77014�

FLAT PANELS IN SHEAR. POST-BUCKLING ANALYSIS

1. NOTATION

cross-sectional area of flange and associated skin excluding associated plate (see Sketch 1.1)

m2 in2

cross-sectional area of flange, associated skin and associated plate

m2 in2

cross-sectional area of stiffener excluding associated plate (see Sketch 1.1)

m2 in2

flange spacing or length of plate m in

stiffener spacing or width of plate m in

parameter correcting fs for plate aspect ratio

compressive end load in flange of area Afe due to tension field N lbf

allowable tensile stress for plate material in simple tension N/m2 lbf/in2

tensile stress in plate parallel to flange at flange to plate rivet line

N/m2 lbf/in2

average compressive stress in stiffener at centre of its length N/m2 lbf/in2

value of fs at which forced crippling of stiffener occurs N/m2 lbf/in2

maximum compressive stress at heel of stiffener (equal to fs in double stiffeners)

N/m2 lbf/in2

tensile strength of plate material N/m2 lbf/in2

shear modulus of material of plate N/m2 lbf/in2

secant and tangent moduli of panel, respectively (see Section 5) N/m2 lbf/in2

distance between centroids of flanges (area Af) m in

second moment of area of flange (area Af) about an axis through its centroid normal to plate

m4 in4

second moment of area of stiffener (area As) about an axis through its centroid parallel to plate

m4 in4

diagonal tension factor

equivalent pin-ended column length of stiffener m in

maximum bending moment in flange due to tension field N m lbf in

Af

Afe

As

a

b

C

F

fall

fpr

fs

fsc

fsh

ft

G

GS, GT

h

I f

Is

k

l ′

MIssued July 1977

1With Amendment A, April 1983

77014�

Both SI and British units are quoted but any coherent system of units may be used.

Sketch 1.1

net panel shear load parallel to stiffeners N lbf

nominal shear stress in plate Q/(ht) N/m2 lbf/in2

allowable nominal shear stress in plate N/m2 lbf/in2

shear stress at which plate first buckles N/m2 lbf/in2

maximum resultant loading per unit run along plate to flange joint

N/m lbf/in

plate thickness m in

thickness of outstand of simple angle stiffener m in

0.2 per cent proof stress in tension of stiffener material N/m2 lbf/in2

distance between centroid of stiffener (area As) and mid-plane of plate

m in

average width of plate assumed to act with each stiffener in resisting instability under end load due to tension field

m in

Q

q

qa

qb

R

t

tso

t2s

ys

βb

2

77014�

uckled.embers,ssible,ed by

imatelydings onnation ofs. The s

r but willy of thes pattern

loads in thewiffnessate and

ailure

etherandccur.

ension

2. INTRODUCTION

This Item provides data for the analysis of flat panels carrying shear loads in which the plate has bA panel is defined as a thin plate, or sheet, reinforced by a system of longitudinal and transverse mas shown in Sketch 1.1. The panels are assumed to be part of a beam, as in an aircraft spar. It is powith suitable modification, to use the data provided to analyse a continuous array of panels formorthogonal stiffeners on a large sheet.

A panel buckled in shear deforms into a set of inclined waves and carries a tensile stress, approxparallel to the waves, together with a smaller perpendicular compressive stress. This leads to loathe panel edge members. Thus, the stress distribution can be conveniently described as a combia pure shear stress and a “diagonal tension field” acting in the general direction of the buckleproportion of the total shear reacted by diagonal tension is termed the “diagonal tension factor”,k, andcurves of k plotted against q/qb are provided in Item No. 77018*. This Item deals with the analysis of thicomplex post-buckled stress system and the following sections provide the data listed below.

3. GENERAL CONSIDERATIONS AND LIMITATIONS

The data have been derived on the assumption that the panels are loaded uniformly in pure sheausually be applied to beams in which the flanges carry tensile or compressive loads. The majoritdata are based upon experiment and therefore include the effects of any non-uniformity in the stresin the panel. The data apply to panels with with a well developed tension field, q/qb greaterthan about 2, in which case the effect of initial irregularities of manufacture is not significant. Forless than this initial irregularities of the plate may become significant and the discontinuity shownfigures with an abscissa of q/qb at a value of q/qb = 1.0 is unlikely to occur. However, in the region beloq/qb of about 2 it may be more efficient to design a panel in which the stiffeners are of reduced stand the plate of increased thickness so that failure occurs by simultaneous buckling of the plstiffeners.

* Data Item No. 77018 “Curved panels in shear. Post-buckling analysis”. The value of k may be obtained from Figure 1 by taking theradius of curvature as infinite.

Section 4.2 Maximum nominal plate shear stress at (a) failure of the plate at a buckle and (b) fof the plate at the rivet line.

Section 4.3 Compressive stress in the stiffener; also (a) the effective length of the stiffener togwith the skin which may be associated with it in resisting stiffener overall buckling (b) the value of the compressive stress in the stiffener at which forced crippling will o

Section 4.4 End load and bending moment acting on the flanges as a result of the diagonal tfield.

Section 4.5 Load per unit run along the flange to plate connection.

Section 5 Secant and tangent moduli of the panel.

