Notes on Aerospace Structures

AME 30341

Edmundo CoronaDepartment of Aerospace and Mechanical Engineering

University of Notre DameNotre Dame, IN 46556

ecorona@nd.edu

August 9, 2006

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Contents

1 Introduction 5

1.1 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.2 Elements of Aerospace Structures . . . . . . . . . . . . . . . . . . . . . . . . 51.3 Work of the Aerospace Structural Engineer . . . . . . . . . . . . . . . . . . . 8

2 A Brief History 9

2.1 Early Aircraft: The Reign of the Wooden Biplane . . . . . . . . . . . . . . . 92.2 The Establishment of the Cantilever Wing . . . . . . . . . . . . . . . . . . . 15

2.2.1 Wood design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2.2 Metal aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.2.3 Pressurized Cabins . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2.4 Composite Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3 High Performance Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3 Materials 23

3.1 Criteria for Material Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2 Typical Aerospace Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4 Structural Nomenclature 27

4.1 Wing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.2 Fuselage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.3 Empennage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

5 Structural Design Definitions 33

5.1 Load Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345.2 Limit Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345.3 Ultimate Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

6 Fracture 35

6.1 Fatigue Design Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356.1.1 Safe-Life Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376.1.2 Fail-Safe Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376.1.3 Choice Between Safe-Life and Fail-Sage Designs . . . . . . . . . . . . 37

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4 CONTENTS

6.2 Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386.2.1 Stress concentration . . . . . . . . . . . . . . . . . . . . . . . . . . . 386.2.2 When will a crack propagate? . . . . . . . . . . . . . . . . . . . . . . 406.2.3 Stress Intensity Factor . . . . . . . . . . . . . . . . . . . . . . . . . . 406.2.4 Fracture Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Chapter 1

Introduction

1.1 Objectives

The objectives of the course are:

Present an overall, introductory view of the subject of aerospace structures and light-weight structures. Topics include:

Historical perspectives and case studies

Load analysis

Materials

Structural concepts

Aeroelasticity

Behavior of thin-walled beams

Fatigue

Buckling

Applications of simple mechanics in relevant examples

Present simple structural theories that yield solutions amenable to hand calculationsor simple computational procedures. Although most of the work in the field is nowconducted using sophisticated computational tools, these will not be used in this course(if you are interested in computational methods in structures, you may want to considertaking AME 50541, Finite Elements, as one of your technical electives).

1.2 Elements of Aerospace Structures

Aerospace structures is a multi-disciplinary field whose objective is to produce structures thatmeet all the requirements of a flying vehicle (or, in other words, actually build the airplane,rocket, etc.). The most important keyword is airworthiness or structural integrity. This

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6 CHAPTER 1. INTRODUCTION

means that the structure will not fail or be damaged under the mission requirements of theaircraft. The second keyword, which is perhaps more of a constraint, is lightweight. Excessweight can result in big penalties in the performance and fuel consumption of aerospacevehicles (as well as land-based ones, although the impact is less dramatic). As an example,it was shown in a PBS program on the development of the Boeing 777 that, once the firstprototype had been finished, the aircraft was actually weighted to see if the design weightobjective had been achieved. Had it not, Boeing would have had to pay the airline that placedthe first order (United) a certain number of Dollars per pound of overweight, presumablyto cover the higher operating expense. In another example [1], one pound of unnecessarystructural weight in a long-range missile may add more than 200 lbs. to the weight of themissile. In summary, the objective of aerospace structural engineers is to produce the lightestairworthy vehicle.

Figure 1.1 shows various elements that are part of aerospace structures and a fewexamples in each category. The figure is not exhaustive, but intended to present a roughidea of the variety of issues that are considered in aerospace structural design and of theknowledge needed to address them. The elements shown are:

Load Analysis: Prior to designing a structure, the type and magnitude of the loads thatneed to be supported have to be established. Load analysis refers to the calculation ofsuch loads based on the mission requirements of the aircraft.

Materials: Every component of an aircraft needs to be made using some material. Manymaterials are available to the structural designer. Careful research and analysis needsto be carried out in order to make the best choices.

Mechanics: Structures need to be designed according to sound mechanics principles to en-sure safety and optimum performance. Mechanics provides the tools needed to conductload and structural analysis.

Physical Factors: These are factors having to do with the physical response of the struc-ture to loads. They influence the form and material choice of each structural memberand of the structure as a whole.

Constraints: This list includes constraints that are dictated by practical and economicissues.

Construction: Several types of construction have been developed for light-weight structuralapplications, the most appropriate one for the application at hand should be chosen.

By judicious considerations of loads, materials, etc. and using the tools of mechanics, thegoal of designing an optimal aircraft structure that meets reasonable design objectives canbe achieved. This process will likely involve iterations, symbolized by the circular arrow inthe figure.

1.2. ELEMENTS OF AEROSPACE STRUCTURES 7

AEROSPACE STRUCTURALDESIGN

Materials- Wood- Plywood- Metals- Composites

Mechanics- Statics- Dynamics- Mechanics of solids- Aerodynamics

Load Analysis- Ground loads- Maneuver loads- Landing loads

Physical Factors- Weight- Strength- Stability- Vibrations- Aeroelasticity- Fatigue- Corrosion

Constraints- Low weight- Low cost- Ease of manufacture- Fit with aircraft requirements

Optimum aircraft structurethat meets the design objectives

Construction- Built-up- Integrally machined- Sandwich construction- Co-cured

Desig

nItera

tions

Figure 1.1: Various disciplines that support aerospace structural design.

