Introduction^[1]

While aerodynamics is the underpinning of atmospheric flight, an aircraft must also have a suitably shaped structure capable of carrying all of the aerodynamic and other loads produced on it. An aerospace structure must be immensely strong and lightweight but also robust and durable, and for these reasons, the structural design options and constraints must be understood. For spacecraft, many structural design goals and engineering challenges are similar to those for aircraft, including the need to use high-strength, lightweight materials. However, special high-temperature capable materials may be needed for supersonic aircraft and reentry spacecraft because of kinetic heating effects.

Early airplanes were simple, glued wood and fabric aircraft structures, and while they could be constructed with simple tools, they were not always so strong and required considerable maintenance. Advances in construction materials and assembly processes led to durable aluminum-stressed skin designs, which have been the preferred construction technique for aircraft and spacecraft structures for nearly a century. More recently, smooth and streamlined aircraft have been made almost entirely of composite materials such as glass and carbon fiber. Composite materials are also used extensively in the construction of modern spacecraft. An advantage of such composite materials is that they can be tailored in shape to carry the applied loads more efficiently, thereby reducing structural weight for a given strength, i.e., the critical metric is the strength-to-weight ratio or structural efficiency, i.e.,

Brief History of Aircraft Structures

George Cayley, the “Father of Aeronautics,” understood the need to build airplanes out of lightweight structures. Cayley had the idea of using stacked wings in the form of biplanes and triplanes to give them a collective structural stiffness and strength. Otto Lilienthal built upon Cayley’s ideas of flight and lightweight structures, building several types of gliders that resembled the wings of birds and bats. Octave Chanute built gliders similar to Lilienthal’s but incorporated external bracing wires to give the wing more structural strength and stiffness. In early 1903, Samuel Langley attempted to launch his tandem monoplane from a catapult, but it crashed after its frail wooden structure failed catastrophically.

By the end of 1903, the Wright brothers had successfully flown their Flyer, which was more strongly built from a wooden skeleton covered with fabric. Their biplane wing design used spanwise spars and chordwise ribs, which were also braced with struts and wires. Wooden structures of that era were typically made of spruce or pine and were relatively lightweight. Nevertheless, such wooden structures were not always as strong or stiff as desired, and structural failures from bending or twisting loads were common.

The main advantage of the biplane is that the two wings, with vertical struts and bracing wires, form a box-like structure, as shown in the photograph below. This type of design is much more resistant to bending and twisting than a single wooden wing, i.e., a monoplane. However, a biplane wing design also has high aerodynamic drag from the bracing struts and wires, a significant overall disadvantage. Nevertheless, this type of wing and airframe construction continued into the 1930s, and many successful biplane aircraft were built.

In 1909, Louis Bleriot of France built and flew a monoplane aircraft made of wood and fabric, although it was extremely fragile. One significant advantage of a monowing is reduced aerodynamic drag compared to braced biplane and triplane wings. Bleriot followed Chatute’s approach, where steel wires supported the single wings from a mast extending above the fuselage. However, the wires still created significant aerodynamic drag on the aircraft. Bleriot also used a truss-type fuselage that was lightweight and strong, and this method became a standard type of early airframe construction.

The German Junkers J-1 of 1910 was a monoplane that pioneered mostly metal construction, the wings skins being covered with very thin gauge sheet steel. Metal also allowed for much stiffer and stronger wings, so wire wing bracing was no longer needed. Steel, however, is three times as heavy as aluminum, which was unavailable then. Nevertheless, by the late 1930s, aluminum alloys suitable for airplane construction were increasingly available, so airplanes made of wood and fabric were increasingly relegated to history. In addition, the years leading up to WW2 led to many advances in aircraft construction techniques, and riveted aluminum “stressed skin” construction techniques were becoming standard for almost all new aircraft.

As airplanes became larger and heavier, other construction methods needed to be developed to obtain structural strength and stiffness, including multi-spar and box beam wing designs. Bonded aluminum honeycomb sandwich panels, developed in the 1960s, have very high stiffness and strength for their weight. These sandwich structures were increasingly used for wing skins, flight control surfaces, cabin floors, launch vehicles, satellites, and many other applications.

Over the last 50 years, there has been a steady increase in honeycomb and foam core sandwich components made from composite materials such as glass and carbon fiber. In the last few decades, advanced materials and manufacturing techniques have allowed a transition from mainly building aluminum airframe structures to those made with a majority of composites. As a result, modern aerospace structures may have 50% or more of their structure (by weight) made of composites, with some new airframe designs reaching as much as 90%.

Types of Loads & Stresses

The aerodynamic and other loads or forces imposed on a flight vehicle cause internal stresses in the material(s) from which the vehicle is made. Stress can be viewed as the internal action that opposes the deformation of the material under load. The corresponding deformation of the material under load is called strain. Therefore, when any material is subjected to external loading, it will become stressed and deformed, i.e., it will always exhibit some strain, regardless of how stiff or strong the material is.

As shown in the figure below, five types of stresses and strains can be produced in the parts comprising aerospace structures, namely compression (pushing or squeezing), tension (pulling), shear, torsion (twisting), and bending. These stresses and strains can be produced individually in a structural component or in combination with other loads.

