TABLE OF CONTENTS

Chapter No.

.. ~ ...Al The Work of the Aerospace Structures Engineer.

STATICALLY DETERMINATE STRUCTURES

(Loads. Reactions, Stresses. Shears. Bending Moments, Deflections>

A2A3

j A4A5A6

! ;, A7

rj,

ASA9A1QAllA12

Equilibrium of Force Systems. Truss Structures. Externally Braced Wings. Landing Gear.Properties of Sections - Centroids. Moments of Inertia, etc.

General Loads on Aircraft.Beams - Shear and Moments. Beam - Column Moments.

Torsion - Stresses and Deflections.Deflections of Structures. Castigliano's Theorem. Virtual Work. Matrix Methods.

THEORY AND METHODS FOR SOLVING STATICALLYINDETERMINATE STRUCTURES

Statically Indeterminate Structures. Theorem of Least Work. Virtual Work. Matrix Methods.Bending Moments in Frames and Rings by Elastic Center Method.

Column Analogy Method.

Continuous Structures' Moment Distribution Method.Slope Deflection Method.

BEAM BENDING AND SHEAR STRESSES.MEMBRANE STRESSES. COLUMN AND PLATE INSTABILITY.

A13 Bending Stresses.A14 Bending Shear Stresses - Solid and Open Sections- Shear Center.

A15 Shear Flow in Closed Thin-Walled Sections.A16 Membrane Stresses in Pressure Vessels.

A17 Bending of Plates.A18 Theory of the Instability of Columns and Thin Sheets.

INTRODUCTION TO PRACTICAL AIRCRAFT STRESS ANALYSIS

A19 Introduction to Wing Stress Analysis by Modified Beam Theory.

A20 Introduction to Fuselage Stress Analysis by Modified Beam Theory.A21 Loads and Stresses on Ribs and Frames.A22 Analysis of Special Wing Problems. Cutouts. Shear Lag. Swept Wing.

A23 Analysis by the "Method of Displacements".

THEORY OF ELASTICITY AND THERMOELASTICITY

A24A25A26

The 3-Dimensional Equations of Thermoelasticity.

The 2-Dimensional Equations of Elasticity and Thermoelasticity.

Selected Problems in Elasticity and Thermoelasticity.

. j 1-3;

;...·,.....l_~ .... •

TABLE OF CONTENTS Continued

Chapter No.

FLIGHT VEHICLE MATERIALS AND THEIR PROPERTIES

81 Basic Principles and Definitions.

82 Mechanical and Physical Properties of Metallic Materials for Flight Vehicle Structures.

STRENGTH OF STRUCTURAL ELEMENTS AND COMPOSITE STRUCTURES

Cl Combined Stresses. Theory of Yield and Ultimate Failure.

C2 Strength of Columns with Stable Cross-Sections.

C3 Yield and Ultimate Strength in Bending.

C4 Strength and Design of Round. Streamline, Oval and Square Tubing in Tension, Compression. Bending,

Torsion and Combined Loadings.

CS Buckling Strength of Flat Sheet in Compression, Shear, Bending and Under Combined Stress Systems.

C6 Local Buckling Stress for Composite Shapes.

C7 Crippling Strength of Composite Shapes and Sheet-Stiffener Panels in Compression. Column Strength.

C8 Buckling Strength of Monocoque Cylinders.

C9 Buckling Strength of Curved Sheet Panels and Spherical Plates. Ultimate Strength of

Stiffened Curved Sheet Structures.

C10 Design of Metal Beams. Web Shear Resistant (Non-Buckling) Type.

Part 1. Flat Sheet Web with Vertical Stiffeners. Part 2. Other Types of Non-Buckling Webs.

ell Diagonal Semi-Tension Field Design.

Part 1. Beams with Flat Webs. Part 2. Curved Web Systems.

C12 Sandwich Construction and Design.

C13 Fatigue.

CONNECTIONS AND DESIGN DETAILS

01 Fittings and Connections. Bolted and Riveted.

02 Welded Connections.

03 Some Important Details in Structural Design.

Appendix A Elementary Arithmetical Rules of Matrices.

INDEX

Accelerated MoUon ofRigid Airplane.

Aircraft Bolts .Aircraft NutsAircrait Wing Sections ­

Type,Aircraft Wing Structure ­

Truss Type.

Air Forces on Wing .Allowable Stresses (and

Interactions) .

Analysis of Frame withPinned Suppor-ts .

Angle MethodApplication of Matrix Methods

to Various StructuresApplied LoadAxis of Symmetry.

Beaded WebsBeam Design - Special Cases.Beam Ftxed End Moments by

Method of Area MomentsBeam Rivet Des IgnBeam Shear and Bending

MomentBeams - Forces at a SectionBeams > Moment Diagrams.Beams with Non-Parallel

Flanges

Beams - Shear and MomentDiagrams

aeams > Statically Deter-minate & Indeterminate .

Bending and Compressionof Columns

Bending Moments - ElasticCenter Method.

Bending of RectangularPlates

Bending Strength - BasicApproach.