8 CHAPTER 1. INTRODUCTION

1.3 Work of the Aerospace Structural Engineer

Structural engineers have very important responsibilities in aircraft/spacecraft design andoperation. Their main responsibility is to ensure the structural integrity of the flight vehiclewhile keeping the weight as low as possible. In order to produce a safe structure that isoptimal, the work of the structures group in an aerospace organization involves [1]:

Applied load estimation: It is obvious that before sizing a structure, the loads that needto be carried must be determined. The load sources in flight vehicles are varied andinclude: aerodynamics forces, power plant thrust, inertia forces, control surface ac-tuators, launching and landing events, armament, thermal loads, docking loads, etc.The results of the load analysis appear as reports with the load design criteria for theaircraft.

Stress analysis: The objective of stress analysis is to specify the geometry (shape) andmaterial for every structural member as well as for joints and connections required toassemble the structure.

Structural dynamics: This subject involves the investigation of the response of the struc-ture to vibration and shock, including aeroelastic phenomena such as flutter. Dynamicphenomena must be studied to determine its effects on the structure and how thestructure should be modified to diminish these effects.

Research: Progress in aerospace structures depends on continued research into analyticaland experimental tools that may improve the accuracy of calculations, into new mate-rials, into new structural concepts, etc. In other words, research leads the way for thedevelopment of new and improved air vehicle structures.

Chapter 2

A Brief History

Anderson [2] wrote very nicely about the importance of structural design and constructionin aerospace vehicles:

In the grand scheme of flight vehicles, the consideration of structural design andanalysis plays a special role. No matter how good the aerodynamics, or howpowerful the propulsion, or how spectacular the flight dynamics, if the vehicledoes not structurally hold together, then it is all for naught.

Actually, structural design has further consequences than just holding the air vehicle to-gether. It actually has a strong bearing on the flight dynamics of an aircraft as will beillustrated in the next section.

2.1 Early Aircraft: The Reign of the Wooden Biplane

Let us compare two very early aircraft, Langleys Aerodrome and the Wright Flyer I. Twoattempts were made in 1903 to fly the Aerodrome, and both resulted in failure. Figure2.1 shows a photograph taken during the second try, at the instant after the aircraft waslaunched from a boat on the Potomac. By then, it was clear that the flight was not going to besuccessful. In fact, the Aerodrome seems to be breaking apart. Note the very large deflectionsof the tandem wings, indicating that the structure was much too flexible. Although structuralfailure may not have been the only factor that caused the Aerodrome to crash, it seemsobvious that it played a role. Nine days after the failure of the Aerodrome, the Wright Flyer1 made the acknowledged first self-propelled, piloted, controlled flight in history, as shown inFig. 2.2. Obviously, the Wright brothers succeeded in the various aspects of aircraft designand construction: aerodynamics, flight controls and structures.

What are the main structural differences between Langleys and the Wright brothersdesigns? The Aerodrome had two tandem wings, whereas the Flyer was a bi-plane, thatis one wing was stacked on top of the other. The bi-plane construction had a significantstructural advantage over the tandem wing design: the two wings and the structure betweenthem formed a truss that was stiff enough to sustain the flight loads. The tandem wingsof the Aerodrome, by contrast, seem to have been much too flexible. Trusses had of course

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10 CHAPTER 2. A BRIEF HISTORY

Figure 2.1: Second launch of Langleys Aerodrome on Dec. 8, 1903. Photograph from [2].

2.1. EARLY AIRCRAFT: THE REIGN OF THE WOODEN BIPLANE 11

Figure 2.2: First flight of the Wright Flyer I. December 17, 1903. Photograph from [2].

been used long before 1903 in building and bridge construction. In fact, the Wright broth-ers adopted the trussed bi-plane design from Octave Chanute who, prior to his interest inaeronautics had been a successful civil engineer.

A schematic of the Flyers truss is shown in Fig. 2.3. Vertical wing struts attachthe two front spars (or span-wise running beams) located at the leading edge of each wing.Similar struts connect the two rear spars. The spars and struts were made of wood. Thediagonal bracing between the wings was made using steel wire. Each wing had a seriesof ribs that served as the truss members that connected the front and rear spars in eachwing. Diagonal bracing in each wing was provided, to some degree, by the cotton fabricused as wing skin. The cotton fabric was sewn so that the threads ran at 45 to the spars.This efficient truss structure was so successful that bi-plane designs were the norm over thedecades of the 1910s and the 1920s, when most airplanes had wooden structures coveredwith fabric. This is not to say that no successful monoplanes existed in this period, buttheir inferior stiffness made them dangerous. In fact, Gordon [5] states that authorities innearly every country frowned on monoplane construction, and in some cases it was actuallyforbidden

Notable examples of early monoplane construction include Bleriots airplanes, oneof which was the first to cross the English channel in 1909. Figure 2.4 shows one of hismonoplanes. Note the wires from the wing to the landing gear and to the apex of the postabove the wing. These wires supported the wing. The upper wires supported the weight ofthe wing when the aircraft is on the ground, while the lower wires held the wing when itwas producing lift. Another monoplane with some claim to fame was the Reissner-JunkersEnte, because it was the first aircraft that incorporated a metal skin.