• Compression is the stress that tends to squeeze and shorten the part. The compressive stiffness of a component is its resistance to compression forces.
• Tension is the stress that resists the force that pulls and tries to extend the part. The tensile stiffness of a component is its resistance to tensile forces.
• Shear is the stress that resists the forces tending to cause one material layer to move relative to the adjacent layer. For example, most fasteners that hold aerospace structures together are subjected to a shearing action. Examples of fasteners include screws, bolts, and rivets.
• Torsion is the stress produced from a torque or twisting effect. A torque is a moment, so it is the product of a force times a distance or “arm.” Therefore, a component’s torsional stiffness can be viewed as its resistance to this twisting action.
• Bending stresses result from a combination of compression and tension in the material. A beam-like spar or other component subjected to a bending moment will be compressed on one side and stretched on the other. In most cases, the individual structural members of aerospace structures are designed to carry mostly tension or compression rather than pure bending.

Stress & Strain Relationships

Stress, given the symbol , is used as a measure of the forces that cause a structure to deform and can be defined as the force per unit area acting on the cross-sectional area of the structure, i.e.,

(1)  

where is the force, and is the area of the cross-section over which the force acts. Stress has units of force per unit area, which is analogous to structural internal pressure. A force pulling on a structural member will cause it to elongate, which creates tensile stress. A force squeezing a member is called compressive stress. A structure subjected to forces from all sides is called bulk stress.

Strain, given the symbol , is a measure of the deformation of an object under such stress and is defined as the fractional change of the object’s length relative to its original length, i.e.,

(2)  

where is the original length and is the change in length. Notice that strain is a non-dimensional quantity.

The stress produced in a structural member also depends on the stiffness of the material used for that member. Many materials exhibit a linear relationship between stress and strain up to a certain point, referred to as the proportional limit. This linear stress-strain relationship is known as Hooke’s Law, and the slope of the stress-strain curve is called the modulus of elasticity, given the symbol , which is usually called Young’s modulus, i.e.,

(3)  

The modulus of elasticity or Young’s modulus is one of the factors used to calculate a material’s deflection under external loading, i.e., the higher the stiffness, the lower the structural deflection. Different materials have different characteristics, as shown in the figure below. There are many online resources where quantitative information on material characteristics is readily available. Notice that a stiff material has a high Young’s modulus and will change its shape only slightly under external loading. A stiff material requires high loads to deform it elastically. A flexible material has a low Young’s modulus, and its shape will change considerably under loading.

Eventually, with increasing applied load, the linear relationship between stress and strain changes and becomes nonlinear. This point is called the yield point, and the material now behaves like a plastic (i.e., the material flows) in that deformations caused by the loads will remain present even after the load is removed. Therefore, the material will take on permanent plastic deformation. Eventually, the material will break or rupture if the stresses become too high. A strong material requires high loads to permanently deform it as well as to break it.

Buckling

Aerospace structures have relatively thin structural members, including thin external skins. Buckling may occur when an aerospace structural component is subjected to high compressive stresses. Buckling is characterized by a sudden out-of-plane deflection of the structural member with increasing compressive loading, as illustrated in the figure below. Different types of buckling may occur depending on the kind of structure and the applied loads.

On aerospace structures, their thin skins need to be designed to prevent buckling under normally expected flight loads. This is done by supporting the skin from below, such as using stringers or with a substrate such as a honeycomb sublayer. However, stringers may also buckle when carrying high compressive loads, as shown in the image above. When they are under load, a certain amount of skin wrinkling of aerospace structures can generally be expected. When such a structure is assembled, the larger unsupported areas of the skin often tend to form mild wrinkles, usually between frames and stiffeners, even under normal loadings. Under these conditions, the skin develops a form of mild elastic buckling and carries the normal compressive loads for which it was designed; it will return to its undistorted shape when the load is removed.

An aerospace structure may buckle, and skins may wrinkle even though the stresses in the structure are well below those needed to cause a material failure. But, if sufficiently severe, buckling can result in permanent material deformations that significantly reduce the structure’s load-carrying capability. Further loading on a structure after severe buckling can lead to structural failure; the example shown in the image below is from a NASA test on a representative spacecraft structure.

The onset of buckling can be predicted using theoretical methods first developed by Leonhard Euler. The Euler buckling formula allows a prediction of the maximum axial load an “ideal” structural member in the form of a column can carry before buckling. An ideal component is perfectly straight, made of a uniform homogeneous material, and free from any initial stress.

When the applied load reaches a critical load, the column reaches a state of unstable equilibrium. In this condition, any small lateral load will cause buckling. The buckling force or critical forces, , can be written as

where is Young’s modulus of elasticity, is the second moment of area of the cross-section of the column, and is the unsupported length. The value of , the effective length factor, depends on the end conditions of the column. For example, if both ends are pin-jointed (i.e., fixed but free to rotate), then . If both ends are rigidly fixed to prevent rotational movement (i.e., encastré), then , and the buckling force is twice as high. There are similar buckling formulae for plates and shells.

Stress Analyses

Determining aerodynamic loads and evaluating the resulting stresses imposed on the structural components is called a structural stress analysis. While a stress analysis may be able to be conducted on separate components or assemblies, it should be appreciated that any single member of the structure may be subjected to a combination of stresses from multiple loading paths. Therefore, a thorough stress analysis generally has to consider the aircraft’s total structure to ensure that it is strong and stiff enough to carry all the flight and ground loads.

This type of stress analysis is performed using a finite-element method or FEM. The FEM is a numerical method in which the aircraft structure is modeled by a set of finite blocks or lattice elements interconnected at discrete points called nodes; an example of a lattice used for an entire aircraft is shown in the figure below. Each block or finite element may have different properties, such as thickness and material characteristics, giving the FEM tremendous optimum design capabilities. In this regard, the design for an aircraft or spacecraft might be to find the strongest and most durable structure for the minimum possible weight, as well as having good fatigue resistance or other desirable characteristics.