Bending Strength - ExampleProblems

Bendtng Strength of Round

Tube'Bending Strength - Solid

Round Bar.Bending StressesBending Stresses - Curved

BeamsBending Stresses - Elastic

RangeBending Stresses - Non­

hcmcgenecus Sections.Bending Stresses About

pr-mcipal Axes .Bending of Thin PlatesBolt Bending Strength.Bolt & Lug Strength AnalysiS

MethodsEolt Shear-, Tension &

Ber:ding Str-engthsBoundary ConditionsBox Beams AnalysisBrazingBuckling CoefficientBuckling of Flat Panels wiui

ntsetmuer FecesBuckling of Flat Sheets under

Combined Loads.Buckli.ng or Rectangular

Plates

A4. 8D1.2D1. 2

A19. I

A2.14A4.4

Cll.36

A9.l6C7.1

A7.23A4.1

A9.4

CIO.16D3.10

A7.32ClO. B

AS.IA5.7AS. 6

en, 9

AS.2

A5.1

AlB. 1

A9. 1

Ala. 13

<:3.1

C3.4

cr. 15

C3.1A13.1

A13. 15

A13. 13

A13.11

A13.2AlS. 10

D1.9

D1.5

D1.3A24.8A22.5D2.4CS.l

C12.25

CS.6

A18.20

Buckling of Stiffened FlatSheets under LongitudinalCompression

Buckling under Bending LoadsBuckling under Shear Loads.

Buckling under TransverseShear

Carry Over Factorcasngnaao'e TheoremCentroids - Center of Gravity.Cladding Reduction Factors.Column Analogy Method.Column Curves - Non-

Dimens tonal .Column Curves - SolutionColumn End Restraint.Column Formulas .Column Strength.Column Strength with Known

End Restraining MomentCombined Axial and Trans­

verse Loads - GeneralAction

COmbined Bending and

Compression.Combined Bending and

Flexural Shear. . •Combined Bending and

TensionCombined Bending and

Tension or Compression ofThin Plates

Combined Bending & Torsion.Combined Stress Equations .Compatability Equations.

Complex Bending' -Symmetrical Section.

Compressive Buckling Stress

for Flanged Elements .COnical Shells - Buckling

StrengthConstant Shear Flow WebsConstant Shear Flow Webs ~

Single Cell - 2 Flange Beam.Constant Shear Flow Webs ­

Single Cell ~ 3 Flange Beam.Continuous Structures ­

Curved MembersContinuous Structures -

Variable Moment of InertiaCOre ShearCorrection for Cladding.Corrugated Core Sandwich

Failure Modes.Cozzone ProcedureCreep of Ma.terialsCreep Pattern .Crippling Stresses

Calculations .Critical Shear StressCrystallization TheoryCumulative Damage Theory.Curved BeamsCurved Sheet Panels ­

Buckling StressCurved Web SystemsCut-OUts in Webs or Skin

Panels .

Deflection Limitations inPlate Analyses. . .

Deflections by Elaanc Weights

C6.4CS.6CS.6

C8.14

All. 4

A7.5A3.1C5.5

AlO.l

C2.2C2.l3

C2.1C4.2

C7.21

C2.16

A5.21

C4.22

C3.l0

C4.23

A18.l7

C4.23ci. 2

A24.7

C3.9

C6.1

CB.22A14.l0

A15.3

A15.5

All. 31

All. 15C12.26

C7.4

e12.27C3.231. 8

B1. 12

C7.7Cll.16

C13.1C13.3

A5. a

C9.1Cll.29

D3.7

A17.4.\7.27

Deflections by Moment Areas.Deflections for Thermal

Strains .Deflections by Virtual WorkDelta Wing Example Problem.Design for CompressionDesign Conditions and Deaign

Weights ..Design Flight Requirements

for Airplane .Design Loads .•Design for Tension ..Differential Equation of

Deflection Surface.Dtsconttnutttes

Distribution of Loads toSheet Panels .

Ductility. . .Dummy Unit LoadsDynamic Effect of Air Forces.

Effect of AxIal Load onMoment Distribution.

Effective Sheet WidthsElastic Buckling Strength of

Flat Sheet in Compression.Elasttc - Inelastic Action.Elastic Latera! SUpPOrt

Columns.Elastic Stability of ColumnElastic Strain Energy .Elasticity and Thermo-

elasticity - One-DimensionalProblems .•..

Elasticity and Thermo­elasticity - Two-DimensionalEquations

Electric Arc Welding ..•End Bay Effects.End Moments for Continuous

Frameworks •.Equations of Static

Equilibrium

Equilibrium Equations

Failure of Columns byCompression.

Failure Modes in CurvedHoneycomb Panels. . .

FaUure of StructuresFatigue AnalySiS - Statistical

Distri.bution ... .Fatigue and Fail-Safe Design .Fatigue of MaterialsFatig-le S-N Curves .

Fillers.Fitting Design .Fixed End MomentsFjxed End Moments Due to

Support DeflectionsFixi.ty cceutcterus.Flange Design .Flan~e Design Stresses .Flange Discontinuities.Flange Loads

Flange Strength (Crippling) .Flat Sheet Web with Vertical

Stiffeners

Flexural Shear FlowDistribution

Flexural Shear Flow ­Symmetr-ical Beam Section

Flexural Shear Stress.