Aerodynamically, it was clear that eliminating as many bracing wires as possible fromthe wing structure would result in decreased drag and improved performance of the aircraft.Structurally, this meant that the internal structure of the wing would have to be stockier

12 CHAPTER 2. A BRIEF HISTORY

Figure 2.3: Schematic of the Wright Flyer 1 structure showing a truss-type construction.Diagram from [3].

Figure 2.4: Bleriot aircraft similar to the one used to first cross the English Channel. Pho-tograph from [4].

2.1. EARLY AIRCRAFT: THE REIGN OF THE WOODEN BIPLANE 13

Figure 2.5: The Fokker Dr-1 tri-plane eliminated much of the wire bracing by employing atubular spar for improved stiffness. Diagram from [3].

to maintain appropriate stiffness. The thicker wings used towards the end of WWI madethis possible. The Fokker Dr-1 tri-plane, famously flown by the Red Baron, was one aircraftwhere most of the bracing wires were eliminated, as shown in Fig. 2.5. Each wing had asingle spar as shown in the figure. The spar, however, was not a single piece of wood, buta relatively wide hollow box with two internal box spars as shown in Fig. 2.6. Tubularstructural members are very efficient structures to resist bending and torsional loads. Infact, nature has many examples of tubular structures, bamboo comes to mind as well as longbones.

By 1917 the allies were achieving air superiority, so Anthony Fokker developed amonoplane with an unbraced wing, sometimes called a cantilever wing, for the Germans.The Fokker D8, shown in Fig. 2.7 had a performance better than anything available or inimmediate prospect on the Allied side [4]. Unfortunately for the Germans, the faster D8suffered from a substantial number of structural failures. The wings tended to come off theairplane during pull-up maneuvers that should have been within the design limits of theaircraft. Obviously, some aspects of structural design were still not well understood at thetime. Fokker discovered that the problem was a lethal form of aeroelastic instability calleddivergent condition that will be discussed in more detail later. By the end of the war, thetraditional biplane had proven to be the safest aircraft structure and was regarded to be asalmost unbreakable [4].

14 CHAPTER 2. A BRIEF HISTORY

Figure 2.6: Cross-section of the Dr-1 spar. Diagram from [3].

Figure 2.7: An example of a single-wing WWI fighter. The Fokker D8. Photograph from[7].

2.2. THE ESTABLISHMENT OF THE CANTILEVER WING 15

Figure 2.8: An example of truss-type construction. Boeing model 40, 1925. Diagram from[6].

The Boeing Model 40B, shown in Fig. 2.8, was an early passenger plane produced inthe late 1920s. The fuselage is made entirely of a steel tube truss structure with the mainpart of the fuselage covered with thin plywood. The construction of the wings was of typicalbraced bi-plane design, with a wooden skeleton covered with cloth. These airplanes weremuch faster than the early planes of the 1900s and could not depend on the wing fabric coverto act as bracing. Instead, note that wires have been used to brace the two spars and someof the ribs in each wing. This structural concept is called a drag-truss because it stiffens thewing against bending induced by drag in the front-to-back direction.

2.2 The Establishment of the Cantilever Wing

2.2.1 Wood design

The problem of producing structurally sound, single cantilever (unbraced) wing airplanesbegan to be solved in the early 1930s. One of the main innovations appears to have beenthe concept of stressed-skin design. This type of design requires that the wing skin carrysignificant shear stress. Therefore, the wing needs to be covered with a stiff material suchas plywood or sheet metal instead of just fabric. The Lockheed Vega, shown in Fig. 2.9 is

16 CHAPTER 2. A BRIEF HISTORY

Figure 2.9: The Lockheed model 1 Vega had a plywood wing cover, in turn covered by fabric.The box made by the two spars and the plywood panels had a high bending and torsionalstiffness. Diagram from [8].

an example of an early successful cantilever wing monoplane. The wing had two woodenspars, with spruce booms (or caps) and plywood webs. The wing was covered with plywoodpanels. Therefore, the two spars and the plywood skin formed a large box that was stiff inboth bending and torsion. Fabric was then used to cover the wood panels. The tail surfaceswere similarly covered with wood paneling. Although it is obvious that wings are subjectedto bending loads, it is not as intuitive to realize that they are also subjected to large torques.The development of the torque tube using stressed skin design resulted in a great structuraladvantage, and it remains a main feature of conventional transport aircraft wing design.

2.2.2 Metal aircraft

During the 1930s metal, particularly aluminum, alloys started to displace wood as the ma-terial of choice for aircraft construction. Boeing, Lockheed, Douglas and other aircraft com-panies started developing aircraft with all-metal structures. The most successful transportaircraft of this period was the Douglas DC-3, shown in Fig.2.10. The DC-3 had a three-sparwing and featured many of the essentials of modern aircraft construction. The DC-3 was

2.2. THE ESTABLISHMENT OF THE CANTILEVER WING 17

Figure 2.10: The Douglas DC-3 was one of the first successful all-metal aircraft. Diagramfrom [9].

the first airplane that made airlines profitable, without government subsidies.