Fuselage Structures

The fuselage is the main structure or “body” of the aircraft. It provides space for the aircrew, passengers, cargo, and other equipment. There are two basic types of fuselage construction: the truss type or the monocoque/semi-monocoque type. In single-engine aircraft, the fuselage also usually houses the engine. In multi-engine aircraft, the engines may be in the fuselage or attached to it, although they may also be suspended from the wings or contained within the wings.

A truss type of fuselage is a lightweight framework of steel alloy tubes that gives stiffness and resists deformation from the applied loads. This type of structure is sometimes referred to as a space-frame design, as shown in the figure below. Diagonal web members give the truss most of its bending and torsional stiffness. The truss type of fuselage frame is usually constructed of light steel alloy tubing that is welded together such that all members of the truss carry mostly tension and compression loads.

In some aircraft, truss fuselage frames may be made of aluminum alloy rods riveted or bolted together at their ends using gusset plates. The truss type of fuselage is generally covered with fabric, although thin plywood or aluminum sheets may give additional stiffness and improve durability. The truss type of fuselage is often used on smaller, general aviation aircraft, but the design does not scale well for use on larger aircraft because it becomes too heavy.

The most common type of fuselage construction for aircraft is monocoque or semi-monocoque. As shown in the figure below, the monocoque (i.e., single shell) fuselage relies mainly on the skin’s strength to carry the primary loads. In this case, the skin must be thick enough to avoid large deformations or buckling, which drives up the structure’s weight. Because the skin is designed to carry significant loads, it is known as a stressed skin design. Skin buckling is most likely under bending, compression, or torsion loads in the monocoque structure shown in the figure below.

Most modern aircraft are of semi-monocoque type of construction, as shown in the figure below. In this design, the skin can be thinner (hence lighter) and is reinforced internally under the skin by longitudinal members called longerons. The longerons are riveted to the skin. The longerons give more structural stiffness and mainly prevent the skin from buckling. The longerons, usually made from single-piece aluminum alloy extrusions in the form of “U” or “T” sections, will extend across several frame members and help the skin support primary bending, torsion, and compressive loads.

Smaller stringers are also used in a semi-monocoque structure, which gives some additional rigidity. They are attached under the skin to form its shape and further prevent it from buckling. The stringers and longerons work primarily in tension and compression from various loads applied to the fuselage. These components are all connected using rivets and perhaps other fasteners such as bolts, which in totality form a very strong and rigid structure.

Most, if not all, commercial aircraft have pressurized fuselages, which means that the cabin pressure is increased to produce a differential pressure between the air inside the cabin and the outside atmosphere. Pressurization is achieved by designing an airtight fuselage pressurized with a compressed air source, usually from engine bleed air. In most pressurized airplanes, the cabin pressure is maintained at an altitude equivalent to about 6,000 ft to 8,000 ft (about 2,000 m to 2,500 m) to allow for good passenger comfort. Nevertheless, some passengers may still exhibit mild hypoxia symptoms (oxygen deprivation) during long-haul flights, contributing to the all-too-frequent malady known as jet lag.

Structurally, pressurization causes significant tensile and hoop stresses to be developed in the fuselage structure, adding not only to the complexity of its design but also increasing its structural weight. Basically, the fuselage is a large pressure vessel that expands like a balloon as the aircraft climbs to altitude. The ceiling for most large commercial transport airplanes is often limited by cabin pressurization requirements, which set a structural stress limit on the fuselage. Naturally, the stresses can be reduced by increasing the thickness of the fuselage skin, but this approach also drives up airframe weight significantly.

Another type of semi-monocoque structure is the geodesic design, pioneered by the British aeronautical engineer Barnes Wallis in the 1930s. The famous Vickers-Armstrong Wellington bomber, shown in the photograph below, was built of a geodesic structure, and it proved its structural integrity after suffering battle damage.

While a less common type of airframe design, this structure is relatively lightweight with good strength and has also been used in spacecraft designs. While this type of geodesic construction has advantages, it tends to be more expensive to build and repair. It is unsuitable for pressurized fuselages because replacing the fabric covering with sheet metal quickly drives up the structural weight compared to other types of construction, such as the more common semi-monocoque design.

Wing Structures

The wings create lift to overcome the aircraft’s weight and are usually the aircraft’s largest structural and heaviest component. Therefore, by design, wings must be extremely strong and lightweight. Wings come in many shapes and sizes, and any particular wing design depends on many factors related to strength, weight, and aerodynamic efficiency. Wings may be externally braced using struts to support the wing and carry the aerodynamic loads, which tends to give a lighter overall design at the expense of some drag.

However, more commonly, wings are of a complete cantilever beam design to reduce drag, i.e., without any external bracing. Most wings have various internal structural members covered by a thin skin, i.e., they are of a typical semi-monocoque stressed skin design, as shown in the figure below.

The internal structures of wings are made up of a lattice of spars and stringers that run spanwise and ribs or other types of formers that are placed chordwise. The main spar is the primary structural member of a wing and carries most applied bending and shear loads. The skin carries much of the torsional loads and transfers the stresses to the wing ribs.

Depending on a specific aircraft’s design criteria, spars may be made of metal, wood, or composite materials. Bolts are usually used to attach the spars to the fuselage, and various fittings are used to carry the loads. Wing main spars are generally variations of I-beam structures made of solid extruded aluminum or several aluminum extrusions riveted together, as shown in the figure below. The I-beam’s top and bottom parts are called the spar caps, which take the compression and tensile loads produced from bending. The vertical section, called the web, carries the shear loads. The web forms the spar’s principal depth portion, and the cap strips are attached.