A fully worked example employing these data is given in Section 7.

0.2 b/a 1.0≤ ≤

3

77014� referredstiffenerse plate.ample

actingessives. As a flange.

sitive to

ed to as

lattn frompported

of whichshows as. Withcomingracture, overFigure

nstantof localn Mises Anmadees are

e

The general method of analysis applies only in the elastic range, although some of the other Itemsto herein include data on the effects of exceeding the elastic range. It has been assumed that the and flanges are manufactured from materials having the same value of modulus of elasticity as thIn the event of significantly differing moduli appropriate adjustments should be made, as in the exin Section 7.

When applying the data to a beam in bending it is necessary to determine an effective width of skinwith the area Af . For the compression flange this is likely to be governed by considerations of comprinstability and reference should be made to Data Items dealing with compressive buckling of plateresult of this the effective area of the compression flange is likely to be lower than that of the tensionUse of the compression flange value of Af will result in slightly conservative stresses if Af /(ht) is less thanabout 2; above this value the plate and stiffener stresses and flange loads are relatively insenvariations in Af .

The stiffeners may be attached either to one side of the plate only, in which case they are referr“single stiffeners”, or else to both sides, back to back, as in Sketch 1.1, when they are termed “doublestiffeners”. Both single and double stiffeners are considered.

4. ANALYSIS OF PANEL STRENGTH

4.1 Initial Buckling of the Plate

Figures 4 to 10 of Item No. Struct. 02.03.02* provide data from which the elastic buckling stress of fpanels that form a continuous beam of the type illustrated in Sketch 1.1 may be calculated. (Note that thaItem requires the calculation of the second moment of area of the stiffener to include a contributiothe plate.) In the application of Item No. Struct. 02.03.02 care must be taken when choosing the unsuvalues for the “length” and “width” of the plate, see the example, Section 7.

4.2 Strength of the Plate

4.2.1 Permanent deformation and failure of the plate away from its edges

The buckled plate is subjected to a combination of shear, tensile and bending stresses, the effectsare most severe at the crests of the waves. Therefore, yielding first occurs at these crests, and slight waviness of the plate after unloading without appreciable change of form of the whole panelincreased loading the yielding progresses through the thickness of the plate with the waviness besufficient to cause appreciable permanent deformation of the whole panel. For ductile materials fof the whole plate, by tearing in a direction normal to the principal tensile stress, will not occur untilsome region of the plate, the average stress through the thickness is sufficient to cause failure. 1presents the allowable value of nominal shear stress, qa , plotted as qa/fall against qb/fall for a range of valuesAs/(bt) for both permanent deformation and failure of the plate; for convenience in use lines of coqa/qb are also given. The permanent deformation curves are provided as a guide to the onset waviness of the plate and have been calculated according to the shear strain energy criterion of voand Hencky. When using these curves fall should be taken to be the proof stress of the plate material.estimate of the value of qa at which permanent shear deformation of the whole panel occurs may be by using the proof stress of the plate material in conjunction with the failure curves. The failure curvbased on the principal stress criterion and when used for strength estimation fall may be taken as the tensilstrength of the material of the plate.

* Item No. Struct. 02.03.02 “Flat panels in shear. Buckling of long panels with transverse stiffeners”.

4

77014�re takestrationsly below

ailing

producesessesrincipal

ariation. Stress

ed for

be made tress n

iagonalers are, and

thatsextentaveragess likely

mn forced

eans ofcented

se of a taken

to theeduced erefore,rom the

Figure 1 has been derived on the assumption that the panel boundary members are rigid and therefono account of any non-uniformity of the stress pattern in the plate or of the effects of stress concensuch as those that occur at rivet holes. Therefore, in practice, the plate may fail at stresses slightthe values obtained from Figure 1.

4.2.2 Failure of the plate at the plate-to-flange joint

In practice the stress distribution in the plate along the joint with the flange is different from that prevnearer the centre of the plate (see Section 4.2.1). Figure 2 gives the nominal shear stress, qa , at which, inthe absence of stress concentration effects, the combined stress field acting at the tensile flange failure of the plate. In Figure 2 fall should be taken as the tensile strength of the plate material. The strhave been combined using either the shear strain energy criterion of von Mises and Hencky or the pstress criterion, depending upon which predicts failure at the lower stress. The small effect of the vof the diagonal tension factor has been eliminated by taking the lower envelope to a family of curvesconcentrations due to flexibility of the flanges or to the presence of rivet holes have not been allowand may lead to failure at stresses below the value obtained from Figure 2.

In the presence of a stress concentration a more detailed calculation of the maximum stress can by taking account of the three individual components of the stress field, used in constructing Figure2, andapplying the appropriate stress concentration factor. The three components are a diagonal tensile skq ,a pure shear stress (1 – k)q and a tensile stress fpr . The value of k and the angle of the diagonal tensiostress may be obtained from Item No. 77018.