2.2.3 Pressurized Cabins

Commercial jet-powered aircraft were developed during the 1950s. One of the first was theBritish deHavilland Comet, see Fig. 2.11 that was put in service in 1952. The Comets had acruise speed of 450 mi/hr and a ceiling of 42,000 ft, and so they provided significant improve-ments in speed and comfort over propeller-driven aircraft. By 1953 , however, three Cometshad crashed while in flight, the first under a storm, but the other two under nominal weatherconditions. It became clear that something was wrong with the Comets. After grounding theaircraft and conducting a historical investigation of the accidents (to be discussed later), itwas found that the cause of the catastrophes was structural and, specifically, metal fatigue.The loading on the structure was causing fatigue cracks to develop on the skin that grewto a sufficient length to result in fast fracture. Comets eventually came back into service,but they faced strong competition from Boeing and Douglas, which had developed moreadvanced jet transports, the 707 and the DC-8, respectively.

In 1958, the Boeing 707 (Fig. 2.12) received FAA certification. It incorporated struc-tural improvements based on the experience of the Comet and also incorporated the fail-safe,or damage tolerant, design philosophy throughout the airframe. Aluminum alloys resistant

18 CHAPTER 2. A BRIEF HISTORY

Figure 2.11: The DeHavilland Comet. Photograph from [10].

to cracking were used to prevent fatigue failure even after millions of loading cycles.

2.2.4 Composite Materials

The shape of commercial aircraft has changed little since the development of the 707 as canbe seen by comparing the Boeing 777 in Fig 2.13, designed in the 1990s, to the 707. The fuelefficiency of the newer aircraft is significantly better, however. It has been said [9] that fuelefficiency has improved by 2% per year over the last few decades. Two-thirds of that is dueto improvements in engine technology, and one-third is due to improved airframe technology.No doubt, this is due to the development of lighter structures, aided in part by the use offiber-reinforced composite materials at various points in the structure. These composites offersuperior strength and stiffness-to-weight ratios to metal alloys. The lessons learned in thepast and cost considerations, however, have made the introduction of composite materials agradual process. Figure 2.14 shows the gradual introduction of composite materials in Airbustransport aircraft. The use of composites has been more prominent in military, experimentaland, surprisingly, general aviation aircraft.

2.3 High Performance Aircraft

Military fighter aircraft, like the F-16, are required to withstand significant inertial forcesthat are generated due to the sharp maneuvers they must be able to accomplish. As a resultthe airframe of such aircraft is very robust, as shown in Fig. 2.15. Note how the constructionof the wing involves multiple, closely spaced spars. In addition the wing skin covers arethick, in the order of 0.5 to 1 inch.

2.4. SUMMARY 19

Figure 2.12: The Boeing 707. Diagram from [6].

2.4 Summary

Structural technology has played a very important role in the development of the air-craft. The constant tradeoff between light weight and stiffness/strength has made modernaerospace structures some of the most optimized structures ever designed. Although thisbrief history has concentrated on aeronautical structures, similar issues arise in rocket andspace structures. These structures must be strong enough to withstand the rigors of rocketlaunch, which include high inertial and aerodynamic forces, and must maintain structuralintegrity either in orbit or space travel to minimize deflections due to maneuvers (pointingmaneuvers, orbit insertion, etc.) and thermal loads, such as when going from sunlight toshadow and vice-versa.

20 CHAPTER 2. A BRIEF HISTORY

Figure 2.13: The Boeing 777. Diagram from [6].

Figure 2.14: Evolution of composite materials use at Airbus. Diagram from [11].

2.4. SUMMARY 21

Figure 2.15: The F-16 fighter. Diagram from [8].

22 CHAPTER 2. A BRIEF HISTORY

Chapter 3

Materials

Every airframe component needs to be constructed using an optimally chosen material. Thisoften involves compromises over various considerations. Some of the criteria for materialchoice are given below.

3.1 Criteria for Material Choice

Static structural efficiency: Two properties are of interest here. The first is the specificstrength, defined by the ratio u/ where u and are the ultimate stress and thedensity of the material, respectively. The second one is the specific stiffness, definedby E/, where E is the Youngs modulus of the material. Obviously, materials withhigh specific strength and stiffness are desirable in aerospace structures.

Fatigue resistance: Fatigue is the deterioration of the structure due to cyclic loading,generally due to crack initiation and growth. Materials with high fatigue resistanceare desired in air vehicles that have long operational lifetimes such as transport aircraft.

Fracture toughness: This parameter represents the resistance a material presents to frac-ture. Materials with high fracture toughness are preferred.

Corrosion and embrittlement: These are results of the chemical interaction between thematerial and the environment. Embrittlement refers to the loss of fracture toughness.

Environmental stability: This represents the resistance to mechanical property changesdue to the operating environment, including mechanical stress.

Availability in desired form: Materials are available in various shapes (bar, plate, tube,sheet, etc.) and sizes. Manufacturing can be simplified if the materials is available inshapes and sizes that are close to those of the finished structural members.

Cost: The purchase cost of the material must be balanced against the physical propertiesof the material.

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24 CHAPTER 3. MATERIALS

Fabrication characteristics: This refers to the easy cutting, drilling, etc. of a materialand influences the manufacturing costs of the airframe.

Materials used in satellites and interplanetary vehicles must meet requirements dic-tated by the space environment. Some of the additional material properties of interest forspacecraft are:

Vacuum properties: The very low pressures in the space environment may cause poly-meric materials to decompose and metals to sublimate.