Today, composite materials are also used to make wing spars because of their excellent strength-to-weight ratio and resistance to fatigue cracking. Fatigue is the weakening of a material caused by repeated cyclic loading, which can result in a catastrophic failure of a wing spar if a fatigue crack grows too much. Sharp corners are a potential source of fatigue cracks, so round holes and smooth transitions increase fatigue resistance. Smaller airplanes may have just one or two spars. “False” or part-span spars are also commonly used in wing construction, which are used as hinge attach points for control surfaces such as flaps and ailerons.

Larger aircraft have multiple spars that may be built into a box beam, a standard structural design for commercial airliners. It uses two main longitudinal spars to connect bulkheads, forming a box shape with tremendous bending and torsional strength, as shown in the figure below.

Secondary spars and stringers may be used for strength and to prevent buckling but for structural redundancy to make the wing fail-safe. In this context, “fail-safe” means that if one critical wing component fails, there is enough remaining structural redundancy and alternative load paths to prevent a catastrophic failure. The FAA’s accepted definition of fail-safe is “The attribute of the structure that permits it to retain its required residual strength for a period of unrepaired use after the failure or partial failure of a principal structural element.”

The interior of box beam wings may also be used for fuel tanks. The wing joints are sealed with a special fuel-resistant sealant that enables fuel to be stored directly inside the structure, known as wet wing design. Alternatively, a separate bladder or tank can be fitted inside the wing.

Wing ribs give the wing its aerodynamic (airfoil) shape and transmit the skin loads and stringers to the spars. The lightweight ribs are usually stamped out from a flat aluminum sheet, and the flanged holes in the ribs lighten the overall assembly. The rib has a cap that stiffens and strengthens the rib and attaches to the wing skin. Ribs can extend from the wing’s leading edge to the rear spar or the wing’s trailing edge. Similar ribs are also used to construct ailerons, elevators, rudders, etc.

A winglet is a vertical upturn of the wing tip, resembling a vertical stabilizer, as shown in the figure below. Winglets are designed to reduce the drag created by wing tip vortices, i.e., the induced drag. Winglets are made from aluminum or composite materials and are often retrofitted to existing wings to improve the airplane’s performance.

Empennage Structures

The tail assembly of an aircraft is called the empennage. The structure of the vertical (fin) and horizontal stabilizers is very similar to that used in wing construction, including spars, ribs, and stringers, all covered with a thin skin. They perform the same functions, shaping and supporting the structures and transferring stresses to the fuselage. However, the stabilators also have control surfaces, which means additional structural requirements exist because of the airloads produced by control deflections. For example, rudder application causes a change in the force on the fin and a torsion or twisting effect. These loads are, in turn, applied to the fuselage as both a bending moment and a torsional twisting moment.

Flight Control Structures

An airplane’s primary flight control surfaces are the ailerons, elevators, and rudder. Other movable surfaces include flaps and spoilers. The ailerons are attached to the trailing edge of both wings and are used for roll control. The elevator is attached to the trailing edge of the horizontal stabilizer and controls the aircraft in pitch. The rudder is hinged to the trailing edge of the vertical stabilizer and gives yaw or directional control.

Control surfaces are typically made from an aluminum alloy structure built around a single spar member or torque tube to which ribs are fitted and skin is attached. However, they may also be made of a honeycomb sandwich structure, built from a core of honeycomb material laminated or sandwiched between thin outer skin sheets using an adhesive, as shown in the photograph below. The paper honeycomb material is called Nomex, but aluminum honeycomb may also be used. The skins may be made of aluminum sheets or composite materials. Primary control surfaces and flaps are often constructed from composite honeycomb materials, especially on larger commercial airliners. Other sandwich construction structures may include cabin floors, nose cones, and engine cowlings.

Helicopter Rotor Blades

Sandwich construction is used extensively in manufacturing helicopter rotor blades, an example being shown in the figure below. The rotor blades must be extremely strong but also lightweight. The dominant loads on the blade are from centrifugal effects caused by their rotation, which produce a tensile load directed along the length of the blade. The blades are also subjected to cyclic lift forces that cause bending and torsional twisting. Early rotor blades were made of aluminum or steel, perhaps using metal honeycomb as a core material.

Using composites has opened up the design of rotor blades to meet an increasingly challenging set of aerodynamic and structural requirements, including fatigue resistance. Using foam such as Rohacell and paper honeycomb such as Nomex allows for a minimum-weight structure highly resistant to skin and web buckling. A leading edge erosion shield of a hardened nickel-steel alloy prevents blade abrasion in dusty or sandy environments.

Material Fatigue

Fatigue is a material failure resulting from repetitive loading cycles, usually at high applied stress levels. In a fatigue failure, a structural component will fail at an applied load well below the average failure load. Aluminum airframe structures are prone to fatigue issues because they are highly stressed and subjected to repetitive loading cycles, e.g., during takeoff, routine and maneuvering flight, rough air, landing, etc. Composite materials tend to have much better fatigue characteristics. Regardless, sharp corners and regions of stress concentration are always potential sources of fatigue cracks, so round holes and smooth transitions are used to increase fatigue resistance. Assessing the fatigue life of an aircraft is an integral part of the design process.

Metal fatigue is the weakening of a metal caused by repeatedly applied cyclic loads, typical of those found in flight structures, resulting in the formation of cracks. The tragic crashes of the de Havilland Comet brought attention to the issue of metal fatigue, which was found to have originated at stress concentrations at improperly drilled rivet holes. The pressurized fuselage, coupled with the thin skin and higher stresses around window cutouts, caused the fuselage of the Comet to suffer explosive decompression, resulting in the loss of two aircraft; the original report explains the details. The subsequent research and understanding of the metal fatigue problem led to significant improvements in the strength and durability of lightweight aluminum structures that benefited all airframe manufacturers.

