0.0692 0.0705 0.0710
16A
0.0630 0.0651 0.0625 0.0644 0.0630 0.0648 0.0632 0.0648 0.0630 0.0650
10B
0.0622 0"0638 0"0623 0-0639 0"0624 0-0639 0.0623 0"0638 0.0623 0.0638
17A
0.0650 0.0622 0.0645 0.0618 0.0645 0.0620 0.0649 0.0620 0.0643 0.0620
l l B
0.0661 0.0661 0.0649 0.0649 0.0649 0.0663 0.~650 0.0660 0-0648 0.0648
18_4.
0.0668 0.0670 0.0668 0.0668 0-0665 0-0665 0.0663 0.0663 0.0661 0.0661
12B
0"0679 :0"0667 0"0680 0"0669 0'0680 0"0672 0"0679 0"0669 0"0675 0"0667
21A
0.0687 . . . . 0.0690 0.0684 0.0688 0.0688 0.0689 0.0686 D : 0 6 8 5 0.0661 0.0684
13B
0.0645 0.0652 0.0649 0-0654 0.0645 0-0652 0.0652 0.0653 0.0654 0.0660
Panel ' 14B 15B 16B 17B 18B
Top 0.0642 0"0638 0.0640 0.0639 0"0635
0-0597" 0-0621 0.0598 0.0623 0.0598 0-0623 0.0598 0.0623 0'0600 0.0627 Bottom
• 0.0660 0.0651 0-0655 0.0649 0.0655 0.0650 0.0655 0.0650 0.0655 0.0650
0.0660 0.0660 0.0655 0.0655 .0.0655
0.0641 0.0627 0.0641 0.0623 0.0644 0.0620 0.0648 0.0620 0.0650 0.0619
0"0660 0-0659 0.0658 0.0657 0.0655 0"0652 0"0655 0.0655 0-0652 0.0652
22
Values of K.
TABLE 7
Panels with Roller Edge Supports
Panel
K1
K=
Panel
K1
Ks
9A
9B
10A
3"67
3"55
10B
4-53
4-56
l lA
3.80
3.71
11B
4.08
4.22
12A
4 "47
4.29
12B
4.65
4.76
13A
4-50
3"85
13B
4"17
3.78
14A
4"31
4"09
14B
3-73
3 "73
15A
5"44
3.75
15B
4.80
4.80
16A
4"20
4.00
16B
4 "30
4 "00
17A
4.76
4.76
17B
5"33
4.75
18A
18B
21A
4.65
5.18
KI found from load vs. strain curve.
Ks found from post-buckled amplitude.
TABLE 8
Slope of (amplitude) 2 vs. strain curves. Panels with Roller Edge Supports
Panel
08
Panel
a a ~
10A
1.6
10B
2-4
l lA
2"0
l lB
2 "4
12A
2"7
12B
3"0
13A
3.7
13B
4.3
14A
6.7
14B
3-2
15A
12-5
15B
7.8
16A
9 . 5
16B
8"5
17A
14.2
17B
13.0
P a n e l 21A i
Wave aa___2 ~ ae
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1-6 2 . 6 2 . 6 3 -0 3 . 4 2 . 6 2-5 2 . 9 3 . 5 2 . 5 3 . 6 2 . 8 2 . 9 2 . 9 3 .1
23
TABLE 9
Panel dimensions. Panels with Stringer Edge Supports
Panel
Skin . . . . .
Str inger 1 . .
Str inger 2 . .
Tota l . .
Panel
Skin . . . .
Stringer 1 : .
Str inger 2 . .
Total . .
Panel
Sldn . . . .
Stringer 1 . .
Str inger 2 . .
Tota l . .
Pane!
Skin . . . .
Stringer 1
Stringe r 2 . .
Tota l . .
Mean Wid th
5
2.684
2-694
5
2.7058
2.6992
5
2.6983
2-6842
5
2.6125
2.6908
Mean thickness
B. 1 A
0"10605
0"06962
0"06608
B. 2 A
0"08345
0-06885
0-06992
B. 3 A
0"06814
0 '06683
0"06889
B. 4 A
0"04918
0"06970
0"06987
Mean Area
0.53025
0.18688
0.17803
0.89516
0.41725
0.1863
0.1889
0.79225
0.3407
0.18033
0-18490
0.70593
0.2459
0.18210
0.1880
0.6160
M~an Width
5
2"7092
2.6992
5
2-6975
2.6792
5
2.6933
2.6917
5
2.7033
2.6733
Mean thickness
B. 1 B
0.10585
0.06941
0-06547
B; 2 B
0.08420
0.07013
0.07017
B. 3 B
0.06865
0 '06818
0.06220
B. 4 B
0-05001
0"06741
0.06848
Mean Area
0.52925
0"18997
0"17672
0.89594
0.4210
0.18918
0.18800
0"79818
0.34325
0-18363
0-16742
0.69430
0.25005
0.18233
0.18307
0.61545
24
T A B L E 10
Experimental value of K. Panels with Stringer Edge Supports
Panel
B. 1 A
B. 1 B
B. 2 A
B. 2 B
B. 3 A
B. 3 B
]3. 4 A
B. 4 B
4"82
4"78
4-76
4-68
4-38
4-56
4-42
4-42
b/t
45 "5
45" 1
57 "0
55 "7
64 "3
66"3
90"0
88"4
10aebl
2"49
2"43
1" 675
1"700
1 "33
1 • 375
1 • 030
1 • 050
10aeb2
2 " 5 2
2"52
1 "67
t" 730
1 "30
1 • 255
0" 845
0" 845
K1
5--15
4-95
5-45
5.28
5-53
6 .08
8 .30
8.21
Ks
5.22
5.11
5 -43
5-40
5-40
5-55
6 .82
6 .60
1 from load vs. strain curve.
2 from post-buckled amplitude.
T A B L E 11
Slope of (amplitude) ~ vs. strain curve. Panels with Stringer Edge Supports
Panel
B. 1 A
B. 1 B
B. 2 A
B. 2 B
B. 3 A
B. 3 B
B. 4 A
B. 4 B
a~la~
9"75
9-75
8"35
7-12
7.12
7"50
4 .50
5"50
25
TABLE 12
Summary of Control Tests
bO 05
. Specimen
E or E1 lb/in. 2
E2 lb/in. 2
L.P. or L.Pa lb/in. ~
L.P.~ lb/in. 2
0.01 P.S. tb/in."
0.1 P.S. lb/im~
0:2 P.S. lb/in. ~
V.P.H. No.
