Skip to main content
OrthoVellum
Knowledge Hub

Study

  • Topics
  • MCQs
  • ISAWE
  • Operative Surgery
  • Flashcards

Company

  • About Us
  • Editorial Policy
  • Contact
  • FAQ
  • Blog

Legal

  • Terms of Service
  • Privacy Policy
  • Cookie Policy
  • Medical Disclaimer
  • Copyright & DMCA
  • Refund Policy

Support

  • Help Center
  • Accessibility
  • Report an Issue
OrthoVellum

© 2026 OrthoVellum. For educational purposes only.

Not affiliated with the Royal Australasian College of Surgeons.

Bending Moment Distribution in Fracture Fixation

Back to Topics
Contents
0%

Bending Moment Distribution in Fracture Fixation

Bending mechanics, stress distribution, neutral axis, working length, and clinical applications in fracture fixation

complete
Updated: 2025-12-25
High Yield Overview

BENDING MOMENT DISTRIBUTION IN FRACTURE FIXATION

Bending Stress | Neutral Axis | Working Length | Plate Mechanics

M/Ibending stress proportional to moment/area moment
L³deflection proportional to working length cubed
h²section modulus proportional to height squared
8xstiffness increase when distance between screws halved

Bending Stress Distribution

Tension Surface
PatternMaximum tensile stress at outer fiber
TreatmentPlate placement optimal
Neutral Axis
PatternZero stress at centroid
TreatmentNo contribution to strength
Compression Surface
PatternMaximum compressive stress opposite tension
TreatmentBone contact preferred

Critical Must-Knows

  • Bending moment creates linear stress distribution from maximum tension to maximum compression
  • Neutral axis at centroid has zero bending stress - material here does not resist bending
  • Stress proportional to distance from neutral axis: σ = My/I where y is distance from neutral axis
  • Working length (distance between screws) affects stiffness as L³ - doubling length reduces stiffness 8-fold
  • Plate should be placed on tension side for optimal biomechanics

Examiner's Pearls

  • "
    Working length inversely proportional to stiffness cubed - critical for bridge plating
  • "
    Section modulus (I/c) determines bending strength - increases with height squared
  • "
    Plate on tension side prevents gap formation and reduces stress shielding
  • "
    Eccentric loading increases bending moment - explains failure in varus/valgus malalignment

Clinical Imaging

Imaging Gallery

Simply supported beam under central point load with moment, shear, and deflection diagrams
Click to expand
Simply supported beam under central point load (P) demonstrating bending moment distribution. Top: beam supported by pin (A) and roller (C) with central load at B. M (magenta): triangular bending moment diagram showing zero moment at supports and maximum at midspan. Q (red): shear force diagram with constant values changing sign at the load point. w (blue): deflection curve showing maximum sag at midspan. This fundamental diagram illustrates how bending moment varies linearly along the span, being zero at simple supports and maximum where the load is applied - principles directly applicable to understanding stress distribution in long bones and fracture fixation constructs.Credit: Bbanerje via Wikimedia - CC BY-SA 3.0

Critical Bending Moment Exam Points

Linear Stress Distribution

Bending creates linear stress profile from maximum tension to maximum compression. Neutral axis at centroid has zero stress. Maximum stress at outer fibers: σ_max = Mc/I where c is distance to extreme fiber.

Working Length Effect

Stiffness inversely proportional to working length cubed: k ∝ 1/L³. Doubling distance between screws reduces stiffness 8-fold. Too stiff = stress shielding. Too flexible = excessive motion.

Plate Placement Principle

Plate should be on tension side of bone. Prevents gap formation, provides compression across fracture, reduces plate stress by allowing load sharing with bone. Compression side can gap without loss of stability.

Section Modulus

Bending strength proportional to I/c (section modulus). Doubling height increases strength 4-fold. Explains why thicker plates resist bending better. Also why hollow tubes efficient.