A7.30

A7.17A7.9

A23.2C4.2

A5.12

A4.6A4.1C4. 1

ALB. 12AZD.15

A2l.2B1. 5A8.6

M.13

All. 22C7.l0

C5.1Bt. 5

C2.l7.'\17.2ci, 6

A26.l

A25.1D2.2

Cll.23

All. 10

A2.lA24.2

A18.4

C12.20

81. 1

C13.4C13.8B1. 14

C13.1303.5

01. ~

All. :3

All. 9C2. 1

CIO.l

ClG.2ClO.7Cll. aCIO.4

CIO.l

AlS.24

A14.5A14.1

INDEX· Continued

Bl.2

C9.S

C4.5

A2.4

.' :''"it':-·"'·A

•

C4.25

C4.26

A8.11

AS. '7C4.5

A.26. 5

Ct. 24

C4.26Cl.I

AS. IS"A9.2

AIO.4

M.tSA9.13

A4.7

Cl1.4CtO.5

Cll.18CIO.10CtO.5

A5.9A19.25

AS. 10A23.11A19.5.'1.19.5

A19.11Al.2

· Al5.11A2l.t

• A19.14

ClO.17A19.2Al9.1

A19.12• A23.14

•••.("r-

Trusses With MultipleRedundancy . . . •

Trusses With SingleRedundancy . . . .

Tubing Design Facts

Two-Dimensional Problems.Two-Cell Multiple Flange

Beam. • One Axis otSymmetry •.•..•.••

Type of Wing Ribs. • • . • •

Wagner Equations ..Web Bending &: Shear StressesWeb Design •.•.•.•••Web Splices ••.•..••.Web Strength. Stable Webs.Webs with Round Lightening.

Holes •••••..••Wing Analysis Problems

Wtng Arrangements. • •Wing Effective SecttonWing Internal StressesWing Shear and Bending

AnaLysis •••...••Wing Shear and Bending

Moments •.••.•..Wing - Sbear Lag . • • •Wing Shears and MomentsWing Stiffness Matrix.. • •Wing Strength ReqUirementsWing Stress Analyl'lis MethodsWing - Ultimate Strength .Work of Structures Group.

tntimate Strength in CombinedBending &: F1exural Shear • •

tnUmate Strength in CombinedCompression, Bending,Flexural Shear &: Torsion.

Ultimate Strength in CombinedCompression, Bending &ITorsion •..••••••.•

illtimate Strength in CombinedTension. Torsion andInternal Pressure p in psi.

Uniform Stress Condition. •Unit Analysis lor Fuselage

Shears and Moments. . •UnsymmetriCal Frame • . .Unsymmetrical Frames orR_ .Unsymmetrical Frames using

P r i n C i ~ Axes. • • . •..'Tnsymmeirical Structures

" ,\t, . 'Jy - Load Factor

" .....

AS.7

A6.10

A6.S

A6.2Cl.5

A7.33A2.9

C4.17

A6.3AS. 4

AS. ISA6.SA5.9

C4.1'7

A8.16

A24.1A16.5

A7.5A8.2

A7.5

AB.39A8.14AB.33

Al9.5A6.l

AS. 10

Bl.5A1B.a

C13.33D3.2

en. 1C11. 2A7.5

AIS. 15

ToUlgent ModulusTangent-Modulus TheoryTaxi Loads ..•.•••Tension CHps . • . . . .Tension-Field Beam Action.'renetcn- Field Beam FormulasTheorem of Castiglta.no ..•Theorem of Complementary

Energy..••••...••.•Theorem of Least Work •.•Theorems of Virtual Work and

Minimum Potential EnergyThermal Deflections by

MatriX Methods • . • • .Thermal Stresses . • . • •Thermal Stresses . . . • •Thermoelasttcity - Three-

Dimensional Equations. •Thin Walled Shells

Three Cell - Multiple FlangeBeam. - Symmetrical aboutOne Axis ..••••..••

Three Flange - Single CellWing ••••••••••••

Torsion - Circular Sections.Torsion - Effect of End

Restraint.••....•Torsion - Non-circular

Sections •..•.•••Torsion Open sectionsTorsion of Thin-Wailed

Cylinder having Closed TypeStiHeners .........•

Torsion Thin Walled Sections.Torsional Moments - Beams •Torsional Modulus of Rupture.Torsional Shear Flow in

Multiple Cell Beams byMethod of SuccessiveCorrections . • • • . .

Torsional Shear Stresses inMulttple4Cell Thin-WallClosed Section - Distribution

Torsional Strength of Round

Tubes •.•.•..•.••Torsional Stresses 1n

Muitiple4 Cell Thin-WalledTubes ••....•...

Transmission of Power byCylindrical Shaft. ...•

TriaXial Stresses . • • • .Truss Deflection by Method

of Elastic Weights •Truss StructuresTrusses with Double

Redundancy. • . .