Metal Fatigue

The mechanism of metal fatigue starts with the development of small micro-cracks in the structure, which grow slowly over many repeated loading cycles to become notable cracks until, eventually, the surrounding material catastrophically fails from a local overstress, as shown in the schematic below. Such cracks often occur in areas of airframe structures that are highly loaded but often difficult to inspect, at least using visual methods. As a result, they can go unnoticed until structural failure occurs, which can be a safety-of-flight issue.

Fatigue failures generally occur in localized regions called stress risers, which can be caused by damage, scratches, or corrosion. Rivet holes are a common source of fatigue cracks, and holes must be adequately prepared after drilling to remove burrs and rough edges before driving home a rivet. After many loading cycles, micro-cracks can be initiated in the metal at any stress riser. These cracks grow in size and length with each loading cycle, although the process is typically very slow. Eventually, the enlarged cracks can reach a size where the stresses at the tip are high enough to cause more rapid crack propagation. The signature of the crack growth in the material is the curved striations emanating radially from the stress riser, which can be seen in the photograph below. The higher stresses acting over the remainder of the (uncracked) material become enough to cause sudden ductile failure from stress overload. However, it may take tens or hundreds of thousands of loading cycles for this process to occur, assuming the cracked part is not noticed during routine inspection and then repaired or replaced.

Fatigue characteristics are measured by testing material coupons, sub-structures, and even complete airframes. By subjecting the structure to the simulated cyclic magnitudes and stress levels encountered during flight, areas prone to fatigue cracking can be identified and remedied. Remediation includes replacing the part or reinforcing the structure with a patch or a doubler. The importance of FEM at the design stage cannot be underestimated, which can predict areas of locally high stresses and those likely to be subjected to fatigue issues before the structure is even built.

Despite best design practices to eliminate stress risers, fatigue cracks will inevitably appear in an aircraft structure over decades of use, e.g., especially on so-called aging aircraft. Therefore, detecting and repairing such fatigue cracks is essential before they result in severe structural failure. In simple, unpressurized structures, the crack growth can be stopped by drilling a suitably radiused hole at the end of the crack to relieve the stresses. In pressurized structures, a complete repair may be required with the addition of a reinforcing structure that is appropriately sealed. Aging aircraft may also suffer from corrosion issues and corrosion-induced fatigue cracking, resulting in serious structural problems that may be difficult and expensive to repair. For these reasons, older aircraft are often retired from service when they experience significant downtime and/or costly repairs.

Wöhler Curves

Fatigue properties of materials are often described using an – curve or Wöhler (Woehler) curve, an example being shown in the figure below. The – curve describes the relationship between cyclic stress amplitude and the number of cycles to failure. On the abscissa, the number of cycles to failure is given on a logarithmic scale, and the ordinate (either linear or logarithmic), the stress amplitude (or sometimes the maximum stress) of the cycle is used.

Ferrous materials, typical of Material A, tend to have good fatigue properties. They generally exhibit an endurance limit below a certain stress amplitude, effectively having infinite fatigue life. Aluminum, typical of Material B, has no such behavior and will continue to show a decreasing fatigue resistance with increased cycles. In most cases, aluminum parts subjected to high cyclic stresses will have to be assigned a safe life in that the part must be withdrawn from service at a certain number of cycles, often measured in takeoff and landings or flight hours. Composite materials, typical of Material C, have good fatigue properties and are much better than most metals. However, their fatigue characteristics tend to have significant variability during testing despite being generally excellent and having much longer fatigue lives than aluminum.

These types of – curves are obtained from fatigue tests done under controlled conditions in the laboratory. Tests are performed by applying cyclic stresses with constant stress amplitude on various types of specimens until the final fatigue failure occurs. Sometimes, the testing may be stopped after many cycles (), the results being interpreted as an infinite service life. Fatigue curves are often obtained for material specimen coupons, which are designed to give the fatigue properties of the material itself rather than a specific part.

Actual flight structures made of multiple components will have more specific – curves. Sometimes, a critical flight structure being tested, such as a wing spar or wing carry-through structure, will have notches cut to initiate fatigue cracking so that the fatigue life of the aircraft is not over-estimated. Complete airframes may also be tested on the ground in a test rig where the cyclic flight loads can be simulated much quicker, and potential issues can be identified before the aircraft ever develops any fatigue cracks in regular use.

Miner’s Rule

An aircraft will be subjected to many types and amplitudes of stresses during normal flight. Unexpected loads, such as the occasional hard landing, may have to be factored into the fatigue life estimate. It is possible to estimate the fatigue life using the method known as Miner’s Rule. This rule states that the cumulative fatigue damage is given by

(4)  

where is the number of load cycles to which the component has been subjected in a certain stress range, and is the number of load cycles in that stress range to reach fatigue failure. The index varies over discrete stress ranges. The ratio is referred to as the partial fatigue damage, and of all partial damage cycles over all occurring stress ranges, it is then a measure of the total fatigue damage. Failure can be expected to occur when .

Miner’s Rule assesses the fraction of the fatigue life consumed at each stress level and then adds the fractions for all the levels to estimate the fatigue damage in aggregate. The stress level damage can be defined as the product of the stress, , and the number of cycles, , operated under that stress, i.e.,

(5)  

Miner’s Rule assumes that the stress level damage to failure is the same for all applied stress levels, so

(6)  

For example, if for a component, it will fail after 5,000 cycles at a stress level of 1, 1,000 cycles at a stress level of 5, or 2,500 cycles at a stress level of 2, etc. Therefore, the cumulative damage can be written as

(7)  

While Miner’s Rule is imperfect, partly because it assumes that the fatigue damage in each stress range is linearly additive, it gives reasonable estimates of structural fatigue life.

