Project

Wing Box Torsional Stiffness Ground Test Project

Project for a wing-box torsional stiffness ground test with torque rig, fixture correction, FEA correlation, lower-bound stiffness and release evidence.

Branch: Aerospace Engineering
Content: Project
Updated: Jul 03, 2026
Revision: v1.1.0 · reviewed

This project builds a ground-test package for wing-box torsional stiffness. The engineering question is whether the tested structure is stiff enough to support aeroelastic, flight-control and structural-load decisions after fixture compliance, measurement uncertainty and model correlation are included.

The project is narrower than a full wing proof-load test. It focuses on one deliverable: a defensible torsional stiffness value and release lower bound for a representative wing-box section.

Scope Boundary

This project does not prove ultimate strength, fatigue life, flutter clearance or control-law safety by itself. It provides a stiffness datum that those analyses may use if the test article, boundary condition, load path and uncertainty statement match the released configuration.

The boundary matters because torsional stiffness is sensitive to root restraint, fastener state, skin repairs, access panels, control-surface installation, load introduction and measurement coordinate definition. A clean torsion number from the wrong boundary condition can make an aeroelastic model look correlated while the installed wing remains under-proven.

Project Objective

Produce a test report that answers:

What torque was applied to the wing box?
What twist was measured between the root and tip reference stations?
How much twist came from the fixture instead of the article?
What installed torsional stiffness should be used for analysis?
Does the lower-bound stiffness meet the release requirement?
Is the finite-element model close enough for the next aeroelastic review?

The answer should be reproducible from calibration records, load-cell data, displacement transducers, angle measurements, fixture characterization and the finite-element model revision.

Test Readiness Controls

Before loading the article, the team should freeze the article configuration, fixture drawing, load introduction hardware, torque-axis definition, sensor coordinate system, data-acquisition rate, zeroing procedure and limit-stop settings. The readiness review should also state whether the test is linear-elastic only or whether any permanent set, fastener slip or local buckling would invalidate the result.

The most important pre-test control is a fixture run without the article or with a known calibration member. If fixture compliance is measured after the article test only, the team may not know whether root rotation changed during loading.

Test Setup

A semi-span wing-box article is fixed at the root and loaded through a tip torque frame. Two vertical actuators apply equal and opposite forces at a known moment arm. String potentiometers and optical targets measure twist between the root reference plane and the outboard reference plane. A separate fixture-characterization run measures root-fixture rotation under the same torque path.

Representative data:

Quantity	Symbol	Value
actuator force magnitude	$F$	$880\ \text{N}$
torque arm	$r$	$1.25\ \text{m}$
measured root-to-tip twist	$\theta_{meas}$	$0.0078\ \text{rad}$
fixture twist correction	$\theta_{fixture}$	$0.0011\ \text{rad}$
finite-element stiffness prediction	$k_{FEA}$	$350000\ \text{N m/rad}$
minimum release stiffness	$k_{min}$	$300000\ \text{N m/rad}$
service aileron torque case	$T_{svc}$	$1800\ \text{N m}$
allowable service twist	$\theta_{allow}$	$0.40^\circ$

Step 1: Applied Torque

The torque from two opposing actuator loads is:

T=2Fr

Using the rig data:

T=2(880)(1.25)=2200\ \text{N m}

This torque value is valid only if both load cells are calibrated, the moment arm is measured from the correct torque axis and parasitic vertical or bending loads are bounded.

Step 2: Article Twist

The article twist removes fixture compliance from the measured twist:

\theta_{article}=\theta_{meas}-\theta_{fixture}

\theta_{article}=0.0078-0.0011=0.0067\ \text{rad}

The corrected torsional stiffness is:

\displaystyle k_\theta=\frac{T}{\theta_{article}}

\displaystyle k_\theta=\frac{2200}{0.0067}=328000\ \text{N m/rad}

Engineering comment: if fixture twist is not removed, the article stiffness would be under-reported. If fixture correction is overconfident, the release lower bound can be non-conservative.

The fixture share of the measured twist is:

\displaystyle f_{fixture}=\frac{\theta_{fixture}}{\theta_{meas}}

For this test:

\displaystyle f_{fixture}=\frac{0.0011}{0.0078}=14.1\%

That is large enough to justify treating fixture compliance as a first-class uncertainty item, not a rounding correction.