4.3 Strength of the Stiffener

After the plate has buckled the stiffeners are required to support compressive loads due to the dtension field and to resist the out-of-plane forces associated with the plate buckles. The stiffentherefore prone to failure by buckling, failure by forced crippling associated with the plate bucklefailure of their attachments. Figures 3, 4 and 5 give the average compressive stress, fs , acting on doublesection stiffeners. Note that Figure 5, for Af /(ht) = 0, is provided as a guide to assist interpolation and the parameter C, used to account for panel aspect ratio, is given by Figure 6. In the case of single stiffenerthe reduced stiffness implied by the offset of the stiffener centroid from the plate is to some counteracted by the tendency of the diagonal tension field to keep the stiffener straight. Thus, the stress is similar to that for a double stiffener of the same area. A conservative estimate of the streto approximate to the stress at the heel of a single stiffener is given by using Figures 3, 4 and 5 but replacingAs by and reading fs as fsh. The stresses fs or fsh, together with any stresses arising frosources other than the shear loading, should be compared with the appropriate failure stress icrippling and the various buckling modes as described in the following sub-sections.

4.3.1 Stability of the stiffener

The overall buckling stress of the stiffeners out of the plane of the plate should be estimated by mItem No. Struct. 01.01.01*. When the stiffeners are resisting buckling an effective width of the adjaplate acts with them and Figure 7 gives the coefficient . The effective width of plate should be includin the calculation of the stiffener radius of gyration when using Item No. Struct. 01.01.01. In the castiffener attached to the plate by more than one row of rivets the effective width of plate should beto extend beyond the outer rivet lines. The tension field in the plate gives some restraintstiffener against overall buckling. This may be accounted for by replacing the stiffener length by the requivalent pin-ended strut length, l' , given by Figure 8, when using Item No. Struct. 01.01.01. Figure8does not include an allowance for constraints due to the attachment of the stiffener to the flanges. Thl' may be further reduced by the rotational restraint at the flanges. Since the stiffener load arises f

* Item No. Struct. 01.01.01 “The strength of struts”.

As/ 1 ys2 As/Is+{ }

βbβ

0.5βb

5

77014�tiffenerstrength.cturing

ld be

t simpleal

ed and

ive load

ection

ress rcegree ofded the

es nds due

direct load,

ure

ble, it of otherhe

normal

r

plate it should be considered as acting through the mid-plane of the plate. Consequently, single sare eccentrically loaded and, as Item No. Struct. 01.01.01 shows, this considerably reduces their sFor both single and double stiffeners an allowance should be made for the effects of manufainaccuracies when applying Data Item No. Struct. 01.01.01.

With open section stiffeners the possibility of failure in a torsional-flexural buckling mode shouinvestigated using the method given in either Item No. 89007 or Item No. Struct. 01.01.10*. The plate willprovide restraint against torsional deformation because of the diagonal tension stress so thaestimates of the type set out in Section 7.8.2.2 of the Example are likely to give values below the actutorsional-flexural buckling strength. Local buckling of the stiffener outstand should also be considerData Item No. Struct. 01.01.08† should be used for this purpose.

Failure of the stiffener by forced crippling occurs when the buckled plate, assisted by the compressin the stiffener, forces the stiffener to deform locally with a plate buckle. Figure 9 gives the value of fsc atwhich this occurs. The figure is derived from limited data for unlipped and lipped angle and Z-sstiffeners.

4.3.2 Stiffener riveting

Where the plate and stiffener are riveted together the possibility of buckling between rivets at stfshshould be checked using Item No. Struct. 02.01.08‡. The tension caused by the buckled plate tends to fothe stiffener and plate apart and may cause the rivets to fail. This effect will depend upon the dedevelopment of the tension field and the thickness of the plate. Limited data suggest that, provitensile load capacity per unit run of the riveted assembly exceeds 0.22tft for single stiffeners and 0.15tft fordouble stiffeners, failure in this mode is unlikely.

The stiffener-to-flange joints are required to transmit the compressive load in the stiffener. Figur3, 4and 5 give fs , the average stress in the stiffener at its centre, but the stress is reduced towards the eto the increase in the effective width of plate. This reduction in end load is about 25 per cent at q/qb = 2falling to about 10 per cent at q/qb = 20.

4.4 Strength of the Flanges

The components of the diagonal tension field parallel to and normal to the flanges introduce acompressive load and a bending moment, respectively, into the flanges. The direct compressiveF,may be determined from Figures 10, 11 and 12 which give F/Q plotted against q/qb for various values ofAs/(bt) and Af /(ht); the set of curves for Af /(ht) = 0 is provided as a guide to assist interpolation. Fig13 gives the maximum bending moment in the flange, M, as M/(qtb2) plotted against q/qb . The curve ofFigure 13 is largely based on experimental evidence and, owing to the limited amount of data availais not possible to distinguish where the maximum value of bending moment occurs. In the absenceinformation it is suggested that the maximum bending moment M should be assumed to occur both at tstiffeners and, with opposite sign, midway between them.

The rivets joining the plate to the flanges must transmit the shear complementary to that portion of Q carriedby the plate in pure shear together with the components of the diagonal tension field parallel to andto the flange. The resultant loading has a maximum value, R, in the region of the stiffeners and Figure 14gives R/(qt) plotted against If /(b3t) for a range of values of q/qb . Note that the rivets joining the stiffeneto the flange must additionally transmit the compressive end load in the stiffener, see Section 4.3.2. Figure

* Item No. 89007 “Flexural and torsional-flexural buckling of thin-walled open section struts”. Item No. Struct. 01.01.10 “Torsional instability of stringers and struts of angle section”.

