An experimental investigation into some of the problems associated with stress diffusion in the vicinity of chord-wise cut-outs in the wing, and a comparison with existing theories

THE COLLEGE OF A E R O N A U T I C S

CRANFIELD

AN EXPERIMENTAL INVESTIGATION INTO

SOME OF THE PROBLEMS ASSOCIATED WITH

STRESS DIFFUSION IN THE VICINITY OF

CHORDWISE CUT-OUTS IN THE WING, AND

A COMPARISON WITH EXISTING THEORIES

by

TECHNISCHE HOGESCHOOL VLIEGTUIGBOUWKUNDE EEFOE*F"1^."^83'° - DELFT SEFTEI.IBBR.1954 1 't FEB. 1955 T H E C O L L E G E O F A E R O N A U T I C S C R > : N F I E L D An E x p e r i m e n t a l I n v e s t i g a t i o n i n t o some of t h e Problems A s s o c i a t e d w i t h S t r e s s D i f f u s i o n i n t h e V i c i n i t y of Chord-Yd.se C u t - o u t s i n t h e liïing, and a Cctnparison w i t h E x i s t i n g T h e o r i e s , b y -La Verne ¥ , Brown, J ro L i e u t e n a n t , U, S, Navy S U H li A R Y

Chord-vid.se openings in the skin between the spars of the wing are designed in some aircraft for undercarriage doors, bomb bay doors, and the vdjig fold joints of naval aircraft,

Stress concentrations exist in the region of these cut-outs where the load is transferred from the stringers and skin into the

concentrated load carrying members. Two theories have evolved

to predict the resulting behavioior of the structure. The 'stringer sheet' theory predicts an infinite shear stress in the comers of the sheet} the 'finite stringer' theory predicts a high, finite shear stress in the comers, the magnitude of which increases with the number of stringers,

Tests Yirere made on a large stringer-skin panel bounded by constant area edge members and subjected to concentrated, equal

end loads. The dimensions of the panel were typical of modem practice J thick skin, multiple stringers, spar cross sectional

area equal to panel area. In these tests variations were made in the lateral stiffness of the spar booms, the method of attach-ment of the end rib to the spar, and the loading between spar and

sheet. The tests showed conclusively that the shear stresses are not only finite in the vicinity of the comer and considerably less than those predicted by either theory but in most cases the shear stress fell off toward zero,

The tests also bixiught out certain other aspects of tliis stress diffusion problem of which little has previously been knovm,

(1) Changing the method of attachment of the end rib to the spar had little effect upon the shear stresses in the comer,

-2-(2) In the tests in which the edge stiffener was attached to the spars, the transverse "^oad applied to the spar by this member was considerable, and it may not safely be ignored

in the design of the spar-to-rib attachment,

(3) Diffusion of the load into the sheet v/as consid-erably slower than predicted by either theory,

(4) At the initia"!. joint betvi/een the spars and the sheet (termed in this report the 'comer') and under certain

conditions of joining the spars and end rib, the sheet is actually putting additional end load into the spars instead of uixLoading

them,

(5) Variation of the lateral stiffness of the spar booms appears in most cases to have little effect upon the

stresses in the sheet. The bendency of the slieet to increase the boom load at the comer is more marked in the design vd.th stiffer booms. The diffusion of load tekies place slightly less rapidly from the stiffer booms»

(,6) Yfhen the slieet was attached to the booms with two symmetrical rows of bolts, the loading by these rows was eccentric, tending to relieve the bending moment due to the lateral shears applied by the rib and sheet. Removal of the outboard row of bolts caused virtually no difference in the resulting behaviour of the panel,

(7) Large bending moments occiu? in the spar booms above the cut-out. The maxinium stresses in the booms due to these moments are of the order of twenty to twenty-five per cent of the boom direct stress,

It is concluded that there are no infinite shear stresses in the comers of a cut-outo The shape of the spor boom cross-section and tlie geometrical relationships among the corner elements have important effects upon the behavio\xr of the structure. The choice of design is extremely complex, and there is at present insufficient knowledge about the problem to enable designers to choose an optimum design for any arbitrary set of conditions,

-5-TABL5 OF COMEIOTS

Item Page

Simmary

Table of Contents 3

Symbols

'+

Introduction 5

Reviev^ of Past Work 5

Practical Consideration of the Problem 9

Experimental Equipment 11

Test Techniciue 12

Presentation of Test Results 14

Discussion of Test Results 15

Conclusions 16

References 21

Appendix

Table I 22

Table II 23

Graphical Illustration of Results

-V-STivIBOLS 2 a panel vddth b stringer spacing

e

XX

e direct strain in the lateral direction

yy

e shear strain in longitudinal or lateral direction

xy

f stress

f^ average tensile stress in boom

f tensile stress in boom belo^v the cut-out

o

f stress measured in (end) rib

f _. direct stress in the longitudinal direction

f direct stress in the lateral di.rection

k non-dimensional coefficient \/Et /Gt

I

length of p;mel

a shear stress in longitudinal direction

txy

t thiclcness of sheet

t thickness of stringer sheet -(t + A /b)

X distance in longitudinal direction, meastired from the

lower right c o m e r upward

y distance in lateral direction, measured from the lower

right c o m e r inward

A cross sectional area of (end) rib

A„ cross sectional ai^ea of one stringer

3 °

E Yoxing's liodulus

F boon cross sectional area

G shear modulus s E / ( 2 + 2cr)

M bending moment in boom

P end load in boora (^^f-o)

R bolt or rivet reaction

S shear" per inch (t,q^)

Tp loading per inch in lateral direction (t.f )

V shear

a

non-dimensional coefficient (a,t /p)

TECHNISCHE HOGESCHOOL

VLilGTülGBOüWKUNDE Kanaalstraat 10 - DELFT

Introduction

Whenever openings are cut in stress carrying materials of an aircraft structure, the load normally cai'ried by these materials must be transmitted around the opening by some system of concentrated load carrying members. The transfer of load into and out of these concentra.ted mer.Tibers is called stress diff-usion, The subject of stress diffdiff-usion, particularly the build-up of stress in the comers of a panel adjacent to an opening, has been comprehensively treated by several authors,

Several aspects of this problem are of interest to the aircraft designer, Pii^st is the problem of producing a struc-turally efficient design, i,e,, a combination of panel and boaas w M c h «Till diffuse th.e load from booms into the panel as quickly as possible, thereby making maxiiiumi practicable use of stringers and skin to carry the load and permitting the boom cross section to be decreased rapidly as the distance from the cut-out grows, The second problem is to design the corners of the cut-out in such a Tv~ay that dangerously high shear stresses in the skin near the rivet line may be avoided. Third, the designer must ascertain that the connections between elements in the comer are safely able to transmit the loads requii^ed \dthout shearing rivets, tearing skins, stretching rivet holes, or other%-n.se exceeding allowable stresses,

The major objective of t M s investigation v/as the

determination of just what does occur in the corner, vd.th a search for effects which may heretofore have been ignored or unknown, A large diffusion panel was constiTicted \ri.th constant area edge members and dimensions similsj? to those of modern design practice, Electrical resistance strain gauges were located on the skin, end rib, and spar boon around one of the comers, Tests were made

to determine in detail the beho.viour of the panel and the results of varying the boom lateral stiffness, the conditions of end rib support, and eccentricity of loading. One additional test was made on the panel \ri.th the end rib removed,

It was found that most of the present theories concerning stress diffusion are incorrect in the vicinity of the comers. The problem is an extremely complex one| there are many variables that have not been treated mathema,tically. Further investigation is required to determine more precisely the effect of these

variables,

Review of Past Work on the Problem

Tvro general theo; etical me-f- ds of solution of the problem of stress diffusion have been devcloperlj the 'Finite Stringer' method in wliich the shear stress in the sheet chanoCs in finite steps at the stringers5 and the 'Stringer Sheet' method in v/hich the stresses very differentially across the

é

-plate, A variation of the second method, in which the panel is solved by a stress-function solution, has been used by a few recent authors,

'Finite Stringer' Theoryj

The first vrork on the finite stringer theory vra-s begun in 1537 "i^ith R, and M. I78O by H,L. Cox, C,G, ComTay, and

H.E, Smith, (Reference I ) , In this report three types of diff-using structures placed betvTeen a concentrated load and a diffused

load, vfere considered, (ycie of these types made use of the sheet

to transfer the load by shear from one stringer to another. The basic assumptions made were that the sheet transmitted shear only (no direct loads), that the stringers carried ell the end loads, and that at any transverse section the shear stress betv/eon adjacent stringers was constant,

In January 1938 V/,J. Duncan published R, and i.i, 1825 (Reference 2) in which he e:'tended somewhat the ^7ork of R, and M, 1780. It is noteworthy that the author foresav/ the need for a different theoretical basis v;hen, in paragraph 1, he v/rotej