A.C.382
10.3 × 10 6
9.8 X 106
18,500
4 3 , 5 0 0
49,600
57,250
59,700
159
A.C.383
10.3 × 106
9.9 x 106
19,100
44,000
50,000
57,850
60,400
158
A.C.384
10.5 X 106
- 9.9,-_× lO s
18,250
41,500
48,800
56,750
59,400
159
A.C.394
10-8 × 106
47,600
55,500
62,700
64,600
157
A.C.395
10.9 × l0 G
48,500
56,200
63,400
65,600
155
A.C.396
10.8 X 10 e
49,000
55,750
63,000
65,000
154
A.C.422
11.0 × lO s
50,000
56,500
64,700
67,100
159
A.C.429
1 1 . 1 × 106
49,500
55,300
64,000
66,400
153
A.C.436
11.1 × 10 ~
47,000
56,100
65,000
67,250
159
," I ~ -rl I ac3ez
t
I ~ f n 9 Z--'P~
I to. t~ l a,o.
7;I ~.~, I r,,, "rs I ~-~'
t
I
t r-~, I,o , T 1 0 1 n c ~ e 7 , ~
I ,o. < I 7 , T iL l
I l Ia
I ~. T'~ I
ISPi 'i' '
f
I , T I l l
I * "ri~,l I ' "M
I r~. TITI ar.~J~o
I(,/~ ~',=..
ITR,
[ 19A
- , ' I f ' t ' e l ~cs~; !
o
¢
clo (aC.3")2)
1 ! ZIFI ¢
SHE~'r X D . T . D . 5 4 b
120
i.,s I ZB Is8
4 B
I EB I~B
h 7B
I I-rZ I
I IT3 (ac~l
I IT4" (~;a,a)l ]
l'rs" (AC ~"}l 'I I
IT/, I I
1, I T7 (Rc3w) I
ITs Cme,3]l
I T~ (A~e) l
IT iO(aC'SSs.}]
I - r . J
[ T 12 (a¢ 4oo X
ITJs I
13 B l-rl4(ae4o01
I 14B I T1b" I
I 1 0 B IT", I
i~B
SHEET Y D.T.D. &z~G
FIG. 1. L a y o u t of sheets for p la tes and tes t pieces.
27
J7 B
I "r;9 I
IOB " J
lIB I I TM I
L,, (nc.qo~) c:::~ 1~z J /
s H EET____..___ZZ /
Sheets were all 16 S.W.G.
I~:. ] ]1
VIEW
WI'tH I -~ lmL/~ l "E. LO~DING ~ Jl~ TOP E;Lmtwlm OMf'I~ED
I ~ E N E R A , L / ~ l ~ I ~ A N <3 F_I~ENT OF I ~ l G FOR TE-STING
I::'L/~T I:: S IN COIV~PR I: S~3i'ON
[ N I C S~ IOIN 'N bJ rTl..( R (::)LLI~IP. a i d I~ SUPPORT...% ]
• ~ E C T I O N ON ~1( - ";/~
• / / ~ , " ' / / . / /~ / / / .
i
pAI:;LIT- ,SECTI ON THROIJ~H E, P~LLS
FL .~ P A R T - ~ E C T I O N I " H ~ O U C N ROLLEI?....~
13EI'.~IL. O~ ~ ~UI::Hc~IL"T DETAIL O~ R O L L E R .SUPPORT
• * * J ; ~ I ~ , N G E H E N T OF ._~lJ~t:::~OR:q'3 & LOA£HN~; 6 A I ~
[Tom. C L , ~ " 4 . OMITTEE::, l
FIG. 2.
28
KH|FE ~J~ffgg.
FIG. 3.
SEcT~Orl ON X - X .
Sketch of contractometer Mk. I I I for measuring mean strain across a plate in compression.
29 (25590) C
0 ' 7
0 ,5
0 -4 Lq z O I,-
cJ 0.3
,-I
a UJ
Q
z_ o.t
O
/ d
O'1
/ /
/ /
0 .2 0 .3 ; 0 . 4 0.5 0 .6 0.7 MEAN PANEL LOAD. TONS
FIG. 4. Ball edge supports. Bolts loose.
o
/
o . o i CONTRACTION. !N .
Friction tests (panel 10A).
/ /
0 " 0 2
.0-
0"!
O'! .U}
O p.
,.¢
..3
ct 0"3
u
O"
O
/ f /
O'1
/ /
12
O-2 O.3 MEAN PANEL
FIG. 5.
/
/ f /
O-4 O.S 0 . 6 O .7 LOAD., TONS
Ball edge supports. Bolts tight.
0-7
0"6
0,! to Z O I -
,60 . ,
O .-I
0 0 . 3 uJ
u N 0.~ _z
O.
O
/ r -
/
O'O1 CONTRACTION. IN.
Friction test (panel 10A).
!
0 " 0 2
30
-- 0"07
--0.06
-- 0'05
- 0 '04
--O'O3
-=-o,o2
Z_-o .o t
~ o
-- o,ol
:~ 0 .02
0"03
0.04 U ,n C.05
-O"15
- 0 . I 0
z-O'OS
z o
uJ O.OS
n -I O ' IC
< 0.15
v o
i j ~
-0.06 "
.04
O
O,OI
0.02
0.03
0-04
O-OS
o-06
\ /
0 '07 N
/ o~ O.IG
t= "EPRESENTS %'I, 3.7~) LENGTH OF PiATE-.-35
-0 - I S
-O, iO
o:j V FIGURES ,AGAINST CURVES ARE TONS
FIG. 6. Plot o1 Skin Buckle Amplitude. Plat.e 19A. Mot / D.T.D. 546 .
L ~
bO
- '0 "07
- 0 " 0 6
-O'OS
- 0 0 4
- 0 - 0 3
-O.C~
;~ -O-OI _z
O
~ 0-01
0.02 ~
~ -03
0 O'O4 ,,n
0"05
O'O6
0'07
,0"9
- 0 - 0 ;
- 0 . 0 ~
- O . O S
-" O'O,~
- 0 " 0 3
- 0 -02
- O . O i
' 0 -
0.0,
LENGTH OF PLATE 35"
REPRESENTS 'b' (=,4,46'~
- 0 . 2 (
- 0 . 1 !