Thermal properties: Low-earth orbit satellites experience wide temperature ranges asthey go from shade to direct sunlight. Atmospheric entry vehicles experience hightemperatures. Thermal conductivity and expansion coefficients are critical parame-ters. Space telescopes are examples of satellites where thermal expansion is of criticalimportance because changes in dimensions can have detrimental effects on optic per-formance.

Radiation properties: Radiation can have the effect of removing structural material andmust be accounted if thin-films are used. Radiation embrittlement can also be a prob-lem.

Magnetic properties: Magnetic fields, such as the earths, can induce in undesired mo-ments that cause orientation change of satellites. Non-magnetic materials are preferred.

The ideal aerospace structural material would have excellent characteristics in all theabove categories. Such material does not exist, so the issue of material choice is usuallya compromise. The structural engineer must decide what properties are most importantfor a given application, and balance those against availability, cost and ease of manufacture.Figure 3.1 gives an idea of what the material property requirements are for different structuralcomponents in the aircraft.

3.2 Typical Aerospace Materials

Many materials are available to the structural engineer, and some of the most commonlyused ones in aerospace structures are listed below.

Aluminum alloys: They are the most commonly used materials in aircraft construction,especially the 2024 and the 7075 alloys because they provide the best material prop-erty package. The former has good fatigue characteristics, the later has a high yieldstress. They can be extruded into complex shapes, but have relatively low meltingtemperature.

3.2. TYPICAL AEROSPACE MATERIALS 25

Figure 3.1: Aircraft material property requirements. Figure taken from [12].

26 CHAPTER 3. MATERIALS

Titanium alloys: Alternative to aluminum alloys for prolonged operation at temperaturesabove 150C. Lighter than steel, stiffer and stronger than aluminum, it can be usedto temperatures in the neighborhood of 1000C. It possesses one of the best structuralefficiency among metals, but it is more expensive and harder to machine.

Steel alloys: Steels are alloys of iron and carbon, with other constituents also added. Theycan develop very large strengths, in the order of 300 ksi, with proper processing. Agreat variety of different steel alloys exist, for example low carbon, tool, stainless, etc.

Composite materials: In aerospace structures, they are generally made of continuousfibers embedded in a matrix. The fibers can be glass, carbon, Kevlar, etc. The ma-trix is usually a polymer, although it could be metal and even carbon (carbon-carboncomposites are used in aircraft brakes). Composites have great structural efficiency inthe direction of the fibers and can be tailored to achieve interesting material properties(one example is zero coefficient of thermal expansion). Composites are slowing replac-ing aluminum parts in airframes. They tend to be expensive and can hide damage,thus making them harder to inspect.

Chapter 4

Structural Nomenclature

The main parts of the anatomy of an airframe are: the fuselage, the wing and the empennage.Each of these is in turn composed of various structural members. Here, the main structuralmembers are presented. Please see Fig. 4.1 showing the structure of the Boeing B-29 tofollow the discussion.

4.1 Wing

The wing is the primary lift-producing part of an airplane. As such, its structure is subjectedto high stresses that arise due to aerodynamics forces and moments as well as loads due tothe weight of engines and stores, reaction loads from the landing gear, etc. The aerodynamicpressure and friction loads act directly on the surface of the wing, or wing skin, usually madeof sheet metal. Depending on the purpose of the airplane, the wing skin thickness can rangefrom 0.016 in. to about 0.75 in. The airfoil-shape of the cross-section of the wing is formedover a set of ribs that also serve to transfer the aerodynamic loads from the skin to the mainstructural part of the wing, a tube-like structure called the wing-box. In the B-29 and manyother aircraft, the wing-box is a tube formed by two spars, which are span-wise beams inthe wing, and the skins in the upper and lower surfaces of the wing between the spars. Sucha torque-box is called single-cell. Aircraft that withstand high wing loads may have morethan two spars, such as the Lockheed C-5 or the Boeing 747. In these cases the torque boxesare called multi-cell. In many airplanes, the outline of the wing-box is easily seen because itis delineated by no-step lines and/or has a different color than the rest of the wing as shownin Fig. 4.2. The bending and torsional characteristics of the wing-box are very importantstructural parameters. Note that the wing-box goes across the fuselage, where it is calledthe wing carry-through box, as shown in Fig. 4.1. The wing skin is stiffened using stringers,which are span-wise bars that are attached to the skin. They are particularly important toresist compressive stresses because they increase the buckling strength of the skin.

The wing spars also serve as attachment points to the many devices that the wing ac-commodates. Examples include flap tracks, aileron and spoiler hinges, landing gear, leadingedge device attachment fixtures, etc. Wing-mounted engines can be attached to mountingribs that are, in turn, attached to the spars. As a first approximation, the wing box can

27

28C

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PT

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4.

ST

RU

CT

UR

AL

NO

ME

NC

LAT

UR

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Figure 4.1: Structure of the B29 Bomber. Diagram taken from [6].

4.2. FUSELAGE 29

Figure 4.2: The Lockheed C141 Starlifter. Note the outline of the wingbox. Photographtaken from [8].

be thought of as a tubular beam that carries both bending and torsional loads. The aero-dynamic loads are distributed over the length of the wing, but point loads induced by theweight of the engines, the reaction from the landing gear, etc. also stress the wing.