'But at any considerable di^'/.-ance f ran the end the sheet must evidently partalce of the longitudinal strain of the stringers, and if the material is isotropic, the sheet must be in direct load. Hence, it a.ppeers that the equations can not be exactly applicable to structures having vrebs of isotropic material,'

Later in I938 H,L, Cox presented R, and li, i860

(Ref-erence 3) in TiYhich the two previous reports xrere am-pl±f±ed. and

generalised to consider a complete monocoque shell ^dth ejny

ni-imber of stringers. He shows that the presence of a constcmt stress stringer divides the structure mathematically and reduces the complexity of the solution. In regard to the effectiveness of the sheet in carridng direct loads, Cox annunciated the fourth basic assumption of the finite stringer theoryi

'In this case, by assuming a small width of sheet on either side of each stringer to act with, and in fact to form part of the stringer itself, the resistance of the remainder of the sheet webs to direct stresses may probably safely be neglected',

He goes on to limit the applicability of tliis theory:

'On the other hand, if the sheet webs are unbuckled, their contribution to the direct load may be consid-erable, and the present method of analysis is prob-ably not adequate to such cases'„

-7-heavy loading, -7-heavy stringers, buckled sheet - and, one might add, probably a very thin sheet,

In R, and LI. 2098, D, miliams, R.D, Starkey, emd R,H, Taylor (Reference 4) reviewed the work of past contributors and enlarged upon the •.rork of Cox and Duncan to obtain solutions for a box beam, using the theorem of minimum potential energy, These solutions include variations in such conditions as stringer area and spacing, sheet thickness, and spar flange area. The work done in tlu.s report is actually applied to the problem of

shear lag, but the method could be applied as v/ell to the problem of stress dd.ffusion. The first mathematical treatment now known as the 'Stringer Sheet' theory v/as devised in this report. It will be discussed farther on,

H,L, Cox and J, Hadji-Argyris in R, and I.i, 15^9 (Ref-erence 5) ga-ve a general method for the ana.lysis of diffusion in a stiffened panel which varies in edge stress and dimensions along its length, 'The authors considered the problem of a flat

plate between irifo corjcentrated edge members under various types

of loading. They obtained expressions for the average stringer stress and the panel edge shear stress, valid for any number of stringers.

In R, and H, 2038 (Reference 6) Kadji-ivrgyris considers using the stringer sheet method but concludes that it is too in-accurate because of the infinite shear stress in the comer. He derives expressions for the edge shear stresses and the average stringer stress for a uniform parallel panel vinder concentrated syTometrical end loads,

In A,R,C, Report No, 9662 (Reference 7) Hadji-J\rgyris e::tends the work of R, and M, 2038 to solve the problem of anti-synmetrical concentrated end loads,

'Stringer Sheet' Theoryi

As previously stated, V'illiams, Starkey, and Taylor in R, and M, 2098 developed a method of mathematical treatment of the diffi:"ion problem laio\.-i as the 'Stringer Sheet' theory. In

this metliod the follovdng assumptions \rerc madej

(1) The stringers and effective sheet are split up into an infinite number of small stringers of uniform thickness capable of carrying end load only. This is knovm as the stringer sheet,

(2) The ribs and effective sheet are split up into a uniform sheet capable of carrying only transverse loads,

(3) The actual sheet is fully effective in resisting shear» (4) Lateral stresses and strains can be ignored,

-8-The stringer sheet theory yields a Laplacian equation for the longitudinal displacem.ent 'u' which can be solved in the usual manner. The stringer sheet solution of R, and i.i, 2058 v/as for

the problem of shear lag only, although the Laplacian equation for the longitudinal displacement is applicable to the problem of any such flat plate,

In R, and K, 2618 (Reference 8) Pine and Hoskins

solved the problem of chord~vd.se cut-outs in a flat sheet between two parallel spar booms, considering a finite length of sheet, cut laterally at each end. The solution for the edge stress gave infinite stress p.t the corners. The authors qualified this solution by assuming that rivet slip, local skin buckling, or plastic elongation would relieve the stresses to a finite

quantity,

Stress Function Solutions

Much recent xrovk has been done by E,H, I/lansfield using

a stress fi..inction solution. His first approach (,Reference 9) v/as to find the stress fiuiction solution for a semi-infinite

sheet subjected to a concentrated load at a distance from the free edge end normal to the edge. By matching sheet strain to the strain of a boom loading the sheet in the direction norrvial to the free edge, he was able to determine the sheet stresses for certain boom-to-sheet shes^r loadings and the sheet stresses for the case of an actual boom diffusing its load into a sheet, His solutions pi-edicted that in the case of a lateral cut-out there vrould be infinite shear stress at the comei- as long as there was any strain in tl'C edge member,

In R,A.,E, Report Stnictures 13 (Reference 10) Ilansfield examines the prob].em of reducing the infinite shear stresses by constructing a rib boom at the cut-out and so attaching it to the corner the.t it is built into the spar boom. Such an attach-ment v/ould obviously not rotate and vrould therefore cause the

shear- stress to be r.sro at the comer. It would also transmit immediately a portion of the boa:i load to the end of the panel, thereby somev/hat hastening the process of diffusion,

In RoA,E, Report Structiires 27 (Reference 11) Ilansfield considers the problem of reducing the infinite shear stress at the corners of the cut-out. As a substitute for the transverse rib boom, he suggests an increase in the spar boom area near the corner to decrease the spar boom strain. In order to avoid the design of a spar boom of infinite cross section at the corner, Mansfield concludes that the spai- boon area may remain finite while the rivets in the comer shall be just flexible enough to permit the requii^ed slip between sheet and boan. This requires the use of rivets of 'graded flexibility',

In R.A.E. Report Structures 31 (Reference 12) Mansfield considers a panel bounded by constant stress boons vdth a trans-verse beam at the edge of the cut-out. He solves the case of the

-9-pin-jointed edge beam as vrell as the built-in case, and shov/s that theoretically the shear stresses at the corner are finite for the pin-jointed beara, zero for the built-in beam, and infinite for the case of no beam,

Practical Consideration of the Problem

•In attempting a practical approach to this problem of stress diffusion one should begin by exploring the limitations to tlie theoretical treatment, examining the assumptions, and considering effects that have been ignored or have resisted mathematical treatment,

In almost every theory of any sort there are some

shortcomings in the assumptions 'irhlch may or may not be of great

iniportance, Certainly when one predicts such effects as

infinite stresses, any flav/s in the assumptions relating to tliis effect are of vital importance, and vre must face up to the

possibility of the resulting limitations to the theory,

In the 'finite stringer' theory the shortccmings of

the theory v:ere foreseen by its early developers and still exist

in the latest reports. In addition, no accoimt v/hatsoever is taken of lateral stresses or displacements. In a centre-loaded panel the lateral stresses and forces on the concentra,ted load carrying members may be safely neglected as self-cancelling, but not so in a panel bounded by concentrated booms. Yet in the Royal Aeronautical Society Data Sheet Structures 02,03,00 it is stated not only that one of the basic assumptions is that the lateral direct strains are aero, but that ',,,,.,in particular

the exact condition of lateral restraint is relatively unimportant', In the 'stringer sheet'-theory the assumption is

inherent that the lateral displcLcement is zero ox" negligible at the spar boundaries. The ribs are assur:ied divided into a rib sheet, giving distributed forces of just the right amount to balance the usual equilibriur.i equation between shear and direct

stresses. This, if true, is fortunate indeed. It is further assumed tlitit the lateral displacement is constant at the edge so one must conclude that the spar boon has infinite stiffness in the plane of tlie sheet. On the other hand, it can be siio\7n that theoretically the plate gives infinite curvature to the spar boom at the corner, so the boom must at the same tinwi have aero stiff-ness,

In the method of solution by stress function Ilansfield painstakingly derives a solution for a semi-infinite sheet vd.th finite spaced concentrated bocras. He then cuts the sheet either midway betv/een booms or in tlie middle of each boora and states

that the previous solution has not been effected, using the /argument , , ,

10-argument that ',,,,,•,,, under the assumptions made in stringer sheet theory, stresses normal to tliese lines do not affect the solution', (Reference 9)» Since he has already predicted an infinite lateral direct stress at the comer, it is a stretch of one's credulity to believe that this stress can be ignored,

There is no question that the stress-function solution for an unbounded plate is reasonable physically and correct math-ematically, but most of the proper boundary conditions of tliis problem are not truly amenable to exact definition. One can not say that the lateral displaxiement along the bocms is zero or that the lateral edge loading of the sheet along the booms is zero, The same is true of the longitudinal displacement at the edge, and, if a rib is attached, of the longitudinal loading. One boundary condition that seems certain is that the shear and

long-itudinal stresses are zero across the transverse (cut) edge if there is no end rib. In this case, theory can be made to predict that the shear stress along the longitudinal edge vd.ll rise to 2/7C at the comer or it can predict infinite shear stress depending upon v/hich theory is used. Both theories use a stress function solution. For the last word on boundary con-ditions, it should be mentioned that from the experimental evidence gained in this investigation, it is difficult to say positively that the sheet partakes of the same strain as the boom, even that portion of the sheet V7hich is rigidly attached to the boom,