- O . I O
z - 0 . 0 5
o
0"05
0 ' 1 0
~O.IS 0.2(
3-2 - 0 - 2
- O - I I
- O ' I C
- 0 0 5
/ ' . 0 . 1 5
i
1.2
!.~7
,'IGURES AGAINST CURVES ARE TONS
F i9 ,7 . P lot of SKin Buckl~ Amplitude P|atQ. 3 0 A . Mat i . DT.D 546.
CLAD PANELS CDTD S4~
OFROM LOAD-STRAIN CURVES ElF ROM AMPLITUDE PLOTS
UNCLAD PANELS (DTD 646)
O O.I
T..~.~QHE O RET IC AL VALUES..._..
[] ,
Note:
C/b D.2
FIG. 8.
®
O O,I c / b
Ball edge supports.
All experimental points have been corrected tor variations in X/b.
[ ] THEOf:ETICAL VALUES
0"2
/,
'CURVES OF ASIN'~ '~ ' {~SIN'~ FOR BI~. = 0 ~ 0"05,0'lO~O'iS.
CROSS-SECTION OF SKIN BUCKLE~PANEL 8~ (STRAINS 0.0 003,0-0006,0'00m,O<XT"~O )
FIG. 9.
(25590)
33 D*
f
/ - - M E A N CURVE
SINE CURVE
'x \
FIG. 10. Buckle cross-section at buckling strain. D.T.D. 646 panels. Ball edge supports.
/
/
5N' 7
5 \ 6
o MEAN CURVE . . . . SINE CURVE
, - / B
B
\ \
FIG. 12. Bnckle cross-section at five times buckling strain. D.T.D. 646 panels. Ball edge supports.
FIG. 11. Buckle cross-section at twice buckle strain. D.T.D. 646 panels. Ball edge supports.
7 / • 6
~// 8
MEAN CURVE ~ /7/ SINE CURVE X~! \ '
/ / . \ \
FIG. 13; Buckle cross-section at ten times buckling strain. D.T.D. 646 panels. Ball edge supports.
0 " ~
7~O,4 o
< 0 . 3 o
£3 ~mO'2
• < (J r~ Z--O, I
/ { /
q
/
/ O.I 0.2 0.3
MEAN
/ . /
/ / /
/I / J
/ /
O '4 O "5 PANEL LOAD. TONS
o3r(
O O'OI 0"02 0 . 0 3 0 ' 0 4 O'O5 0 ' 0 6 O'O7 0 ' 0 8 CONTRACTION. IN.
FIG. 14. Roller edge supports. 13olts loose. Friction test (panel 10A).
0 , 7
O '~
Z o
4 0 . 4
8
u~ 0 " 3
o_ z o.2
O'1
/ / / / 1
/ /
/ / /
/
/ / / ~
O' l O . 2 O,3 0.4 O-5 0-6 MERN PANEL LOAD. TONS
FIG. 15.
/ J
/ / i
Roller edge supports.
O O431 O.O2 0.O3 0 ' 0 4 O -O5 CONT P, ACTIO N, IN.
Bolts tight. Friction test (panel 10A).
~a
0 '06
O.';
O'~
O 0"~
z
o O - 4 <
s ~O '3
No.2
O O'l O'2 MEAN
FIG. 16.
/Y
0"3 O '4 0"5 0"6 PANEL LOAD ~N TONS
Lubricated roller supports.
~7 I / 0 . 6
iy , ~ J
0.6
2 Z f /
/
/// O.I 0.2 0"3 Q'4 0"5 0.6 0'7 0.8 0"9 I.O 1.1 1'2 1-3 1'4
STRA1N x IO 3
Bolts tight. Friction test (plate 21A).
35
SO~OO0
40,DO0
Yz ¢0 ..I
30 ,000
20,000
IO, OOO
/ 0 ¸
0
/ / PLATE 9A: //++ CONTRACTION
I 0-00 .0-002 0"003
FIG. 17.
/ . / J/
E1.=10"2 x IO 6 LB tiN2
F.== 8 .45x iO + LB t i n 2
E,=IO-3 x I06 LB/IN 2 F~= 8.47x I06 LB/IN 2
I MEASURED WITH HEADPLATE DIALS
I I. 0.00.4 ' 0.005 0"006 0.007 . " O-008
S T R A I N
Stress v s . strain curve for plates 9A and 182%. Material D.T.D. 646.
60,000: / / / !
/ 50,00C /
"z_ PLATE 9 ,T
// 20,00C
t / / PLATE 98 El=lO'67xlO ~ LB/IN 2
PLATE t88 E I =lI.OOx IO* LB/IN 2
1 I I I CONTRACTION MEASURED WITH HEADPLATE" DIALS
O O'OOI O -OO2 O-OO3 O-QO4 0.005 O-OO6 0"007 STRAIN
FIG. 18. Strain curve for plates 9B and 18B. Material D.T.D. 646.
0 -008
- O ' O 7 -
- O - O 6 "
-O,O5 -
-0.04
-O.03
-0 '02
z -0.01 .0_.=
~ o ~
i • ~ .o.o~- ~,~. N
m O . C ~
0.05
0.06
0"07
-O '14
-O.i ;
-O- IC
- 0 - 0 8
- 0 . 0 6
-0.0~I
~2 - 0 ' 0 2 z
Lu 0
~ 0 .02 -
J 0 , 0 "~
0"06
u~ 0 .08 • u D 0 . 1 0 •
0 " 1 = •
O - I d •
- - 3 '3
- - 3~8
4 . 0
-- 4-SO I ' " /
-o.o7-
-O-O~
-O-C
O.C
_.6 REPRESENTS
LENGTH OtF PLATE = 35"
c~os6'9
-O-14-
- 0 . 1 2 -
-O . IO-
~ 0.0,
0"08
O ' lO
0 . 1 2
O ' l # FIGURES AGAINST CURVES ARE TONS,
1 FIG 19. Plot of Buckl~ Amplitude for Plate. 2'~A b / t
Mot I D.T.D. 546. ~lg~s Clamp~l
=45.
