Bruhn - Analysis And Design Of Flight Vehicles Structures Episode 3 part 9 potx

In general, this type of beam web design is not widely used in flight vehicle structures because it is heavy construction since the web thickness must be relatively large to prevent buck

ANALYSIS AND DESIGN OF FLIGHT VEHICLE STRUCTURES

of 398 lb Thus rivets could be spaced further

apart as margin of safety is rather large

The rivets attaching the skin to the upper

flange should be spaced to prevent inter-rivet

buckling of the skin, since the skin was

assumed effective in computing the beam moment

of inertia The rivets attaching the lower

skin to the lower angles would be checked for

the shear flow load and not for inter-rivet

buckling since skin is in tension The general

subject of rivet design for structures is

treated in Chapter Dl

The web stiffeners at the external load

points and at the beam support points must be

designed to transfer the concentrated load to

the beam web Refer to Chapter A2Z1, which

treats of loads in such stiffeners

General Comments

The reader should understand that the

margin of safety for the beam web in the pre-

ceding beam check was based on the design

requirement of no initial buckling under the

design load The buckling stress as calculated

is not the stress that would cause wed to fail

or collapse, as the web could take considerably

more load in the buckled state The subject of

beam design with buckling webs is treated in

Chapter C11

In general, this type of beam web design

is not widely used in flight vehicle structures

because it is heavy construction since the web

thickness must be relatively large to prevent

buckling and the cost of fabrication and

assembly is relatively high because of many

parts and much riveting The aerospace

structures engineer decreases these disadvant-

ages by using a web sheet with closely spaced

C10 15 peads or a series of flanged lightening holes which stabilize web against buckling and provide low fabrication and assembly cost This type of web design is treated in Part 2 of this chapter

C10, 15a Use of Longitudinal Stitfener to Increase Bending

Buckling Stress of Web Sheet

The strength check of the beam in the example problem showed that the compressive stress on the wed due to beam bending was the factor that had great effect in producing the wed buckling This web weakness can be improved

by adding a single longitudinal stiffener on the compression side as illustrated in Fig C10.16

Theoretical and experimental information on the effect of such a stiffener is quite limited (see Ref 3) Such a stiffener can raise the buckling coefficient kp to around 100 or more, thus the web can be made somewhat thinner if bending stresses are critical Adding this longitudinal stiffener means another structural part and more assembly cost and therefore such construction is not widely used although it

is a structural arrangement that will save structural weight under certain conditions of peam depth, span and external loading

C10, 16

DESIGN OF METAL BEAMS WEB SHEAR RESISTANT (NON-BUCKLING) TYPE

PART 2 OTHER TYPES OF NON-BUCKLING BEAM WEBS

(BY W F McCOMBS)

C10.16 Other Types of Web Design

At this point it should be noted that the

web design discussed in Part 1 required a large

number of parts (the stiffeners) to achieve

lightness To keep manufacturing costs down,

the number of parts must be kept to a minimum

A balance, or economic compromise must be

found between manufacturing expense and weight

penalty This can be arrived at since in avery

airplane design some “dollar” penalty can be

assigned to every extra pound of weight The

exact figure will depend upon the type of

airplane being designed Thus, eliminating

parts may incur some weight penalty but if the

savings in manufacturing cost is greater, then

the reduction in parts is economical

Three types of shear resistant, non~

buckling webs are frequently used in aircraft

design to save the expense of stiffeners

Actually, the web in most cases is as light,

or lighter, than a web with separate stiffeners

There is a general limitation, however, in

that a stiffener must be provided wherever a

significant load is introduced into the beam

The web types are:

a) web with formed vertical beads at a

minimum spacing

b) web with round lightening holes having

45° formed flanges at various spacing

€) wed with round lightening holes having

formed beaded flanges and vertical formed beads between holes

he webs with holes, (b) and (c}, also provide

lots of built-in access space for the many

nydraulic and electrical lines and control

linkages in alrplanes

C10,17 Beaded Webs

Figure C10.17 shows 2 web having "male”