Even the concept of the comer itself defies an exact definition. The comer in an actual diffusion panel may be

markedly different from the equivalent mathematical panel. First, the loads are actually applied in finite amounts by rivets or

bolts of finite vd.dth, often in tvro or more lines of attachment, The edge of the panel must extend a finite distance beyond the la^t rivet connection and may be attached to an edge rib with several rov/s of rivets or bolts. So there are not tvro mathemat-ical lines intersecting in a point to be defined the comer» Ïïe could define the comer as the intersection of the inboard rov/s of longitudinal and transverse connections, and that is the comer as used in this report, ¥e are, hov/evor, still left vri.th the consideration of the sheet outboard of the comer,

One further consideration is the method of applying loads to the sheet. In theory they are applied at points or in a line I in actuality they are distributed and limited to certain stresses in the area of application. It is difficult to believe that the action of the sheet vill have cny effect other than to reduce those stresses at increasing distances from the point of application,

Certain other effects have 30 far been ignored in the handling of the theories or else are not amenable to mathematical consideration vd.thin the probleme The lateral stiffness of the spar booms has already been mentioned. In addition there are

nCHNISCHE HOGESCHOOL

VLliiCIjiGBOUWKUNDE Kanaalstraat 10 — DELfT

1 1

-such factors as the elasticity of the connections bet\reen sheet and boccis, the possibility that a thick skin tends to support itself at the corner, eccentricity of loading, rnd shortening of the bocsn due to curvatijre,

It does seem that tliLs problem of stress diffusion, although it can be treated vdth ptore mathematics, is too complex to yield one exact solution to the v/hole problem» The necessary 3.ssiJmptions are too greeit, and the factors ignored arc probably too important, Yflaile an approximately correct ans".7er can be obtained over much of the prnel, there is no resemblance at all between actual behaviour in the comer and the jjredictions of

theories,

Experimental Equipment

In order to measure relatively close to the comers of the cut-out, a very large test specimen had to be chosen. In addition to l2rge size, the test specimen viras designed to have the follovdng characteristics of the tension skin and booms of a typical t\TO spar torsion boxS

(1) Thick skin (14 gauge) of high strength alloy, (DTD52f6) (2) Large number of closely spaced stringers, (20 stringers

at 2-inch pitch),

(3) High ratio of skin-plus-stringer area to bocm area, (Unity).

(4) High ratio of skin area to stringer area, (Over 2jl) (5) Medium rib spacing,

Photographs of the test panel are shovm. in Figs, 1 and 2, The folloviring details should be notedi

(a) Length/mdth ratio is only about 9/8, This vrould be lov/ for ordinary diffusion testing but is believed satisfactory for investigating the localised effects in the comers. See R, and M, 26I8 (Ref, 8 ) , (b) Stringers are replaced by equivalent flat strips,

Since the panel is tested in tension only, the effect of the stringer can be represented by its ability to carry tensile loads,

(c) Panel is symmetrical about its centre-line. This is a departure from ordinary designs but assures that eccentricity of loading out of the plane is minianised,

-12-(d) Large edge rib. It has relatively high lateral stiff-ness but rather lov/ bending and shear stiffstiff-ness in the plane of the plate. In a later test the edge rib was removed and the psmel tested \d.th the edge free,

(e) End rib attachment to booms can be varied to simulate built-in support (as shovm) or single support, or the rib can be left free frcm support by the boons,

(f) Booms are bolted to the plate by tv7o rovra of bolts,

equidistant frctn the centre-line of the bocms. Bolting gives a poorer joint between bocans and plate than rivet-ing, but permits interchange of sets of boons of different properties, A later series of tests v/as performed vdth

only the inboard row of bolts in use, (As sho\7n in Pig. 2 ) ,

Location of electrical resistance strain gauges is shovm in Fig, 2, A dial gauge was rigged to record relative lateral motion between tlie tvro boons. Its reading was so small, hovrever

-0.0025 inches for a load of 34,000 pounds - that it v;as felt to be of little practical use,

Tvro sets of boons v/ere tested, one a 3/8 inch slab, the other a tee section of about the same area, both three inches -idde, They were not tapered. All parts of the test panel, except the bolts, were of light alloy,

Details of Panel Length: 51 inches

Y/idth (between centre-lines of boons): 45 inches Width (betv/een inboard rows of bolts): 42,3/4 inches Boom area per side: Slab boons - 2,23 square inches

Tee booms - 2,17 square inches . Boon moment of inertia per side: Slab bocms - 1,689 inches,

Tee boons - 0,970 inches ¥eb (slcin) thicknessi 0,0813 inches

Stringer area: 0,0732 inches^ Stringer spacing: 2,0 inches

End rib area: 0,684 square inches

Test Technique Loading System

The desired aim in loading vras to apply symmetrical loads to the tvro spar booms, Arrangeiient of the loading system can be seen fron Figure 2, The purpose of the links bet."/een the steel

-13-channels and the connections to tlie bocms v/as to minimise the introduction of spurious bending moments or side forces,

In order to ascertain that loads applied were equal and symmetrical, strain gauges v/ere fixed on both booms belov/ the edge of the panel, and tensile loads and bending moments determined, The position of the hydraulic jacks was varied laterally until the loading v/as as desired,

Tests

Ten tests vrere performed. In each the total load v/as varied in 4000 pound increments from 14,000 pounds to 34,000 pounds, readings of all strain gauges taken at each loading. The conditions of the panel for each test are described belovir:

Test 1 • The Tee booms were bolted to the panel vd.th both rows of bolts. The edge rib was given 'built-in' support

at the spar booms,

Test 2, Same as Test 1 except that the edge rib was given 'simple' support at the spar boons,

Test 3. Same as Test 1 except that the edge rib v/as not attached to the spar boons,

Test 4» The Tee booms vrore removed and replaced by

slab booms, connected vdth both rears of bolts. The edge rib v/as

given 'built-in' support at the spar boons,

Test 5. Same as Test 4 except that the edge rib Viras given ' simple' support at the spar boons»

Test 6, Same as Test 4 except that the edge rib v/as not attached to the spar boons»

Test 7. Same as Test 4 except that the outboard row of bolts was removed,

Test 8» Same as Test 5 except that the outboard rav of bolts v/as removed,

Test 9» Same as Test 6 except that the outboard raw of

bolts was removed»

Test 10» The edge rib v/as removed from the panel and the rivet holes in the rib enlarged. The edge of the panel v/as coated vdth a light grease and the rib v/as replaced and bolted on loosely vd-th small bolts. This gave support to the edge of the panel against buckling in compression or shear but permitted no direct load to be transmitted betvreen sheet and rib. In all other respects the test v/as the sarae as Test 9,

-14-General Remarks About Testing

It v/as found that bolted connections required a consid-erable amount of loading before transmitting forces in direct proportion to the applied loads. By starting the readings at a high loading (14,000 pounds) it v/as possible to get strains linear v/ith load, and there was no trouble ivith pronounced nonlinearity

in any of the readings,

A loading link was used to measure the applied load but did not turn out to be an unqualified success. It v/as very

sensitive to changes in cii'cuit current and moreover seemd to vary a bit from day to day. As a result, the average stress indicated by strain gauges on the booms belov/ the edge of the panel v/as used

as the basis for computations,

As mentioned previously, the loading system was adjusted to give symmetric loading. In actuality the strain gauges shoT,TCd loads v;ithin one per cent of each otheri the bending moments were usually both in the positive direction (shear outboard) but v/ere rarely alike in magnitude. Since they represented sheajrs of the order of ten pounds for a tensile load of ten thousand pounds, it T/as felt that exsictitude here v/as not required,

In analysing the test results, Poisson's ratio effects v/ere accounted far in determining direct stresses in the sheet, Poisson's ratio v/ai3 assumed to be 0,30, Tests on control speci-mens showed that all elements had a modulus of elasticity v/ithin

tv/o per cent of 10,5 x 10° pounds per square inch, so in deter-mining the results presented it v/as not necessary to use the modulus of elasticity, only to assimie that it was the same for

all elements,

Presentation of Test Results

A tabulation of the measured results of the ten tests is appended as Table II, For the skin, both strain mea^surements and relative stresses are indicated. For the end rib, strain, relative stress, and ratio of rib load to boon load. For the boom, average strain, rela^tive stress, difference betv/een inside

and outside edge stresses, and that difference divided by the average stress in the boon at that location. By relative stress is meant the ratio of the particular stress to the average stress in the boom below the cut-out. It is felt to be best to reduce the stresses to non-dimensional figures in order for them to liave the most significance and to compare one test vdth another or v/ith theory,

Graphical illustration of the tests has been used, since this is considered to be the best available method of comparing the

-15-relative effects of the different variations (the boom and the end rib fixation),

