Introduction^[1]

Now that some understanding of the anatomy of flight vehicles has been gained, it is logical to delve deeper into their structural design characteristics. 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, such as engine loads, undercarriage loads, landing vertical/side-loads, etc. Indeed, any aerospace structure must be immensely strong and lightweight but also robust and durable. Therefore, the structural design options and constraints must be well understood.

Many structural design goals and engineering challenges for spacecraft are similar to those for aircraft, including the need for optimum-shaped structures made of high-strength, lightweight materials. However, unique high-temperature-capable materials may be needed for particular spacecraft because of kinetic heating effects, i.e., during re-entry into the Earth’s atmosphere. Supersonic aircraft may also have to use certain structural design features to allow the aircraft to safely expand during flight without creating high internal structural stresses.

Brief History of Aerospace 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 capitalized on 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 1907, the Wright brothers had successfully flown several versions of their Flyer, a biplane type more strongly built from a wooden skeleton covered with fabric. Their wing design used spanwise spars and chordwise ribs braced with struts and wires. The main advantage of the biplane is that the upper and lower wings are tied together with vertical struts and bracing wires, forming a strong 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. However, a biplane wing design also has high aerodynamic drag, 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 its reduced aerodynamic drag compared to the braced wings of biplanes or triplanes. Bleriot followed Octave Chanute‘s approach, where steel wires supported the single wings from a tall mast extending above the fuselage. However, the wires still created significant aerodynamic drag on the aircraft and reduced its performance. Bleriot also used a welded truss-type of fuselage that was lightweight and strong, and this method became a standard type of early airframe construction.

By the 1920s, aluminum alloys suitable for airplane construction became increasingly available, so airplanes made of wood and fabric were increasingly relegated to history. In addition, the years leading up to WWII led to many advances in aircraft construction techniques, and riveted aluminum “stressed skin” construction techniques were becoming standard for almost all new aircraft. In 1925, Ford Motor Co. entered the aviation business with the 4-AT Trimotor, a three-engine, all-metal plane using corrugated aluminum skins. Dubbed “The Tin Goose,” it quickly became successful and was used by over 100 airlines worldwide.

By the mid-1930s, more airplanes were becoming larger and heavier and made almost entirely of stressed-skin aluminum construction. Other construction methods were developed to obtain the needed structural strength and stiffness of the wings, including multi-spar and box beam designs, one such concept being shown in the figure below. Box beam designs use multiple spar caps, webs, and shear panels to achieve high bending and torsional stiffness, efficient material use, and overall structural robustness.

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. 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, helicopter rotor blades, and many other applications. Sandwich construction is used extensively in manufacturing helicopter rotor blades, an example of which is 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 composite materials has opened up the design of helicopter rotor blades and propeller blades to meet an increasingly challenging set of aerodynamic and structural requirements, including fatigue resistance. A leading edge erosion shield of a hardened nickel-steel alloy prevents blade abrasion in dusty or sandy environments.

In the last few decades, advanced materials and manufacturing techniques have allowed a transition from mainly building airframe structures made entirely to those made with a majority of composites, such as carbon fiber reinforced polymer (CFRP).  CFRP offers several advantages over traditional aluminum. Its higher strength-to-weight ratio means that structures made from CFRP can achieve the same or greater strength while using less material. This reduction in material not only lightens the overall structure but leads to better fuel efficiency per unit of payload carried. For example, the fuselage barrel shown in the photograph below is approximately 30\% lighter than it would be if made from aluminum alloy.

Modern aerospace structures can be tailored using advanced computational techniques, such as the finite element method (FEM). FEM enables engineers to simulate and analyze the structural performance of complex shapes and materials under various conditions. This tailoring ensures that every component is optimized for maximum structural efficiency, balancing strength, stiffness, and weight. Additionally, CFRP’s resistance to fatigue and corrosion, coupled with its superior mechanical properties, means that it offers longer service life and reduced maintenance costs compared to traditional materials. As a result, the shift towards composites like CFRP in aerospace engineering represents a leap forward in creating lighter, stronger, and more efficient airframes that meet the stringent demands of modern aviation.