At a Glance

Bending creates a linear stress distribution from maximum tension at one surface to maximum compression at the opposite surface, with zero stress at the neutral axis (centroid). The fundamental equation σ = My/I describes bending stress (proportional to moment M, distance from neutral axis y, and inversely to area moment of inertia I). Critical clinical concept: working length (distance between screws) affects construct stiffness as L³—doubling working length reduces stiffness 8-fold. The section modulus (I/c) determines bending strength, explaining why thicker plates resist bending better (strength increases with height squared). Plates should be placed on the tension side of bone to prevent gap formation and reduce plate stress through load sharing. Understanding these principles is essential for bridge plating, plate selection, and analyzing construct failure.

Mnemonic

MY ICIBending Stress Formula Components

M
Moment
Bending moment at cross-section (N·m or N·mm)
Y
y-distance
Distance from neutral axis to point of interest
I
I (area moment)
Second moment of area - resistance to bending
C
c-distance
Distance from neutral axis to extreme fiber
I
I/c ratio
Section modulus - determines maximum bending stress

Memory Hook:MY ICI determines bending stress: σ = My/I with max at c!

Mnemonic

PLIESFactors Affecting Working Length Stiffness

P
Plate modulus
Material stiffness (E) - titanium vs steel vs carbon fiber
L
Length (working)
Distance between screws - L³ relationship to stiffness
I
I (area moment)
Plate cross-section - width × thickness³/12 for rectangle
E
Empty screw holes
Stress concentration points - reduce fatigue life
S
Screw configuration
Number and spacing affects load transfer

Memory Hook:PLIES together determine construct stiffness!

Mnemonic

TENTOptimal Plate Application Principles

T
Tension side
Place plate on tension surface for best biomechanics
E
Eccentric loading
Consider physiologic loading direction (varus, valgus)
N
Neutral axis
Material at centroid doesn't resist bending
T
Three-point bending
Most common loading mode in long bones

Memory Hook:Put your TENT on the tension side!

Overview and Fundamentals

Bending moment distribution is fundamental to understanding fracture fixation mechanics. When a long bone or plate is loaded in bending, internal stresses develop that vary linearly from maximum tension on one surface to maximum compression on the opposite surface. The neutral axis, located at the centroid of the cross-section, experiences zero bending stress and contributes nothing to bending resistance.

The bending stress at any point is given by the flexure formula: σ = My/I, where M is the bending moment, y is the perpendicular distance from the neutral axis, and I is the second moment of area. Maximum stress occurs at the outer fibers where y is maximum (y = c), giving σ_max = Mc/I. The ratio I/c is called the section modulus and determines bending strength.

Why Bending Matters in Fracture Fixation

Most long bone fractures experience bending loads during physiologic loading. Understanding bending stress distribution explains: (1) why plates should be on tension side, (2) how working length affects construct stiffness, (3) why eccentrically loaded fractures fail in predictable patterns, (4) how to optimize screw spacing for biological fixation.

Pure Bending vs Combined Loading

Pure bending: M only, linear stress distribution, neutral axis at centroid

Combined axial + bending: Axial stress shifts neutral axis, asymmetric stress distribution

Clinical: Most fractures experience combined loading - eccentric axial loads create bending moments (varus/valgus stress)

Material at Neutral Axis

Material at neutral axis contributes ZERO to bending resistance

Explains why:

  • Hollow tubes as efficient as solid rods (same I/c)
  • Trabecular bone in marrow cavity doesn't resist bending
  • Intramedullary nails optimized with hollow design

Neutral Axis and Stress Distribution

Location of Neutral Axis

The neutral axis passes through the centroid of the cross-section and is perpendicular to the plane of bending. For symmetric sections (circular, square, I-beam), the neutral axis is at the geometric center. For composite sections (plate plus bone), the neutral axis shifts based on relative stiffness and area.