O0
EDGES CLAMPED (THEORETICAL)
@
FOt EDGES PINNED (THEORETICAL)
CLAD PANELS (DTD546)
OFROM LOAD-STRAIN CURVES O FROM AM ~LITUDE PLOTS
O
6
5 " '
K
3
3 •
EDGES CLAMPED (THEORETICAL)
'EDGES PINNED (THEORETICAL)
¢
FI 9. 20 . R,oli~r zd9 e supports. Not.~: E.~p~r.im~ntol points ore ~ correc~.¢d "for variott0ns in ~,/b,
v
"17
#11 lj~71 14 / , , ' / ;
/--,40 ." r3ls ,, fl6 11 /"
," II 7,/
t1"7~5 //" l/ "15 i
t:N L ~ t 3, "x M~
SINE CURVE ' ' \ o
12~bB~ THEORET ICAL CLAMPED-EDGE CURVE
FIG. 21. Buckle cross-section at buckling strain. D.T.D. 646. Roller edge supports.
~ f ,.27t~l,
¢i "1 i11 /
t ~ / 7 / t t /
@/ /"
",~, SINE C U R V E ~ •
I '~' \ " , - x i
THEORET IC A L - - " ~ ~,~l CLAMPED EDGE . ~ "~,?~
CURVE ~
FIG. 22. Buckle cross-section at twice buckling strain. D.T.D. 646. Roller edge supports.
c~ c.D
,',~,'" ~ ~,~ / \ 4.
•
/ ~ : / / \
14/.~/, , / SINE CURVE " - ~ l ~ / V P / / THEORETI(;AL ~ ~\
I J / " ~
FIG. 23. Buckle cross-section at five times buckling strain. D.T.D. 646. Roller edge supports.
I / / L7 /
FIG. 24.
• \ \ ~ \
.SINE CURVE " \ \>
\ \ " \
THEORETICAL ~ \ ¢ \ CLAMPED- EDGE CURVE , . , ~ \
t I I ' - ~
Buckle cross-section at ten times buckling strain. D.T.D. 646. Roller edge supports.
0
A
BALANCE tVEI6NT
iCTlOkl
'L&TTEI~
~IDE ~UPPORT5 FOR CARRYINEI UI~IVERSAL ~E~R
VIEW A 0F. PANEL ONLY
SH EWING CONTRACT0~'I ETE R$
C O~ T~ ~.C TOt,4 F~T~ R ,S
~ ~_ T E S T ~ G M / c
5ECTJ0N C ' C
FI~. 25.
51FI2$N~IE ~ S F02 ,~EYIN 6 P,~O D 5
Jv~£'r~,L TO "PAP,IELS
I ' 0JA . ('.SK+ 14o. RI91~'tS
2"Dba. Co,~.K+ 14o. ~J'/E"/~
~. ;G5/50~ FOR igA~L,S ~1.
r r C~K 120 ° ml ~+~-.IN
~PA;'- IEL ENDS C~,~'i' J N WOODS HET/,.t . ~ / 8 ~r~iCY~
i~"; "2"
71 4 +o.
oem'rl~+mc,~.'nom l oa f ~+¢xa~+5.s r~.cK~es¢ p4a+rm'Rr~,~t. ,,+,vn~l+~. B,L 2 12 'S W~. 16 S~.~ OTO- 6,¢6 DT~, 64~
~4. 2 18 S ~ t(~ SW~ 01" ~646 gt'O641
! . - - - - -
+' ! ~.5. + 6 5 / 4 0 4 H
CU T . " .SK | ~ 0 + 11,4 SK+N
i z p ~ I E L E~tO<~
~,~OOOS H E T A L /15 THICK. I ~" " " -
_ 8 s ~ s
_ ,401"
c K . . j ' ~
I " 4-~. ~AD
FzG. 26.
D ~ N ~ t ~ I O N OFF TH'CK~SS T~,~.K~S~ ~ ¢ , , n ~ l ~ )-,ArEIZfAC TI "~ 14.SwG, 16 5w~. 0TO 6 4 6 O'~D 6 4 6 "1"2 2 IG St~C], e6SL,,I~. I~'t'l~ 6 4 6 DrD 6ZL6 T3 ~ ~8 s ~ i . 1,6 $t4~. b~D 646 OTO~.4-& T+¢ 2 2 o g r e . ~osw¢4 OrO 646 ¢~'D6A6
41
o m
+ p~
+I ~ to "t < - - ,a
- - e .
;45w'C~. SKINS ~ CONTROL TEST
P I E C E S
I
,~, ~ ~ ~ 2
[ 1 - - o .
m ~ ~1
2OswE. SKINS & CONTROL T E S T
P IECES
I i J F
• < - - ~ ~ ~ - ~ m
[ + + + ~] + +, + iz ;z 2 Z
,I; I~ "++ i I • +m F :+-:l
16EWE. S K ~ E & CONTROL T E S T P I E C E S
!
r-
18 5W¢=. SKtNS Jk CONTROL T E S T 2 2 Sv,/C~ SK•INS ~ CONTR.OL T E S T 12 BW~,• SKINS R, CONTROL TEST
P I E C E S P I E C E S P I E C E S '
~ A C H PANEL SKIPJ 15 NARi<,ED W I T H THE P A N E L I D E N T I F I C A T I O N T O ~ E T H E R Y41TH THE ~ A T C H ~ ~;HEET N °6, FROM
W H I C H IT W A S H ~ D E . E A C H S T R I N G E R IE H A R K E D ' ~ / I T ~ T H E P A N E L I D E ~ I T I F I C A T I O N TO WHICH IT BELO~IGS TOGETHER. W i T H T H E I~ATC~ ~, S H E E T N O6* FROFI WPIICH IT W ~ S N A D E . STRIN~.ER.S Ok[ B p A N E L S S U F F I X E D J ~. ~ R . E S p E C T t ~ ' E L y ADDIT iONALLy ' . 6~S, 53E.~r, AC4$E,~tO3~S£ EL~.I,JKS ~OR. CONTg.OL. T E S T S P e C i M E N : 5 P- I o ~ ( '2 E FOR T E N S I L ~ T E S T S & 3 ~' ~ I ~ FOr?. cOr , lPR.ESSION T E S T S EACH T E S T P I E C E IS MA.R.KED WITH IT5 I D E N T I F I C A , T I O ~ ~AS SHEWt.I AEOVE~ TOGETHER. WITH T H E ~'~,TCH, ~ SHEET ~05. FROt"~ W H I C H IT t/~'~,E GU'T. FOR. SKINS. "~1.6, TIE.S1 FOR STRINGER T E S T PIECES A B L A N K 31/2 m L O ~ W~S CUT FROH " ~ S E~CESS LEIdG, TH OF EACH STRIklGER. AFTE.R FORMINg. TZ~.+ T?A-SI, .:
TEST P~ECEE H~,RK~O WITH THE BATCH J~ SHEET N o$, OF THE SHEET FR.Ot~I WHICH THEy WERE CUT TOGETHER ~V~THT~G 10~NTIFICATION T~'B T2SSI • T3+~. T3A, Sl
OF THEIR. ~EEPECTIVE STi~INEERS. TS.S, T36.SI.