Worked Example #4 – Estimating Fatigue Life

It is required to estimate the “cycles to failure” of a thin aluminum rod. Preliminary experiments suggest that the angle between the two arms of the bent rod affects the number of cycles to failure. Therefore, the “angle” can be treated as a surrogate for the “stress.” The first test suggests that it takes 63 repeated bends to an angle of 30 degrees for the rod to suffer a fatigue failure. A subsequent test on a new rod subjects it to the following repeated bends and loading cycles.

Bend angle (deg)	Cycles
15	40
40	15
45	10

Based on Miner’s rule, how many cycles with a 30-degree bend can be expected to break the rod?

It is necessary to calculate the cumulative damage for each stress cycle, i.e.,

   

In this case, , so the cumulative fatigue damage, in this case, can be expressed as

   

where is the remaining number of cycles. Performing the arithmetic gives

   

Therefore, , and so .

Fail-Safe & Safe-Life Designs

Aerospace engineers have developed safe-life and fail-safe design philosophies for structural design. Fail-safe designs incorporate various techniques, such as structural redundancy and multiple load paths, to prevent catastrophic failure in the event of a single component failure. Safe life design is the philosophy that a component or system is designed not to fail during operational use within a specific period. This period may be defined by the number of flight hours, takeoffs and landings, years of operation, or some combination. Testing and analysis can estimate the expected life of the component or system, with a margin of safety also being applied. The part or component must be removed from operational service and scrapped at the end of its expected life.

The decision between a safe life and a fail-safe design in structural design depends on a cost-benefit analysis of the likelihood and the potential consequences of failures. The benefit of a safe-life design includes freedom from specific inspection processes and maintenance cycles, which can save an operator much time and money. However, fail-safe designs are usually heavier and more expensive. Safe-life designs are often simpler and lighter and aim to minimize unplanned maintenance and the possibility of failure by designing components to last for a specific period. However, this period may still be thousands of flight cycles or hours.

An example of a safe-life versus failsafe structure is shown in the figure below for a wing spar, a critical aircraft component. Notice that in the event of a failure of the lower spar cap, such as from fatigue cracking, the fail-safe structure has enough redundancy using an alternative load path to carry the bending moment loads. Unless the fatigue cracking of the safe-life structure is identified before progressing too far, the spar will fail catastrophically under load.

The final decision to employ one or the other design philosophy must be made on a case-by-case basis, and the specific application of the parts or systems to different types of airframes. For example, a commercial airliner is designed using fail-safe principles, as are military aircraft. The use of the fail-safe design philosophy in the aircraft industry provides structural redundancy against damage that may occur during an aircraft’s service life. By incorporating fail-safe design features, the consequences of a single component failure can be minimized, ensuring the safety of the aircraft and its passengers.

However, a small general aviation (GA) airplane may be designed using safe-life principles to save weight and cost, recognizing that a GA airplane will likely be flown much less frequently and accumulate a much lower number of loading cycles over its life. This approach assumes that the components will not be subjected to a critical number of cycles during their lifespan and so do not require the same level of durability and safety factors as commercial or military aircraft. Nevertheless, catastrophic structural failures do occur on aging GA airplanes.

Composite Structures

Composite materials are increasingly important in the construction of aerospace structures. The aerospace industry constantly strives to improve airframe manufacturing by reducing weight and costs, and composite materials are very attractive to this end. Today, larger, lighter, and more integrated aircraft and spacecraft structures are built from composite materials such as carbon fiber epoxies. Modern composite airframe construction also improves aerodynamics by eliminating surface joints and rivet heads, providing an exceptionally smooth airfoil shape and reducing drag.

A composite structure consists of a core fiber material, some reinforcing material, and a resin binder. Each of these substances alone has poor strength, but when appropriately combined as a matrix, they become a very stiff and strong structure. The fibers are the primary load-carrying elements of a composite material. Still, the material is only strong and stiff in the direction of the fibers, as shown in the figure below.

The fibers can be laid up at any combination of angles in an optimum arrangement to carry the applied loads most structurally efficiently. Airframe components made from composites can be designed using FEM so that the fiber orientations produce the optimum mechanical properties of the component in response to the applied loads. Making an anisotropic material (e.g., bidirectional or multidirectional fibers) is critical to the high strength-to-weight ratio of composite components compared to using isotropic materials such as aluminum.

In the 1960s, secondary airframe structures, such as fairings, spoilers, and flight controls, were developed out of composites for weight savings over aluminum parts. New generations of aircraft are being designed with entire fuselages and wing structures made of advanced composites, although the manufacturing techniques and tooling require considerable financial investments. Advanced composites are typically classified as those containing fiber volumes greater than 50%. The photograph below shows a composite wing spar being laid up for curing in an autoclave. The fibers can be laid up anisotropically, with the fibers best aligned at the angles needed to carry the applied loads. The resulting structure will have a higher strength-to-weight ratio than a metallic structure.

There are two main classes of advanced composites: thermoset and thermoplastic, but ceramic and metal matrix types also exist. The manufacturing processes are designed to create high-quality composite parts at the standards required for the airworthiness certification of aerospace products. The advantages of using advanced composite materials for structural design are their high strength-to-weight ratios, optimum load-carrying capabilities, elimination of many rivets and other fasteners, and fatigue and corrosion resistance. Eliminating rivets alone may save 5% of the structural weight over conventional aluminum construction methods.