peads formed into it at the minimum spacing

forming will allow The cross-section of the

bead ts described in Table C10.5

Fig, C10 17

Table C10 5

t B R t B R 080 | 95 | 38 0T2 |.1.65 | 1.15

925 | 1.05 | 40 081 | 1.73 | 1.30 1

.032_,| 1.16.) 82 -091 | 1.81 | 1.45 {

.040 | 1.27 | 64 102 |1.92 | 1.63 U51 | 1.42 | BL 125 |2.12 | 2.06 084 | 1.55 | 1,02 {

The allowable shear flow, q in pounds per inch at collapse, is given in Fig C10.18, by the solid lines The dotted lines indicate initial buckling setting in but this is not failure (which is given by the solid lines)

This is the strongest of the web systems not having separate stiffeners failure occurs

ANALYSIS AND DESIGN OF FLIGHT VEHICLE STRUCTURES when the beads collapse an example will follow

later in Cl0.19 A suitable stiffener must be

used (replacing 4 bead) wherever a load is

introduced to prevent earlier collapse of the

bead The allowables are for pure shear only,

no normal loads (see art 03.3)

10.18 Webs With Round Lightening Holes Having

Formed 45° Flanges

This is a simple easily formed web Fig

€10.19 shows such a beam with a cross-section

through the web at the holes The geometry of

the hole and its flanges is given in Table

CLO.6 for typical rorming

The N.A.C.A has developed, from an extensive

test program, an empirical formula that gives

the allowable shear flow (collapse) for webs

having this type of hole Referring to Fig

C10.19, the allowable shear flow is, from

Ref (2)

= ‘ (Dy 2 fx | ct Maun.” * t[s, Œ - g9) + se fr 3

fs, = Collapsing shear stress of a long plate of width c and thickness t, obtained from Fig C10.20

pb = hole centerline spacing

h = height of web, between flange to wed rivets

Cc! = C-2B where B is given in Table C10.5 for a typical hole

Cc =b~0D

For this type of web design, in general, those webs designed to take ultimate load will probably not show any permanent set at yield

Fig C10 20

material, ca

over the net sections, C' x t and xt, is

In general, it will be found, from formula

(18), that the larger holes (about D * 8h) with

wider spacings, b, will give the lightest web

in designing for a given shear flow q, but the

stiffness will de less, of course

Again, the allowables per formula (18) are

for pure shear only, no normal loads on the

wed Thus a stiffener must be provided wherever

a load is introduced into the beam and also in

areas where the beam may nave significant

curvature as in round and elliptical bulkheads,

An example is given in see Chapter D3.8

DESIGN OF METAL BEAMS WEB SHEAR RESISTANT (NON-BUCKLING) TYPE

In addition to the above (collapse), the

wed should be checked for met shear stresses

through the holes to be sure that ÝSNgp “ Psu

at ultimate load, q x h

For a more complete discusston of this type

of web design and the test data, the reader should review Refs (2) and (1) Design charts can be prepared from formula (18), Fig ¢10.18, and Table C10.6 for use in designing without having to resort to formula (18) Figure Cl0.21 shows such a chart taken from Ref (2) for the cases of D/n = 80 and D/h = 50,

10.19 Webs With Round Beaded Flange Lightening Holes

and Intermediate Vertical Male Beads

A third type of web has round

beaded flanges and vertical "male”

between the holes Such 4 beam is Fig C10.e2 The vertical bead is

in Table C10.5 The beaded flange described in Table C10.7 For the

9.0

a

holes with beads shown in

as described shown ts particular

case where ™ 6 and the hole spacing is equal to h, the allowable shear flows shown in Fig C10.23 apply