Graphical results are presented in the appendix, arranged as listed in Table I, in groups in v/hich one element is held con-stant while the other element is varied. Three sets of curves are presented for each group» one to show stresses along the longitudinal edgej one to shov/ stresses along the lateral edgej and one to shov/ the diffusion of load fron the boon into the sheet, In addition there is a group to illustrate the comparison of a free edge vdth a stiffened edge and a group to compare typical results of this series of tests v/ith the predictions of certain theories,

Stresses in the end rib are not shown in any of the graphs. It is felt that the stresses along the rib are of less importance than the rib loads, v/hich must be taJcen out by the booms as shear's. Both the rib and its stresses are rela^tively

large, so these loads may be considerable. In the CCLSCS in v/hich

the rib is attached to the boon, thelib load enters the boon at one or three bolts and therefore malces up a proportion of the bolt reactions v/hich may not be ignored,

Discussion of Test Results

It must be noted that the so-called 'edge stresses' v/ere actually measured a finite distance av/ay from the edges, both long-itudinal and lateral. This distance is the sum of the overlap of the boon or rib beyond the line of bolts or rivets, plus the vd.dth of the strain gauges, and amounts to about two per cent of the effective panel v/idth. It is believed that tliis is close enough to consider the results to be relia.ble quantitatively as v/ell as qualitatively,

In comparing the tvro booms, it must be pointed out that

the slab boons are scxae three per cent greater in area than the

tee sections. Making aLlowance for the material removed for bolt holes, the difference is less than tvro per cent. This, it is believed, has little effect upon the edge stresses but should be

considered when conparing the diffusion of load from the boons, Strains in the set of slab boons were measured in three places across the boom for each longitudinal location - on each edge and along the centre-line. In all positions except the first two above the comer there v/as close agreement bet\""/een the strain in the centre and the average of the edge strains. In the readings of the first t;vo groups above the comer the agree-ment v/as poor, and it was necessary to v/eigh each reading in

order to arrive at a realistic average strain, taking into account the direct strains in the sheet along the two edges. The results /so obtained •»•

-16-so obtained should not be considered as being completely reliable,

Conclusions

1, The results presented, particularly the comparison of theory and test, shov/ conclusively that the edge stresses in the corner are finite and in most cases drop off tov/ard zero near the comer. These results represent a large, though localised, departure from the predictions of the theories considered. Little effect can be attributed to either spar stiffness or condition of end rib fixity,

The agreement v/ith the finite stringer theory is fairly good as long as the longitudinal distance fron the comer is greater than two-tenths of the semi-span and provided we mak:e the reasonable assumption that the shear stress has decreased in tlie distance

isetween the 'edge' and the strain gauges, (although this is con-trary to one of the basic assuLiptions of the theory), It is possible that these predicted shear stresses could safely be used as an envelope around the maximum shear stresses that will actually occur in the sheet, applicable to vdtliin, say, tv/o-tenths of the semi-span from the corner, at v/hich point its 2-iagnitude v/ould be the maxiinim encountered anyvThere in the sheet. Further tests on sheets of different tliickness would have to be carried out before this hypothesis could be accepted,

The correlation between the stringer sheet theory and the tests results is so poor that there is no basis on which to discuss the two further,

2, The diffusion of load seems to be a very complex

problem, affected by many vrjriables. Certainly the actual rate of load diffusion lags far behind the rate predicted by the theories,

Boca lateral stiffness appears to loave some effect,

particularly upon the phenomenon observed in certain tests in vAiich

the booms tc^e additional load frcm the sheet at the first

connec-tions rather than transfer load into the sheet. Of the tliree tests using the flexible boons, this occurred oncej in seven tests vdth the stiff boons it occurred five times. It was most marked in the tests vdth the end rib free and in the tests in which the loading v/as eccentric. Since tests on the Tee booms loa.ded eccentrically were not carried out, this is perhaps an unfair conparison, but from Figures 5» 8, and 11 it appears that the flexible booms do load the sheet much more rapidly in and near the corner,

The lag in the comer betiveen the predicted and the actual load diffusion is probably related to the drop-off of edge shear stress. It is reasonable to conclude that since the sheet is not experiencing the shear strain predicted by theory the boon

-17-is not loading the sheet as predicted,

Eccentricity of loading undoubtedly has sane effect, as the load diffused in Tests 7f 8 and 9 was less than the load diffused in Tests 4, 5» and 6, Since the shear load bends the boon in the positive direction, the tensile loads bend it in the negative direction, and the whole panel probably behaves so as to minimise the total strain energy, it is possible that there is

some optimum eccentricity, perhaps a function of radius of gyration and lateral sliear stiffness, to give best load diffusions

The presence of an end rib also speeds up load diffusion, even vAien it is not connected to the spar, as seen fron Figure 25» The method of attachment of the rib to the spars makes a considerable difference in the load diffusion at the comer, although there is no significant difference eight or ten inches av/ay, Tlie effect of rib airea has not been investigated except \d.th a rib of zero area (no rib), in v/hich case the diffusion v/as considerably slov/er,

It may be that the load diffusion predicted by the theories represents the maxii:.iun possible rate of load diffusion, Prom the results of the two 'blieories, the finite stringer theory again appears to be much the more reasonable,

3« Contrary to the Royal Aeronautical Society Data Sheet Structures 02,05oOO on stress diffusion, the lateral loads in the end rib are of such magnitude that they can not safely be ignored, In these tests the end loads in the rib area are of the order of seven to nine per cent of the boon tensile loads. Since this is entering the boo.i as a concentrated load and, moreover, as a shear, it demands careful consideration both from the standpoint of the connection between the end stiffener and the spar and fron the

standpoint of designing the spar booms for maximum allo\/able stress, These lateral loads are higher in the tests v/ith the flexible spar booms, (probably because they deflect more under bending)„ The effect of rib cross sectional area has not been investigated, but there is little doubt that a smaller rib vdll introduce smaller loads. In the test with a rib of zero cross section (no rib) the lateral stress in the skin v/as zero at the corner (no transverse load), 4. Large bending moments existed in the boons above the

comer. These caused average additional tensile stresses of a^ much as twenty-five per cent of the average stress in the bocm at

that location. Localised additional stresses may be considerably greater» These additional stresses v/ere highest for the

flexible boons and they v/ere higher when the boon v/as loaded eccentrically than v,hen tv/o rows of attachment v/ere used» It is concluded that designers should increase the factor of safety for the spar booms in the first semi-span av/ay from the comer in order to allov/ for tliese additional stresses,

5» Decreasing the end rib cross sectional area should produce the same qualitative effect as removing the rib. These effects

-18-should bc as follows:

(a) Lov/er maximum shear stress. Shear stress drops off more markedly to zero at the corner,

(b) Higher compressive stresses in the rib and liigher transverse compressive stresses in the skin across the cut edge,

(c) Lov/er direct stresses at the comer,

(d) Probably a lov/er transverse load applied to the boom. (e) Less rapid diffusion of load frcti booms into the sheet, (f) Slightly higher bending monents in the booti.,

6, Sane of the effects of incr-easing lateral stiffness of the booms may be predicted fron the tests of the two boons. Not all of these are conclusive,

(a) Essentially no change in mcocimum shear stress. The drop off in shear begins farther up the boons v/hcn the

stiffer booms are in use,

(b) Higher direct stresses in the corner, Tliis v/as part-icularly marked in tests 6 and 9 in v/hich the rib v/as not attached to the boois,

(c) The stresses in the rib are lov/er, and the transverse load applied by the rib is less,

(d) Less rapid diffusion of load from boons into the sheet, (e) Lov/er stresses due to bending monent in the boom above

the comer,

(f) Possibly more tendency for the stiffer boom to take additional load from the sheet at the corner, instead of a^pplying load to the sheet,

7» All the effects of changing the condition of support of the end rib can not be predicted conclusively from the tests, The differences are sometimes small or even conflicting. There are some effects, hov/ever, and they are as follows:

(a) No marked difference in maximum shear stresses or the v/ay in vtó.ch the shear stresses drop off,

(b) Higher direct stresses in the comer when the rib vras

TECHNISCHE HOGESCHOOL

VLIEGTUIGBOUWKUNDE Kanaalstraat 10 - DELFT

1 9

-not attached, No significant difference betiiveen the built-in case and the simply supported case,

(c) No significant difference bet\/een rib stresses in built-in ca^e and simply supported case. Slightly lower stresses all the v/ay across the rib for the case of no support,

(d) A large proportion of the boom loc^ v/a>.s transferred directly to the sheet via the end rib v/hen the rib was supported, except v/hen the boon-to-sheet attachment v/as eccenti"ic. This v/as more mrrked for the flexible boons. There v/as no consistent tendency for either

condition to transfer the higher proportion of load, (e) Bending monents in the boon are lov/est for the cases

of no rib attachnent. There is little difference

hetvoen the built-in and sijnply supported cases, (f) The phenonenon of the boon increasing its end load at

the first connection to the sheet occurred every time the rib v/as not connected to the boon, ViTien the rib v/as supported by the boom this did not occur except v/hen the loading v/as eccentric,