A2.7

A2.3

AB.lC2.14

Al2.7

A24.5A7.l

A14.2

A.6.7B1.7

A24.6A22.1

Cll.17

C4.22Cll. 15

All. 29

Cll.32ci, 6

A2.2D3.12

AlS.24

Static Tension Stress­Strain Diagram . . .

Statically DeterminateCoplanar Structures and

Loadings .Statically Determinate and

Indeterminate StructuresStatically Indeterminate

Frames - Jomt RotationStatically Indeterminate

Problem ..••.•...Stepped Column - StrengthStiliened Cylindrical

Structures - illUmate3trength .•.•.•.

Stiffness &I Carry-overFactors lor CUrved Members All. 30

Stiffness Factor. • . . All. 4Strain - Displacement

Relations •.....Strain Energy . . . . .Strain Energy of Plates Due

to Edge Compression andBending A18.19

Strain Energy In Pure Bendingof Plates. • • • . . . . . . . AlB. 12

Streamline Tubing - Strength. C4. 12Strength Checking and

Design - Problems • . . .Stren~··_ ".: Round Tubes

_ ..nder Combined Loadings .sn-ess Analysis FormulasStress Analysis of Thin Skin -

Multiple stringer CantileverWing •..........•• A19.10

Stress Concentration Factors. C13.10Stress Distribution & Angle

of Twist for 2-Cell Thin4

Wall Closed Section . .Stress-Strain Curve •.•.•Stress-Strain Relations .••Stresses around Panel Cutout.Stresses in UprightsStringer Systems in Diagonal

Tension ...•.•.•••.Structural Design Philosophy.Structural Fittings • • • • . .

Structural Skin Panel Details.Structures with Curved

Members •.•.•...Successive Approximation

Method for Multiple CellBeams .....•..

Symbols for ReactingFitting Units ....•

Symmetrica sections ­External Shear Loads

Y Stiffened Sheet Panels C7.2C

CHAPTER Al

THE WORK OF THE

AEROSPACE STRUCTURES ENGINEER

AI. 1 Introduction.

The first controllable human flight in aheavier than air machine was made by OrvilleWright on December 17, 1903, at Kitty Hawk,North Carolina. It covered a distance ot 120feet and the duration of flight was twentyseconds. Today, this initial flight appearsvery unimpressive, but it comes into its trueperspective of Lmportance when we realize thatmankind for centuries has dreamed about dOingor tried to do what the ~ r l g h t Brothersa:campllshed in 1903.

The tremendous progress accompliShed in thefirst 50 years of aviation history, with mostof it occurring in the last 25 years, 1s almostunbelievable, but without doubt, the progressin the second 50 year periOd will still be more~~believable and fantastic. As this is writtenin 1964, jet airline transportation at 600 MPHis well established and several types ofmilitary aircraft have speeds in the 1200 to2000 ~ range. ?reliminarJ designs of asupersonic airliner with Mach 3 speed have beenccmpleted ~ ~ d the government is on the verge ofsponsoring the development of such a flightvehicle, thus supersonic air transportationshould become co~on in the early 1970's. Therapid progress i ~ ~ ! s s i l e design has usheredin the Space Age. Already many space vehicleshave been flown in search of new knowledgewhich is needed before successful explorationof space such as landings on several planetscan take place. Unfortunately. the rapiddevelopment of the missile and rocket powerhas given mankind a flight vehicle when combinedwith the nuclear bomb, the awesome potential toquickly destroy vast regions of the earth.TMhile no person at ~ r e s e n t ~ ~ o w s where or whatspace exploration will lead to, relative tobenefits to ~ n k i n d , we do know that the nextgreat aviation expanSion besides supersonicairline transportation will be the full develop­~ e n t and use of vertical take-off and landingaircraft. Thus persons who will be livingthrough the second half century of aviationprogress will no doubt witness even morefantastic progress than oceurred in the first50 years of aviation history.

A!. 2 General Organization of an Aircraft CompanyEngineering Dfvtetcn,

scientific machine and the combined knowledgeand experience of hundreds of engineers andscientists working in close cooperation isnecessary to insure a successrul product. Thusthe engineering division of an aerospace companyconsists of many groups of specialists whosespecialized training covers all fields ofengineering education such as PhySics, Chemicaland Metallurgical, MeChanical, Electrical and,of course, Aeronautical ~ ~ l n e e r i n g .

It so happens that practically all theaerospace companies publiSh extensive pamphletsor brochures explaining the organization of theengineering division and the duties andresponSibilities of the many sections and groupsand illustrating the tremendous laboratory andtest facilities which the aerospace industrypossesses. It is highly recommended that thestudent read ~ ~ d study these tree publicationsin order to obtain an early general under­standing on how the ~ o d e r n flIght vehicle isconceived, deSigned and then prOduced.

In general, the engineering department ofan aerospace company can be broken down into saxlarge rather distinct sections, which in turnare further divided into specialized groups,which in turn are further divided into smallerworking groups of engineers. To illustrate, thesix sections will be listed together with someat the various groups. ThiS is not a completelist. but it should give an idea or the broadengineering set-up that is necessarJ.

