Structural Loads, Stress and Fatigue

Every part of an airframe is loaded all the time. On the ground the wings hang from the fuselage and the landing gear carries the weight; in flight the wings bend upwards under lift, the fuselage is inflated by cabin pressure, and gusts and manoeuvres add loads that come and go in seconds. How a structure carries these loads, and how its material responds, decides whether it bends and springs back, deforms permanently, buckles, or cracks after thousands of flights.

This article covers the kinds of load, the measures engineers use to describe a material's response, stress and strain, and the mechanism of fatigue. How the airframe is built to carry the loads is described in airframe structure and construction; the limit and ultimate loads, the factor of safety and the safe-life, fail-safe and damage-tolerant philosophies are in structural design and design loads.

Types of Structural Load

Three basic loads act on a structural member:

• A tensile load (tension) tends to stretch it. Control cables work in tension, as do parts of the structure pulled apart by aerodynamic loads. A member designed to resist tension is a tie.
• A compressive load (compression) tends to shorten it. Undercarriage legs are in compression carrying the aircraft's weight on the ground. A member designed to resist compression is a strut.
• A shear load tends to slide one face of the material over the adjacent face. Rivets, bolts and skin panels are the classic shear carriers; rivets transfer load between skin panels in shear and have little strength in tension.

Two further loads are combinations of these. Bending puts the outer, convex edge of a member in tension, the inner, concave edge in compression, and the material across it in shear. A wing bending upwards in flight has its upper skin in compression, its lower skin in tension and its internal structure in shear; on the ground, hanging under its own weight, the loads reverse. Torsion is twisting about the member's axis. It sets up shear stress in the material, greatest at the outer surface and zero on the axis, which is why a closed tube or box resists it far better than an open section of the same weight. The wing meets torsion from aerodynamic pitching moments and from deflected ailerons, and carries it as shear in the skins and spar webs of its closed torsion box.

Stress and Strain

A load on a member produces stress, the internal force per unit area of the material: stress = force ÷ area. It is expressed in N/mm² or MN/m², which are the same quantity (both equal to 1 MPa). Tension produces tensile stress, compression compressive stress. Stress is what a material "feels", so the same load is more severe in a thinner part.

The material responds by deforming. Strain is that deformation, expressed as the change in a dimension divided by the original dimension, as a fraction or a percentage. Because it is a ratio of two lengths, strain has no units. A tensile stress produces a tensile strain, an elongation.

The distinction matters in maintenance as much as in design. Strength ratings, such as yield stress or ultimate stress, are stated in stress units; damage is often detected as strain, a wing or a skin panel that has taken a permanent set.

Elastic and Plastic Deformation

If a metal specimen is loaded gradually in tension, its strain at first rises in step with the stress. Remove the load and the specimen returns to its original dimensions: this is elastic deformation. The highest stress at which this remains true is the elastic limit.

Beyond the elastic limit, part of the deformation remains when the load is removed. This is plastic deformation: the part is permanently stretched, bent or dented. Loaded further still, the material reaches its ultimate tensile strength (UTS), the greatest stress it can carry in tension, and then fails.

Aircraft structure must work within the elastic limit. Permanent deformation is evidence of serious overstress, which is why the design limit load is defined as the load the structure must carry without detrimental permanent deformation, and why an overstressed aircraft is inspected for buckled skins, pulled rivets and bent members before it flies again.

Hooke's Law and Young's Modulus

Within the elastic limit, stress is proportional to strain. This is Hooke's law. The constant of proportionality is Young's modulus of elasticity, E:

E = stress ÷ strain

Young's modulus measures stiffness, how much a material deforms under a given stress, not strength, how much stress it can carry before it yields or breaks. A stiff material has a high modulus and stretches little. Stiffness matters to the airframe in its own right: a wing that twists too easily loses aileron effectiveness at high speed and is more prone to flutter, even if it is strong enough.