STRIH6ER,~f.,OHPRES$fON TEST PIECE~ .
p~IJEL J 5TRI~JGGR IDENTiPtCATIOM+ ID2~nFIC~TJOH I ~NO TeST m~ce~.
El. ~ , ~IJLBI.A¢,448 t181A.St,~C +49 El, S ~1 B, ~1. AcJ.50,~. t,i m 52. AC 451 B2.A. 5~A~SI.AC4S2~B2A.S~,AC4S~ E?.E+ ~,'2 g,.S L AC,,CS 4- ~ J] 2 I~ S 2.AC4~ 5~'.A+ B 3 A,Sh A C,45& ~, b3A,S 2,A¢ 4gl
t OS~S2.~SS S4,A+ ~,A+SJ ACA60 I, E4A. 5~.AC 461 ~4. S BAB.SI ~ C ~ & B4B.S~,~C4~Z TL A. TIA.$1
T4. ~,, T4A.51. T4.E, T4.B, Sl TS. A, TEA* Sl. TS+E T58.SI.
FI~. 27.
4 2
0.15
0'10
0,05
-0.05
0.07
- 0 - I 0 ".
0"05
-0 .15
0,03
0"02
0 ,0 !
-0-0
-O -O
-O-O3
- 0 - 0 5
- 0 . 0 7
\ \--
F-' kW
CJ,
.35
4"
z O ~ UJU-Z
w _ J - -
Om> , . i-x< Om~ "0
-- 0 " 0 I
-- 0
- - o . o i . . . . .
-0 .02
--0"05
0,07 ~ 0
0 '05 - -
' ' ~ 0 ' 0 3
_lO.2S - - - - - - - - - " - I ~ 10'5
,,, I I 'O I I "25 I I "75
': "12"5 - '
/
V - -0'15. ~ / " ~ J~.25
]hO-
10.5 " ~ ~ , o . 2 5 - - - - - ~ 8 " 7 5 ~
o~,
~,,<,
JO
-0.05
- 0 -07
NUMBERS CURVES ARE TONS
- \ \
,,u~ , e~ 0
\
\ \
- \ - \
\
\
FIG. 2B. Panel 81A. Mot / DTD 646. Plot of Wove Ampl!4ude'on Centre Line of Panel.
-0.07
-005 -O,OS
-0-03 -O-O3
-0.15 z - 005
\ ~ . 12.75
0,10 ~ 11-75 / ~ ~ -O.O2 ~ OF MEAN FLEXURE \ ' |1"2S FROM WJ~VE LENGTHS / . o o ~ Io._...jlllgr~
Oil 5 ~ i / ~ " ~ '-- IO:5 ~ _ _ 4 N
O.OI $5" ~, FIGURES AGAINST C JRVES ARE TONS
HEADPLATE
25
~.%~ ',
1217S
- - I 1.7S
0
FIG. 20. Panel B,I.~. Mat / DTD 646. Plot of W~v~ Am,~litud~ on C~ntr¢ Line of Pdnel.
- 0 " 0 7 - 0 " 0 7
-0,05
LOAD
4=
-0,03
" 0 ' 0 2
- O O l
0
; 0 ' 0 1
z 0'02 z
~0'03
I - 0 . 0 4 - 0 . 1 5 g
~o.
w, O ' 0 6 - 0 ' 1 0
~ o .
- O ' O 5
0.05
O ' I 0
0 , I 5
- O ' O 1 - - ~ ~ ~ ~ ~
t~ ~ ~ ~ . " ~ 0 -15 35
O ' O 1
F I G U R E S A G A I N S T C U R V E S A R E T O N S
o
IO-B J --9"6
• .r~-~- 4 PITCH
,-- Z~ I , _ - - - - - - - _ _ 2 . + + ~ '< _, 7 .6 ' ~ "
: 0 0 1..1~
6 . 2
FIG, 30, Pon~l B2A: Plot of Buckle Amplizud~ down ~ of Panel .
u~ ,,i
_Z
Z
MJ
F-
U
-0-07
-O .OS
- 0 ' 0 3
- 0 " 0 2
- O ' O I
O
0 " 0 I
0 ' 0 2
0 " 0 3
-O' IS
0 " 0 5
-0 -10 - -
0 " 0 7
-O'OS
0 . 0 5
0 . 1 0
0-1 5 "
\ \ \
"F- uJ
°0.07~
- O . O 5 L
0 ' 0
\
\
~ 7'4
7-8 9.2
0'0~
0"07
- - 1 - 0 ' 1 0
: , , j
\ ,
O
0-010 ~ " " - ' - " ~ - -
FIGURES AGAINST CURVES ARE TONS
I
4 "
7-0
FIG.3|. Panel B2 m. Mot [ 'DTD 646, Plot of Wove Amplitude on Cencre Line of Pon¢ l .
LL ~ o ~1
z \1 LU = - \1 0 -< ,j "~,~ ')-- i .al- w l <<, _ , ~ I
w , ' , ~ 4
j - r
} \ l '\1
- ' \1 - \ 1
- \1 \ 1
\ 1
~ l o . e \ I
- \ I
- " q
\ I \ I
/ I-- I
N u~ - - 0
\ 1
O0
~. u. \ I
- 0 " 0 7
-O'O5
- 0 ' 0 7
LOAD
'=--,-I
-O'O3
- 0"02
- 0 , 0 1
0
Z 0'01
_..z. 0 . 0 2
w o 0.03 p-
• "i 0 '04-O.~
,¢ 0-05
w J 0 .06 u
~o 0 .07
O -
0"0;
0'01
-0 '03
~ - - : Z w -FIGURES AGAINST CURVES - _ ~ ~ - ~ . . . ,< J
ARE TONS . . ~ ' ~ 0 .02 7-2 ~ - - - ~ ~>u
. . . . . . _ - - - - - - - - - ~,~ - - - - - - . ~ - - . . . . . _ . .