(g) Despite (d) and (f) above, there v/as, at a distance of a ha.lf semi-span above the corner, no difference in the amount of load diffused,

8, At the end of a cut-out, on the tension surface at least, a rigid stiffener must be employed to prevent huddling of the cut edge. It seems logical to attach that stiffener to the booms in order to taJce advantage of its capacity to relieve the boons inmediately of a portion of their loa.ds. In considering

the support of the rib, there appears to be little to choose betv/een built-in and simple support as far as transfer of load is

concerned. It should be pointed out, ho\/ever, that built-in support requires the application of a large bending monent beti,.noen rib and boon as v/ell as a longitudinal loa.d. This in turn

requires the means of applying that bending moment. Such means are almost certain to be very costly fron the standpoint of v/eight, so it is possible that the use of a built-in rib vdll achieve no -.veight savings a.t all, A simply supported rib, on the other hand, requii*es the application of only a longitudinal load. By proper design it can be attached to the spar in such a way as to minimise the introduction of undesired bending monents,

9» Some of the conclusions th^it nay be drawn from the results of this investigation ere directly applicable to any diffusion design, but all the results must be considered in the light of the follcad.ng limitations» the panel v/as synmietrical

-20-on both sides of the skinj the tests were made -20-on CL flat plate,

not a box sectionj and the edge mer.ibers of the test panel v/ere constant in area,

The as symmetry of the actual aircrcift wing about the skin v/ould add some bending monents out of the plane of the skin which v/ould tend to buckle tlie skin or bend the spars. An actual stmcture is v/ell bra.ced by the spar v/ebs agednst any such deform-ation of the flanges J the stringers v/ould tend to relievo the monents in the skin as v.'oll as stiffen itj so it appears likely

that the as symmetry of loading v/ould have little effect,

A box section, being considerably stiffer out of the

plane of the sheet end having, normally, e. full plate rib cct the

cut-out to give lateral stiffness, night tend to raise the overall stiffness at the cut-out end hence increase the shejir stresses in the comer end probably the rate of load diffusion. In the design in which only one surface is cut, as for undercarriage doors or bonb bey doors, the v/eb would probably absorb a higher than usual proportion of the boon load end thus relieve the stresses in the comer. The total effect v/ould probably be to raise the corner stresses soncv/hat, but it is not likely to be of more then secondary importance,

Constant area edge nonbers are unlikely to crise in a practical vd.ng design, so the results should be exainined to see which \vould be changed markedly in a design of constant stress boo-is. The drop off of the sheer- stress tov/erd zero in the

comers is a localised effect end occurs even v,hen the boon stress increases at the first connection to the sheet, therefore it

would undoubtedly occur in a constant stress design. The nax-ioun shear stress measiired by test occurs well up the skin, usually between one end tv/o tenths of a semi-spen, so it is probable that in a constent stress design the naxiinu:n shear stress vdll be

greater in magnitude and vdll occur farther fron the comer. The diffusion of load v/ill probably be slov/er than predicted by the theories for constant stress boons, the sene as for constant area boons. The effects of boon stiffness, eccentricity of loading,

end rib area, and end rib support are probably sinilar. The lateral loads in the end rib and the moments in the spar boon v/ould still exist and vrould probebly be higher because of the lov/er lateral stiffness of the boons at a distance awey fron the corner,

10, The problem of stress diffusion is extremely complex,

and there are many variables that hscve narked effects upon the

behgViour in the vicinity of this cut-out. There is insufficient

quantitative knowledge about these variables to enable designers

to obte.in en optinun design for any arbitrery set of conditions, The results of the tests perfor.:ied leetd to the conclusion that the theories are incapable of handling the problen in the

-21-c o m -21-c r or of obtaining even qualitative indi-21-cations. It is felt that sone other neens of solution, such as the relaxation of restraints, could v/ell be attempted for a specific problen, but it is also believed that there should be further testing to obtain quantitative results that v/ould be of value to designers,

REFEKENDES No» Author(s)

1.

9.

H,L. Cox, H,E. Snith, and C.G, Conv/ay 2» WoJ» Duncan 3* H»L. Cox D, Williams, R,D, Starkey, and R,H. Taylor 5» J. Hadji-Argyris, and H.L, Cox 6, J, Hadji-Argyris J, Hadji-Argyris 8, M , Fine, and HoG, Hopkins E,H, Mansfield Title, Etc,

Diffusion of Concentrated Loads into Monocoque Structures, A,R.C, R, and M, I78O, 1937. Diffusion of Load in Certain

Sheet-Stringer Conbinations, A,R,C, R, and M, 1825, I938, Diffusion of Concentrated Loads into Monocoque Stimctures III, A,R,C, R, and M , I86O. 1938, Distribution of Stress betv/een

Spar Flanges emd Stringers for a Y/ing under Distributed Loading» A,R,C, R. and M , 2098, 1939. Diffusion of Load into Stiffened Panels of Varying Section,

A.R.C, R. and M , I869, 1944, Diffusion of Symmetrical Loads into Stiffened Parallel Panels v/ith Constant Area Edge ilembers, A.R.C, R, and M , 2038, 1944. Diffusion of Antisyi^netrical Concentrated End Loads,

A,R,C, Report No. 9662, 192^6. Stress Diffusion Adjacent to Gaps in the Inter-Spar Skin of a

Stressed-Skin v/ing,

A,R.C, R, and M , 26l8, 1942, Diffusion of Load into a Senii-Infinite Sheet, Part I,

R,A.E, Rep, Structures 11, 1947. /IO, ,,,

-22-NOQ Author(s) 10, E,H. Mansfield 11, E,H« Mansfield 12, E,H, Mansfield Title. Etc,

Effect of SpenvdLse Rib-boon Stiffness on Stress Distribution Near a Yidng Cut-out,

R,A,E, Rep, Stmctures 13, 1947, Diffusion of Load into a

Semi-Infinite Sheet, Part II«

R.A.E, Rep, Structures 27, 1948, Diffusion of Ijoad into Panel Bounded by Constant Stress Boons and Transverse Beam,

R,A,E, Repc Structures 31, 1948,

TABLE I

/jrrcngenent of Presentation of Test Results

Element Fi.xed Element Varied Tests

Group Figures

1 3-4-5 End Rib Support (Built-in) Boon Stiffness 1-4-7 6-7-8 End Rib Support (Sijnple) Boon Stiffness 2-5-8 9-10-11 End Rib Support (Free)

12-13-14 Boon (Tee Boons) • 15-16-17 Boon (Slab Booms)

18-19-20 Boon (Eccentric Loading)

2

3

4

5

6

7

Boon Stiffness 3-6-9

End Rib Support 1-2~3

End Rib Support 4-5-6

Hid Rib Support 7-8-9

21-22-23 I l l u s t r a t e s Effect of Removing End Rib 3-6-10

8 24, 25

26

27

Ccciparison of load diffusion and longitudinal edge shear stresses by finite stringer theory

( R . A , A , Data Sheets) and stringer sheet theory (Reference 8) v/ith results of tests 6 (end rib free) and 10 (end rib removed).

Conparison of longitudinal edge shear stresses predicted by Reference 10 for built-in end rib Td.th results of tests 1 and 4.

CCT.iparison of longitudinal edge shear stresses predicted by Reference 12 for simply supported end rib with results of tests 2 and 5.

TABLE II

TEST DATA __ -_ DIFFUSION PANEL

Gauge! 'GrcDupj

1' '

1 j

1 2

1 ^

^ 1

5 ^

7

8 1 2

3

1 ^

1 5

i ^

i 7

1 8

( i n s ) -0 . 9 Oo9 0 . 9 0 , 9 2.75 4 . 7 2 8,67 2.75 i 0 . 9 iO.9

io.9

io.9

J2.75

i4.72 (8.67

12,75

\

" 'i

y 1

(ins)l

7.4 j

5.4 1

3.4 j

0 , 8 j 0 . 8 0 , 8 0 , 8 j ,3.40 i

7.4 1

|5.4 1

l3.4

\

1 1 | 0 , 8 f ;0,8 j

b,& 1

!0.8 f ^3.4 i e ,10^1 XX 2 . 5 1

3.5

6 , 0 13.1 1 3 . 8 , 1 5 . 6

il9«é

^ 3 . 8

i

1 1.6 4 , 5 + 3 . 3 - 1 . 1 + 8 . 7 +15.1 21.1 2 . 3

e ,10^1

-8.9 1

-7.6 I

-6.0 i

-8.0 1

-6.9 j

- 9 . 2 - 6 . 2 - 3 . 4 . - 8 . 9 - 8 . 9 - 9 . 9 j - 5 . 3 - 5 . 0 j - i o . i

j -5.7

1 -4.6

T e s t 1 e .10^ xy* 14.2 2 0 . 7 2 9 . 8 5 2 . 3 49.1 4 0 . 9 3 4 . 0 2 9 . 8 Tes-t 16,5 2 3 . 2