bh Load

ANALYSIS AND DESIGN OF FLIGHT VEHICLE STRUCTURES

The solid lines of Fig C10.23 give the

ultimate strength, q, of the wed as a function

of web height, h This represents the total

collapsing strength of tne wed The dotted

lines indicate the shear flow, q, at which

initial buckling begins if the 0.0 1s greater

than 6 x 1, or if the spacing of holes is

Fig C10 23

CHANCE VOUGHT AIRCRAFT, INCORPORATED REFERENCE: STRUCTURAL DESIGN MANUAL SECTION 4.230

ME

1 Vatuen are for room temperaters ze only oo,

L Curnes sgpty vuen 2:2: 6;

h - HEIGHT OF PANEL - INCHES

DESIGN CURVES FOR CLAD 2024-T4 AND 7075-T6

SHEAR PANELS WITH CVC-3030 LIGHTENING HOLES AND STIFFENED BY MALE BEADS

BEADED SHEAR PANELS WITH LIGHTENING HOLES

reduced, the 2 data is included fo other cases, Arts

is for pure shear only, no n loading stiffeners must be u vertical bead locally} and ar

In such cases some extra margin of safety aocve the shear load is usually used, depending upon the designers judgment and/or substantiating element tests Where large distributed loads are involved, aS ina Deam supporting a fuel cell, or where the beam curvature is significant (See 03.8), stiffeners should be used for the lightest cesign

AS @ final note, whenever using webs with formed beads as in 010.16 and C10.18, it is important that the beads be formed with a length long enough to extend as close to the beam flanges as assembly will allow Short beads, ending well away from the flanges, will not develop the strength indicated by tha allowadles given in the figures Rivets attaching the web

so the flange above a hole also need be more closely spaced to take the nigher "net" shear locally,

C10.20 Example Problems

determine For the beam shown tn Fig 010.24,

the web gages required Zor a) a beaded web, as in C10.16

bd) a 45° flanged hole web as in C10.17

c) a beaded flange hole wep with inter- mediate beads as in C10.18

Tne beam shown in Fig ©10.24 has the external dimensions and design load $ beam son tn Tig 010.14 and used for example problem in Part 1 of this <

chese example problems, we are replac web design by the three variations fal, fe)

(0) and Since the webs cannot be considered full;

3750# Ị 37504!

j~H— 25" 25 a a 25" —

Fig C10 24

C10 20

effective in resisting beam bending stresses,

the flanges would be stressed slightly higher

than found in the example problem of Part 1,

Using the same Deam dimensions and beam design

loading will provide a comparison of the web

weights for the various web designs

Using the simplified formula, the shear

flows in bays A and B are

Thus, for lightest weight, 2 web gages

should be used, the lighter one for bays "8",

and these could be spliced at the loading

stiffeners introducing the 2400 lb loads

a) Beaded web Gage Requirements

Entering Fig ClO.18 with q = 526 1b./in

and 4 = 7.125" we find that the minimum

acceptable gage is 051" Thus the wed

of Bay A should be 051", giving

41iox,Š 770 lb./in., from ?ig C10.18,

M.S = zo “==“~ S26 1= — „46

Repeating for the web of Bay B, enter with

q = 189 1b./in and h = 7.125" and find

the minimum acceptable gage is 032, which

has Vr ° 310 lb./in Thus for Bay B,

~ 310

“ES = "Teg ~ ls 64

bd) a 45° Flange Round Lightening Hole

Since the larger diameter (and more widely

spaced) holes are more efficient weight-

wise, try a nole having D = 8h or D =

5.61" from Table €10.6 Spacing two holes

1n the 25" bays would indicate a Spacing

2 = 12.5" Then, from C10.19

C=b-D = 12.5-5.5 = 6.9

B = 19, from Table Cl0.6 o'= 0-28 = §.9~2 (.19) = 5.52 Now determine the allowable value of q

for, say, t = 081" for Bay a

te = —Y_ = 526 (7.125) = 3750

SNET (n-D)t (7.125-5.61)(.081) .1

= 30,500 Thus, MS.) 3 22 - 1 09

m

=_ 5u, „ 27,000 5

T5 nượn Toypp 50,500 ~ + * 28h

Repeating with the above geometry and using

t = 051 for Bay "B" where q = 189 lb./in.,

be obtained It can be seen that the example gages are confirmed by the data of Fig C10.21 extrapolating in the case of the 081 wed