L~ z
FIG 32 Ponel B3A : P lo t of ~,u¢~l~ Arnplltude down ~ of P~n~l
4x CO
--0.07
-- 0'05
- - 0 "03
-- 0"02
- -0 "01
0
~ 0 . 0 1 2:
O-02
w 0 .03 -r~
,J CL
0.05
0 .07
--0.15
--0.I0
--0'05
- -O 'O7
- - 0 ' 0 5
- - 0 . 0 3
- - O.O2
0 -05
0- I0
LOAD 5 ' 0
4"5 4 ' 0
3 . 5 \
2 . 7 \
8 -6 - - - ~
0"05
O'iO
- - 0 ' 0 1 O-IS
0
0"01
FIGURES AGAINST CURVES ARE TONS
0"15
4 t/ PITCH 8"6
/ 7.4
) 5 ' 8
~o
z
FIG. 33. Panel B3B: Plot of Buckle Amplitude down ~ of Panel.
" O ' 0 5 L ~
- 0 - 04~.'~-.-
- 0"03 ~ "1'--
- 0 '02 I,~ ~"-
- 0-001 k~ ,,~_..-
0.01 \
- 0 " 4 0"02 \ ! \ 0.03 \
- 0 . 3 0 ' 0 4 \ - -
0.05\
~-o-2 i - \
o-0"I J
< .0
..J " i u m 0"1
0 .2
. 0.3 ~
0"4 ~
0 '5 " ~ - -
FIG. 34. Panel B4A
- O'O5 • 2' 7-O.O4
-O.O3
. - - - - ~ 2 "3_O.O 3
o o,
0-03 --
- 0 . 3 o . o 4 i - -
0"05 --
-0"2
-7-6 I~ ~'--.
2"7
2"3 2"0 1"7
- - - - 7 " 6
7-6
S'6
UJ
<< rcuJ LdI
JO
uj-r _jI--
;~LU
-o.o, I----~ ~
35" J
Mot / DTD 646. Plot of Wove Amplitude on Centre Line of Ponel.
\ \ \ \ \ \ \ \ \
Y\ ,..J
,Lu
"O -- O.
\ - \
\ _ \
\
0
0"2
0.15
0"I
0 ,05
0
U _z - o . o s
Z -- 0 ' 0 9
-O 't
-0'15
U 0 '03 m
-O'2 0.02
0"01
-O-OI
-0 "02
-0 "03
- 0 ' (
z ~,
o
ii 35
4" O 2.6 " - ~ , ~ - - ~ ~ \
~ ~ ~ ~ 3-8 - - - - ~ . / ~ ~ / / - -
7'4 0 . 0 4
6 .0 _~ - 0 4"7-- ~ .
3"8--
, _ / \
-o.,s 004 ~ . . j _ 003 ~ \
-o2
05 FIGURES AGAINST CURVES ARE TONS j
FIG. 35 Panel B4 B. Mat L DTD 646. Plot of WaVe AmplltudQ. on Centre Line of Panel.
CREST
MEAN FLEXURE . CORRECTIONS_ ] " - ~ - I__ ;==r 3 ,~ s T ~
FOR PLOTS OF BUCKLE SHAPE, PLOT x x MAX
AS ORDINATE
'b'
- o . o l ? ~ASE UNE FOR TR_R_ouGH
-oo,_.1 / /
SKIN SIDE
Z
ZERO l INE OF O:)NTOUR MEASURING DEVICE
- 0 0 4 ~ , N ~ . S,OE
.O.O~'CORR~CTED . ~ o ~ .
-z ~ . " ~ ' ~ U NCO R RECTE D TROUGH
FIG. 36. Method used to find b, the distance between longitudinal skin nodal lines, and to obtain co-ordinates for the cross-sectional buckle shape. (As drawn for panel B.3B at five tons load.)
0 " 0 5
7- 0
n~ -0"05
-010
.) ,.
CREgT
I CORRECTED
I I I
"\\
\
PANEL B I A
2 oS °
'I ......-- -.....
J J
f
%.
TROUG H I I
2:S"
SKIN ~;IDE
ST RINGEP~ SIDE i i i i
FIG. 37.
? ? 4 ,s .~ 7 _ _ B9 . . . . . . . . lo l l t2 i s l4 t s l s t7 ,o.2s T o N s - o~,
0 -O,O!
IO-5 TONS - O-O1 .,~ ~ O
-O.01
I I TONS ~ 0"01
" - - - ~ -8'01
I 1"25 TONg 0.01 /
I 1"7S TONS 0"01 0
t-o o, ToNg . 4 g.o,
, , , t i i , , I , i i i , ~
Cross -sec t i ona l mean mode
Readings obtained on test of cross-sectional buckle shape.
E "0 t -
O m
i
2
5 1 (25520) F
17
CIAESi I . SKIN SlOE
~- -o.o. ~ , , ,
~ _ _ _ _ _ . . . . . / - \ \ i \ .
CORRECTED TP, OUGN "-"-- """ STAINGER ,SIDE
- o . I I I t ' / ross ' -~e~ i 'oZo l ' 'me'o~ 'm'od;
PANEL BIB I 2 3 4 S 6 7 8 9 I0 II 12 13 14 15 16 2 3 4 S 6 7 8910111213141SI617
i , id .2s TONS ' ' ' O.OI
O O'OI
O.OI
• O.OI ~. "O
O.OI __ -- I C
"O.OI o im
O'OI _ z
-0.01
OOI z
-O.OI
.OI
;"00I
FIG. 38. Readings obtained on test of cross-sectional buckle shape.
;£
uJ (3 I - . J n :E <
----. - - ~ SKIN S IDE .
,...~ ~
• ~ ~ . - - - - . .~ ~ ~ ~//
/ _O. I C - - - C O N N E C T E D TROUGH ~ STRINGER SID
I I I ,
-O'IO
PANEL B2A II 12 13 14 15 16 17 2 3 4 5 6 7 8 9 I011 121314151617
' ' 6.2TO~S' ' ' ~ O'OI O
.O.OI
6.6TONS ~ O.O| O -O.OI
--...._ 7 0 TONS ~ O.OI 0 "~
i ' -
-...._.._.._7~7 - 6 TON S 0'01 ¢) 0 m
-o.ot
0.01_ B'6 TONS 0 Z
-O'OI "
9- 6 TONS / O.O10 -(3.O1
O.O1 O
"~,~.~BTON S J "0.01
i i i I l i I i i i , , i , t
Cross-sect ionol meon mode
FIG. 39. Readings obtained on test of cross-sectional buckle shape.