Cross-Section TypeNeutral Axis LocationSection Modulus (I/c)Clinical Example
Solid circular (diameter d)Centerπd³/32Intact long bone, IM nail
Hollow circular (outer D, inner d)Centerπ(D⁴-d⁴)/32DCortical bone, hollow nail
Rectangular plate (width b, height h)Centerbh²/6Compression plate
Plate-bone compositeShifts toward stiffer materialComplex calculationFixed fracture

Key Principles:

  • Stress increases linearly with distance from neutral axis
  • Maximum tensile stress on one surface, maximum compressive on opposite
  • At neutral axis: σ = 0 (no contribution to bending resistance)
  • Stress sign changes across neutral axis (tension to compression)

Composite Beam Behavior

When plate and bone share load, neutral axis shifts toward the stiffer material (steel plate). This means bone near the plate experiences less stress (stress shielding), while bone far from plate experiences higher stress. Proper working length balances load sharing to promote healing while preventing excessive motion.

Stress Distribution Across Section

For a rectangular cross-section in pure bending:

  • Outer tension fiber: σ = Mc/I = M/(bh²/6) = 6M/bh²
  • Neutral axis (center): σ = 0
  • Outer compression fiber: σ = -Mc/I = -6M/bh²

The linear distribution means stress gradient is constant: dσ/dy = M/I.

Why Section Modulus Matters

Q: Why is a plate twice as thick more than twice as strong in bending? A: Section modulus I/c increases with height squared. For rectangular section, I/c = bh²/6. Doubling thickness (h) increases section modulus 4-fold, thus strength increases 4-fold for same bending moment. This is why small increases in plate thickness dramatically improve bending resistance.

Working Length in Fracture Fixation

Definition and Biomechanical Significance

Working length is the distance between the two innermost screws on either side of a fracture. It determines construct stiffness and affects fracture healing, stress shielding, and implant failure risk.

Beam deflection under three-point bending: δ = FL³/48EI

Where F is load, L is working length, E is elastic modulus, I is area moment of inertia.

Key relationships:

  • Stiffness k = F/δ ∝ 1/L³ (inversely proportional to length cubed)
  • Doubling working length reduces stiffness 8-fold
  • Halving working length increases stiffness 8-fold
Working Length StrategyStiffnessStress ShieldingFracture MotionClinical Application
Short (compression plating)Very highMaximumMinimalSimple fractures, absolute stability
Intermediate (standard bridge)ModerateModerateModerateMost fractures, relative stability
Long (flexible bridge)LowMinimalExcessiveRisk of delayed union, implant failure
Optimal (3-5 cortices)BalancedBalancedMicromotion onlyModern locking plate technique

Clinical Implications

Too short (stiff):

  • Excessive stress shielding
  • Reduced fracture site strain (may impair healing)
  • All load through implant (fatigue risk if no healing)
  • Higher stress at screw-bone interface

Too long (flexible):

  • Excessive fracture motion (may prevent healing)
  • Increased implant stress (bending moment ∝ L)
  • Cantilever beam effect if fracture doesn't heal
  • Risk of implant failure before union

Optimal working length:

  • 3-5 cortices (1.5-2.5 screw holes) on each side of simple fracture
  • Longer for comminuted fractures (bridge entire comminution zone)
  • Balance stiffness for healing while allowing micromotion
  • Modern locked plating allows increased working length vs conventional

Working Length and Screw Density

Current principle: fewer screws, longer working length for biological fixation. Traditional AO teaching (6 cortices per fragment) too stiff. Modern bridge plating: 3-4 screws per fragment with working length chosen for appropriate flexibility. Exception: periarticular fractures need short working length for stable articular reduction.

Working Length Calculation

Q: How do you calculate working length in a plated fracture? A: Distance between innermost screws on opposite sides of fracture. NOT the distance between screw holes, but actual occupied holes. Empty holes within the working length act as stress risers and should be avoided. For comminuted fractures, bridge the entire comminution zone - working length is from end of comminution to first screw.

Plate Placement and Tension Band Principle

Tension Side vs Compression Side

Plates should ideally be placed on the tension surface of bone for optimal biomechanics. This principle is based on bending moment distribution and composite beam behavior.

