Exercise set

Biomedical Device Structural Load, Fatigue, and Fixation Exercises

Solved biomedical device structural exercises for stress, contact pressure, bending, fatigue, fracture, micromotion, fixation and buckling.

These exercises focus on biomedical device structural integrity and body-interface mechanics. They cover stress, contact pressure, bending, static safety factor, fatigue, fracture, micromotion, fixation, buckling, torsion, bearing, proof loading and structural release gates.

Assume simplified screening models unless an exercise states otherwise. Real device release should also use intended-use loads, anatomical boundary conditions, material processing, sterilization effects, manufacturing variation, fatigue scatter, inspection evidence and applicable medical-device risk controls.

Release Evidence Notes

Structural evidence must identify the load path, material lot, geometry revision, surface condition, body interface, sterilization state, manufacturing tolerance and acceptance criterion. A calculated pass is weak if the part cannot be manufactured, inspected, cleaned, sterilized and used within the assumed boundary conditions.

For body-interface calculations, the result should be tied to tissue tolerance, micromotion, fixation quality, clinical use case and validation evidence. A low average stress can still be unsafe if local contact, fatigue, fretting or misuse loads dominate.

Engineering Boundary Notes

These exercises are screening calculations. They do not replace full finite-element validation, cadaver or benchtop testing, fatigue test planning, implant standard testing, clinical risk analysis, biocompatibility review or regulatory submission evidence.

Scenario Map

ScenarioExercisesPrimary checkEngineering decision
Static structural screening1, 3, 4, 11, 12, 13Axial, bending, yield, torsion, bearing and compressionDecide whether the device geometry has static margin.
Interface and fixation2, 7, 8, 16Contact pressure, micromotion, pullout and screw load sharingDecide whether the body interface can be released.
Durability and damage tolerance5, 6, 10, 14, 17Fatigue, fracture, strain signal, snap retention and proof loadDecide whether lifecycle evidence is strong enough.
Slender-device stability and release9, 15, 18Buckling, guide support and all-of structural gateDecide whether insertion or use conditions are releasable.

A device link carries 180\ \text{N} through a cross-section of 12\ \text{mm}^2. Compute axial stress.

Solution

\sigma=\dfrac{F}{A}=\dfrac{180}{12}=15\ \text{N/mm}^2

Since 1\ \text{N/mm}^2=1\ \text{MPa}:

\sigma=15\ \text{MPa}

Engineering Comment

This is a nominal stress. Local holes, fillets, surface damage and sterilization effects can raise the true critical stress.

Plausibility Check

A few hundred newtons over about ten square millimeters should produce tens of megapascals, not hundreds.

Exercise 2: Contact Pressure Under a Wearable Pad

A wearable pad applies 24\ \text{N} over 18\ \text{cm}^2. Compute average pressure in \text{kPa}.

Solution

Convert area:

18\ \text{cm}^2=0.0018\ \text{m}^2

Pressure:

p=\dfrac{24}{0.0018}=13333\ \text{Pa}=13.3\ \text{kPa}

Engineering Comment

Average pressure does not capture edge pressure or motion. Body-interface release should include fit, duration, skin condition and user variability.

Plausibility Check

Tens of newtons spread over a few square centimeters gives pressure in the low kilopascal range.

Exercise 3: Bending Stress in an Instrument Arm

A reusable instrument arm has bending moment M=2.4\ \text{N m}, distance to outer fiber c=3.0\ \text{mm} and second moment I=85\ \text{mm}^4. Compute bending stress.

Solution

Convert moment:

M=2.4\ \text{N m}=2400\ \text{N mm}
\sigma=\dfrac{Mc}{I}=\dfrac{2400(3.0)}{85}=84.7\ \text{MPa}

Engineering Comment

The screen should be checked at the smallest section and at any feature that creates stress concentration.

Plausibility Check

The moment is substantial for a small section, so stress near one hundred megapascals is plausible.

Exercise 4: Static Safety Factor Against Yield

A component has yield strength 520\ \text{MPa} and maximum guarded stress 170\ \text{MPa}. Compute safety factor.

Solution

SF=\dfrac{520}{170}=3.06

Engineering Comment

A static safety factor above three may be acceptable for screening, but fatigue, impact and cleaning damage can still govern.

Plausibility Check

The yield strength is about three times the stress, so the safety factor is about three.

Exercise 5: Fatigue Stress-Amplitude Screen

A cyclic device member has maximum stress 140\ \text{MPa} and minimum stress 40\ \text{MPa}. Compute stress amplitude.