† Item No. Struct. 01.01.08 “Local instability of struts with flat sides”. ‡ Item No. Struct. 02.01.08 “Buckling in compression of sheet between rivets”.

6

77014�

duced. in

.

ibility. cent ifde to

14 may also be used to obtain values of R for plate joints that are parallel to the stiffeners by taking If /(b3t)as infinite.

5. PANEL STIFFNESS

With the development of the diagonal tension field the overall in-plane stiffness of the panel is reThe reduction is represented by the secant modulus, GS , which is the ratio of the nominal shear stressthe plate to the total shear strain of the panel, and by the tangent modulus, GT , which is the rate of increaseof nominal shear stress in the plate with total shear strain of the panel. Figures 15 to 17 and 18 to 20 givethe ratios GS/G and GT /G , respectively, plotted against q/qb for various values of As/(ht) and Af /(ht) . Thecurves of Figures 17 and 20 give a theoretical limit only and are presented as a guide to interpolation

Figures 15 to 20 are derived on the assumption that the flanges do not bend. The effect of flange flexin the plane of the panel is to reduce the value of both GS /G and GT /G below that shown by the curvesThe reduction is less than 10 per cent if is less than 0.5, and less than 5 perit is less than 0.2. For further information on the effect of flange flexibility, reference should be maDerivation 10.

A( s βbt)b3/ 360I f h( )+

7

77014�

o.

rt I -aft

rt IIaft

III -aft

IV -t No.rch

s beenSO,

icaln

ce.n

ity.

6. DERIVATION

1. NADAI, A. Plasticity. Chapters 12 and 13. Published by McGraw-Hill Book CInc., New York, 1931.

2. CROWTHER, F.HOPKINS, H.G.

An experimental investigation into plate web spars under shear. PaSpar with 24 S.W.G. web. Report No. SME 3276, Royal AircrEstablishment, Farnborough, UK, February 1944.

3. CROWTHER, F.SANDERSON, N.

An experimental investigation into plate web spars under shear. Pa- Spar with 20 S.W.G. web. Report No. SME 3383, Royal AircrEstablishment, Farnborough, UK, October 1946.

4. CROWTHER, F.SANDERSON, N.

Experimental investigation into plate web spars under shear. PartSpar with 16 S.W.G. web. Report No. Structures 7, Royal AircrEstablishment, Farnborough, UK, February 1948.

5. CROWTHER, F.SANDERSON, N.

Experimental investigation into plate web spars under shear. Part Destruction tests on spars with 24, 20 and 16 S.W.G. webs. ReporStructures 8, Royal Aircraft Establishment, Farnborough, UK, Ma1948.

6. LEGGETT, D.M.A. The stresses in a flat panel under shear when the buckling load haexceeded. R and M No. 2430, Aeronautical Research Council, HMLondon, 1950.

7. KUHN, P.PETERSON, J.P. LEVIN, L.R.

A summary of diagonal tension. Part I - Method of analysis. TechnNote No. NACA-TN-2261, National Advisory Committee oAeronautics, Langley Field, Va, USA, October 1951.

8. KUHN, P.PETERSON, J.P. LEVIN, L.R.

A summary of diagonal tension. Part II - Experimental evidenTechnical Note No. NACA-TN-2662, National Advisory Committee oAeronautics, Langley Field, Va, USA, January 1952.

9. KUHN, P. Stresses in aircraft and shell structures. Chapter 3, pp. 47-94.Published by McGraw-Hill Book Co. Inc., New York, 1956.

10. SIMMONS, J. Shear moduli for flat panels and the effect of flange flexibilJ. R. aeronaut. Soc., Vol. No. 61, pp. 694-700, October 1957.

8

77014�

on

7. EXAMPLE

7.1 Additional Notation for this Example

It is convenient to declare the following additional symbols for use in the example described in Secti7.2.Note that where other Data Items are employed their notation will be used without definition.

modulus of elasticity of material N/m2 lbf/in2

tangent modulus of material N/m2 lbf/in2

compressive stress in flange N/m2 lbf/in2

tensile stress in flange N/m2 lbf/in2

stress at which ET = ½E (see Item No. 76016) N/m2 lbf/in2

tensile stress acting along flange at flange-to-plate rivet line N/m2 lbf/in2

tensile strength of plate material N/m2 lbf/in2

torsion constant of cross-sectional area of stiffener (area As) m4 in4

radius of gyration of stiffener (area As) about an axis through its centroid parallel to plate

m in

material characteristic (see Item No. 76016)

direct load acting on flange (area Afe) due to bending moment applied to panel in plane of plate

N lbf

distance between centroid of flange (area Af) and mid-plane of skin

m in

distance between centroid of flange (area Afe) and innermost fibre of flange

m in

distance between centroid of flange (area Afe) and innermost rivet line

m in

Suffixes

The following suffixes may be applied to the notation of Section 1 as well as to the above notation.

effective value calculated including a contribution from plate

relates to flange

relates to stiffener

Both SI and British units are quoted although only SI units are used in this example.