I. Preliminary Design Section.

II. TecrJlical _ ~ a l y s i s Section.

(1) Aerodynamics Group(2) Structures Group(3) ~eight and 3alance Control Group(4) Power Plant Analysis Group(5) Materials and Processes Group(5; Centrols AnalYSiS Group

III. Component DeSign Section.

(1) Structural DeSign Group(~lng. Body and Control Surfaces)

(2) Systems Design Group(All mechanical, hydraulic, electricaland ther.nal installations)

IV. Laborato~J Tests Section.The ~odern commercial airliner, militarJairplane, missile and space vehicle is a highly

Al.I

Al.2 THE WORK OF THE AEROSPACE STRUCTURES ENGINEER

(1) Wind Tunnel and Fluid Mechanic5 ~est

Labs.(2) Structural Test Labs.(3) Propulsi~n Test Labs.(4) Electronics ~ e s t Labs.(5) Electro-Mechanical Test Labs.(6) Weapons and Controls Test Labs.(7) A r ~ l o g and Digital Computer Labs.

v. Flight Test Section.

VI. Engineering Field Service Section.

SinCe this textbook deals with the subjectof structures, it seems appropriate to discussin some detail the work of the Structures Group.For the detailed discussion of the other g r o u ~ s ,

the student should refer to the various air­craft company publications.

At. 3 The Work of the Structures Group

The structures group, relative to number ofengineers, is one of the largest of the ~ a n y

groups ot engineers trat make up Section II,the technical analySis section. The structuresgroup is primarily responsible for thestructural integrity (safety) ot the airplane.safety may depend on sufficient strength orsufficient rigidity. This structural integritymust be accompanied with lightest pOSSibleweight, because any excess weight has detri­mental etfect upon the p e r f o ~ c e of aircraft.For example, in a large, long range missile,one pound of '~ecessary structural weight mayadd mora than 200 Ibs. to the overall weight ofthe missile.

The structures group is usually divided'into sUb-groups as tollows:-

(1) Applied Loads Calculation Group(2) Stress AnalySiS an~ Strength Group(3) Dynamics AnalYSiS Group(4) Special Projects and Research Group

THE '"ORK OF THE APPLIED LOADS GROUP

Before any part ot the structure can befinally proportioned relative to strength orrigidity, the true external loads on the air­craft must be determined. Since critical loadscame tTom many sources, the Loads Group mustanalyze loads fram aerOdynamiC forces, as wellas those forces from power plants, aircraftinertia; control system actuators; launching,landing and recovery gear; a ~ e n t , etc. Theetrects of the aerOdynamic forces are initiallycalcUlated on the assumption that the airplanestructure 1s a rigid bOdy. Atts: the aircraftstructure is Obtained, its true rigidity canbe used to obtain dynamic effects. Results ofwind t~~el model tests are usually necessaryin the application of aerodynamic principles toload and pressure analYSiS. •

The final results of t.he work of thisgroup are formal reports g l v ~ n ~ complete a ~ p l i e d

load design criteria, with ~ n y graphs ~ n d swu­mary tables. The final results ~ y 61v8 com­plete shear, moment and no~l forc~s =e~er=~d

to a convenient set of :CY2 axes for major air-c ra.r t units such as the Wing, rus eIage , e t c .

THE WORK OF STRESS ANALYSIS ~\m S~R~~GTH GROUP

Essentially the primary job of :he stressgroup is to help specify or deter.nine the kindof material to use and the : h : c ~ ~ e s s , size andcross-sectional shape Jt every s t r u c t ~ l ~ e Q ­

ber or unit on the airplane or ~issile, andalso to assist in the deSign of all jOints andconnections for such ~ e m b e r s . safety with ~ i g h t

weight are the paramount s t r ~ c t u r a l j e s l ~ re­quirements. ~ h e stress group ~ust consta~tly

work closely with the Structural DeSign Sect:Gnin order to evolve the best structural over-allarrangement. Such factors as ~ower ~lants,

bUilt in fuel tanks, landing gear retractingwells, and other large cut-outs can d ~ c t a t e thetype of wing structure, as for example, a twospar single cell wing, or a multiple spar~ u l t i p l e cell wing.

To expedite the initial s t r u c t ~ r ~ l ~ e s i g n

studies, the stress group ~ u s t s ~ ~ p l y initialstructural sizes based on approximate loads.The fi~l results of the work by the stressgroup are recorded in elaborate reports whichshow how the stresses were calculated and hewthe reqUired member sizes were obtained to carrythese stresses efficiently. The r:nal size ofa member may be dictated by one or more rae torssuch as elastic action, tne Ias t t c action, ele­vated temperatures, fatigue, etc. To insurethe accuracy of theoretical calculations, thestresS group must have the assistance of thestructures test laboratory in order to obtaininformation on which to base allowable designstresses.

THE WORK OF THE DYNAMICS A~LYSIS GROUP

The Dyna~ics AnalysiS Grou) has rapidlyexpanded in recent years ~ e l a t i v e to number ofengineers required because supersonic airplanes,missiles and vertical riSing a i ~ c r a f t have pre­sented many new and complex problems in thegeneral field of dynamics. In some airc~tt

companies the dynamiCS group 1s set up as aseparate group outside the Structures Group.