Hoop and Axial Cabin Stresses

A pressurised fuselage is a pressure vessel. The cabin differential pressure, which ATPL texts quote at up to 65.5 kN/m² (9.5 psi), loads the skin in two directions:

• Hoop stress acts around the circumference and tries to expand the cross-section.
• Axial stress (longitudinal stress) acts along the length and tries to make the fuselage longer.

For a thin-walled cylinder of radius r and skin thickness t under a pressure differential P, the hoop stress is P × r ÷ t and the axial stress P × r ÷ 2t. The hoop stress is therefore twice the axial stress, and a larger fuselage diameter needs a thicker skin for the same differential. Both stresses are applied once and removed once on every flight, so the pressure hull accumulates one major fatigue cycle per flight however long the flight is (see pressurisation principles and control).

Buckling and Stress Concentration

Buckling is the failure of a thin or slender member under compression: it bows sideways and collapses at a load far below what the material could carry in direct compression. Thin skin panels buckle under end loads, and slender members designed as ties buckle if the load reverses and puts them in compression. Stringers and stiffeners prevent it by dividing the skin into shorter panels, each far more resistant to buckling than a large unsupported sheet. A wrinkled skin panel after a heavy landing or a severe turbulence encounter is a sign that buckling has occurred.

A stress concentration is a local rise in stress wherever the smooth flow of load through a part is interrupted: a rivet or fastener hole, a sharp corner at a cut-out, a scratch, a crack or a contaminant in the material. Windows, doors and access panels are unavoidable stress raisers in a fuselage. Designers reduce the peak with smooth radii at corners, polished surfaces and doublers around openings, and by cold-working fastener holes to leave a residual compressive stress around them that delays cracking.

Static and Dynamic Loads

Static loads are generally constant and build slowly, like the weight of a parked aeroplane on its landing gear and wing structure. Dynamic loads build quickly as flight conditions change, in manoeuvres, gusts, turbulence and landings. They are often more severe than static loads and can induce additional loads elsewhere in the structure. A wing spar sees both kinds: bent downwards by weight on the ground and upwards by lift in flight, with the gusts of every flight superimposed.

The size of the flight loads is measured by the load factor, and the structure is designed for limit load factors set by the certification codes (see load factor and flight envelope). The pilot's control over dynamic loads is speed and handling: slowing to the turbulence penetration speed, avoiding abrupt control inputs at high speed, and making a firm but not heavy landing.

Structural Fatigue

Structural fatigue is progressive failure under cyclic, repeated loading at stresses far below those that would break the material in a single application. A fatigue crack begins at a stress concentration, grows a little with each load cycle, and causes sudden failure when the remaining material can no longer carry the load. Fatigue cracks almost always start at stress concentrations: rivet holes, sharp corners at cut-outs and brackets, surface defects such as scratches and manufacturing flaws, and contaminants in the material.

The number of cycles a metal survives depends very strongly on the stress. ATPL texts illustrate it with a part loaded to 80 per cent of its ultimate stress failing after about 100 cycles, and one loaded to 20 per cent surviving 10 million cycles or more. The relationship is so non-linear that a modest reduction in working stress greatly extends fatigue life, one reason for the margins built into airframes and one reason load limits matter even when an exceedance breaks nothing.

An airliner experiences millions of load cycles in its life, one large pressurisation and wing-bending cycle per flight and many smaller ones from gusts, so structural life is counted in flight cycles as well as flight hours.

Composites behave differently from metals. ATPL texts note that fatigue is not generally a concern in composites at stresses below about 80 per cent of their ultimate stress and that they lose their properties gradually, whereas a metal keeps its design strength up to a critical point and then fails rapidly as the crack runs. Undetected fatigue in metal is therefore the more dangerous, which is why metal primary structure is inspected on a schedule designed to find cracks while they are still small.

Both of the accidents that every structures course recalls, the de Havilland Comet losses of 1954 and Aloha Airlines Flight 243 in 1988, began at stress concentrations in a pressure hull cycled on every flight; they, and the safe-life, fail-safe and damage-tolerant philosophies that followed, are described in structural design and design loads.

Library articles are written for study and exam preparation. They do not replace your aircraft's approved documentation, your operator's procedures or the regulations themselves.