Solution

\sigma_a=\dfrac{\sigma_{max}-\sigma_{min}}{2}
\sigma_a=\dfrac{140-40}{2}=50\ \text{MPa}

Engineering Comment

Fatigue release needs stress concentration, surface finish, sterilization, environment and expected cycle count, not only amplitude.

Plausibility Check

The stress range is 100\ \text{MPa}, so amplitude is half of that.

Exercise 6: Fracture-Toughness Screening

A flaw of depth a=0.25\ \text{mm} is found in a component. Use K=Y\sigma\sqrt{\pi a} with Y=1.1 and \sigma=180\ \text{MPa}. Compute K using a in meters.

Solution

a=0.25\ \text{mm}=0.00025\ \text{m}
K=1.1(180)\sqrt{\pi(0.00025)}
K=198(0.0280)=5.54\ \text{MPa}\sqrt{\text{m}}

Engineering Comment

This is a flaw-tolerance screen. Release needs inspection sensitivity and material fracture toughness with appropriate environmental condition.

Plausibility Check

A sub-millimeter flaw at moderate stress gives a single-digit stress-intensity value.

Exercise 7: Interface Micromotion Under Load

An implant interface has stiffness k=12000\ \text{N/mm} and cyclic load amplitude F=180\ \text{N}. Estimate micromotion amplitude.

Solution

\delta=\dfrac{F}{k}=\dfrac{180}{12000}=0.015\ \text{mm}
\delta=15\ \mu\text{m}

Engineering Comment

Micromotion should be compared with tissue integration or fixation criteria. The stiffness model must represent the actual interface.

Plausibility Check

A stiff interface under a few hundred newtons should move only micrometers to tens of micrometers.

Exercise 8: Fixation Pullout Screen

Four fixation features each have tested pullout capacity 95\ \text{N}. Required guarded pullout load is 300\ \text{N}. Check margin.

Solution

Total capacity:

F_c=4(95)=380\ \text{N}

Margin:

M=380-300=80\ \text{N}

Engineering Comment

The arithmetic passes, but equal load sharing is an assumption. Misalignment or bone quality variation can reduce effective capacity.

Plausibility Check

Four features just under one hundred newtons each give capacity just under four hundred newtons.

Exercise 9: Cannula Buckling During Insertion

A cannula has Euler critical load 14\ \text{N} with current unsupported length. Guarded insertion load is 11\ \text{N}. Compute buckling margin.

Solution

M=14-11=3\ \text{N}

Percentage margin relative to insertion load:

\dfrac{3}{11}=0.273=27.3\%

Engineering Comment

The margin is useful but should be checked against worst insertion angle, guide support and manufacturing straightness.

Plausibility Check

The critical load is only a few newtons above the guarded insertion load, so the margin is modest.

Exercise 10: Strain-Gauge Signal from Device Flexure

A flexure strain is 420\ \mu\varepsilon. Gauge factor is 2.1 and bridge excitation is 3.0\ \text{V}. Estimate quarter-bridge output:

V_o\approx\dfrac{GF\varepsilon}{4}V_{ex}

Solution

\varepsilon=420\times10^{-6}
V_o=\dfrac{2.1(420\times10^{-6})}{4}(3.0)=0.000662\ \text{V}
V_o=0.662\ \text{mV}

Engineering Comment

The signal is small. Release evidence should include noise, calibration, temperature drift and overload protection.

Plausibility Check

Microstrain bridge outputs are usually millivolt-level or lower before amplification.

Exercise 11: Torsional Shear in a Handle Shaft

A handle shaft carries torque 0.75\ \text{N m}. Its polar section modulus is 42\ \text{mm}^3. Compute torsional shear stress.

Solution

Convert torque:

T=0.75\ \text{N m}=750\ \text{N mm}
\tau=\dfrac{T}{Z_p}=\dfrac{750}{42}=17.9\ \text{MPa}

Engineering Comment

The shaft may pass nominal torsion while failing at notches, flats, pins or molded transitions.

Plausibility Check

The torque divided by a few tens of cubic millimeters gives shear stress in tens of megapascals.

Exercise 12: Bearing Stress Under a Pin

A pin transfers 160\ \text{N} through a lug with pin diameter 3\ \text{mm} and lug thickness 2.5\ \text{mm}. Compute average bearing stress.