1 34.6

5 2 . 4

158.7

1 47.2

( 3 7 . 4 ! 2 7 . 5 ^ x x / ^ o 0 . 0 3 4 .119 .300 .330 .359 .495 .077 ' 3 I-.031 +.049 +,007

J-.073

;+.195 i .330 j .525 ! . 0 2 4 SMN

Vol

- . 2 2 8 - , 1 8 4 ' - , 1 1 9 ' - , 1 1 4 - , 0 7 7 - , 1 2 6 - , 0 0 7 L.-»065_J - . 2 3 0 - . 2 0 2 -,2h2 - . 1 5 3 - . 0 6 6 - . 1 5 3 + ,016 - , 0 1 6 STRESSES 1 1 q, / f ' e .10^ T C / 01 XX

.138 3.2 1

.203 \ 3.7 1

.291 \ 5 . 3 ,511 1 13.1 ,430 15,0 j ,400 j 1 8 . 4 .332 18.2 .291 i 8 . 4

i

.148 1 3.2

i .210 1 4.4

1 .313 j 3-4

I .473 0,9

i .530 3.7

1 .las i 13.1

i .539 1 14,0

! .250 1 4.8

: 1

V^^"'

- 7 . 4 - 6 , 7 - 5 . 5 - 7 . 4 - 3 . 4 - 3 , 7 - 3 . 7

u-J-.o J

- 6 . 7 1 - 7 . 3 - 1 0 , 1

j -3.0

j +0,9

1 -6.2

1-3.2

j -4.4

Test 2 e .10^ xy* 15.6 2 0 , 4 3 1 . 0 4 9 . 9 4 4 , 0 4 0 . 9 3 1 . 5 2 6 . 8 XX o< .030 .050 .107 .313 ,403 .453 ,492 ,216 T e s t 4 1 6 , 3 2 0 , 4 24,1 : 2 5 , 9 4 1 . 3 ! 3 9 . 9 2 6 , 4 \ 2 0 , 6 +.043 +,078 .025 0 .153 ,401 ,466 ,124 1 f / f .•VT 0 - . 1 8 4 ! - , 1 6 2 - , 1 1 2 ! - . 0 9 9 +,032 - , 0 9 2 +,052 - , 0 1 5 - , 2 0 5 - . 2 1 4 - , 3 2 6 , - . 0 9 6 +.071 1 - , 0 8 4

j +.037

! -.1O9 i 1 )

.157 i

.2041

i .311 i

,5001

.4431

.410} .3161 .269 • ; .208 1 ! i . 2 5 8 ! ! .301

1.3261

! .519i

.500 i

.3331

1.2581

f Gaugd Group 1

2 1

3

4 1

5 1

6 1

7

8 1

t '' 1 2

3 :

4

i 5 I

6 ;

j 7 1

1 8 '

' 1 « IVI J

s

o

•- O 5. I i-i iS w

TS^W: I I , Contd,

j

i

1

1 1 Gauge Group 1 2 3 4 5 6 7 8 i j ! 1 2 3 4

1 5

6 7 8 X ( i n s ) 0 , 9 0 , 9 0 . 9 0 . 9 2 . 7 5 ( i n s ) i i 1

7,4

5.4

3o4

0 , 8 0 . 8

4.72

0.8 1

8 . 6 7 0 . 8 I 2o75 3 . 4 ; 1 i 0 . 9 0 , 9 0 , 9 0 , 9 2.75 4 . 7 2 7 . 4 5 . 4 3 . 4

0.8 1

0 . 8 Oc3 8.67 0 . 8 2 , 7 5 i 3 . 4 SKEN STRi3S:'3ES T e s t 5 1 * e ,10^1 e . 1 0 ^ XX yy 2c3 3 . 9 4 , 1 1,1 7 . 3 1 4 . 4 1 9 . 7 - 8 . , - 8 . 7 - 9 , 2 - 6 . 6 - 3 . 9 - 8 . 7 -5,5 2 , 5 1 - 4 . 4 1 i 2»5 3o7 + 4 , 8 - 1 . 3 + 3 . 9 13 «8 1 9 . 5

1 2.5

- 1 0 . 6 - 1 1 . 2 - 1 4 . 5 - 6 . 2 -2^,6 -10o3 - 6 . 9 - 7 . 8 e . 1 0 ^ 1 7 . 7 2 4 . 5 3 4 . 9 4 5 . 0 5 6 . 7 4 9 . 3 3 4 * 4 2 6 . 6 Te si 2 0 . 2 27.1 3 5 . 3 3 8 . 8 5 5 , 8 . 5 1 . 2 3 6 . 5 2 6 . 9 XDC O - . 0 1 2 + . 0 3 5 i + . 0 3 5 - . 0 2 4 + , 1 6 5 . 3 2 6 , 5 2 0 , 0 3 3 •' 7 - . 0 2 4 + . 0 0 7 + . 0 1 2 - . 0 8 8 +0O69 . 2 9 5 , 4 7 7 . 0 0 5 f / f JV 0 -o 224 - . 2 0 3 - . 2 1 7 - . 1 7 0 - . 0 4 6 - . 1 2 0 1

S c / ^ o

, 1 7 0 . 2 3 4 . 3 3 3 . 4 3 0 . 5 4 1 . 4 7 0 +.012 1 c328 -.099^ .2^-6 1 - , 2 7 1 - . 2 7 7 - . 3 5 9 - . 1 8 0 - . 0 9 3 - , 1 6 9 - . 0 2 4 . 1 9 5 . 2 5 9 . 3 3 7 , 3 7 3 . 5 3 4 1 .493 1 o350 - . 1 9 2 ! , 2 5 9 1 i 1 T e s t 6 l . . . _ ) e «10^ 2o3 5 . 5 + 3 . 7 - 1 3 . 1 + 6 . 6 1 2 , 6 21 „1 1,1 1 3o4 4 . 4 1.1 1 , 8 5 . 0 1 4 . 9 2 0 , 0 3 , 9 e J O ^ .yy - 1 0 , 5 - 1 2 , 1 - 1 5 . 8

v^°^

2^-H.5 2 6 . 9 3 1 . 0 - 1 1 . 2 5 3 . 3 - 4 c 4 j 5 9 . 2 - 8„7 i 5 4 , 0 - 6 , 2 3 8 . 4 - 5 , 7 ' 2 5 . 2 Te si - 8 , 7 - 9 . 4 - 1 1 . 0 - 4 , 6 - 3 . 0 2 0 , 0 2 5 . 7 3 0 . 5 4 4 . 0 5 1 , 2 - 8 . 7 5 1 , 6

- 5.7 36.3

- 6.2 j 27.5

f / f DOC 0 -0O23 + . 0 5 1 - , 0 2 8 -o437 . 1 4 0 . 2 6 5 + . 5 1 0 - 0 O 1 6 ; 8 , 0 2 2 + . 0 4 3 - , 0 6 0 + . 0 1 2 . 0 9 6 . 5 4 0 , 5 0 6 . 0 5 5 f / f - . 2 6 0 - , 2 7 9 - . 3 9 1 - . 4 0 0 - . 0 6 4 - , 1 3 1 0 - . 1 4 2 - . 2 1 3 - . 2 2 3 - . 2 9 2 - . 1 1 3 - . 0 4 1 - . 1 1 5 +,007 - c 1 3 ^ S c / 0 „228 «251 „288 . 4 9 5 . 5 5 0 . 5 0 2 . 3 5 7 . 2 3 4

1

. 1 9 4 . 2 5 0 1 * . 2 9 5 , 4 2 7 . 4 9 6 . 5 0 1 . 3 5 3 , 2 6 6 Gauge Group 1 l • 2 3 ! 4 1 5 6 7 : 8 1 2 3 4 5 6 7 8

TABLE I I , Contd, SKIN STRESSES 1 - - • - - - - • - i [Gauge! [Group'

1 ""

! 2 3 4

1 5

1 6

! 7

1 Ö

X ( i n s ) 0 . 9 0 . 9 0 . 9 0 . 9 2.75 4.72 8.67 2.75 1

y 1

( i n s ) i 7 . 4 5 . 4

3.4 1

0,8 1

0 . 8 0 . 8 1 i 0 . 8

[3.4

T e s t 9 e .10^ XX 2 . 5 5.5 +3,9 - 1 3 . 3 +4.1 12.1 2 0 . 4

1 2.8

e . 1 0 ^ - 9 . 6 - 1 1 , 0 - 1 4 . 7 - 7 . 3 - 5 . 3 - 8 . 0 - 5 . 7 - 7 . 6 e ,10^ :<y i 2 3 . 4 27.1 3 2 . 8 54.1 52.1 5 1 . 5 37.6 2 6 . 4 f / f rcxr 0 - . 0 1 2 + .059 - . 0 1 4 - . 4 2 5 + ,069 ,265 ,510 , 0 1 4

f yf

yy^ 0 - , 2 4 2 - , 2 5 6 - . 3 7 0 - . 3 0 8 - . 1 1 1 - . 1 2 1 - . 0 1 2 - . 1 8 7