52
0 ' I 0
• 0 . 0 5
Q
- O ' O 5
'-0.I 0
-0 " I 5
PANEL 8 2 B I 2 3 4 5 6 7 8 9 IO ,, 12 13 ,4 ,5 ,6 ,7 2 3 4 5 6 7 8 9 lOll 12131415,617
i d i 1 2 . 5 . 1 I I I I , I I I I I I 1 1 , I 2.5 . . . .
I > '< I - 7 ' 0 TONS
~ . ~ SKiN SI iE.
/ ~ / / / - - ~ " - 7-4 T O N S / . . . . ' ~
- T O N S ,
4 -
~ - - ~ ~ 9-2 TONS /
\ ~._ ///
• C O R R E C T E D T R O U G H S T R I N G E R S I D E
1 I I I I I 1 I I i ~ ' ~ ' ' ' ' ' ' ' ' ' , l ~ I Cross-Sect iona l Mean Mod¢
FIG. 40. Ri~ac~ngs obtained on test of cross-secdonal buckle shape.
0'01 O,
- 0 . 0 1
0"01 0
-0.01
0.01 ~, 0
-O'OI "~ i -
O.OI c ~ O O
- 0 - 0 1 m
o Z, - O ' O I "
O'OI
-O'OI
ua
i-
Q'IO
0"05
O
-O.10
I 2 . 3 • PANEL B 3 A
4 5 "6 7 O 9 I0 II 12 "-13 14 15 [6 17 2 3 4 S 6 7 8 9 [OIII21314151617
J l ' l::l 2 . 5 " ~
f ......_ ~ ..... ~ SI
f
I I T R O U G H S T R I N G E R SiDE
I I I I I I
FIG. 41.
I I I I I I I I I I I I I I I i
O'Ol 4 ' 3 T O ~ . . - ~ 0
- -0 '0~
4-.6 T O ~ 0"01 0
- - O . O i
s.o TONS .......- - - ~ O.b, O
°0-01
~ 0'01 0
~ - 0"01
0.01
8.2. T O N S / -O'O1
I I I I I I I i i t i i i i I I
Cross -S¢c t t ona l Mean Mode
C O R R E C T E D
- o - i s . I I I
Readings obtained on test of cross-sectional buckle shape.
?
Z I Z
5 3 (25590) F*
=_ UJ
-0.0.=
"O'10
"O' 15
I 2 3 4 s e ? e 9 Io II I~ I3 14 as I6 I7
I I 2"s: 2 . s " I I I C R E S T S K I N SIDE
RECTED TROUGH I I t I
J f
/
/ , /
/ / t / STRINGER SIDE
I I i
PANEL 8=3 B 2 3 4 5 6 7 8 9 IOIII21314151617
3- s i'oN.~ ~ O-OI O
"O'Ot
...... - 4.OTONS ~ 0 "0 l
O - - " O ' O I
, ~ 4 ' 5 T O N S ~ 0"01 0
- - " O ' O I E
"--....._~.OTONS ~ 0'01 r- o ~ - - - O . O I o
m
To. - - - - 0 , 0 1 z
- - 0 . 0 1 7'4 TONS I ~ O
- - - - " O O I
~ O w O J 8.6 TONS ~ _./ 0
- - " O ' O I l I f I l I I I l I I I I I l
C r o s s - - Sectional Mean Mode
FIG. 42. Readings obtained on test of cross-sectional buckle shape.
O'10
CREST 0 ,05
I 2 PANEL B 4 B
3 4 5 6 7 8 9 IO 1t 12 13 16 17 2 34 5 6 7 8 9 IO I1121314 (516 I7
O,O2 2"5" ~ .- 2.5" 3'2 TONS
. , . , ~ = " ' ' ' ~ , ~ . . . SKIN SIDE " - - " ' ~ ' ~
- 0 , 0 2
3,8 TONS - - O
' - O - O 2
O-O2
~O
-O.O2
• O, O4
I I I I I I I I I I I I I I t
Crc~s-S~ctional Mean Mode
FIG. 43. Readings obtained on test of cross-sectional buckle shape.
/ / I
o ,--,,
- ~ ~ ' ~ j t
- J / I / / -O, IO
STRINGER SIDE
\-,.. \
-O.15 CORRECTED TROUGH--
-0"02 E
O "O i'- m -4
-O'O2 C m
Z
Z
5 4
. S a
Y "z1" u
J /
,g t
J ~ J Q /
-;I0 O- I0 20 30
\
KEY ' pOINT-- PANEL,
o B I A • B I B x B 2 A u B 2 B m B 3 A A B 3 B
FIG. 44.
40 50 60 70 °/o of 'b"
-SINE CURVE
Buckle shape at buckl ing strain.
%
BO 90 IOO
t t
ItO
,F //
#
7
/ f = ",
-% ° \
KEY POINT PANE~
o B I A o B I B x B 2 A o B 2 B e B 3 A A B 3 B
~x
~ -SINE CURVE
\,,
- IO O IO
FIG. 45.
20 30 4o so 6o 70 so 9o too % of "b'
Buckle shape at one-and-a-quar ter t imes buckl ing strain.
IIO
55
- I 0
j
/m
:.4
O
\
X N X¥
KEy POINT PANEL
x B 2 A ,', B 2 B m B 3 A a B 3 B v B4B
\ I0 20 3 0 4 0 50 6 0 7 0 80 9 0 I 0 0
% o, I ;
Buckle shape at one-and-a-half times buckling strain. FIG. 46.
IIO
- I O O
/ / /
/ t / " ~Z
//
IO 2O
FIG. 47.
/
POINT PANEL
= B 3 A
a B 3 B
\ ~x x\x
B 4 B
30 40 50 60 70 80
°/o o! 'b'
Buckle shape at twice buckling strain.
_ _ . S I N E CURVE
\
90 , IOO IIO
56
O1
I0
9
8 K
7
6
S
4
3
2
I
0
b 2 K DEFINED AS • b ( -~ '~ , THE VALUE OF b BEING T H E M E A N DURING THE T E S T
/ f
@ ®
0 @
J f
POST- BUCKLED AMPLITUDE LOAD- STRAIN CURVE THEORETICAL, BASED ON 02.01. 18
I O.S ts / t I'0
INS 2 ~ 3 f 4-6
2 4
4-2 | VARIATION OF b WITH | NUMBERS ON PLOTTED POINTS TO PANEL NUMBER)
4"°.o 2!o e/oh 3!0 FIG. 48. Variation of K.