7he engineers in the dynamiCS group areresponSible for the investigation ot Vibrationand shOCk, aircraft flutter and the establish­~ e n t of desig~ requirements or c~2nges for itscontrol or correction. Aircraft contain dozensof mechanical installations. Vicration of ~~y

part of these installations or systems ~ y beof such character as to cause faulty operationor danger of failure and therefore the dynamic

ANALYSIS AND DESIGN OF FLIGHT VEHICLE STRUCTURES A1.3

characteristics must be changed or modified inorder to insure reliable and safe operation.

The major structural units of aircraft suchas the wing and fuselage are not rigid bodies.7hus when a Sharp air gust strikes a fleXiblewing in high speed flight, we have a dynamicload situation and the wing Nill vibrate. Thedynamicist must determine whether this vibration1s serious relative to induced stresses on thew i r ~ structure. The dynamics group is alsoresponsible for the determination of thestability and performance of miSSile and flightvehicle guidar.ce and control systems. Thedynamics group must work constantly with thevarious test laboratories in order to obtainreliable values of certain factors that arenecessary in many theoretical calculations.

THE ',jaRK OF THE SPEC IAL PROJECTS GROUP

In general, all the various technical

groups have a speCial SUb-group which are work­ing on deSign problems that Nill be encounteredin the near 1r distant future as aviation pro­gresses. For example, in the r.t r-uc tur-ea Group,this sub-group might be studying such problemsas: (1) how to calculate the thermal stressesin the wing structure at super-sonic speedS;(2) how to stress analyze a new type of wingstructure; (3) what type of body str~cture isbest for future space travel and what kind ofmaterials will be needed, etc.

Chart 1 illustrates in general a typical~ k e - u p of the Structures Section of a largeaerospace company. Chart 2 lists the manyitems which the structures engineer must beconcerned with in insuring the structuralintegrity of the flight vehicle. Both Charts1 and 2 are from Chance-Vought StructuresDeSign Manual and are reproduced with theirpermi saton.

~ E I l O E ' - ' \ S T l c : ' · · · 4 U..f ,.

~ ' I l O E ' - ' \ S T I C ,..---lcU"", i, I STWCTVI~S I

""lAKlIlATo'" I' ~~u,11:'I. "'",ru,,, 1'liSI U,,"T

J i, -.c...."I.IC

'NO "Owu' .....1 ""ST

: UN"

, .....c:.. 'H~COMPUIATICH

~ ' ' ' G ' ' GIlOU'~ ~ ,

Chart 1. Structures Section OrganizationChance- Vought Corp.

