Aircraft Structures

Aircraft structures represent a complex engineering challenge: creating a framework that can withstand extreme loads while remaining as light as possible. Unlike ground vehicles, every pound of structural weight has a direct impact on performance, payload capacity, and fuel efficiency.

Structural Loads and Requirements

Primary Loads

Aircraft structures must withstand several types of loads:

G-loads: Acceleration forces during maneuvers
Aerodynamic loads: Pressure distributions over the aircraft surface
Inertial loads: Forces due to acceleration and deceleration
Landing loads: Impact forces during touchdown
Ground loads: During taxiing, takeoff, and maintenance

Load Factors and Safety Margins

Aircraft are designed to withstand load factors beyond normal operations:

n = \frac{L}{W}

Where:

$n$ = load factor
$L$ = lift force
$W$ = aircraft weight

Typical design load factors:

Normal category aircraft: +3.8g to -1.52g
Utility category: +4.4g to -1.76g
Acrobatic aircraft: +6.0g to -3.0g

A safety factor of 1.5 is typically applied, meaning structures must withstand 1.5 times the limit load without failure.

Stress and Strain Analysis

Basic Stress-Strain Relationship

Hooke's Law defines the relationship between stress and strain:

\sigma = E \varepsilon

Where:

$\sigma$ = stress (force per unit area)
$E$ = Young's modulus (modulus of elasticity)
$\varepsilon$ = strain (dimensionless deformation)

Types of Stress

Tensile stress: Pulling forces that stretch material
Compressive stress: Squeezing forces that compress material
Shear stress: Forces that cause sliding between material layers
Torsional stress: Twisting forces

Stress Concentrations

Geometric discontinuities cause stress concentrations:

K_t = \frac{\sigma_{max}}{\sigma_{nom}}

Where $K_t$ is the stress concentration factor, $\sigma_{max}$ is the maximum stress at the discontinuity, and $\sigma_{nom}$ is the nominal stress.

Structural Elements

Fuselage Construction

The fuselage serves as the backbone of the aircraft structure:

Monocoque: Skin carries all loads (like an eggshell)
Semi-monocoque: Skin and internal framework share loads
Truss-type: Framework of beams and struts

Wing Structure

Wings must resist bending, torsion, and shear:

Primary elements:

Spars: Main spanwise beams carrying bending loads
Ribs: Structural members maintaining airfoil shape
Skin: Outer surface carrying aerodynamic loads
Stringers: Longitudinal stiffeners preventing skin buckling

Load paths:

Lift loads cause upward bending moment
Wing weight creates downward bending moment
Engine loads create local bending and torsion

Structural Analysis Methods

Beam Theory

For basic bending analysis:

\sigma = \frac{My}{I}

Where:

$M$ = bending moment
$y$ = distance from neutral axis
$I$ = area moment of inertia

Finite Element Analysis

For complex structures, engineers use FEA to solve:

\{F\} = [K]\{u\}

Where $\{F\}$ is the force vector, $[K]$ is the stiffness matrix, and $\{u\}$ is the displacement vector.

Materials in Aircraft Design

Aluminum Alloys

Aluminum remains the most common aircraft material:

Common alloys:

2024-T3: Good fatigue resistance, used for skins and structures
7075-T6: High strength, used for critical structural components
6061-T6: Good corrosion resistance, used for non-critical parts

Advantages:

Good strength-to-weight ratio
Excellent fatigue properties
Easy to fabricate and repair

Disadvantages:

Susceptible to corrosion
Lower strength than composites

Composite Materials

Fiber-reinforced composites offer superior properties:

E_c = E_f V_f + E_m V_m

Rule of mixtures for composite modulus, where:

$E_c$ = composite modulus
$E_f$ = fiber modulus
$E_m$ = matrix modulus
$V_f$ , $V_m$ = volume fractions

Types:

Carbon Fiber Reinforced Plastic (CFRP): High strength, high stiffness
Glass Fiber Reinforced Plastic (GFRP): Lower cost, good for non-critical parts
Aramid Fiber (Kevlar): High toughness, impact resistance

Titanium Alloys

Used for high-temperature applications:

Jet engine components
Fasteners in high-stress areas
Landing gear components

Fatigue and Fracture

Fatigue Life Prediction

Materials fail under repeated loading at stresses below ultimate strength:

S = A(N_f)^b

Basquin equation, where $S$ is the stress range, $N_f$ is the number of cycles to failure, and $A$ , $b$ are material constants.

Fracture Mechanics

Critical crack size before failure:

a_c = \frac{1}{\pi} \left(\frac{K_{Ic}}{Y\sigma}\right)^2

Where:

$a_c$ = critical crack length
$K_{Ic}$ = fracture toughness
$Y$ = geometry factor
$\sigma$ = applied stress

Structural Design Considerations

Damage Tolerance

Modern aircraft use damage-tolerant design:

Multiple load paths (fail-safe design)
Slow crack growth properties
Inspection access and intervals

Environmental Considerations

Structures must withstand:

Temperature variations (-55°C to +70°C)
Humidity and corrosion
Lightning strikes
Bird strikes

Real-World Application: Wing Spar Design

Consider the critical main wing spar of a general aviation aircraft that must support both lift loads and engine weight.