E

ET

ffc

fft

fn

ffr

ftp

Js

ks

m

Pf

yf

yfie

yf re

e

f

s

9

77014�

sidel puttingin Tabled by this

7.2 Panel Description and Loading

The panel shown in Sketch 7.1 is subjected to a downward shear load of 49.9 kN from the right-handand a bending moment in the plane of the plate of magnitude 200 kN m at the centre of the panethe upper flange in tension. The material properties of the various elements of the panel are given 7.1. The following sub-sections set out an analysis of those aspects of the panel strength covereItem.

Sketch 7.1 All dimensions in mm.

TABLE 7.1

Property Units PlateStiffeners,

flanges and skin

E MN/m2 74 500 63 400

G MN/m2 28 600 24 400

t2 MN/m2 341 332

ft MN/m2 386 417

fn MN/m2 305 296

m 19 17

10

77014�

n inanges

loyed inas given

7.3 Geometric Properties of the Panel and its Elements

From the dimensions given in Sketch 7.1 the geometric properties of the panel and its elements giveTable 7.2 may be calculated. The following values assume that the skin directly in contact with the flacts as part of the flanges and similarly, with flange and stiffener properties suffixed e, that the plate directlyin contact with them also acts as part of the flange or stiffener. These simple assumptions are empthis example to illustrate how the different properties may be used. It should be noted that the arein Table 7.2 make no allowance for the loss of area due to rivet holes.

From the properties given in Table 7.2 and the overall dimensions given in Sketch 7.1 the following valuesmay be determined.

mm,

mm

and mm.

Thus,

and .

7.4 Panel Shear Loading

The net panel shear load is 49.9 kN so that q, which is based upon h, is

MN/m2.

TABLE 7.2

The flanges The stiffeners

= 2000 mm2 = 2060 mm2 = 125 mm2

= 521 000 mm4 = 522 000 mm4 = 20 000 mm4

= 14.7 mm = 15.6 mm = 11.2 mm

= 40.2 mm = 12.6 mm

= 28.2 mm = 120 mm4

= 200 mm4

Afe Afe As

I f I fe Is

yf yfe ys

yfie ks

yfre Js

Jse

a 448=

h 448 2 551.62

------- 14.7–+

+ 530= =

he 530 2 15.6 14.7–( )– 528= =

Af

ht-----

2000530 1.2×------------------------ 3.14= =

As

bt-----

125283 1.2×------------------------ 0.368= =

q49.9 10

3×

530 103–

1.2 103–×××

---------------------------------------------------------------= 78.5=

11

77014�

es are

ach

7.5 Plate Buckling Stress (Section 4.1)

This is calculated using Item No. Struct. 02.03.02 and, working in the notation of that Item, gives

,

and .

Thus, from Figures 7 to 10 of Item No. Struct. 02.03.02, by extrapolation, K = 9.2 so that

MN/m2.

Therefore, .

7.6 Flange Strength (Section 4.4)

7.6.1 Flange loads and moments

The average load in both flanges due to the applied bending moment is

kN.

The average load in the flanges due to the shear loading is found from Figures 10, 11 and 12. The valuesof the moduli of the stiffeners and flanges are different from those of the plate. However, the valusufficiently close to allow for the effect by simply factoring Af and As by the ratio of the moduli. Therefore

and .

Thus, from Figures 10, 11 and 12, at q/qb = 6.38, F/Q = 0.23 and hence the compressive end load in eflange due to the tension field is

kN.

The bending moment in the flanges is obtained from Figure 13. At q/qb = 6.38, M/(qtb2) = 0.0336 giving

= N m.

µEsIb

Ea2t3

---------------

1/263 400 10

620 000 10

12–283 10

3–×××××

74 500 106

448 103–×( )

21.2 10

3–×( )3

×××------------------------------------------------------------------------------------------------------------------------

1/2

3.73= = =

GJEsI--------

24 400 106

200 1012–×××

63 400 106

20 000 1012–×××

-------------------------------------------------------------------------------- 0.0038= =

ab---

448283--------- 1.58= =

qb 9.2 74 500 106

1.2 103–/283 10

3–××( )2

×××= 12.3=

q/qb78.512.3----------= 6.38=

Pf200 10

3×

528 103–×

----------------------------= 379=

Af

ht----- 3.14

63 40074 500-----------------× 2.67= =

As

bt----- 0.368

63 40074 500-----------------× 0.313= =

F 0.23 49.9 103××= 11.5=

M 0.0336 78.5 106

1.2 103–

283 103–×( )

2×××××= 253

12

77014�

is

re and is

n,

7.6.2 Flange stresses

The flange stresses are given by the addition of the direct and bending stresses; thus,

.

The maximum stress in the compression flange occurs at the stiffeners at the innermost fibre and

MN/m2.

The maximum stress on the tension flange occurs midway between the stiffeners at the innermost fib

MN/m2.

The maximum stress at the inner rivet line of the tension flange is

MN/m2.

7.6.3 Flange riveting

The load transmitted by the rivets is obtained from Figure 14.

and, at

giving kN/m.