Step 3: FEA Correlation

Compare the test-derived stiffness with the finite-element prediction:

\displaystyle \epsilon_k=\frac{k_\theta-k_{FEA}}{k_{FEA}}

\displaystyle \epsilon_k=\frac{328000-350000}{350000}=-0.062=-6.2\%

The model is stiffer than the test by about 6 percent. If the correlation target is within 10 percent for this preliminary stiffness release, the model can be retained with an updated uncertainty note. If later flutter or aileron-reversal margins are tight, the stiffness model should be updated rather than treated as exact.

Model-Use Decision

The test result should be assigned to a model-use category. For preliminary load and control-surface trend work, a 6 percent stiffness difference may be acceptable with a lower-bound margin. For flutter, aileron reversal or control-law clearance, the same difference may require updating the finite-element stiffness, rerunning sensitivity cases or restricting the envelope until correlation improves.

The release package should therefore say whether analysts may use the nominal FEA stiffness, the measured stiffness, or the lower-bound stiffness. Leaving that choice implicit is a common source of inconsistent margins across loads, controls and aeroelastic teams.

The project should also preserve the load-unload repeatability check. If twist does not return close to zero after unloading, the stiffness result may include slip, seating or damage rather than purely elastic torsion.

Step 4: Lower-Bound Stiffness

Use relative standard uncertainty components:

Source	Standard uncertainty
torque from load cells and arm	$1.5\%$
corrected twist measurement	$3.0\%$

For a stiffness ratio $k=T/\theta$ , the relative standard uncertainty is:

u_r(k)=\sqrt{u_r(T)^2+u_r(\theta)^2}

u_r(k)=\sqrt{0.015^2+0.030^2}=0.0335=3.35\%

With an approximate coverage factor of 2:

U_r(k)=2u_r(k)=6.7\%

The release lower bound is:

k_{LB}=k_\theta(1-U_r)

k_{LB}=328000(1-0.067)=306000\ \text{N m/rad}

The lower bound exceeds the minimum release stiffness:

306000>300000\ \text{N m/rad}

This is a pass, but it is a narrow one.

Step 5: Service-Twist Check

Use the lower-bound stiffness for the service aileron torque case:

\displaystyle \theta_{svc}=\frac{T_{svc}}{k_{LB}}

\displaystyle \theta_{svc}=\frac{1800}{306000}=0.00588\ \text{rad}

Convert to degrees:

\displaystyle 0.00588\frac{180}{\pi}=0.337^\circ

The lower-bound twist is below the allowable value:

0.337^\circ<0.40^\circ

The test supports release for this torque case, provided the article configuration, boundary condition, fastener state, repair status and control-surface installation match the released model.

Release Package

The release package should include:

load-cell calibration and torque-arm measurement;
actuator command history and force balance;
twist sensor calibration and coordinate definition;
root-fixture compliance characterization;
article configuration, fastener torque, repairs and temperature;
finite-element model revision and mesh-correlation notes;
uncertainty budget and lower-bound stiffness calculation;
service-torque and allowable-twist check;
decision on whether aeroelastic margins need model update.

For this case, the ground test supports conditional release. The lower-bound stiffness clears the minimum requirement and the service twist limit, while FEA correlation is within the preliminary target. The condition is that future flutter, aileron-reversal or control-law reviews use the measured stiffness or a conservative lower-bound update, not the uncorrected nominal model value.

The release is also configuration-limited. A repair, added access panel, fastener rework, control-surface change, mass-balance change, local delamination or different root fixture can invalidate the stiffness evidence. The report should state what changes require retest, model update or engineering disposition.

Common Mistakes

A common mistake is treating measured twist as article twist without subtracting fixture compliance. Another is comparing test and FEA stiffness with different torque axes, boundary conditions or reference stations. A third is releasing a nominal stiffness while ignoring uncertainty even though the lower bound is close to the requirement.

A strong torsional-stiffness ground test states the torque path, twist coordinate, fixture correction, calibration evidence, model boundary condition, uncertainty, lower-bound value and the engineering decisions the stiffness is allowed to support.

Other mistakes include using actuator command instead of calibrated force, measuring twist in mixed coordinate frames, overlooking root slip, extrapolating a small-angle linear test into a nonlinear load case, and giving the aeroelastic team a stiffness value without the configuration and uncertainty limits attached.

REF

Disciplines