Plate on tension side:

  • Prevents gap formation on tension surface (plate resists tensile stress)
  • Creates compression across fracture (pre-loading effect)
  • Bone compression side can tolerate contact and load sharing
  • Reduces plate stress by allowing composite action with bone
  • Minimizes interfragmentary motion

Plate on compression side:

  • Gap opens on tension surface (uncontrolled)
  • Plate experiences higher bending stress
  • Less stable construct
  • Risk of delayed union or nonunion from gap
Bone SegmentPhysiologic Tension SurfaceOptimal Plate PositionRationale
Femur - lateral cortexLateral (tension band of IT band)LateralResist varus moment from body weight
Tibia - medial cortexAnterior or medialAnteromedialSubcutaneous position, resist anterior bow
Humerus - anterolateralAnterior with forward flexionAnterolateralAccessible, resist AP bending
Forearm bonesVariable with rotationDorsal radius, volar ulnaBased on anatomy and soft tissue

Eccentric Loading and Bending Moment

Axial loads applied eccentric to the bone's mechanical axis create bending moments: M = P × e, where P is axial force and e is eccentricity (perpendicular distance from load line to neutral axis).

Clinical examples:

  • Varus knee: medial compartment overload creates varus bending moment
  • Hip joint reaction force lateral to femoral shaft: creates varus bending moment in proximal femur
  • Patellar tendon pull anterior to tibial axis: creates anterior bending moment

This explains why:

  • Varus malunion of femur fracture leads to increased implant stress and failure
  • Proper alignment critical to minimize bending moments
  • Plates should resist the direction of expected bending from eccentric loading

Tension Band Plating Example

Q: Why place lateral plate on distal femur fracture? A: Hip joint reaction force creates varus bending moment. With body weight medial to femoral shaft, lateral cortex experiences tension. Lateral plate resists this tensile stress, prevents lateral gap formation, and creates medial compression across fracture. Medial plate would allow lateral gap and higher plate stress.

Beam Theory and Implant Design

Second Moment of Area (Area Moment of Inertia)

The second moment of area (I) quantifies a cross-section's resistance to bending. It depends on how material is distributed relative to the neutral axis.

For rectangular cross-section: I = bh³/12 (b = width, h = height perpendicular to bending axis)

Key insights:

  • I proportional to height cubed (h³): doubling height increases I by 8-fold
  • Material far from neutral axis contributes more to I (y² term)
  • This is why I-beams, hollow tubes are efficient - material concentrated at extremes

For circular cross-section:

  • Solid: I = πd⁴/64
  • Hollow: I = π(D⁴ - d⁴)/64

Hollow tube advantage: Can remove material near neutral axis (low contribution) while maintaining I by preserving outer diameter. Explains efficiency of cortical bone, intramedullary nails.

Plate Thickness Effect

For a plate of width b and thickness h:

  • Area moment: I = bh³/12
  • Section modulus: I/c = bh²/6 (c = h/2)
  • Maximum bending stress: σ_max = 6M/bh²

Doubling plate thickness:

  • I increases 8-fold (h³ relationship)
  • Section modulus increases 4-fold (h² relationship)
  • For same bending moment, stress decreases 4-fold
  • Stiffness increases 8-fold

Clinical implication: Small increase in plate thickness dramatically improves bending strength and stiffness. However, may increase stress shielding. Modern locked plates can be thinner due to different load transfer mechanism (angle stability vs friction).

Locking vs Conventional Plate Mechanics

Conventional plate: Load transfer via friction (plate compression to bone). Bending creates friction force at plate-bone interface. Requires precise contouring.

Locking plate: Load transfer via screw-plate construct acting as internal-external fixator. Less dependent on plate-bone contact. Can use longer working length, maintain bending stability with fewer screws. Allows biological fixation principles.

Evidence Base

Working Length and Fracture Healing: Biomechanical Study

3
Stoffel K et al • Injury (2003)
Key Findings:
  • Increasing working length from 2 to 6 screw holes decreased construct stiffness 27-fold
  • Optimal working length balances stability and flexibility for healing
  • Empty screw holes within working length reduced fatigue life by 30-40%
  • Locked plates allow longer working length than conventional plates while maintaining stability
Clinical Implication: Modern bridge plating uses longer working length (3-5 cortices per fragment) to reduce stress shielding while maintaining adequate stability. Avoid empty holes within working length.
Limitation: Biomechanical study in synthetic bones - fracture healing biology may differ from mechanical model.