Vo;

. 2 2 5 .261 j

.312 1

.520

.500

.494 j

.360 j

.254 j

Test 10 1

e .10^ j XX + 6 . 2 +3.9 + 4 . 4 0 + 6 , 9 +12,9 +16.5

1

+2,5

e .10^1 yy - 1 7 . 9 - 1 4 . 0 - 1 1 . 7 - 2 . 5 - 3 . 7 - 8,9 - 5 . 5 - 6,9 e ,10^1 4 . 8 6 , 4 1 1 , 5 2 0 . 0 31.6 3 2 . 8 2 5 . 7 13.1 f / f x x 0 +.035 - . 0 0 9 +.035 - . 0 2 8 +.210 : +.364 +.536 ' +.016 f / f .yy 0 - . 5 8 0 - . 4 6 5 - . 3 7 6 - . 0 9 1 - . 0 5 6 - . 1 8 2 - . 0 1 9 - . 2 2 2

V'o

.060 ^082 .147 . 2 5 4 .402 .417 .326 .166 Gauge Group!

'

i

2 ^ ! j \

4 1

1 5

! 6

1'

1 Ö

TABIE I I , C o n t d , ! EbT) RIB STRESSES I 1 1 Gcuge ! ': No, 25 26 27 28 29 X ( i n s ) -~ y ( i n s ) 2 1 . 4 1 1 . 4

7,4

5.4

3 . 4 .

T e s t 1 e^ i 1 0 " ^ R • - 1 3 . 8 - 1 2 , 4 - 1 1 . 3 - 1 1 . 5 - 1 1 . 1 Gauge Group 30-41 31-40 32-39

33-38

34-37

35-36

X ( i n s ) - 4 . 0 + 0 , 8 2 . 8 4 . 6 8 . 4 1 2 . 4 y ( i n s ) -! _ —

-V^o

- . 3 2 - . 2 9 - . 2 6 - . 2 7

i-.26 1

SPAR

VR/^O

- , 1 1 2 - , 1 0 0 - . 0 9 1 - . 0 9 3 - . 0 8 9 T e s t 2 1 i

-R ^ ^ ° ' '

- 1 3 . 3 - 1 1 . 7 - 1 1 . 7 - 1 1 . 3 ! 1

-10,6 1

V^o

-.35

- . 3 1 - . 3 1 - . 3 0 - . 2 8 BOOM STRESSES

Test 1 1

e i l O " ^ ave . 3 8 , 0 3 6 . 4 3 2 , 6 3 1 . 3 2 9 . 6 - i 27.1

1 '1

fVf

^ 0 1.00 .883 .832 .800 ^^fplpsi) (DUE BI) 1000 -2600 -1540 -1620 ,760 - 780 .692 - 280 1^ _ . i

^'

V^B

+ . 2 4 4 - . 7 4 6 - . 4 4 8 - . 4 9 2 - . 2 5 0 - . 0 9 8

W ^ o

- , 1 1 0 - . 0 9 6 - . 0 9 6 - . 0 9 5 - . 0 8 7

Test 2 1

e i l O " ^ _{ave •} 3 8 . 2 3 6 . 4 32.1 3 0 . 8 2 8 . 4 26.2

V^o

1,00 .950 ,840 .805 .742 ,688 . . . . A f g l p s i ) (DUS H/I) 1030 -1230 -1380 -1640 - 800 - 320

^-^V^B

+.256 - . 3 2 2 - . 4 0 8 - . 5 0 7 - . 2 6 8 - . 1 1 6 Gauge No. 25 26 27 28

1 29

Gauge Group 30 31 32

33

34

35

i

TABLE I I , C o n t d . i i iGauge [ X i No, i ( i n s ) '

j 25 1

-1 26 -1 - -1

1 27 \

\ 28

1 29

1

-y J

( i n s )

21,4 1

11.4 1

7.4 1

5 . 4 !

;

^R ^^°"^

-12.7

-11,3

, - 9.9

' - 9.7

3.4 |i 1 - 6.9

' i . i

Test 3

V^o

- . 2 9 - . 2 6 - . 2 3 - . 2 3 E^ID

! ! - . 1 6 !

1 ! ! RIB STRESSES 1

kv^o

- . 0 9 8

1 -.087 1

j - . 0 7 6 !

-.075 1

i - . 0 5 3 \

c \

Test 4

j

^R

•i 10"^

_{• i \}

10,6 t

9.0 j

7.6

7.1

5.1 i i

V^o

- . 3 5 - . 2 9 - . 2 5 - . 2 3 - . 1 7

V R / ^ O

- , 1 0 6 - . 0 9 0 - . 0 7 6 - . 0 7 1 ! - , 0 5 1 Gauge No,

1— —

25

1 ^^

27

28 I

1 29 j

t • '

SPAR BOQivI STPJiSSES |

! 1 1 i

i A

b-auge

JGroup

[30-41-50

hi-40-49

^2-39-48

33-38-47

l34-37-4£

135-36-45

1

, i n s )

- 4 , 0

+0,8

2.8

4.6

8.4

12.4

y 1

( i n s ) j

i

-1 "•

1 -: - i je -ilO"^ ave •

1 40.8

1 41.5

34.7

5^*°

31.6 1

28.4 1

? 1

Test 3

V^o

1.000 1.014 .849 .805

Üfg(psi) j

(DUE m,i)

730 1

+230 1

-1210 j -1260 „772 j -1080 1 . 6 9 3 ; -480 i 1

1

.170 i

+.053 1

-.331 1

- . 3 6 4 }

-.325 j

- . 1 6 6 j

le -10

ave •

1 30.7

30.5

28,5

26,5

1 23,6

; 21.8

1

Test 4 1

-5

V^o

1,000

.992

.930

.864

.772

.710

j A ^B^Psi)

{.DUE H'l)

190

j +850

I -190

- 8 5 0 -650

1 -390

i

^ V^B

.059 i +,266 1 - . 0 6 3

-.305 1

-.262 1

-.162 11

1 Gauge 1 No. ; 30 1 1

31 1

32 :

33

34

35 1

TABIE I I , Contd.

! END RIB STRESSES : 1 l' L 1 p-auge No, j

1 ^^ 1

1 26

27

28 1

29 1 X j ( i n s ) j l \

-y 1

( i n s ) i 2 1 . 4 ! 1 1 . 7 !

7.4|

5.4!

3.4i

1

Test 5 j

-R T ^ ° " - 1 3 . 4 - 1 2 , 2 - 1 0 , 6

1 - 9.4

] - 8.1 1 )}

V^o

- . 3 3 - . 3 0 - , 2 6 - . 2 3 - . 2 0 I V R / ^ O ! - . 1 0 1 j 1 - , 0 9 3 - , 0 8 0 i - . 0 7 2 j - , 0 6 1 j T e s t 6 e , ^10-5 - 1 3 . 4 - 1 2 . 0 - 1 0 . 4 - 8 . 8 ! : - 4 . 6 ! 1 ! J

V^o

- . 3 2 - . 2 9 - . 2 5 - . 2 1 - . 1 1

k ^ R ^ o

1 -.099 1

- . 0 8 9 - . 0 7 7

1 -.065 1

i - . 0 3 4 ! Gauge No.

1 ^^

₂₆

27

28 j

1 29

1 SPAR BOOM STRESSES

! i

p-auge iGroup 130-41-50 J51-40-49

J32-39-48

133-38-47

134-37-46

P5-36-45

( x n s ) - 4 , 0 + 0 . 8 2 . 8 4 . 6 8.6 1 2 . 4

y 1

^ins)j

; -'

i

-i I

1 Test 5

e - i i o ' i

ave • 4 0 , 5 3 8 . 1 5 6 . 2 3 5 . 1 3 1 . 6 ]

1 28,9

V^o

1,000 . 9 4 2 , 8 9 4 ,870 ,782 A f 3 ( p s i ) (DUE H.I) 1 320 I +530 ; - 5 6 0 i , -1160 - 610 . 7 1 3 t - 680

i

^ - ^ ^ B / ^ B

.075 1

+.132 ' - . 1 4 7

-.315 1

- . 1 8 3 - . 2 2 4

1 Test 6 1

e i 1 0 ' 5 ave •

j 41.5

1 42.0

1 39.2

1 36.8

I

32.5

1 29.5

V^o

1.00 1.014 .947 . 8 8 8 . 7 8 4 .712 1 (DUE BI) -+1010

1 - 460 i

- 920 1 - 8 5 0 j - 700

1 i

^ ' ^ B / ^ B -+ . 2 2 8

-.115 1

- . 2 3 8 - . 2 5 9 j - , 2 2 6

1 30

1 ^^

32 1

1 5^ 1

i ^^ i

t

''