-:3

e.13W m = r ETT? 5ZWF

AI. 4 THE WORK OF THE AEROSPACE STRUCTURES ENGINEER

THE LINKS TO STRUCTURAL INTEGRITY••••• ARE NO BETTER THAN THE WEAKEST LINK

STRESS

ANALYSISSKIN PANElS

BEAM ANALYSISSTRAIN COMPATIBILITY

STRAIN CONCENTRATIONJOINT ANALYSIS

BEARI~G ANALYSISBULKHEAD ANALYSI S

fITTING ANALYSISi1'ERMAL STRESS

,'oIECHAN1CAL COMPONENTSD:PERIMENTAL STRESS ANALYSIS

MATERIALS OFCONSTRUCTION

FA.STENERS

WELDINGBONDING

?LATE~ND BAR

FORGINGSCASTINGS

€XTRUSIONSSHEET METAL

SANDWICH?tASTIC l,OMINAIT

BEARINGS

MATERIALS AND

QUALITY CONTROLDUCTILITY

STRESS-STRAIN

HOMOGENEOUS MATERIAL

RESIDUAL STRESS

HEAT TREAT CONTROL

STRESS CORROSION

STABILITY AT TE~P£RATURE

SPECIFICATION CONFORMANCE

BLUE PRINT CONFORMANCE

ALLOWABLESYIHDING

FRACTURE

°ATlGUE

WEAR, BRINELLING

CREEP

DEFliCTIONS

Tl'ERMAl O"FECTS

STIFFNESS

COMBINED LOADINGS

3UCKlING

COMPONENT

ANALYSISUNIT SOLUTIONS

INOffiRMINATE STRUCTURES

WING ANALYSIS

TAIL ,l,NAlYS1S

FUSElJ.GE SHElL A""lYSIS

THERMAL ANALYSIS

DfFlICTION ANALYSIS

STIFFNESS

STIFFNESSCRITERIA

FLUTTER

CONTROL SYSTEM STABILITY

PANEL fLIJTTER-SKIN CONTOURS

CONTROL SYSTEM DEfLECTIONS

THERMAL EFFECTS

MtCHANICAL VIBRATIONS

ROLL POW£R-O IVERGENCE

AEROtWtAMIC CENTER SHIFT

DYNAMIC RESPONSE

LOADS ANDENVIROMENT

FLIGHT LOAD CRITERIAGROUND LOAD eRITER IA

FLIGHT LOAD DY~M'CS

LAUNCHING DYNAMICSLANDING DYNAMICS

DYNAMIC RESPONSEaECOVERY DYNAMICS

,UGHT LOAD DISTRIBUTIONSINERTIAL LOAD DISTRIBUTIONS

Fl..D:IBILITY EFFECTSGROUND LOAD DISTRIBUTIONS

REPEATEO LOAD SPECTRUMSTEMPERATURE DISTRIBUTIONS

LOADS FROM TllERMALDEFORMATIONS

PRESSURES-IMPACT

Chart 2From Chance- Vought Structures Destgn Manual

CHAPTER A2

EQUILIBRIUM OF FORCE SYSTEMS. TRUSS STRUCTURES

EQUILIBRIUM OF S?AC::; ?J..RALLEL FORCE SYSTlli

force system pass through a cammon point. ThereSUltant, if any, must therefore be a forceand not a moment and thus only 3 equations arenecessary to completely define the conditionthat the resultant must be zero. The equat10nsof equilibrium available are therefore:-

A combir~tion of force and moment equationsto make a total of not more than 3 can be used.For the moment equations, axes through the pointof concurrency cannot be used since all forcesof ~ h e system pass through this point. Themoment axes need not be the same direction asthe directirns used in the force equations butof course. they could be.

In a parallel force system the direction ofall forces is known, but the magnitUde andlocation of each is unknown. Thus to determine~ g n i t u d e , one equation Is required and forlocation twa equations are necessary since theforce is not confined to one plane. In generalthe 3 equations commonly used to make the re­sultant zero for this type of ~ o r c e system areone force equation and two moment equatiOns.For example, for a space parallel force systemacting in the y direction, the equations ofequilibrium would be:

} - - - - -(2.2)

ooo

m, =m, =m, =

orl:Fx = aZFy = al:Fz =0

•A2.2 Equations of Static Equilibrium.

To completely C e f l ~ e a force, we must knowits ~ a g n l t u d e , direction and ~ o l n t of ann1ica­tion. These facts regaTding the ~ a r c e aregenerally r e f e r ~ e d to as the characteristics ofthe ~ o r c e . S o ~ e t i m e s the more ~eneral te~ ofline Of act~on or lecation is used as a forcec r ~ r a c t e r i s t i c in Place of paint of applicationdesignation.

A force acting in space is completelydefir-ed :: we %now its components in threedirections and its ~ o m e n t s about 3 axes, as forexample FX J F~, Fz ~nd ~x, tly and Xz • ~or

equilibrium o ~ a force system there can be noresultant force and thus the equations ofequllibri'4n are obtained ~ y equating the forceand moment cCill~onents to zero. The equations~ f static equilibrium for the various types offorce systems 'Nill now be suear-tzeo .

A2.1 Introduction. The equations of static

equilibrium must constantly be used by thestress analyst and structural designer 1 ~ ob­taining unknown forces and reactions or u n k n o ~ n

internal stresses. They are necessary whetherthe structure ..or machine be s tmp.Le or complex.The ability to apply these equations 1s nodoubt best developed by solving ~ n y problems.This Chapter l ~ l t l a t e s the application of theseimportant phySical laws to tt.e force and stressa r ~ l y s l s of structures. It 1s assumed that astudent has completed the usual college coursein engineering mecrznlcs called statics.

SG.UILIBRIUM OF GE:N""'..2.AL CO-PUu'JAR ~ O R C E SYSTEM

EQ.UILI3RIUi1 SO.UATICNS FOR GSNERAL

SPACE: urCN-COPLANAR) ?ORCE SYSTE?:

ZFy = 0, ZI1x ::: 0, n1z:= 0 - -(2.3)

C o ~ c u r r e ~ ~ 7 ; e ~ n s that all forces of the

sq,UILI3RI'L11 OF' SPACE ::CNCJEP,S::T ropes SYS':'~

rhus :or a general space ~ o r c e system,there are 6 equations of static eqUilibriumavailable. T ~ r e e of these and ~ o ~ o r 8 can beforce equations. It is or t en acr-e convenientto ~ a k e the moment axes, 1, 2 ~nd 3. as any setot X, y and z axes. All 6 equat10ns could beno~ent equaticns about 6 ciffere~t axes. ~ ~ e

force equations are written for 3 ~utually

~er?endiC~lar ~es ~nd need not be t~e x, yand z axes.

l:Fx = 0ZFy = 0

ZFz = 0

~ ... = 0

m, = am, = 0

} - - - - -(2.1)In this type ot farce system all forces lie

in one plane ~ d it t a ~ e s only 3 equations todeter.Aine the magnitUde, direction and locationor the resultant of such a force system. Eithertorce or moment equations C3n be ~sed. exceptthat a ~aximum of 2 :orce e q u a ~ l o n s can be used.For example, for a force system acting in thexy plane, the follcwiig c o ~ b l n a t i c n of equili­b r i ~ equations could be used.