The history of spacecraft structures spans from the simple stainless steel shells of early satellites to the complex modular designs of the International Space Station (ISS). Key milestones include the Apollo Lunar Module’s lightweight aluminum and titanium construction and the Space Shuttle’s intricate aluminum airframe covered with reinforced carbon-carbon tiles. Modern 3D printed and inflatable structures allow for cost-effective and adaptable designs. At the same time, projects like SpaceX’s Starship push boundaries using lightweight stainless-steel structures, embodying the continuous evolution of spacecraft structures in response to technological advancements and exploration goals.

Types of Structural 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 an 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. A component’s compressive stiffness is its resistance to compression forces.
• Tension is the stress that resists the force pulling and trying to extend the part. A component’s tensile stiffness 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 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.

Structural 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 (or sometimes ), 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 dimensionless 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 elastic relationship between stress and strain, as shown in the figure below, at least up to a point referred to as the proportional limit.

The elastic nature of materials means that after the load is removed and the stress is released, the material returns to its original undeformed state. This linear stress-strain relationship is known as Hooke’s Law, and the gradient or 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)  

Stiff materials have a higher Young’s modulus value but tend to be brittle and fracture easily. Soft and easily extendable materials have a low value of Young’s modulus.

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 aluminum sheet 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 most of the torsional loads and transfers the stresses to the wing ribs.

Wing ribs give the wing its aerodynamic (airfoil) shape and transmit the skin loads and stringers to the spars. The lightweight ribs are stamped out from a flat aluminum sheet, then flanged holes are cut into the ribs to lighten the overall assembly; flanging the hole increases the resistance to buckling. The rib has a cap around its periphery, often in the form of a “T” or “L” shape, which stiffens and strengthens the rib and is then attached to the wing skin using rivets. 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 the ailerons, elevators, rudders, etc.

Depending on a specific aircraft’s design criteria, spars may be made of metal, wood, or composite materials. Bolts usually attach the spars to the fuselage, with various fittings 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, which is called the web, carries the vertical shear loads. The web forms the spar’s principal depth portion to which the cap are attached.

The stress, , in a wing spar can be calculated using the bending stress equation as given by

(4)  

where is the bending moment, is the second moment of area of the cross-section, and is the distance from the neutral axis to the point where the stress is being calculated, as shown in the figure below. The highest stresses will arise in the spar caps, the lower cap being in tension and the upper cap in compression. The second moment of area for the cross-section of the spar (or the wing as a whole) depends on the geometry of the cross-section. Values for common shapes are available and include rectangles, L-shapes, T-sections, U-sections, and I-beams. For a symmetric cross-section, the neutral axis will be halfway between the top and bottom of the section.

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 or other structural component 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. Rear “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, as shown in the figure below, a standard structural design for commercial airliners. It uses two or three main longitudinal spars to connect ribs and bulkheads, forming a box shape with tremendous bending and torsional strength. The interior of 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 a wet wing design. Alternatively, a separate fuel bladder or tank can be fitted inside the wing, a more typical implementation on smaller aircraft.

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.”

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 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 compared to other designs.

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 compressive 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 likely under bending, compression, or torsion loads in the monocoque structure.

Most modern aircraft are of semi-monocoque 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, giving it 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, as shown in the figure below, adding not only to the complexity of its design but also increasing its structural weight. The fuselage is a large pressure vessel that expands like a balloon as the aircraft climbs to altitude. The ceiling for most 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 Wellington bomber was built of a geodesic structure, shown in the photograph below, and it proved its structural integrity even after suffering significant combat 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.

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. Primary control surfaces and flaps can also be constructed from composite honeycomb materials, and this method is used especially on larger commercial airliners where excessive weight growth is a concern. Other sandwich construction structures may include cabin floors, nose cones, and engine cowlings.