A Beaded Flange Hole with Intermediate Vartical Seads

Tne geometry for this is as previously

discussed (0.0 ~ 6n and b =n}

First determine gage for Bay A Entering Fig Cl0.23 with h = 7.125" and q =

526 lb./in., the closest acceptable gage

1s t = 064 (solid line), giving

Repeating for Bay B with q = 189 and

h = 7.125" the closest acceptable gage is

Actually, a hole with 0.D = 4.43 (from

Table C10.7) could be used even though

O.D 4.43 = TSS 62 is a little larger

than 6, since the M.S above 1s well

above zero

A comparison of the total weights of each

of the 3 types of webs is given in Table

C10.8, using 4 hole diameter of 5.61" for

webs (b) and 3.31" (from Table C10.7) for

webs (c) and a density of 10 1b./in

Type Weight in Pounds

of Web | pays "A" (2) | Bays "B" (2) | Total Web Wt

Thus for a "non-distributed" load, web

(a), a beaded web, is lightest for Bays

"aA" and (c) is lightest for Bays "B" If

"access" for lines is required then a web

of type (c) or (b) should be used for

Design a butt web splice for the beam section of C10.13 for a design shear load

¥ = 3000 1b and a bending moment of 50,000 tn lbs

Fig C10.26 shows a simply supported beam carrying 4 2000 lb design load located

as shown The cross-section of the beam

is shown in Fig Cl0.27 The design re- quirement for the web is no initial buckling under the design external load

Check the given design for strength and modify if too weak or too strong, or in other words, improve the design Assume peam flanges are braced against lateral column failure

2000 th

stiffeners designed for no initial buckling

under combined bending and shear gave a

value of 5.82 lbs., or much heavier than

30" J" yi row vé eam rÍY hat 1-1/8"

the other designs

PROBLEMS Fig C10.25 shows the cross-section of a

wing beam Calculate the ultimate

resisting moment for the beam section

using the stress-strain curve for the

extruded 24ST material given in Fig C10.4

Use 008 unit strain at the extreme fiber

of the upper flange Compare the results

with the resisting moment given by the

general beam formula M = fy//y (4)

Fig C10, 26 angte on one side of web

Re-design the beam of Problem (3) to use the 3 types of stiffened web as presented

in Part 2 of this chapter Compare the web weights with the web weight required

in Problem 3

Fig C10.28 shows the external dimensions

of a tapered cantilever beam carrying the distributed design load as shown The wed

is not to buckle under the design load

272

C10, 22 DESIGN OF METAL BEAMS

1 fe— 1-1/2" — vis

WEB SHEAR RESISTANT (NON- BUCKLING) TYPE

Make a complete structural design of beam showing size of all parts For flange use 7075-T6 extrusion material and 7075-16 clad material for web and web stiffeners, Show rivet design

Same as Problem (4) but use web with vertical beads

REFERENCES Kuhn, Paul:- The Strength and Stiffness

of Shear Webs With and Without Lightening Holes NACA ARR June 1942

Kuhn, Paul:- The Strength and Stiffness

of Shear Webs with Round Lightening Holes Having 45° Flanges NACA ARR L~-323 Dec 1942

Bleich, F.:~ Buckling Strength of Metal Structures - Book - Publisher, McGraw-Hill

