Aircraft Wing Spar Stress Analysis

Objective: Performed structural stress analysis of a Cessna 172 wing spar to evaluate load-bearing performance under flight conditions. 

Requirements: Model the spar geometry, apply aerodynamic loading scenarios, and assess deflection and stress distribution to validate structural integrity. Combined numerical simulation with classical analytical methods to ensure accuracy. 

Top Skills: stress analysis (Ansys Mechanical, SpaceClaim), analytical mechanics (Euler-Bernoulli beam theory, Rayleigh-Ritz method), mechanical modeling, simulation validation 

Overview

Our group analyzed the wing spars of a Cessna 172 to determine whether the structure could withstand lift forces during takeoff. We modeled the right wing using CAD and simulated stress and deflection using ANSYS Mechanical. Results were validated through hand calculations based on Euler-Bernoulli beam theory and the Rayleigh-Ritz method. 

Design

• Modeled a 5.675 m half-span right wing with constant NACA 2412 airfoil geometry

• Designed main and rear spars as I-beams positioned at 25% and 58% of chord length

• Used OnShape to create a 3D rib-spar-skin assembly

• Selected CFRP for spars and ribs; Aluminum 2024-T3 for the outer skin

• Total wing weight: 6,730 N (including skin, spars, and ribs)

Simulation & Analysis

• Performed structural simulation using ANSYS Mechanical

• Maximum tip deflection from FEA: 6.75 mm

• Maximum shear stress: 2.32 MPa (well below 193.7 MPa allowable)

• Maximum normal stress: 5.45 MPa (well below 335.6 MPa allowable)

• Results validated by hand using Euler-Bernoulli and Rayleigh-Ritz; predicted tip deflection: 6.70 mm

Key Takeaways

This was a fun final project for my sophomore year and a step beyond the 2D problems we focused on in class. We used both Bernoulli-Euler and PMPE hand calculations to estimate tip deflection and stress, and found strong agreement with FEA results. This gave us confidence in our assumptions despite simplifications like ignoring the slanted flanges of our I-beams. We experimented with CFRP throughout the model, though separating rib and spar materials (e.g., aluminum ribs) would better reflect real designs. A small plane would typically use steel, not CFRP. Our choice led to unusually low deflection, well below the allowable limit.

Our simplified geometry also lacked features like stringers, ailerons, and tapering, which would have affected stress and deflection, especially under dynamic loads. Finally, although our design passed all constraints, its high factor of safety revealed material overuse, an important lesson in cost-efficiency and realistic design margins. Our basic stress assumptions used uniform pressure, but running CFD would better show how stress is distributed across the wing.