7.7 Plate Strength (Section 4.2)

The plate strength away from its edges is estimated using the curves of Figure 1 with q/qb = 6.38 andAs/(bt) = 0.313 (Section 7.6.1). The figure gives, for failure, qa /fall = 0.457 and, for permanent deformatioqa/fall = 0.307. Thus, using these ratios with the values of the plate material data gives:

nominal shear at plate failure

MN/m2,

Pf F+( ) /Afe Myf+ /I fe

ffc379 10

311.5 10

3×+×

2060 106–×

------------------------------------------------------------ 253 40.2 10

3–××

522 000 1012–×

----------------------------------------------+=

190 106

19 106×+×= 209=

fft379 10

311.5 10

3×–×

2060 106–×

------------------------------------------------------------

19 106×+=

178 106

19 106×+×= 197=

ffr 178 106 253 28.2 10

3–××

522 000 1012–×

----------------------------------------------+×= 192=

I f

b3t

--------521 000 10

12–×

283 103–×( )

31.2 10

3–××----------------------------------------------------------------------- 0.019= =

q/qb 6.38,= R/ qt( ) 1.12=

R 1.12 78.5 106

1.2 103–××××= 106=

qa 0.457 386 106××= 176=

13

77014�

nominal shear stress at local permanent deformation is

MN/m2

and the nominal shear stress at general permanent deformation is

MN/m2.

The plate strength along the plate-to-flange joint is estimated using Figure 2. From Section 7.6.2 ffr is192 MN/m2 . The corresponding tensile stress in the plate at the same strain* as ffr is

MN/m2.

Then, using the value of ft for the plate given in Table 7.1,

so that, from Figure 2, giving MN/m2.

7.8 Stiffener Strength (Section 4.3)

7.8.1 Stiffener stresses

The average compressive stress acting at the centre of the stiffener is determined using Figures 3 to 6. Thus,with q/qb = 6.38, As/(bt) = 0.313 and Af /(ht) = 2.67 Figures 3 to 5 give, by interpolation, fs/(qC) = 0.605.Then, from Figure 6, at b/h = 283/530 = 0.534, C = 1.16. Therefore,

MN/m2.

The stiffeners are single-sided and the stress at the stiffener heel is obtained by replacing As/(bt) by

.

Then using Figures 3 to 5 as before but with As/(bt) = 0.176 gives fs/(qC) = 0.77 = fsh/(qC). Therefore,

MN/m2.

* If the stress in either the flange or the plate exceeds the limit of proportionality Item No. 76016 should be consulted.

qa 0.307 341 106××= 105=

qa 0.457 341 106××= 156=

fpr 192 106 74 500 10

6×

63 400 106×

---------------------------------

××= 226=

fpr

ft------

226386--------- 0.585= =

qa

ft----- 0.47= qa 0.47 386 10

6××= 181=

fs 0.605 78.5 106

1.16×××= 55=

As

bt 1 ys2As/ I s+( )

-----------------------------------------125

283 1.2 1 11.22

125/20 000×+( )×

------------------------------------------------------------------------------------------63 40074 500-----------------

0.176= =

fsh 0.77 78.5 106

1.16×××= 70=

14

77014�

r is ;

wing

7.8.2 Stiffener stability

7.8.2.1 Overall buckling

This is checked using Item No. Struct. 01.01.01. The average width of plate acting with the stiffeneand, from Figure 7, . Thus the effective area of the stiffener becomes

mm2,

the effective second moment of area becomes

mm4,

giving an effective radius of gyration of

mm

and the offset of the combined neutral axis from the mid-plane of the plate is

mm.

From Figure 8, at q/qb = 6.38 and b/h = 0.534 (Section 7.8.1), l'/h = 0.882 so that l' = 0.882 × 530 = 467mm. Then, in the notation of Item No. Struct. 01.01.01,

,

mm

and allowing for initial eccentricity of manufacture of 1.0 mm then

.

Taking , from Table 7.1 .

Then interpolating and extrapolating from Figures 3 to 6 of Item No. Struct. 01.01.01 gives f/fn = 0.61 so that

N/m2 = 181 MN/m2.

The average stress in the stiffener at overall buckling = 181 MN/m2. (From Section 7.8.1, applied stress= 55 MN/m2.)

7.8.2.2 Torsional-flexural buckling

This is checked using Item No. Struct. 01.01.10. Working in the notation of that Item the folloproperties and ratios are determined mm, l is taken as the stiffener length of 530 mm , is calculated using Item No. Struct. 00.07.01* (assuming no bulb) as = 1.05 × 1.63 × 39.23/18 = 14 400

* Item No. Struct. 00.07.01 “Torsion and secondary warping constants for a bulb angle”.

βbβ 0.31=

Ase 125 0.31 283 1.2××+ 125 105+ 230= = =

I se 20 000 105+ 11.22 105 11.2×( )2

230-----------------------------------–× 27 200= =

kse 27 200/230( )1/210.9= =

11.2 105 11.2/230×– 6.1=

l ′k---

fnE----

1/2

46710.9----------

29663 400-----------------

1/2

2.93= =

c k2/y 10.9

2/ 6.1 1.2/2+( ) 17.7= = =

e/c 1.0 6.1+( ) /17.7 0.40= =

fall t2s= fall / fn 332/ 296( ) 1.12= =

f 0.61 296 106××=

k( ks)≡ 12.6= Γ2Γ2

15

77014�

ling. so that

mm6 , mm4 giving

and .