Stress Distribution in Plated Fractures: Finite Element Analysis

3
MacLeod AR et al • J Orthop Res (2012)
Key Findings:
  • Plate on tension side reduced peak bone stress by 40% vs compression side
  • Maximum plate stress 3-fold higher when plate on compression surface
  • Working length inversely proportional to construct stiffness (L³ relationship confirmed)
  • Stress concentration at screw holes increased with increasing working length
Clinical Implication: Plate should be positioned on tension surface to optimize load sharing and reduce implant stress. Balancing working length critical - too short causes stress shielding, too long risks implant failure.
Limitation: Computational model with idealized geometry and loading - actual physiologic loading more complex.

Plate Fixation Principles: AO Evolution from Rigid to Flexible

4
Perren SM • Injury (2002)
Key Findings:
  • Traditional compression plating (rigid fixation) caused stress shielding and bone resorption
  • Bridge plating with longer working length preserves periosteal blood supply and reduces stress shielding
  • Relative stability (micromotion) promotes callus formation in indirect healing
  • Modern locked plates allow biological fixation with fewer screws and longer working length
Clinical Implication: Evolution from absolute stability (compression plating, short working length) to relative stability (bridge plating, longer working length) represents paradigm shift in fracture management. Current principle: minimum fixation necessary for adequate stability.
Limitation: Expert opinion and biomechanical rationale - clinical outcomes depend on fracture pattern, patient factors, surgical technique.

Exam Viva Scenarios

Practice these scenarios to excel in your viva examination

VIVA SCENARIOStandard

Scenario 1: Bending Stress Distribution and Neutral Axis

EXAMINER

"Examiner shows cross-section of a long bone and asks: Explain the stress distribution when this bone is loaded in bending. What is the neutral axis and why is it important?"

EXCEPTIONAL ANSWER
When a long bone is subjected to bending, a linear stress distribution develops across the cross-section. On one surface, there is maximum tensile stress, and on the opposite surface, maximum compressive stress. The stress varies linearly between these extremes according to the flexure formula: sigma equals My over I, where M is the bending moment, y is the distance from the neutral axis, and I is the second moment of area. The neutral axis is located at the centroid of the cross-section and is the plane where bending stress is zero. Material at the neutral axis contributes nothing to bending resistance. This is why hollow tubes such as cortical bone or intramedullary nails are efficient - material near the neutral axis can be removed without significantly affecting bending strength, as bending resistance depends primarily on material distribution at the outer fibers. For fracture fixation, this explains why plates should be positioned on the tension surface where stress is maximum, allowing the plate to resist tensile loads and prevent gap formation while the compression surface of bone provides contact and stability. Maximum stress occurs at the outer fibers a distance c from the neutral axis, giving sigma max equals Mc over I. The ratio I over c is the section modulus and determines the maximum bending stress for a given moment.
KEY POINTS TO SCORE
Linear stress distribution from maximum tension to maximum compression
Neutral axis at centroid has zero stress
Stress formula: σ = My/I where y is distance from neutral axis
Maximum stress at outer fibers: σ_max = Mc/I
Material at neutral axis doesn't contribute to bending resistance - explains hollow tube efficiency
COMMON TRAPS
✗Saying stress is uniform across section (it's linear, not uniform)
✗Not explaining neutral axis location or significance
✗Missing the clinical application to plate positioning
✗Confusing bending stress with axial stress (different distributions)
LIKELY FOLLOW-UPS
"How does plate thickness affect bending strength?"
"What is the section modulus?"
"Why place plate on tension side of bone?"
VIVA SCENARIOChallenging

Scenario 2: Working Length in Bridge Plating

EXAMINER

"You are treating a comminuted mid-diaphyseal femur fracture with a locked plate. Explain how you would determine the optimal working length and why it matters for fracture healing and construct stability."

