5.1 Structural Loads and Stress Analysis

Aircraft Structural Loads

Every structure on an aircraft exists to carry loads safely from one part of the airframe to another. Understanding where those loads come from, how they distribute through the structure, and how engineers analyze them is the foundation of aircraft structural design.

Types of Aircraft Structural Loads

Aircraft experience five main categories of loads during their operational life. These loads rarely act in isolation; during a gusty landing, for example, aerodynamic, inertial, ground, and environmental loads all act simultaneously.

Aerodynamic loads are generated by airflow over the aircraft's surfaces.

• Lift acts perpendicular to the freestream airflow and supports the aircraft's weight in flight. It's concentrated along the wings but also acts on the tail and fuselage.
• Drag opposes the aircraft's motion through the air. It creates tension and bending loads along the fuselage and nacelles.

Inertial loads come from the aircraft's own mass being accelerated.

• Gravity pulls the entire aircraft downward at all times, so every structural member carries some portion of the aircraft's weight.
• During maneuvers (pull-ups, banked turns, rapid pitch changes), the effective load on the structure increases well beyond 1g. A 60° banked turn, for instance, doubles the load on the wings.

Propulsive loads originate from the engines.

• Thrust pushes the aircraft forward and must be transferred from the engine mounts into the airframe.
• Engine torque (especially on propeller-driven aircraft) creates twisting moments that the structure must resist.

Ground loads occur during takeoff, landing, and taxiing.

• Landing gear absorbs the impact of touchdown. Landing loads can be several times the aircraft's weight, depending on sink rate.
• Taxiing over uneven surfaces produces repeated, lower-magnitude loads on the gear and fuselage.

Environmental loads result from external conditions.

• Gust loads from atmospheric turbulence cause sudden changes in angle of attack, producing rapid spikes in aerodynamic force.
• Thermal loads arise because different parts of the aircraft heat and cool at different rates. Temperature gradients cause materials to expand or contract unevenly, generating internal stresses.

Stress Analysis and Load Distribution

Once you know what loads act on the aircraft, the next step is figuring out how those loads travel through the structure and what stresses they produce. This is the core of structural analysis.

Stress Analysis in Structural Components

The general process for analyzing a structural component follows these steps:

1. Identify the load paths. Trace how external forces travel through the airframe. Wings, spars, ribs, stringers, and skin panels each carry specific portions of the total load.

2. Determine internal forces. At any cross-section of a structural member, four types of internal forces can exist:

   • Axial forces (tension or compression along the member's length)
   • Shear forces (acting perpendicular to the cross-section)
   • Bending moments (causing the member to curve)
   • Torsional moments (twisting the member about its longitudinal axis)

3. Apply equilibrium and free-body diagrams. Cut the structure at the section of interest, draw all forces and moments, and use static equilibrium ($\sum F = 0$, $\sum M = 0$) to solve for unknowns.

4. Account for stress concentrations. Holes (like rivet holes and access panels), notches, and abrupt changes in cross-section amplify local stresses far above the average. These are often where cracks initiate, so engineers pay close attention to them.

Stress and Strain Distribution Methods

Analytical methods give exact (closed-form) solutions for idealized geometries. They're fast and provide physical insight, but they only work well for relatively simple shapes.

• Beam theory treats structural elements like wing spars and fuselage frames as beams. Two key formulas come up constantly:

  • The flexure formula gives the normal (bending) stress at a distance $y$ from the neutral axis: $\sigma = \frac{My}{I}$ where $M$ is the bending moment and $I$ is the second moment of area. Stress is zero at the neutral axis and maximum at the outermost fibers.
  • The shear stress formula gives the shear stress due to a transverse shear force $V$: $\tau = \frac{VQ}{It}$ where $Q$ is the first moment of area above (or below) the point of interest, and $t$ is the width of the cross-section at that point.

• Thin-walled structure analysis applies to aircraft skin panels, stringers, and spar webs, which are thin relative to their other dimensions.

  • Shear flow (force per unit length along the wall, $q = \tau \cdot t$) is used to track how shear loads distribute around open and closed cross-sections.
  • Torsion in thin-walled closed sections is analyzed using the Bredt-Batho formula, which relates applied torque to shear flow around the enclosed area.

Numerical methods handle the complex, real-world geometries that analytical methods can't.

• Finite Element Analysis (FEA) is the workhorse of modern structural analysis:

  1. Divide (discretize) the structure into many small elements (triangles, quadrilaterals, tetrahedra, etc.).
  2. Apply loads and boundary conditions (e.g., fixed supports at the wing root, distributed lift along the span).
  3. Solve a large system of equations to find displacements at every node, then compute stresses and strains from those displacements.

  FEA can handle irregular shapes, composite layups, and combined loading that would be impossible to solve by hand.

• Computational Fluid Dynamics (CFD) complements structural analysis by predicting the aerodynamic loads that feed into FEA:

  1. Discretize the air volume around the aircraft into a mesh of small cells.
  2. Solve the governing fluid equations (Navier-Stokes equations) with appropriate boundary conditions.
  3. Extract pressure distributions on the aircraft surfaces, which become the aerodynamic loads for structural analysis.

Load Factors and Dynamic Loads

Load factor ($n$) is the ratio of the total aerodynamic lift to the aircraft's weight:

$n = \frac{L}{W}$

In straight-and-level flight, $n = 1$. During a 2g pull-up, $n = 2$, meaning every structural component effectively carries twice the aircraft's weight. Regulatory agencies (like the FAA) specify design load factors based on aircraft category. For example, normal category aircraft must withstand $n = +3.8$ to $n = -1.52$, while acrobatic aircraft require $n = +6.0$ to $n = -3.0$.

Gust loads arise from sudden changes in wind velocity. A sharp vertical gust increases the wing's angle of attack almost instantly, producing a spike in lift. Engineers calculate gust load factors using standardized gust profiles (defined in regulations like FAR Part 25) and apply them alongside maneuvering load factors to determine the critical design case.

Dynamic loads vary with time and introduce two additional concerns:

• Aeroelastic phenomena occur when aerodynamic forces and structural flexibility interact.
  • Flutter is a self-excited oscillation where aerodynamic energy feeds into a structural vibration mode. If it occurs, the amplitude grows rapidly and can destroy the structure in seconds. Flutter speed must always be well above the aircraft's operating envelope.
  • Divergence is a static aeroelastic instability where aerodynamic twisting moments exceed the wing's torsional stiffness, causing the wing to twist uncontrollably. It sets an upper limit on how flexible a wing can be.
• Fatigue results from repeated cyclic loading (pressurization cycles, gust encounters, landing impacts). Even stresses well below the material's ultimate strength can cause cracks to initiate and grow over thousands of cycles. Engineers use the S-N (stress-life) approach, which plots stress amplitude against the number of cycles to failure, to estimate how long a component can safely operate before inspection or replacement is needed.