Therefore, from the figure of Item No. Struct. 01.01.10,

.

The section constant Ip is the polar moment of inertia of the stiffener about its point of rotation on buckThe point of rotation will be assumed to be mid-way between the heel and the stiffener-to-plate rivet

mm4.

Hence, MN/m2.

Thus, the average stress in the stiffener at torsional buckling = 61 MN/m2. (From Section 7.8.1, appliedstress = 55 MN/m2.)

7.8.2.3 Local buckling

This is checked using Item No. Struct. 01.01.08. Working in the notation of that Item, d/t = (40 – 1.6/2)/1.6= 24.5 and (fn/E)1/2 = (296/63 400)1/2 = 0.068 so that f/fn = 0.21 giving

MN/m2.

Thus the average stress in the stiffener at local buckling of the outstand = 62 MN/m2 . (From Section 7.8.1,applied stress = 55 MN/m2.)

7.8.3 Forced crippling of the stiffener

From Figure 9, at q/qb = 6.38 and tso/t = 1.6/1.2 = 1.33, fsc/t2s = 0.29 giving

MN/m2.

Thus the stiffener heel stress at which forced crippling occurs = 96 MN/m2. (From Section 7.8.1, appliedstress = 70 MN/m2.)

J ( Js)≡ 120=

EΓ2

GJk2

-------------63 400 10

614 400 10

18–×××

24 400 106

120 1012–

12.6 103–×( )×

2×××

--------------------------------------------------------------------------------------------------------------------- 1.96= =

l /k 530/12.6 42.06= =

ft Ip

GJ-------- 1.015=

I p1.63

------- 403

303

103

+ +( ) 49 100= =

ft1.015 24 400 10

6120 10

12–××××

49 100 1012–×

--------------------------------------------------------------------------------------------- 61= =

f 0.21 296 106×× 62= =

fsc 0.29 332 106×× 96= =

16

77014�

Item

earanges of

ners of

7.8.4 Stiffener riveting

7.8.4.1 Inter-rivet buckling

This is checked using Item No. Struct. 02.01.08. Working in the notation of that fn/(KE) = 305/ (3 × 74 500) = 0.00136, l/t = 50/1.2 = 41.6 and, at m = 19, fe/fn = 0.347 giving

MN/m2.

Thus the stress at which inter-rivet buckling occurs = 106 MN/m2. (From Section 7.8.1, applied stress =70 MN/m2.)

7.8.4.2 Load on flange-to-stiffener rivets

The average stress acting in the stiffener is 55 MN/m2 which implies a load of 55 × 106 × 125 × 10–6 =6.87 kN. As described in Section 4.3.2 part of this load is picked up from the flanges by the plate. Lininterpolation between the reduction values indicated in that section suggests a stiffener load at the fl

kN.

Thus the load on each rivet = 2.7 kN.

7.9 Panel Stiffness (Section 5)

The secant and tangent moduli of the panel are determined from Figures 15 to 20. Checking for flangeflexibility as described in Section 5

.

Therefore since 0.052 « 0.5 the curves may be used without correction. From Section 7.6.1, Af /(ht) = 2.67and As/(bt) = 0.313 so that, at q/qb = 6.38 (Section 7.5), Figures 15 to 20 give

and

The lower of the above two shear moduli implies a panel shear deflection over the pitch of the stiffe

m or mm.

fe 0.347 305 106×× 106= =

6.87 103× 1 0.25

0.1520 2–( )

--------------------- 6.38 2–( )–

– 5.4=

As βbt+( )b3

360I f h----------------------------------

125 106–

105 106–×+×( ) 283 10

3–×( )3

360 521 000 1012–

530 103–××××

---------------------------------------------------------------------------------------------------------- 0.052= =

GS/G 0.71,= so that GS 0.71 28 600 106××= = 20 300 MN/m

2

GT/G 0.62,= so that GT 0.62 28 600 106 ××= = 17 700 MN/m

2.