D.T.D. 646 panels with stringer edge supports.
e /¢ b REFER
t
ts -i-- =0,8
t---~- s = I '00
]
I ' 0 I'S . 2 0 2.5 eleb ~-
t MAX ! M U M STRESS
L~ DI FFERENEE AT HEELOFtlSOOOO STRINGER,BY METHOD OFIIooooo
' - ~ / / / / / / " TECH.OFF.REPORT Feb/4S150000 CPLASTIC REGION SHADED)Io LB/IN2
I-0 1.5 2<) ~5 ¢/¢b -~" J
f
f sooQo 00000 500OO
o L~/tN 2 1.0 I.S 2.0 2-S ~/e b - -~
L ~ ~ R 15OOOO OR SKIN(STRESSES EQUAL3hooooO
. . . . . . . . . ~ " I5oooo
t-O I-S 2.O 2.5 */¢b
t s = 1.36
FIG. 49. Location of skin nodal line on stringer flange.
I ' O '- '
0.5
0 0 0 0
_.%o
o ~ - ~ o " ~ o~o
t";,a ._ K REDUCED 20 ~o /
N.A.C.A~ T.N. 75,~
. ~ O
o o 0 0
NAC.A. TN. 75~
o K FOUND FROM LOAD-STRAIN CURVES o K FOUND FROM AMPLITUDE PLOTS
I I I I
I 2 3 4 K 5 6 7 O I 2 3 4 K S CLAD PANELS ('DTDS4d.) UNCLAD PANELS (DTD 646)
FIG. 50. Comparison of K and ~lb with results of N.A.C.A.T.N. 752.
6QO00
so, ooo f edge LB/IN"
40~000
3qooo
2opoc
IC~O00
DTD 564 PANELS.
3/~ 0.4/
/2 / / I/ 9Q 4
DTD 646 PANELS. 6qo00 I
0.I
, / I 0 . 2 . ~ ~ . 5ODOO . 2 ~ - ' - I
.,ooo/// 2Qobo ' o.s
O
overolae ~qooo a ~
IOpOO 2CXOC)O 3C~OOO 40,0OO 5OPO0 60~O0 O I q o o o 20,000 3Qooo 40,000 sQO00 60,000 fb LB/IN ~
FIG. 51. Panels with ball edge supports. D.T.D. 546 panels.
Note: Numbers on plotted points give ten times the value of df.wr.ge/Efedge.
58
0.6
0.5 at average
8t edge
0"4
0 .3
0-2
O-I
0
Fzc. 52.
I 2 f edge 3 4 fb
D.T.D. 546 panels with ball edge supports, Curves of Ofaverage/~.fedge.
5;
0.6
0,5
~ overage ~fedg¢
0"4
0-3
O-~
O.I
O
FZG. 53.
I 2 3 4 eddie f b
D.T.D. 646 panels with ball edge supports. Curves of Of a . . . . ge/0fedge-
Note: Up to 52,000 lb/in. ~, e = 0.935 × 10-~feag~.
59
eo, o o o DTD 546 PANELS
5o, ooo
t ~dg<~ ~ .~4 O~2 LS/IN" /~[ ...2----~ 4~o6o - ~ / % / ~o.~-~
f f 2 J / , , o.4
30000 - ~ l F
5 5
.
~ ~ , ~
0
m . , ~
, 5 / o / | / ~ o / NOTE. /do NUMBERS ON -
/ PLOTTED POINTS io GIVE IOx VALUE ~,.... OF ~ fo~/~ f¢
.~faveraq~ Bfedge
~),ooo 2o~oo 3o, o o o 4qooo sqooo eopoo fb LB/m. ~
FIG. 54,
60 ,000
sqooo fed9¢ LB/IN. 2 40,000
30,000
2 O,(300
! O, OO O
O
Panels with roller edge supports.
• DTD 646 PANELS
,/
5/
I t ~ O . I - "
-----'- j = v ' j / .4 0 ~ ' ~ / , ~
, / 1 / ' ° / 5 to ' overQqe I ( ~'fedge
Jqooo 2qooo aQpoo 4oooo fb LB/I N?
D.T.D. 546 panels.
5 0 ~ 0 0 6qO00
0.6
0.5 Bf average
8t edge 0.4
O.
0-;
O.
0 0
FIG, 55.
fb, LB/IN. a
0
I 2 " f cdCe i r fb
3 4 5
D.T.D. 546 Panels with roller edge supports. Curves of ~faverage/~fedge.
60
0"6
0 . 5 at ov~r.og¢
a f eage 0.4
0-3
0 '~
o:1
0 0
fb LB / IN. 2
l \
FIG. 56.
I 2 • f edge 3 4 fb
D.T.D. 646 panels with roller edge supports. Curves of Ofaver.g~/ofeage. Note: Up to 52,000 lb/in.L e = 0.935 × 10-Tfedge.
0
0 . 6
0 . 5 ~f clver'oge
. I
2 1 ~ 2 . o__L/.-~"3~ 23~~
-o2_~/~ """
.0. L -~-,~--~-,~4" • /..-...~,So~C
o s L 5,o/ I / I0
_ _ ,,e-.-----'-- 8f edge
to, o o o 2o, ooo 3o, o o o fb LB/IN. ~
FIG. 57.
af edge
0 . 4
0 . 3
0 - 2
0 - 1
0 0
% \
fb L B / I N )
5 . 0 0 0
\
I f edge 2 3 fb
D.T.D. 646 panels with stringer edge supports. Apparent skin af.~o~.g~/~f~dg~ curves. Note: Up to 52,000 lb/in. 2, e = 0.935 × 10-Tfed~e.
4
61
0-5
0 . 5 Bf av(rage
Be Itdg¢ XlO'70. 4
0 -3
0-2
0-1
0 0
FIG. 58.
2 ~ 3 cb
~ O ALL VALUEs ot fb
A"LE VA'[UE'S'-oT Fb"
CURVES FROM 02. 01. 02.
Curves of ~faver.ge/~eedge from Data Sheet 02.01.i (draft). 35-65 material. Practical edge conditions.
(25590) Wt. 16-680 K9 8/53 F. M. & S.
62 PRINTED IN GREAT BP~TAIN
IL & M. No. 2652 (11,036, 11,037, 11,038)
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