Winglets

A winglet is a vertical upturn of the wing tip, as shown in the figure below. Winglets are designed to reduce the drag created by wing tip vortices, i.e., the induced part of the total drag. Winglets are made from aluminum or composite materials and are often retrofitted to existing wings to improve the airplane’s performance. A winglet must be structurally attached to the main wing box to create a fully integrated design.

Stress Analyses

A structural stress analysis involves determining aerodynamic and other loads and evaluating the resulting stresses imposed on the structural components. While a stress analysis may 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. The process begins with creating a geometric model of the aircraft and its detailed components using Computer-Aided Design (CAD) software. Each block or finite element may have different properties, such as thickness and material characteristics, reflecting the characteristics of aerospace materials like composites and metal alloys, giving the FEM tremendous optimum design capabilities.

Material properties, such as Young’s modulus, Poisson’s ratio, and density, are assigned to each element. Boundary conditions, including constraints, loads, and perhaps even thermal effects, are applied to the model, representing the operating environment and mission requirements. The assembly of system equations involves the formulation of the stiffness matrix by aggregating the contributions from individual finite elements and the assembly of the load vector to account for applied loads and environmental conditions. For linear systems, the displacement vector is determined by solving the equation

(5)  

where represents the stiffness matrix and is the load vector comprising of forces and moments. This equation describes the relationship between the loads acting on all of the nodes in the mesh and the displacements and rotations at the nodes. The nodal displacements and rotations of the structure are the unknowns in the FEM.

Solution techniques in the FEM encompass various numerical methods. One approach that could be used is rho invert the stiffness matrix and solve for . However, direct inversion of a large matrix is not a numerically efficient process. Instead, preferred methods iteratively approximate the displacement vector to converge to a solution. Post-processing tools are then employed to visualize and interpret the results, an example being shown in the figure below for a spar lug. Notice the higher stresses around the bolt holes. The idea is to distribute the stresses so that they “flow” smoothly into the primary attachment points without large concentrations.

From the FEM results, engineers can then assess the structural integrity of the flight vehicle by analyzing the stresses, strains, and overall deformations to ensure that the vehicle and its components meet safety, performance, and certification requirements. In this latter regard, the design for an aircraft or spacecraft might involve finding the strongest and most durable structure for the minimum possible weight, as well as having good fatigue and corrosion resistance or other desirable characteristics.

Fail-Safe & Safe-Life Structural 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. The upper spar cap will be in compression and the lower cap in tension; the lower cap is more critical regarding the likelihood of fatigue failure. Notice that in the event of a failure of the lower spar cap, the fail-safe structure has enough redundancy because of the alternative load path to carry the bending moment loads. Unless the fatigue cracking of a 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. Using 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, at the expense of some extra airframe weight, the consequences of a single component failure can be minimized, ensuring the safety of the aircraft and its passengers.

A small general aviation (GA) airplane may be designed using safe-life principles to save weight and cost, recognizing that it 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 occur on aging GA airplanes, increasing the burden on the owner/operator for more frequent inspections.

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 force, , 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.

Thermal Considerations

Thermal expansion issues in aerospace structures may be a consideration in airframe design. Spacecraft and aircraft structures can encounter wide swings in temperature, ranging from the cold of high altitudes or space to the kinetic heating in supersonic flight to the intense heat of atmospheric re-entry. When materials expand or contract with temperature changes, it can lead to significant structural stresses and potential structural failures if not properly managed.

Different materials will expand at different rates, a property quantified by the coefficient of thermal expansion (CTE). In aerospace structures, materials with mismatched CTEs can lead to differential expansion or contraction, causing stress concentrations at the interfaces where these materials meet. For example, composites and metals in the same structure might expand or contract differently when exposed to temperature changes, potentially leading to delamination or cracking.