However, one concern for aircraft is that composite materials can be more difficult to repair after damage than metallic construction. New repair methods are constantly being developed for composite materials that can restore the structure’s original design strength. Nevertheless, composite structural repair needs specialized tools and materials and is only easily accomplished at specialized repair facilities, which will not exist at most airports. In this regard, damaged aircraft may need to be ferried empty to these special facilities, the damage repaired, and the aircraft eventually returned to service.

Worked Example #5 – Considerations with Aging Aircraft

What might be some of the specific airworthiness concerns that the FAA might be associated with “aging aircraft,” i.e., those flying aircraft 20 to 30 or more years old? Also, look at Part 26 of the FARs – what do these FARs say about older aircraft and their required maintenance?

The FAA is concerned with the airworthiness of aging aircraft, as these aircraft may experience deterioration of materials, systems, and components over time. To ensure their continued safe operation, the maintenance and inspection requirements for older aircraft may become more frequent and complex. Part 26 of the Federal Aviation Regulations (FARs) establishes requirements for the continuing airworthiness of aircraft and related products, parts, and appliances. It covers the maintenance, preventive maintenance, rebuilding, and alteration of aircraft, engines, propellers, and appliances. These FARs specify the inspection and maintenance requirements for aging aircraft, including requirements for repetitive inspections and structural assessments. The requirements for older aircraft may be more stringent than newer aircraft and may include more frequent inspections and particular maintenance tasks. Part 26 also outlines the FAA’s policies and procedures for certifying aging aircraft and granting an extension of time for compliance with airworthiness directives. These FARs aim to ensure the safe operation of older aircraft and reduce the risk of in-flight structural failures.

Airframe Weight Estimation

A goal in flight vehicle design is always to obtain the maximum performance for the lowest structural weight and lowest cost. However, this goal is not always so readily obtained in practice. In this regard, “cost” includes both the acquisition cost of the vehicle or its “price,” as well as its operational costs. A flight vehicle comprises many parts, generally combined into major groups or sub-assemblies such as wings, fuselage, tail, undercarriage, propulsion system, etc. Of course, the weight of a new aircraft design is never known a priori and must be obtained iteratively as an integral part of the design process.

For preliminary airframe design, weight estimates can be performed using historical data for existing aircraft, such as the approaches discussed by Ramer and the related approaches documented by Torenbeek and Roskam. As the design process is refined, which will inevitably include computer-aided design (CAD), finite element methods (FEM), and computational fluid dynamics (CFD), the estimated weight of the components and sub-assemblies can be obtained more accurately. The effects of weight on performance and cost can then be reassessed, and the structural design iteratively refined toward closure. It should be recognized that the weight of an airframe design generally grows disproportionately quickly with increasing size (i.e., the so-called “square-cube law“), which becomes a significant design challenge for commercial aircraft, in particular.

Advanced materials and sophisticated manufacturing techniques may be considered, reducing the required material and lowering airframe weight. The extra design time and investments in tooling in accomplishing significant airframe weight savings may result in a higher useful weight for the aircraft (i.e., fuel load and payload) but not necessarily a lower cost or acquisition price. Nevertheless, the long-term economics of higher payloads and lower operational costs for airliners are very attractive to an aircraft operator such as an airline.

What is the payload?

Payload refers to the weight, , carried on the aircraft that pays the bills. The payload comprises the passengers and their baggage as well as cargo. Useful load, , includes everything on board the aircraft that is not part of the aircraft’s empty weight, . The empty weight comprises the weight of the airframe, engines, and all necessary systems for flight. Fuel is not a payload but part of the useful load. The useful weight, , therefore, is the sum of the payload weight, , and the fuel weight, , i.e.,

   

The useful load and, hence, the payload weight can vary depending on the aircraft type, the intended purpose of the flight, the altitude the aircraft flies at, and the distance of the flight. For most aircraft, the payload and fuel load can be traded off with each other in that more payload can be carried with a lower fuel load. Payload is an essential consideration for airlines because they need to have as much payload as possible but also ensure that they take sufficient fuel for the flight and do not exceed the maximum certified gross takeoff weight, , for any given aircraft, i.e.,

   

Spacecraft Structures

Many of the structural design challenges for spacecraft are similar to those for aircraft, including the need for high strength-to-weight materials and low manufacturing costs. Consequently, spacecraft structures are mainly of thin-walled, semi-monocoque design. They are subject to most, if not all, of the issues associated with aircraft structural design, an example being shown in the photograph below. Today, most space vehicles are constructed with a significant amount of metallic and composite sandwich materials, which are strong and lightweight and help to avoid buckling under high applied loads.

Launch and reentry vehicles are subject to high aerodynamic loads and severe kinetic heating effects, which pose additional challenges in the design of the structure and the selection of the appropriate structural materials. There can be a significant softening and weakening of all types of materials at high temperatures caused by aerodynamic heating. So besides designing for strength and stiffness, additional methods of protecting the structure may be needed, e.g., silica tiles on the Space Shuttle to protect the airframe from kinetic heating during re-entry. An example of a state-of-the-art thermal protection system, which is based on an inflatable concept, is shown in the figure below. A further engineering challenge is that these re-entry environments cannot be easily simulated on Earth or fully modeled analytically under the expected combined mechanical and thermal loads. Hence, the design risks are higher than for an aircraft.

Another major challenge in the design of launch vehicles is the structural design of fuel tanks, which are large pressure vessels, often filled with cryogenic liquids. In this case, the embrittlement of metals at low temperatures is a significant consideration, and internal stresses are caused by differential temperatures, e.g., between hydrogen and oxygen tanks. Composite materials have also seen much use in the design of fuel tanks for rockets.