\

1 i

TABLE I I . C o n t d . 1 1 Gauge No, 25 26 27 28 29 X ( i n s ) -y ( i n s ) 2 1 , 4 1 1 , 4 7 . 4 5 . 4 3 . 4

END RIB STRESSES T e s t 7 ^R T10-5 - 1 3 . 8 - 1 2 . 2 - 1 0 , 6 - 9 . 2

1 1 - 6 , 7

1

V^o

- . 3 4 - . 3 0 - , 2 6 - . 2 3

:

- ^ 7

i

V R ^ C ^

- , 1 0 5 - . 0 9 3 - . 0 8 1 - . 0 7 0 - . 0 5 1 i T e s t 8 ®P f 10"^ - 1 3 . 1 - 1 2 , 0 - 9.7 k

V^o

-.33 - . 3 0 - . 2 4 - 8.8 1 - . 2 2 - 6,7 ' - . 1 7

W ^ o

- . 1 0 2 - . 0 9 3 - . 0 7 5 - , 0 6 8 - , 0 5 2 Gauge No, 25 26 27 28 29 SPAR BOOM. STRESSES

Gauge Group 30-41-50 31-40-49 32-39-48 33-33-47 34-37-46 35-36-45 1 X ( i n s ) - 4 , 0 + 0 , 8 2 . 8 4 . 6 8 , 4 1 2 . 4 il 1! y ( i n s ) -i e i 1 0 " 5 ave • 40.1 42,1 3 9 . 4 3 6 . 0 3 1 . 5 2 9 . 2 T e s t 7

V^o

1,000 1.050 .982 .900 .787 .728

Z^i^psi)

(DUE BM) 340 +460 - 1 0 6 0 -1520 - 820 - 630

^ V^B

0O81 + . 1 0 4 - . 2 5 6 - . 4 0 2 - . 2 4 8 - . 2 0 5 i e i ave . 39.7 4 4 . 3 40.1 3 5 . 7 3 1 . 5 2 9 . 0 T e s t 8 10"^

_V^o

1.000 1.114 1.008 .900 . 7 9 4 .730 / i f g ( p s i ) (DUE BI) 290 +610 - 9 0 0 -1500 - 870 - 630 1

^V^B

.070 + ,131 - . 2 2 4 - . 4 0 0 - . 2 6 3 - . 2 0 7 Gauge Group 30 31 32 33 34 35 i .

TABIE I I . C o n t d . Gauge No, 25 26 27 1 X ( i n s )

; 28 1

-( i n s ) j 2 1 . 4 1 1 . 4

7.4 1

5 . 4 i

29 1 - 1 3.4!

1 ' 1 • jGauge jGroup 30-41-5C 131-40-49 32-39-38 33-38-47 34-37-46 35-36-45 i x ( i n s ) - 4 . 0 + 0 . 8 2 . 8 4 . 6 1 8 . 4 [ 1 2 . 4 y l ( i n s ) i

i

-i !

ENE ) PIB STRESSES T e s t 9 ^R -^^^ - 1 2 . 9 - 1 1 . 5 - 9 . 0 - 7 . 6 - 4 . 2 !

V^o

- . 3 2 1 - . 2 8 7 - . 2 2 - . 1 9 - . 1 0 SP/JF

: V i / ^ o

1 -.098

-o088 - . 0 6 8 - . 0 5 8 j - . 0 3 2 j : T e s t i e j ^ . 1 0 5 NO El^b PJB j l BOOM STRESSES j Test 9 e , 10^ ave

1 40.2

4 0 . 8 3 8 . 3 3 5 . 8 32.2

1 29.3

V^o

1.000 1.017 .952 .890 .803 .730 / ) f B ( p s i ) (DUE BI) i +1110 1 - 600 -1600 - 1 0 6 0 - 680 ^ ^ B ^ B -+.259 - . 1 4 9 ! - . 4 2 5 \ - . 3 1 2 1 - . 2 2 0 10

V^o

V R / ^ O

i 1 T e s t 10 ! ' 1 1 e . 1 0 ^ _ave 3 0 . 4

1 31.5

2 9 . 5 28.1 2 5 . 6 2 3 . 3

V^o

1.000 1.040 .972 .925 .842 .768 (DUE EM) 560 +1060 -220 -1140 - 870 - 720 .. / i f / f . .176

+.320 1

- . 0 7 1 ! - . 3 8 6 j - . 3 2 3 1 - . 2 9 4 Gauge No. 25 ; 26 1 : 27

28 1

29 1 Gauge Group 30 31 ; 32 33 34 35 !

GENERAL ARRANGEMENT

OF TEST PANEL

FIG. I.

DETAILS OF CORNER

FIGS. 3, 4 & 5.

8 IO

LONGITUDINAL EDGE STRESSES END RIB BUILT-IN.

FIG. 3.

IO 8

. 4 -2 -—Va O

LATERAL EDGE STRESSES END RIB BUILT-IN.

FIG. 4.

x / c — i

LOAD DIFFUSION END RIB BUILT — IN.

-* IP-TEE BOOMS. SLAB BOOMS. SLAB BOOMS ECCENTRIC LOADING. FIG. 5.

FIGS. 6.7. & 8.

o x / a — . - -2 . 4

LONGITUDINAL EDGE STRESSES END RIB SIMPLY SUPPORTED

FIG. 6.

1 —

11a O

LATERAL EDGE STRESSES END RIB SIMPLY SUPPORTED

FIG. 7.

6 « / a — ^ "^ "^

LOAD DIFFUSION END RIB SIMPLY SUPPORTED FIG. 8. - O Q— TEE BOOMS SLAB BOOMS SLAB BOOMS ECCENTRIC LOADING 2a F^, Ffo

FIGS. 9, 10 & 11.

LONGITUDINAL EDGE STRESSES END RIB FREE.

FIG. 9.

LATERAL EDGE STRESSES END RIB FREE.

FIG. IO.

LOAD DIFFUSION END RIB FREE. FIG. 11. TEE BOOMS. SLAB BOOMS. SLAB BOOMS ECCENTRIC LOADING. ////////////_ 2a Ffo Ffo

f' P ló»

« / , ' 2 -"/a O

LONGITUDINAL EDGE STRESSES TEE BOOMS

FIG. 12.

LATERAL EDGE STRESSES TEE BOOMS FIG. 13. 1-0 " / f o ^ e - ^ ^ ^ -^'—' / ^ ^ ^ ^ „ J i - - " ' / '.. - - X .^'^"^•^ • a ' . v j ^ ^ © - i t

-si

• ^ — - - ^ =^ o / 2" X—" A" 6 8 10" 12 14 f>-« / a — -2 LOAD DIFFUSION TEE BOOMS FIG. 14. - 0 Q— Ffo

END RIB BUILT-IN END RIB SIMPLY SUPPORTED

END RIB FREE

2a y

FIGS. 15, 16 & 17 2 ' X — • 4 ' 8 IO -Vy/,

w

IO 8 4 " — y 2" x / -_'a •2 — ' / < ,

LONGITUDINAL EDGE STRESSES SLAB BOOMS.

FIG. 15.

LATERAL EDGE STRESSES SLAB B O O M S

FIG. 16.

LOAD DIFFUSION SLAB BOOMS. FIG. 17

END BIB BUILT-IN.

END RIB SIMPLY SUPPORTED.

END RIB FREE.

////////////_

2a

TECHNISCH!: HOGESCHOOL

VLIhGTÜiGüOUWtfUJ^DE

Kanaalstraat 10 - DELFT

FIGS. 18.19. & 20.

o x^,_> .2 .4

LONaTUDINAL EDGE STRESSES ECCENTRIC LOADING .(SLAB BOOMS)

FIG. 18.

10" 8"

2 —y/a

LATERAL EDGE STRESSES ECCENTRIC LOADING (SLAB BOOMS)

FIG. 19.

x / o — -2

LOAD DIFFUSION

ECCENTRIC LOADING (SLAB BOOMS)

END RIB BUILT- IN

END RIB SIMPLY SUPPORTED END RIB FREE

2a

Ffo Ffo

FIGS. 21, 22 & 23 • 6 "/a-—F— •2 Vy-4, ^'\ 'wC-, > i / .-^

7

. = ^ 2

Ho

S%

10 4 -.—y 2 •2 — Va

LONGITUDINAL EDGE STRESSES EFFECT OF END RIB REMOVAL.

FIG. 21.

LATERAL EDGE STRESSES EFFECT OF END RIB REMOVAL.

FIG. 22.

'%

W

LOAD DIFFUSION EFFECT OF END RIB REMOVAL. FIG. 23.

Ft

SLAB BOOMS. END RIB FREE. TEE BOOMS END RIB FREE. NO END RIB. $ L A B BOOMS}

2a