Engineers address these thermal issues through careful material selection, designing joints and interfaces that can accommodate movement, and incorporating thermal isolation or control techniques to minimize temperature gradients. A good example is the wing ribs used on the Concorde, an example being shown in the photograph below. Some of the webs were made of pin-jointed rods, allowing the structure to expand thermally from kinetic heating in supersonic flight without creating high stresses—some stringers in the wing skins fitted in sliding joints in the ribs for the same reason. Concorde also used high-temperature stainless steel honeycomb structural components. Today, advanced materials like carbon composites and thermal barrier coatings can mitigate thermal effects and enhance the durability of aerospace structures.

Launch and re-entry 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. Aerodynamic heating can cause significant softening and weakening of all types of materials at high temperatures. 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 spacecraft 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.

Airframe Weight Estimation

A goal in flight vehicle design is always to obtain the maximum performance for the lowest structural weight and lowest cost. For a given type of aircraft, its price is roughly proportional to its empty weight. 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 the airframe weight. The extra design time and investments in tooling necessary to accomplish significant airframe weight savings may result in a higher useful weight for the aircraft (i.e., more fuel load and/or 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.

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. Most space vehicles are constructed using components made of metallic materials such as aluminum and titanium and composite sandwich materials, which are strong and lightweight and help avoid buckling under high applied loads. As with aircraft structures, spacecraft structures are mainly thin-walled, semi-monocoque designs. They are subject to most, if not all, of the issues associated with aircraft structural design, an example being shown in the photograph below. This spacecraft structure is made of aluminum, and to maximize its strength to weight, it has a triangular iso grid pattern with curved conic sections similar to a geodesic construction.

A significant 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 liquid hydrogen and oxygen tanks. Cryogenic propellants need to be kept at extremely low temperatures to remain in a liquid state. The most common cryogenic propellants include liquid hydrogen (LH2), liquid oxygen (LOX), and liquid methane (LCH4). Their storage tanks are made from lightweight materials such as aluminum alloys, stainless steel, or advanced composites. They are equipped with multilayer insulation and vacuum jackets to minimize heat transfer. The hemispherical and cylindrical shapes help evenly distribute the structural stresses produced by the internal pressures, while their structural integrity against buckling is maintained through integral support structures.

Cryogenic tanks are vital for space launch vehicles like the SpaceX Falcon 9 and NASA’s Space Launch System (SLS) and for deep space missions where long-term propellant storage is necessary. An example of the liquid hydrogen fuel tank used on NASA’s SLS rocket is shown below. This tank was made using friction welding, which relies on the friction generated between a rotating tool and the material to heat and soften but not melt the workpieces. The tool then stirs the softened material across the joint, producing a solid-state weld. This process results in high-quality welds with minimal defects, reduced distortion, and improved mechanical properties compared to traditional welding methods. Composite materials have also been used to design fuel tanks for rockets.

Managing boil-off gases and maintaining the low temperatures of cryogenic propellants are significant challenges. These are addressed through both active cooling systems and passive insulation. Tanks are integrated with sophisticated feed lines and monitoring systems to ensure a controlled supply of propellants to rocket engines, along with sensors to track pressure, temperature, and liquid levels. Pressure management systems with vents and relief valves are also needed to handle the high pressures of cryogenic liquids.

Summary & Closure

Aerospace structures require a unique combination of strength and lightness. The finite element method (FEM) is widely used to design structures that meet specific requirements while minimizing weight. Stressed skin structures made of aluminum alloys have been the dominant material for aerospace applications for many years and have provided 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 structural design flexibility, making them an excellent alternative to aluminum alloys in many aerospace applications.

The design of spacecraft structures parallels that of aircraft in many ways. Advanced materials and fabrication techniques, such as carbon fiber composites and friction stir welding, are employed to achieve high strength-to-weight ratios. Spacecraft structures designed for cryogenic applications face unique technical challenges because they must store and manage cryogenic propellants at extremely low temperatures, such as liquid hydrogen and oxygen. The design and engineering of spacecraft structures are critical to mission success, ensuring reliability and durability while optimizing for weight and efficiency.