CHAPTER Cll DIAGONAL SEMI-TENSION FIELD DESIGN PART 1 BEAMS WITH FLAT WEBS PART 2 CURVED WEB SYSTEMS

PART 1

C11.1 Introduction

The aerospace structures engineer is

constantly searching for types of structures

and methods of structural analysis and design

which will save structural weight and still

provide a structure which 1s satisfactory from

a fabrication and economic standpoint The

development of a structure in which buckling

of the webs is permitted with the shear loads

being carried by diagonal tension stresses in

the web is a striking example of the departure

of the design of aerospace structures from the

standard structural design methods in other

fields of structures, such as beam design for

bridges and buildings The first study and

rasearch on this new type of structural design

involving diagonal semi-tension field action

in beam webs was by Wagner (Ref 1), and de-

cause of this fact, this tyne of beam design

is often referred to as a Wagner beam

In Chapter C10, Part 1, the subject of

beam design with shear resistant (non~buckling)

flat webs was covered This type of web design

leads to a comparatively heavy weight, which

fact prevents its wide use in asrospace

structures Part 2 of Chapter C10 dealt with

webs stiffened by closely spaced beads, flanged

lightening holes, etc., a design which shows an

improvement relative to wet weight over the

flat sheet web with vertical stiffeners

However, a large proportion of sheet panels

used in aerospace structures is part of the

external surface and holes and deep beads in

the surface skin cannot be permitted, thus

continuous sheet is required and to save

structural weight, semi-tension field action

in the webs and surface sheet panels must be

permitted, which means a wrinkling type of

structure

Since the original work by Wagner, much

further study and testing of structures

involving semi-tension field design has been

carried out by both industry and government

agencies, nence a fairly accurate procedure

for the design of such structures has been

developed and this chapter is concerned with a

limited presentation of the principles involved

and the design procedures that have been

C11.2 Elementary Approximate Explanation of Tension-

Field Beam Action

Fig Œ11.1 shows a single bay truss with double diagonal members (A) and (B) and carrying an external load P The load P will cause 2 compressive load in member (A) and a

tensile load in member (B) If member (A) 15

quite flexible it will buckle as a long column

as shown in Fig Cll.1b, when load P is relatively small, however, panel will not collapse As the load P is increased, the member (A) cannot take any more load but it will practically hold its column buckling load as the bending deflection or bowing gets larger

However, member (B) being in tension can take further load until it reaches its ultimate tensile strength Thus any increase of the shear in the panel due to an increase of load

P after diagonal (A) has buckled can be carried

by a further increase of tension load in member

(B)

is shown in Fig C11.2a, and fo = f¢ = fg where

fg is the shear stress in the web at this

particular point on the web Now thin flat

sheet 1s relatively weak under compression, thus when panel load P {s increased, the compressive stress fg reaches the buckling stress of the panel in the diagonal direction and the web buckles, however, the panel dees not collapse

as further increase in load P can be handled by C11.L

G112

further increase in f, or diagonal tension in

the web sheet The web has an ability to hold

the f, stress that caused buckling but cannot

increase it Fig Cll.2b shows the web stress

picture after the load P has been increased

onsiderably, thus increasing the diagonal web

stile stress as snown by che Length or the

vector for £; Since the shear load on the

panel is transferred by diagonal tension in the

weo and since flat sheet is erficient in

tension, this method of carrying the shear load

permits the use of relativaly thin webs because

of the nigh allowable design stresses in

tension Fig Cl11.2 shows a photograph of a

thin web beam under load Since the diagonal

wrinkling appears severe, the external load

yeing carried is no doubt approaching the

failing point of the web The student should

realize that such a degree of web wrinkling

dees not occur under normal flying accelerations

since the loads carried in normal flying

conditions are only a fraction of the design

leads, and thus the buckling and wrinkling is

barely noticeable under accelerations cf 1/2

gravity, which may be encountered often in

flying in gusty weather conditions,

€11.3 Elementary Derivation of Approximate Tension-

Field Beam Formulas

In order to give the student a general

picture of the influence of web tension field

action upon the beam component parts, an

salemantary approximation of the beam equations

DIAGONAL SEMI-TENSION FIELD DESIGN

Fig 711.4 showg a cantilever team with parallel chords and vertical stiffeners sub- jected to a single shear load ¥ at the free end,

he dashed diagonal lines indicate the direction

of the wrinkles as the thin sheet ouckles under the load V,

Assuming that the flange angles develop all the bending resistance, the vertical and hori- gontal shearing stress is constant over the web and equals