ZFx = 0 ZFx = 0 ZFy • a zr1z .. =aZFy =0 or L:!":z..= 0 or ZMz... :: 0 or 1:1z II = 0 2.4

z:1z = 0 Z!"!Zil= 0 z:M:Zll= 0 mz" =a

(':'he subsc=-lpts 1, 2 and 3 refer to differentlocations for z axes or moment center-s . )

A2.1

.AC

A2.2 EQUILIBRIUM OF FORCE SYSTEMS. TRUSS STRUCTURES.

reacted 'Jy other ext er-ne; -or-ces , ccmnorLyreferred to as reactions which hold the j:,cwnforces on ~he str~cture in equiliJri~ll. Sl~ce

the static e q u a ~ i o n s of equil:bri:2n ~ v a i : ~ ~ : e

for the various t ~ ? e s ot force s y s t e ~ arelinited, the s t r ~ c : u r a l engineer resorts tc theuse of fitting units w h i c ~ establ:sh thsdirection 8f an ~n}~i8~TI fc~ce C~ ~~s ~o:nt Jfap~11c8:~on or both, t ~ ~ s decreasins th3 ~ ~ b e r

of UIL~owns t8 be determi~ed. ~~e ~l~ures

which follow illustrate t ~ e ty;e of ~ i t t 1 ~ g

units employed or o:her g e n e ~ ~ l I e t h ~ d s ~ J r

establiShing the ~ o r c s c ~ a r a c t e r i s t 1 c s ofdirsction and pOint of application.

or ZFxl:Fx : 0

ZFy : a

Since all forces lie in the s s ~ e plane andalso pass thr8ugh a c~~,on ~oint, the ~ a ~ ~ i t u d e

and direction of the r ~ s ~ l t a n t of this type offorce system is unknown ~ut the location ~ s

£ ~ o w n s i n ~ e the ;oint of c o n c ' ~ i e n c y is on thelin8 of action cf the resultant. ~ h u s only twoequations 0: equilibri~ are necessary to definethe resultant and ~ke it zero. T ~ e combin­ations available are,

= a or ZFy = a or Z M z ~ =0 } 2.5

=0 ZI'1z = O ZI'1z a = O

EQUILIBRIUM: OF CO-PLANAR P.4RALLt:L FCRCE SYS'I'~

(The moment centers 1 and 2 cannot be on thesame y axis)

For any space or coplanar f8rce s u c ~ as ?and Q acting on the bar, the line o ~ action ofsuch forces must act t..u-cucn the cent.cr- 0': theball ~ ! rotation of the bar is prevented. ~ h u s

a ball and socket joint can be used to establ:shor control the d i ~ e c t i o n and line action of aforce applied to a struct~re through : ~ i ~ : j ~ e

of fitting. Since the ~ o i n t has ~o rctaticTzlreSistance, no couples in any plane can beapplied to it.

Ball and Socket Fitting

~ ' l

II- p

-----2.6}4I'1z Ii = a

l:l1z. : aor

l:Fy : 0

n1z = 0

Since the direction of all forces in thistype or rorcs system 1s known and since theforces all lie 1n the same plane, it only takes2 equations to define the magnitude and locationof the resultant of such a force system. Hence,there are only 2 equations of equil1bri~ avail­able for this type of force system, namely, aforce and :noment equation or two momentequations. For example, for forces parallel toy axis and located in the xy plane the equili­brium equations available would be: -

(The z axis or moment center locations must beother than through the paint of concurrency)

EQUILIBRITJr1 OF COLINEAR FORCE SYSTEM

A2.3 Structural Fitting Units for Establishing the ForceCharacteristics of Direction and Point of Application.

where moment center 1 is not on the line ataction of the force system

To completely define a force in space re­qUires 5 equations and 3 equations if t ~ e forceis limited to one ?lane. In ~ e n e r a l a structureis loaded by ~own forces ar.d these !orces aretransferred tPIough the s t r u c t ~ r e in some~nner of internal stress distribution and then

A collnear torce system 1s one where allforces act along the same line or in otherwords, the direction and location of the forcesis known but their nagnt tudes are unknown, thusonly magnitude needs to be found to define theresultant of a collnear force system. Thusonly one equation ot equilibrium is a'ffiilable,namely

If a bar AB has s i ~ G l e pin f ~ t ~ i n g s ate a c ~ end, then any :orce P lying in the xyplane and anplied to end B ~ust have a directionand line of action co tnc tc t ng .... ith a line jo tn-.i~g the pin centers at end ~it~1ngs A ar.d 3,since the :lttings cannot resist a ~oment aboutthe 3 axis.

A ,B

-<@o========:j):Jl_

For any force such as P and Q acting i ~ thexy plane, the line of action of such a ~~rce

~ust pass through the ,in center since t ~ e

fitting unit cannot resist a ~cme~t about a zaxlo through the pin center. Therefore, fJrforces acting in the xy plane, t h ~ direct:cn~ ~ d line of action are established by th8 pinjoint as illustrated in the f:gure. Sir.ce aSingle pin fitting can resist :noments atou: axesperpendicular to the ~ i n axis, the cirectlon andline of action of out of ,lane :orces is ~ t e r e ­

fore not established by s tngl e pfn ~ i t - : l n g umt.s .

----2.7ZI1 1=OorZF =a