Design Scenario

A wing spar must withstand a maximum bending moment of 150,000 N·m during a 3.8g maneuver. The spar uses an I-beam configuration with:

Flange area: 0.002 m² each (top and bottom)
Web thickness: 0.005 m
Height: 0.3 m
Material: 7075-T6 aluminum (yield strength = 500 MPa)

Stress Analysis

The bending stress in the spar is:

$\sigma = \frac{M \cdot c}{I}$

Where $c$ is the distance to the outer fiber and $I$ is the area moment of inertia.

For an I-beam:

# Given parameters
bending_moment = 150000  # N·m
safety_factor = 1.5     # Required safety factor

# I-beam dimensions
flange_area = 0.002     # m² each
height = 0.3            # m (distance between flanges)
web_thickness = 0.005   # m

# Calculate moment of inertia approximation
I_approx = 2 * flange_area * (height/2)**2  # Approximation for I-beam

# Distance to outer fiber
c = height / 2

# Calculate bending stress
stress = (bending_moment * c) / I_approx

# Calculate maximum allowable stress (with safety factor)
material_yield = 500e6  # Pa for 7075-T6 aluminum
allowable_stress = material_yield / safety_factor

print(f"Applied bending stress: {stress/1e6:.2f} MPa")
print(f"Allowable stress: {allowable_stress/1e6:.2f} MPa")
print(f"Factor of safety: {allowable_stress/stress:.2f}")

# Check if design is adequate
is_safe = stress < (material_yield / safety_factor)
print(f"Design is safe: {is_safe}")

Your Challenge: Composite vs. Aluminum Wing Design

Compare the weight and performance of a wing structure using aluminum versus composite materials.

Goal: Calculate the weight difference and assess the structural benefits of using composite materials.

Design Parameters

# Wing section properties
wing_section_length = 4.0    # meters
required_bending_stiffness = 2e10  # N·m² (typical for light aircraft wing)

# Material properties
aluminum_props = {
    'density': 2700,      # kg/m³
    'modulus': 70e9,      # Pa
    'strength': 500e6     # Pa
}
composite_props = {
    'density': 1550,      # kg/m³ (typical CFRP)
    'modulus': 140e9,     # Pa (can be tailored)
    'strength': 1200e6    # Pa (can be tailored)
}

# Cross-section: Simplified rectangular box beam
cross_section_depth = 0.25  # m
cross_section_width = 0.15  # m

# Calculate required cross-sectional area for aluminum and composite
required_area_aluminum = 0  # Calculate based on stiffness requirement
required_area_composite = 0  # Calculate based on stiffness requirement

Determine the minimum cross-sectional area required for each material to achieve the required bending stiffness, then compare the resulting weights.

Hint:

Bending stiffness = $E \cdot I$
For a rectangular cross-section: $I = \frac{bh^3}{12}$
Weight = Volume × Density = Area × Length × Density

# TODO: Calculate required areas and weights
area_aluminum = 0      # Required cross-sectional area for aluminum
area_composite = 0     # Required cross-sectional area for composite
weight_aluminum = 0    # Total weight for aluminum structure
weight_composite = 0   # Total weight for composite structure

# Calculate percentage weight savings
weight_savings = 0     # Percentage weight savings with composites

# Print results
print(f"Required area - Aluminum: {area_aluminum:.6f} m²")
print(f"Required area - Composite: {area_composite:.6f} m²")
print(f"Total weight - Aluminum: {weight_aluminum:.2f} kg")
print(f"Total weight - Composite: {weight_composite:.2f} kg")
print(f"Weight savings with composites: {weight_savings:.1f}%")

What additional factors would influence the material selection beyond just weight and stiffness?

Aircraft Structures

Aircraft Structures

Structural Loads and Requirements

Primary Loads

Load Factors and Safety Margins

Stress and Strain Analysis

Basic Stress-Strain Relationship

Types of Stress

Stress Concentrations

Structural Elements

Fuselage Construction

Wing Structure

Structural Analysis Methods

Beam Theory

Finite Element Analysis

Materials in Aircraft Design

Aluminum Alloys

Composite Materials

Titanium Alloys

Fatigue and Fracture

Fatigue Life Prediction

Fracture Mechanics

Structural Design Considerations

Damage Tolerance

Environmental Considerations

Real-World Application: Wing Spar Design

Design Scenario

Stress Analysis

Your Challenge: Composite vs. Aluminum Wing Design

Design Parameters

ELI10 Explanation

Self-Examination