The wings of fighter aircraft have low aspect ration and must be very strong to resistthe high loads that result from abrupt maneuvers. As such, they have different construction,as can be seen in Fig. 4.3. In this case multiple spar-like members are used to give the wingthe appropriate strength. Also note the absence of a carry-through box. The placementof the engine makes it impossible to use this structure. Instead, the wings are attached tostrong bulkheads and frames in the fuselage. Low aspect ratio wings cannot be modeled asbeams, instead they should be thought of more as plates.

4.2 Fuselage

The fuselage is the body of the airplane that carries the payload. In flight, the fuselagebasically hangs from the wing, so it is subjected to significant bending loads from its own andthe payloads weights. These loads can be augmented by inertial forces during maneuvers andlanding. As such, the fuselage can usually be thought of as a beam, as a first approximation,if it is relatively long as in the B-29. Like wings, fuselages have a skin that covers the

30 CHAPTER 4. STRUCTURAL NOMENCLATURE

Figure 4.3: The F-16 fighter. Diagram taken from [8].

structure. The thickness of the skin in the fuselage is usually smaller than that used inthe wing. The fuselage skin thickness of a pressurized, narrow-body aircraft such as theBoeing 737 is in the order of 0.040 in. Torsional loads also arise in the fuselage duringrolling and yawing maneuvers. Pressurized fuselages must also serve as pressure vessels thatresist the pressure differential between the inside of the cabin and the outside environment.Fuselage structures can be of truss-frame construction, as shown in Fig. 4.4(c), of monocoqueconstruction, where the skin alone resists all stresses, or of semi-monocoque construction,where the skin stiffened using length-wise running stringers/longerons. In the latter twocases, the skin is formed over frames that maintain the shape of the cross-section of thefuselage. Frames near the wing have to be stronger since they also have to transfer loadsbetween the fuselage and the wing. Semi-monocoque construction, as in the B-29 has beenpreferred for many aircraft. Bulkheads are used to cap longitudinal sections of the fuselage.In the case of the B-29 these bulkheads must be able to withstand pressure differentials. Inmany fighter aircraft, the fuselage also contains and supports the engine, as shown in Fig.4.3.

4.3 Empennage

The empennage contains the horizontal and vertical stabilizers, which generally have similarconstruction characteristics as the wing, although the rear spar may be stronger, which isopposite to the construction of the wing. The elevators are the main control surfaces in

4.3. EMPENNAGE 31

Figure 4.4: Types of fuselage construction. Diagram taken from [12].

32 CHAPTER 4. STRUCTURAL NOMENCLATURE

the horizontal stabilizer and the rudder in the vertical stabilizer. These control surfacescause the center of pressure to move towards the rear of the stabilizers, thus requiring morestrength farther aft [12].

Chapter 5

Structural Design Definitions

It is clear that any structure must be sized according to the loads that it is supposed tocarry. Generally, once the service loads are determined, the structure is actually designed tocarry higher loads in order to establish a margin of safety. Such margin of safety is generallyestablished by government agencies based on the work of committees made of engineersworking on a particular field.

In the case of airplane structures, the applied loads depend on the mission of theaircraft, that is, whether the aircraft will have a transport mission, or a fighter mission, oran aerobatic mission, etc. In each case, an aircraft mission can be roughly divided into fourparts [13].

Taxi and takeoff

Cruise

Maneuvers

Landing

Design loads must be carefully established for every segment of the aircraft mission.In the US, the Federal Aviation Administration (FAA) is the government agency responsiblefor establishing factors of safety for the structure of civilian aircraft. The FAA guidelinescan be reviewed on line by going to www.faa.gov. The military, of course, dictates therequirements for military aircraft.

The objective of structural design is to maintain the shape and integrity of the air-craft during each part of the mission. In other words, the structure must prevent excessivedeformations that can interfere with the operation of the aircraft, and it must not fail (break).

It is important to become familiar with certain terms and definitions used in thedesign of aircraft structures. These are presented next.

33

34 CHAPTER 5. STRUCTURAL DESIGN DEFINITIONS

5.1 Load Factor

The load factor (n) is a multiplying factor that defines the load on the airplane or any partof it in terms of its weight. For the whole airplane in flight, the load factor along the yawaxis is given by

n =L

W(5.1)

where L is the lift and W is the weight of the airplane. For example, the load factor understeady, level flight is n = 1, but n can increase or decrease during maneuvers. It caneven become negative. Furthermore, in some instances, different parts of the airplane mayexperience different load factors.

5.2 Limit Loads

Limit loads are the maximum loads that are anticipated during the service life of the aircraft.When the structure is loaded to the limit load, the resulting deformations must not interferewith the safe operation of the aircraft. These loads are often determined statistically byassessing the probability that such load will arise. A common practice is to establish thelimit loads through a limit load factor that an airplane must withstand and still satisfy thecriterion above. Such limit load factors depend on the mission. Examples of positive limitload factors for different aircraft types are [12]: Fighters (5.3-8.7), passenger transports (2.5),private aircraft (3.8), etc.

5.3 Ultimate Load

The ultimate load is defined as the product of the limit load times the factor of safety:

Ultimate load = Limit load Factor of safety. (5.2)

In aircraft structures, generally the factor of safety is 1.5 to take into account unexpectedcircumstances. This factor of safety is relatively low compared to other structures in civiland mechanical engineering because the weight of the aircraft must be as low as possible.Therefore, aerospace structural design must be very carefully done, paying attention tocareful and accurate analysis and testing. According to the FAA regulations, an aircraftstructure must be able to withstand the ultimate loads for at least three seconds withoutfailure [14].