EXCEPTIONAL ANSWER
Working length is the distance between the two innermost screws on either side of the fracture and is a critical determinant of construct stiffness and fracture healing. I need to balance adequate stability with appropriate flexibility to promote healing. The relationship between working length and stiffness is described by beam theory: stiffness is inversely proportional to the working length cubed. This means if I double the working length, stiffness decreases by a factor of eight. For this comminuted femur fracture, my approach would be to first bridge the entire zone of comminution with the plate to avoid stress concentration in the fracture zone. I would then place my screws to achieve a working length of approximately 3 to 5 cortices on each side of the comminution zone. This provides what we call relative stability - enough stiffness to maintain alignment and prevent excessive motion, but sufficient flexibility to avoid complete stress shielding. If I make the working length too short by placing screws too close to the fracture, I create a very rigid construct that completely shields the bone from physiologic stress, which can impair callus formation and lead to stress shielding osteopenia. The plate alone bears all the load, increasing risk of fatigue failure if healing is delayed. Conversely, if the working length is too long with screws very far from the fracture, the construct becomes excessively flexible. This can allow too much motion at the fracture site, potentially preventing healing, and also increases bending stress in the plate itself since stress is proportional to the bending moment, which increases with span. Modern locked plating allows me to use fewer screws and longer working length compared to conventional plating while still maintaining adequate stability through angle-stable screw-plate construct. I would also avoid leaving empty screw holes within the working length as these act as stress concentration points that reduce fatigue life. My goal is 3 to 4 bicortical screws per main fragment with working length chosen to provide micromotion at the fracture site while preventing gross instability.
KEY POINTS TO SCORE
Working length = distance between innermost screws on opposite sides of fracture
Stiffness inversely proportional to L³ - doubling length reduces stiffness 8-fold
Optimal: 3-5 cortices per fragment for relative stability
Too short = stress shielding, impaired healing; too long = excessive motion, implant failure
Bridge entire comminution zone to avoid stress concentration
Avoid empty screw holes within working length (stress risers)
COMMON TRAPS
✗Not explaining the L³ relationship quantitatively
✗Saying 'maximum screws for maximum stability' (outdated principle)
✗Not addressing the balance between stress shielding and excessive motion
✗Missing the difference between locked and conventional plate working length principles
LIKELY FOLLOW-UPS
"What if the fracture hasn't healed at 6 months?"
"How would you modify working length for a simple transverse fracture?"
"What is the role of far cortical locking screws?"
VIVA SCENARIOStandard

Scenario 3: Plate Positioning and Tension Band Principle

EXAMINER

"You are treating a distal femur fracture with lateral locked plate. The examiner asks: Why do we place the plate laterally? What would happen if you placed it medially?"

EXCEPTIONAL ANSWER
The lateral plate position for distal femur fractures is based on the principle that plates should be placed on the tension side of the bone to optimize biomechanics. During stance phase of gait, the hip joint reaction force passes medial to the mechanical axis of the femur, creating a varus bending moment. This causes tensile stress on the lateral cortex and compressive stress on the medial cortex. By placing the plate laterally on the tension surface, we achieve several biomechanical advantages. First, the plate directly resists the tensile stress, preventing a gap from opening on the lateral side. Second, the plate pre-loading and load sharing creates compression across the fracture, particularly medially where bone contact is present. This compression provides stability and promotes healing. Third, the plate experiences lower stress when on the tension side compared to the compression side, because it works in concert with the bone rather than against it. If I were to place the plate medially on the compression surface instead, several problems would occur. The lateral cortex, which is in tension, would have no direct support, allowing a gap to form. The plate would experience much higher bending stress because it must now resist both the tensile stress and the bending moment alone without bone load sharing. The construct would be less stable, with increased risk of loss of reduction, delayed union or nonunion from the lateral gap, and higher risk of implant failure from fatigue. Additionally, the eccentric loading from body weight creates a bending moment equal to the load times the eccentricity - that is, M equals P times e - where e is the perpendicular distance from the load vector to the neutral axis. For the femur, this eccentricity causes varus moment, further supporting lateral plate placement. This same principle applies throughout the skeleton: tibia anteriorly or medially, forearm bones on their respective tension surfaces based on loading. Modern precontoured locked plates are designed specifically for this anatomically appropriate tension-side positioning.
KEY POINTS TO SCORE
Hip joint reaction force medial to femoral shaft creates varus bending moment
Lateral cortex in tension, medial cortex in compression
Plate on tension side prevents gap formation and reduces plate stress
Medial plate would allow lateral gap, higher implant stress, less stable construct
Bending moment M = P × e from eccentric loading
COMMON TRAPS
✗Not explaining the biomechanical rationale (varus moment)
✗Saying 'because that's what we do' without explaining why
✗Not discussing what would happen with medial plate placement
✗Missing the load sharing and compression principles
LIKELY FOLLOW-UPS
"What about for a medial femoral neck fracture?"
"How does this principle apply to tibial fractures?"
"What is the role of plate contouring in conventional vs locked plating?"