Materials Selection Charts

Material selection charts are often used when choosing materials for a particular engineering application. In this type of presentation, one material property is plotted on the ordinate of the chart and another property on the abscissae. A particularly relevant material selection diagram for flight vehicle applications is one with strength on the ordinate and density on the abscissa, as shown below. In this case, the value of Young’s modulus describes how stiff the material is. This type of chart helps expose the relative benefits of particular materials so that the most appropriate material can be selected for a specific structural application.

In reference to this type of chart, some materials look very attractive for the light, stiff components needed for flight vehicles. Unfortunately, there are few inexpensive, strong materials. Wood is not strong enough as a primary airframe construction material other than for small airplanes, and composites might be too expensive. Metals like aluminum give an excellent overall performance regarding their strength, lightness, durability, cost, etc., and have traditionally been used to construct flight vehicles. Composites offer a good compromise, but they are usually quite expensive regarding the material itself and the tooling needed to manufacture the components, e.g., the need for layup facilities and autoclaves.

Three possible metallic construction materials for flight vehicle structures are aluminum, steel, and titanium. Steel is by far the heaviest, being approximately three times as heavy as aluminum or titanium, which rules it out as a primary construction material for most aerospace structures. However, steel is used for components where much strength and durability are needed, such as landing gear. Aluminum is, in fact, lighter than titanium, but titanium is stronger than aluminum.

However, many other factors must be considered when selecting materials, particularly manufacturing methods and costs. For example, regarding price, titanium is at least five times more expensive than aluminum. Nevertheless, titanium in the airframe is attractive for high-speed flight vehicles because it offers the most balanced choice regarding strength, weight, and heat resistance. For example, the SR-71 Blackbird was primarily made of titanium, comprising over 90% of its structural weight.

It is usually advisable that any material selection based on a “clean-sheet” airframe design using these charts be left quite broad to keep the options open. One way to approach the material selection problem for an aerospace structure is to use the charts to eliminate possible materials (e.g., wood, steel, etc.) rather than trying to identify the single best material too soon in the design process. Today, the choices often come down to using aluminum, composites, or both.

Additive Manufacturing & 3D Printing

Additive manufacturing, sometimes called 3D printing, involves the construction of a part manufactured directly from a CAD model. The basic principle is that an appropriate material is deposited, joined, and solidified, typically layer by layer, to make a part. Fused filament fabrication or fused deposition modeling is the most common method for making 3D-printed parts. This process uses a continuous filament of a thermoplastic material, which is melted at a printer nozzle and deposited on the part in incremental layers. Techniques such as direct metal laser sintering and direct metal laser melting can also produce 3D-printed metal parts.

An advantage of 3D printing is the ability to produce complex shapes that would be difficult, time-consuming, and expensive to construct by conventional manufacturing methods. An advantage for aerospace applications is that 3D-printed parts can also be made with internal geodesic structures to reduce weight. The attractiveness of 3D printing technologies is such that the range of available materials has increased exponentially over the last decade. Some materials are now of the strength, surface finish, and overall quality for which the industry uses 3D printing for production parts.

One of the concerns with 3D-printed parts for aircraft applications is to ensure their airworthiness, i.e., can they be safely used? In the U.S., the FAA requires that all aircraft parts be manufactured to comply with airworthiness standards under FAA production approvals. To this end, aerospace manufacturers using 3D printing will need to continue to develop processes that comply with regulatory requirements and can prove their airworthiness. Recently, the FAA approved the production of a 3D-printed fuel nozzle for the GE LEAP engine. This part was previously made using 20 pieces welded together, but 3D printing technology allowed it to be made from a single piece, which also cut its weight by 25%.

Summary & Closure

Aerospace structures require a unique combination of strength and lightness, which is why aluminum alloys have been the dominant material for use in aerospace applications for many years. Aluminum alloys are used to build semi-monocoque or “stressed skin” structures that provide the necessary strength and durability for most aircraft and spacecraft. However, composite materials, such as carbon fiber reinforced polymers, have become increasingly popular in recent years, especially for primary structures such as wings and fuselages. Using composites allows for improved strength-to-weight ratio and greater design flexibility, making them a good alternative to aluminum alloys in many aerospace applications.

Using advanced lightweight materials and optimized structures is crucial to achieving lighter airframe components. Finite element methods are widely used to design structures that meet specific requirements while minimizing weight. The manufacturability of the structures is also an important consideration because it affects the feasibility and costs of mass-producing the components. The development of advanced technologies, such as additive manufacturing, has the potential to help reduce airframe weight even further. Using 3D printing techniques, for example, complex structures can be created with minimal material waste, potentially yielding significant weight savings.

5-Question Self-Assessment Quickquiz

For Further Thought or Discussion

• List some of the relative advantages of wood and fabric airplane construction versus stressed metallic skin construction.
• Research the manufacturing methods used to make airplanes using conventional riveted construction. Explain how a rivet is “bucked.”
• Consider the expected costs of making airplane structures from molded composites versus traditional riveted metallic construction. Which method is likely to be more expensive, and why?
• The elimination of many fasteners in composite construction also improves fatigue resistance. Explain.

Other Useful Online Resources

To learn more about flight vehicle structures, try some of these online resources:

• Video lecture on aircraft structures and loads applied to an airframe.
• A short video explaining wooden airframe structures and the selection of the wood.
• Great video lecture on aerospace structures – airframe basics.
• Test your knowledge of the construction of an aircraft: Engineering a Jetliner. 
• Lecture series on advanced aircraft structures by Dr. Goyal.
• Learn how to buck a solid rivet for an airplane structure.
• Titanium – The Metal That Made The SR-71 Possible.
• Aircraft conversion XXL – A cargo plane is born.