Guidelines for the calculation of the aircraft loads in compliance with FAA regulationscan be found in the FAA website.

Chapter 6

Fatigue and Fracture

Fracture is a failure mechanism of great concern in structures that can result in unexpected,catastrophic events. Figure 6.1, for example, shows a one-day old Schenectady tanker, whichfailed by splitting as shown in 1943 in clear weather upon returning to harbor after successfulsea trials. Up to 30% of the early Liberty Ships failed catastrophically as a result of an allwelded structure, poor workmanship and the use of materials with low fracture toughness.For more information on the Liberty Ships see [15].

Fracture has not forgiven aerospace structures. In these structures, the problems havegenerally been associated with fatigue. Fatigue is the deterioration of the structure due tocyclic loading, generally due to crack initiation and growth. One catastrophic example ofthe results of fatigue is shown in Fig. 6.2 The following excerpt of the abstract of the NTSBreport explains what happened [17]:

On April 28, 1988, at 1346, a Boeing 737-200, N73711, operated by Aloha AirlinesInc., as flight 243, experienced an explosive decompression and structural failureat 24,000 feet, while en route from Hilo, to Honolulu, Hawaii. Approximately18 feet of the cabin skin and structure aft of the cabin entrance door and abovethe passenger floor-line separated from the airplane during flight. There were89 passengers and 6 crew members on board. One flight attendant was sweptoverboard during the decompression and is presumed to have been fatally injured;7 passengers and 1 flight attendant received serious injuries. The flight crewperformed an emergency descent and landed at Kahului Airport on the Island ofMaui.

The fields of fracture mechanics and fatigue of materials are immense. Here we willbriefly review some of their most basic concepts.

6.1 Fatigue Design Criteria

Fatigue considerations are important parts of aircraft structural design. The effect of fatiguemust be established during design. Two major design philosophies are used in aerospacestructures with respect to fatigue [3]:

35

36 CHAPTER 6. FATIGUE AND FRACTURE

Figure 6.1: Fractured Schenectady Liberty ship. Photograph taken from [16].

6.1. FATIGUE DESIGN CRITERIA 37

Figure 6.2: Aloha Airlines flight 243, April 28, 1988, after an emergency landing.

6.1.1 Safe-Life Design

In safe-life design the structural component must remain crack-free during service. In otherwords, no cracks are allowed and fatigue is seen as a safety problem.

6.1.2 Fail-Safe Design

In fail-safe design the structure can be safely operated even if there is some degree of damage(damage-tolerant structure), but the damage will not lead to structural failure before it isdetected. This requires that the structure be able to absorb failure of a component withoutoverall failure, and that periodic inspections of the airframe be conducted. Inspections haveto be carried with a frequency that will ensure that undetected damage in one inspectionwill not grow to the extent that it can result in failure before the following inspection.

6.1.3 Choice Between Safe-Life and Fail-Sage Designs

Safe-life design is used with parts that cannot be duplicated without paying severe weightpenalties and that can be replaced relatively easily. The landing gear is one example. Fail-safe design is used for major structural components such as the fuselage.

The design requirements for fail-safe design have to specify what a reasonable maxi-mum damage can be allowed in an airframe. Roughly, it is recognized that the strength ofthe structure will decrease from that required to sustain the calculated ultimate loads, but itshould not be allowed to decrease more than it is required to sustain the design limit loads.

38 CHAPTER 6. FATIGUE AND FRACTURE

6.2 Fracture

The subject of fracture addresses the breaking of splitting of objects due to the growth ofcracks. Why things break was a mystery up until the beginning of the 20th century, but bythen it had been observed that catastrophic failure could occur even when the calculatedstresses were much less than the strength of the materials used (hence the need for safetyfactors). Figuring out how fracture proceeds took several steps and people with good physicalunderstanding.

6.2.1 Stress concentration

The issue of stress concentration is a very important first step in the study of fracture.Stress concentrations are local areas of high stress introduced by discontinuities (generallygeometric) in structures. Such discontinuities may be intentional (windows and doors in afuselage, rivet holes, etc.) of unintentional (scratches, dents, cracks, etc.). You can easilyfeel the effect of stress concentrations by taking a strip of paper and tearing it by pullingonly. First take the intact strip as in Fig. 6.3(a) and feel how much force it takes to tear it.Then take an identical strip and put a small tear (about one twentieth or one tenth of thewidth in length) in the middle as shown in Fig. 6.3(b). If you pull this strip, you will find ittakes much less force to tear this strip, even though the cross-sectional area has only beenreduced by a small fraction. The reason is that the small tear leads to the development ofvery high stresses at its tip, in other words, it creates a stress concentration.