MCQ Practice Points

Bending Stress Formula

Q: What does the flexure formula σ = My/I represent? A: Bending stress at distance y from neutral axis. M is bending moment, y is perpendicular distance from neutral axis, I is second moment of area. Stress is linear across section, maximum at outer fibers (y = c).

Section Modulus

Q: How does doubling the thickness of a plate affect its bending strength? A: Increases strength 4-fold. Section modulus I/c = bh²/6 for rectangular section. Doubling h increases section modulus by factor of 4, thus maximum stress σ_max = M/(I/c) decreases 4-fold for same moment.

Working Length Relationship

Q: If you double the working length in a plated fracture, how does construct stiffness change? A: Stiffness decreases 8-fold. From beam theory, stiffness is inversely proportional to working length cubed: k ∝ 1/L³. Doubling L means new stiffness is 1/(2L)³ = 1/8 of original stiffness.

Neutral Axis Significance

Q: Why is material at the neutral axis not effective at resisting bending? A: Stress at neutral axis is zero. From σ = My/I, when y = 0 (at neutral axis), σ = 0. Material contributes to bending resistance proportional to its distance from neutral axis. This explains efficiency of hollow tubes.

Plate Positioning

Q: Why should plates be placed on the tension side of bone? A: Prevents gap formation and reduces plate stress. Plate directly resists tensile stress, creating compression across fracture. Allows load sharing with bone. Plate on compression side would allow gap on tension surface and experience higher stress.

Eccentric Loading

Q: How does varus malalignment affect bending moment in a femoral fracture? A: Increases bending moment via eccentric loading. M = P × e where e is eccentricity. Varus shifts load line medial, increasing distance to lateral cortex, thus increasing varus bending moment and lateral cortex tensile stress.

Australian Context

FRACS Examination Relevance

Basic Science Viva:

  • Bending mechanics is a core basic science topic for FRACS Part 1
  • Expected to explain flexure formula and neutral axis concept
  • Working length principles commonly tested with clinical correlation
  • Section modulus and area moment of inertia calculations

Clinical Viva Integration:

  • Plate positioning rationale (tension vs compression side)
  • Working length selection for bridge plating
  • Stress shielding and its prevention
  • Implant failure analysis from biomechanical perspective

Common Examination Scenarios:

  • Distal femur fracture - explain lateral plate positioning
  • Comminuted shaft fracture - working length selection
  • Implant failure analysis - identify biomechanical factors
  • Comparison of locked vs conventional plating mechanics

Australian Training Resources

AOA Training Program:

  • Basic science modules cover beam theory and bending mechanics
  • Cadaveric courses incorporate biomechanical principles
  • Regional fellowship programs include biomechanics rotations

Key Australian Resources:

  • AO Foundation online modules (aotrauma.aofoundation.org)
  • University biomechanics laboratories (QUT, UNSW, Melbourne)
  • Australian Chapter AO Trauma courses
  • RACS surgical science examination preparation courses

Continuing Professional Development:

  • AOA Scientific Meeting biomechanics symposia
  • Specialist society workshops on fracture fixation
  • Industry-sponsored biomechanics education programs