W

foe

~ nat where

rd d

Fig C11.3 Loaded Cantilever Beam Showing Severe Diagonal Web Wrinkling (Ref 3)

ANALYSIS AND DESIGN OF FT

Fig C1ll.5 shows the free body diagram of

a small triangular segment of the web cut from

the upper portion of the beam

Fig C11.5

From elementary mechanics the horizontal

and vertical shearing stresses produce com—

pressive and tensile stresses on planes at 45°

with the shearing planes

The web, being very thin, can carry very

little compression stress on the surface (AC)

of Fig CLL.S before buckling; thus this small

stress which produces buckling on AC will be

neglected or fo = 0, The edge BC is subjected

to tensile stresses which the sheet can carry

effectively The forces acting on the sheet

element are shown in Fig C1l.5

, For equilibrium of the element:

rivets are subjected to two loads, one parallel

to AB and one normal to AB; and each force equals fg tdx The resultant rivet load there~

fore equals V2 f, tdx; and 1í dx Is taken as

one inch, the resultant load will be VZ fs t

But f, = v/nt, hence Rivet load/inch = 1.41 V/n Web Stiffener Load

The tendency of the web 18 Fig C11.4 which has broken down into the tension bands, is to pull the flanges together; this action is prevented by the vertical stiffeners which keep the flanges apart Thus if a pure tension field

is assumed, the axial compressive load Pg in the stiffeners from Fig Cll.6 equals the vertical component of the

web tensile

fy = 2 fg and fg = V/nt

whence Stiffener load Ps = Vd/n (compression)

(7)

Flange Axial Loads Fig Cll.7 shows a free body of the portions of the beam to the right of a section

a distance x from the end of the beam

Let M, = external bending moment at Section

AB For equilibrium the internal resisting moment on Section AB must equal external vending moment My

Taking moments about point B:

IMy = My-Fen' -fpcos 450n' t.c

h ENN SYS SN NAY N SY Axial force in stiffeners

Fe ——4d d Vv In the above equations:

Fig C1L.7 VY = applied shear load

h = distance between centroids of flange- web rivets

h's distance between centroids of flange

where sections

t = web thickness n' = distance between flange centroids d = vertical web stiffener spacing

a= angle of wed buckle (see Fig C11.7)

But

av In deriving equations (10) to (13) Wagner

fy 22 fg and f, = F/n't, hence ft “tt assumed that the beam flanges were infinitely

stiff in bending Actually the flanges due to

Substituting this value of fy in Sq (8) act somewhat as a continuous beam over the web

“xX t Cll.8a The deflections of the beam flanges

whence relieves the web stress in the midportion of

Then to make ZH =

Thus the compressive flange axial load dues

to bending is increased by a value equal to V/2

lbs and the tension flange load due to bending

is decreased by V/2 due to the horizontal com~

ponents of the web tension field

C11.4 General Wagner Equations for Tension Field Beams

The approximate elementary derivation given

in the previous article was for the purpose of

giving the student a general idea of the

influence of a complete tension field beam on

the various beam stresses The angle a is in

general not 459 but depends on flange areas,

beam height, stiffener spacing, etc

The

(Ref 1} general equations derived by Wagner are as follows:

For

parallel deams with infinitely rigid and flanges with vertical web stiffeners:

Diagonal tensile stress in web:

a ee

‘tht’ gin2a

the panels and concentrates the web stress near

the stiffeners where deflection of the flange

is prevented (see Fig Cll.8b)

This stress ratio factor is obtained from Fig

C1l.9 and the following equations:

sin*asVYatta-a -+ - (18)

1 men

a 7a he Tt (16)

Ag âu * AL