Solution

Projected bearing area:

A_b=dt=3(2.5)=7.5\ \text{mm}^2
\sigma_b=\dfrac{160}{7.5}=21.3\ \text{MPa}

Engineering Comment

Bearing stress should be checked with wear, creep and sterilization exposure if the lug is polymeric.

Plausibility Check

The projected area is small, so even a modest load produces tens of megapascals.

Exercise 13: Compression of a Spacer

A polymer spacer has stiffness 850\ \text{N/mm} and assembly preload 120\ \text{N}. Estimate compression.

Solution

\delta=\dfrac{F}{k}=\dfrac{120}{850}=0.141\ \text{mm}

Engineering Comment

Compression affects alignment and seal preload. Creep and cleaning exposure may reduce retained load.

Plausibility Check

The stiffness is less than one thousand newtons per millimeter, so one hundred newtons gives a few tenths of a millimeter.

Exercise 14: Snap Retention Load Margin

A snap feature has measured retention 38\ \text{N} after aging. The release requirement is 30\ \text{N} with a 4\ \text{N} guard. Check status.

Solution

Guarded requirement:

F_g=30+4=34\ \text{N}

Margin:

M=38-34=4\ \text{N}

Engineering Comment

The snap passes narrowly. Release should verify worst material lot, cleaning exposure and repeated use.

Plausibility Check

The measured value is only eight newtons above nominal requirement and four above guarded requirement.

Exercise 15: Guide Support Buckling Improvement

Reducing unsupported cannula length raises critical load from 14\ \text{N} to 24\ \text{N}. Guarded insertion load is 11\ \text{N}. Compute new safety factor.

Solution

SF=\dfrac{24}{11}=2.18

Engineering Comment

Guide support strongly improves buckling margin. The guide must be part of the controlled design and use procedure.

Plausibility Check

The critical load is a bit more than twice the insertion load, so safety factor just above two is expected.

Exercise 16: Bone Screw Load Sharing

Three screws share a peak interface load of 270\ \text{N}. If load sharing is assumed equal, compute load per screw and compare with guarded screw capacity 110\ \text{N}.

Solution

F_s=\dfrac{270}{3}=90\ \text{N}

Margin per screw:

M=110-90=20\ \text{N}

Engineering Comment

Equal load sharing is often optimistic. Bone quality, screw angle and plate fit should be considered.

Plausibility Check

Dividing 270\ \text{N} over three screws gives a clean 90\ \text{N} per screw.

Exercise 17: Proof-Load Acceptance

A structural subassembly must survive proof load 2.5 times intended-use load. Intended-use load is 140\ \text{N}. The test fixture reached 330\ \text{N} before stopping. Check status.

Solution

Required proof load:

F_p=2.5(140)=350\ \text{N}

The test stopped at 330\ \text{N}:

330<350

so acceptance is blocked.

Engineering Comment

Stopping below proof load is not a pass even if no damage was observed. The test must reach the required load or the plan must be revised.

Plausibility Check

Two and a half times 140 is clearly above 330.

Exercise 18: Structural Release Gate

A structural release gate requires static margin pass, fatigue margin pass, fixation pass, buckling pass and proof-load pass. Results are pass, pass, pass, conditional pass and pass. Decide status.

Solution

The rule is all-of:

G=R_s\land R_f\land R_{fix}\land R_b\land R_p

A conditional buckling pass is not full release evidence, so release is blocked.

Engineering Comment

Biomedical structural release should not average evidence across unrelated failure modes. A weak buckling condition can invalidate an otherwise strong package.

Plausibility Check

Any conditional required gate blocks an all-of release rule.

Common Release Mistakes

  • Treating nominal stress as local stress at holes, notches or molded transitions.
  • Ignoring sterilization, cleaning, surface finish and material-lot effects.
  • Assuming equal fixation load sharing without evidence.
  • Using static safety factor as fatigue evidence.
  • Releasing body-interface contact from average pressure only.
  • Counting an incomplete proof-load test as accepted.

Validation Package Checklist

  • Intended-use and foreseeable-use load cases with traceable requirements.
  • Material lot, geometry revision, manufacturing tolerance and surface condition.
  • Static, fatigue, fracture, buckling and fixation calculations with guards.
  • Body-interface contact and micromotion evidence where applicable.
  • Inspection or NDT capability for critical flaws and features.
  • Proof-load, fatigue or benchtop validation tied to acceptance criteria.
  • Risk-control linkage for every structural failure mode.
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See also