The calculation of stress concentrations are in general treated in Elasticity graduatecourses, so only a few important results will be quoted here. One of the most basic cases infracture is that of a large plate with an elliptical hole [16], [19] as shown in Fig. 6.4, subjectedto a uniaxial stress . The stress field around the hole turns out to be complex including allin-plane stress components (x, y, xy). The maximum normal stress occurs at the pointswith x = a, and it is

max = (1 +

2a

b

). (6.1)

In terms of the root radius of curvature of the ellipse = b2/a at those locations, themaximum stress is

max =

(1 + 2

a

). (6.2)

Note that a crack can be approximated by an ellipse with a >> b, which leads to

6.2. FRACTURE 39

(a) (b)Figure 6.3: (a) Uniform plate and (b) Plate with discontinuity

40 CHAPTER 6. FATIGUE AND FRACTURE

and decreasing crack tip radius. Stress concentration factors for many different geometricconfigurations are provided in handbooks.

6.2.2 When will a crack propagate?

Now, supposing a crack is present in a component, what would be the maximum stress thatcould be applied before the crack grows uncontrollably? Or asking the same question inanother way, if a part is stressed to some given level, what would be the maximum cracklength that could be tolerated? The basic theory was developed by Griffith in the 1920sbased on an energy argument that goes as follows [5]: Imagine a crack in a plate under fixededge displacements, and let the crack extend a little increment. Some of the material unloadsjust behind the crack tip, because the sides of a crack are free of forces. Therefore, somestrain energy is released and is available to do work. As the crack advances, however, newsurfaces are created, and it takes energy to create a surface. If the released strain energy isless than the energy required to create the new surface, the crack will not grow. If on theother hand, more energy is released than required to create new surface, the crack becomesunstable and extends rapidly.

6.2.3 Stress Intensity Factor

The stresses near the crack tip for an opening crack deformation are dictated by the geometryof the crack. For plane stress and the coordinate system shown in Fig. 6.5, they are givenby [19]:

x =K2pir

cos

2

(1 sin

2cos3

2

)

y =K2pir

cos

2

(1 + sin

2cos3

2

)(6.4)

xy =K2pir

cos

2sin

2cos3

2

whereK is the stress intensity factor, a constant that depends on the geometry and loading ofthe component. Also note that the magnitude of the stress field varies as 1/

r as measured

from the crack tip. Values for K for many loading configurations are available in fracturehandbooks. For example, for a very large plate with a central crack, loaded uniaxially by afar-field stress applied perpendicular to the crack, as shown in Fig. 6.6:

K = pia. (6.5)

6.2.4 Fracture Criterion

Fracture criteria are generally stated in terms of the stress intensity factor. Once the stressintensity factor is known for a sample of given geometry, such sample can be subjected to a

6.2. FRACTURE 41

x

y

2a2b

Figure 6.4: Plate with an elliptical hole under uniaxial tension.

x

y

xy

r

Crack faces x

y

Figure 6.5: Region near the crack tip.

42 CHAPTER 6. FATIGUE AND FRACTURE

2a

Figure 6.6: A large plate with a central crack.

test to determine the value of K at which the crack extends. This critical value is called Kc,the fracture toughness of the material. It is a material property. Any specimen shape maybe used to determine Kc provided its stress intensity factor is known.

So the answers to the questions posed above are obtained from knowledge of thefracture toughness of materials and the stress intensity factor for the geometry and loadingof the structural member being considered.

Bibliography

[1] Bruhn, E.F., Analysis and Design of Flight Vehicle Structures, Tri-State Offset Com-pany, 1973.

[2] Anderson, J.D., Introduction to Flight, 4th Edition, McGraw-Hill, 2000.

[3] Curtis, H.D., Fundamentals of Aircraft Structural Analysis, Irwin, 1997.

[4] http://www.wpafb.af.mil/museum.

[5] Gordon, J.E., Structures-or Why Things dont Fall Down, Da Capo, 1978.

[6] Badrocke, M. and Gunston, W., Boeing Aircraft Cutaways. The History of BoeingAircraft Company, Barnes and Noble books, 2001.

[7] Bisplinghoff, R.L., Ashley, H. and Halfman, R.L., Aeroelasticity, Addison-Wesley, 1955.

[8] Badrocke, M. and Gunston, W., Lockheed Aircraft Cutaways. The History of LockheedMartin, Barnes and Noble Books, 2001.

[9] Badrocke, M. and Gunston, W., The illustrated history of McDonell Douglas Aircraft,Osprey Publishing, Oxford, 1999.

[10] http://surf.to/comet

[11] Hinrichsen, J., The Material Down-Selection Process for the A3XX, Around Glare, anew aircraft material in context,Klug C. Vermeeren Editor, Kluwer, 2002.

[12] Welch, J. F., Bjork, L. and Bjork, L.,Van Sickles Modern Airmanship, 8th Edition,McGraw-Hill, 1999.

[13] Batill, S., Class notes for Aerodynamics and Design, US Air Force Academy, 1978.

[14] http://www.faa.gov

[15] http://www.mech.uwa.adu.au/DANotes/fracture/maritime/maritime.html

[16] Hertzberg, R.W., Deformation of Fracture Mechanics of Engineering Materials, JohnWiley & Sons, 1976.

43

44 BIBLIOGRAPHY

[17] NTSB Report NTSB/AAR-89/03, Aircraft Accident Report Aloha Airlines, Flight243, Boeing 737-200, N73711, near Maui, Hawaii, April 28, 1988, June 14, 1989.

[18] Niu, MCY, Airframe Structural Design, Conmilit Press, 1988.

[19] Bedford, A. and Liechti, K.M., Mechanics of Materials, Prentice Hall, 2000.