78.5 106×

17 700 106×

--------------------------------- 283 103–×× 0.00126= 1.26

17

77014�

FIGURE 1

FIGURE 2

qb

fall

0.0 0.1 0.2 0.3 0.4 0.5 0.6

qa

fall

0.2

0.3

0.4

0.5

0.6

Failure

Permanent deformation

As

bt

0.3

1.0

∞

0.3

1.0

∞

20

qa

qb125

fpr

fall

0.0 0.2 0.4 0.6 0.8 1.0

qa

fall

0.0

0.1

0.2

0.3

0.4

0.5

18

77014�

FIGURE 3

FIGURE 4

qqb

0 2 4 6 8 10 12 14 16 18 20

fsqC

0.0

0.2

0.4

0.6

0.8

1.00.1 0.2

0.5

1.0

2.0

As

bt

Af

ht----- 10≥

qqb

0 2 4 6 8 10 12 14 16 18 20

fsqC

0.0

0.2

0.4

0.6

0.8

1.0 0.1 0.2

0.5

1.0

2.0

As

bt

Af

ht----- 1.0=

19

77014�

FIGURE 5

qqb

0 2 4 6 8 10 12 14 16 18 20

fsqC

0.0

0.2

0.4

0.6

0.8

1.00.1 0.2 0.5

1.0

2.0

As

bt

Af

ht----- 0=

20

77014�

FIGURE 6

bh

0.0 0.2 0.4 0.6 0.8 1.0

C

1.0

1.1

1.2

1.3

1.4

1.5

1.0

1.5

20.0

15.0

10.0

7.06.05.0

4.0

3.0

2.5

2.0

qqb

21

77014�

FIGURE 7

FIGURE 8

qqb

0 2 4 6 8 10 12 14 16 18

β

0.0

0.1

0.2

0.3

0.4

0.5

∞

bh

qqb

0 2 4 6 8 10 12 14 16 18

l'h

0.5

0.6

0.7

0.8

0.9

1.0≥ 1.5

0.2

0.5

1.0

∞

22

77014�

FIGURE 9

qqb

2 6 10 14 18 22 260 4 8 12 16 20 24

fsc

f2s

0.0

0.1

0.2

0.3

0.4

0.5tso

t

0.5

0.75

1.0

1.25

1.51.752.0

tso

t

23

77014�

FIGURE 10

FIGURE 11

qqb

0 2 4 6 8 10 12 14 16 18 20

FQ

0.1

0.2

0.3

0.4

As

bt

0.1

1.0

≥ 20

Af

ht----- 10≥

qqb

0 2 4 6 8 10 12 14 16 18 20

FQ

0.1

0.2

0.3

0.4

As

bt

0.1

1.0

≥ 20

Af

ht----- 1.0=

24

77014�

FIGURE 12

FIGURE 13

qqb

0 2 4 6 8 10 12 14 16 18 20

FQ

0.1

0.2

0.3

0.4

0.1

1.0≥ 20

As

bt

Af

ht----- 0=

qqb

0 1 2 3 4 5 6 7 8 9

M

qtb2

0.00

0.01

0.02

0.03

0.04

∞

25

77014�

FIGURE 14

FIGURE 15

If

b3t

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

Rqt

0.0

0.5

1.0

1.5

2.0

2.5qqb

2010531 Asymptotic to

1.151.101.051.00

qqb

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0

Gs

G

0.0

0.2

0.4

0.6

0.8

1.0As

bt

≥ 20

1.0

0.5

0.1

∞

Af

ht----- 10≥

26

77014�

FIGURE 16

FIGURE 17

qqb

0 2 4 6 8 10 12 14 16 18

Gs

G

0.0

0.2

0.4

0.6

0.8

1.0

∞

As

bt

≥ 20

1.0

0.5

0.1

Af

ht----- 1.0=

∞qqb

0 2 4 6 8 10 12 14 16 18

Gs

G

0.0

0.2

0.4

0.6

0.8

1.0

As

bt

0.1

0.5

1.0

≥ 20

Af

ht----- 0=

27

77014�

FIGURE 18

FIGURE 19

qqb

0 2 4 6 8 10 12 14 16 18

GT

G

0.0

0.2

0.4

0.6

0.8

1.0

As

bt

≥ 20

1.0

0.5

0.1

∞

Af

ht----- 10≥

qqb

0 2 4 6 8 10 12 14 16 18

GT

G

0.0

0.2

0.4

0.6

0.8

1.0

As

bt

≥ 20

1.0

0.5

0.1

∞

Af

ht----- 1.0=

28

77014�

FIGURE 20

qqb

0 2 4 6 8 10 12 14 16 18

GT

G

0.0

0.2

0.4

0.6

0.8

1.0

As

bt

≥ 20

1.0

0.50.1

∞

Af

ht----- 0=

29

77014�

2.03.12llowing

ertookequent

THE PREPARATION OF THIS DATA ITEM

The work on this particular Item, which supersedes Items Nos Struct. 02.03.00, and 02.03.03 to 0(inclusive), was monitored and guided by the Aerospace Structures Committee which has the foconstitution:

The work on this Item was carried out in the Strength Analysis Group. The member of staff who undthe technical work involved in the initial assessment of the available information and the subsdevelopment of the Item was

ChairmanMr K.H. Griffin – Cranfield Institute of Technology

Vice-ChairmanMr I.C. Taig – British Aircraft Corporation Ltd, Preston

MembersMr H.L. Cox – IndependentDr T.W. Coombe – British Aircraft Corporation Ltd, FiltonMr R.S. Dabbs – Hawker Siddeley Aviation Ltd, KingstonDr G.Z. Harris – Royal Aircraft EstablishmentProf W.S. Hemp – University of Oxford

Dr W. Lansing*

* Corresponding Member

– Grumman Aerospace Corp., Bethpage, NY, USA

Mr K.R. Obee – Hawker Siddeley Dynamics Ltd, HatfieldMr J.G. ten Asbroek – Fokker-VFW N.V., Schiphol-Oost, The NetherlandsMr F. Tyson – Scottish Aviation Ltd

Mr K. van Katwijk* – European Space Agency, Noordwijk, The Netherlands.

Mr M.E. Grayley – Group Head.

30