Laboratory Facilities:

  • Queensland University of Technology - Biomechanics & Mechanobiology Laboratory
  • UNSW Sydney - Surgical & Orthopaedic Research Laboratories
  • University of Melbourne - Orthopaedic Research Unit

AOANJRR Insights

Implant Failure Data:

  • AOANJRR Annual Reports document revision rates for fracture fixation
  • Plate failure and nonunion contribute to revision burden
  • Working length optimization reduces implant-related complications

Relevant Statistics:

  • Locked plate technology adoption in Australia well-established
  • Bridge plating techniques now standard for comminuted fractures
  • Registry data supports modern biological fixation principles
  • Declining rates of stress shielding-related complications

Quality Improvement:

  • Registry feedback informs surgical technique evolution
  • Outcome data supports evidence-based working length principles
  • Australian surgeons contribute to international biomechanics research
  • Collaboration between academia and clinical practice

Management Algorithm

📊 Management Algorithm
Management algorithm for Bending Moment Distribution
Click to expand
Management algorithm for Bending Moment DistributionCredit: OrthoVellum

BENDING MOMENT DISTRIBUTION IN FRACTURE FIXATION

High-Yield Exam Summary

Bending Stress Fundamentals

  • •Bending creates LINEAR stress distribution from max tension to max compression
  • •Flexure formula: σ = My/I (M = moment, y = distance from neutral axis, I = area moment)
  • •Maximum stress at outer fibers: σ_max = Mc/I where c is distance to extreme fiber
  • •Neutral axis at centroid: zero stress, no contribution to bending resistance

Section Modulus and Strength

  • •Section modulus I/c determines maximum bending stress for given moment
  • •For rectangle: I/c = bh²/6 - proportional to height squared
  • •Doubling plate thickness increases strength 4x (h² effect) and stiffness 8x (h³ effect)
  • •Hollow tubes efficient: material at neutral axis removed, outer fibers preserved

Working Length Principles

  • •Working length = distance between innermost screws on opposite sides of fracture
  • •Stiffness ∝ 1/L³ - doubling length reduces stiffness 8-fold
  • •Optimal: 3-5 cortices (1.5-2.5 holes) per fragment for relative stability
  • •Too short = stress shielding; too long = excessive motion and implant stress

Plate Positioning

  • •Plate on TENSION side for optimal biomechanics
  • •Prevents gap formation, creates compression, reduces plate stress
  • •Femur: lateral plate (varus moment from medial hip reaction force)
  • •Tibia: anteromedial plate (resist anterior bow, subcutaneous access)

Clinical Applications

  • •Eccentric loading creates bending moment: M = P × e
  • •Varus/valgus malalignment increases bending stress and implant failure risk
  • •Empty screw holes within working length = stress risers (avoid)
  • •Locked plates allow longer working length than conventional (angle stability)

Key Numbers to Remember

  • •I/c for rectangle = bh²/6 (width × height squared / 6)
  • •Deflection ∝ L³ (length cubed relationship)
  • •Area moment ∝ h³ (height cubed for rectangular section)
  • •Modern bridge plating: 3-4 screws per fragment (vs old rule of 6 cortices)

References

  1. Perren SM. Evolution of the internal fixation of long bone fractures: The scientific basis of biological internal fixation: choosing a new balance between stability and biology. J Bone Joint Surg Br. 2002;84(8):1093-1110. doi:10.1302/0301-620X.84B8.0841093

  2. Stoffel K, Dieter U, Stachowiak G, et al. Biomechanical testing of the LCP - how can stability in locked internal fixators be controlled? Injury. 2003;34(Suppl 2):B11-B19. doi:10.1016/j.injury.2003.09.021

  3. MacLeod AR, Pankaj P, Simpson AH. Does screw-bone interface modelling matter in finite element analyses? J Biomech. 2012;45(9):1712-1716. doi:10.1016/j.jbiomech.2012.04.008

  4. Gautier E, Sommer C. Guidelines for the clinical application of the LCP. Injury. 2003;34(Suppl 2):B63-B76. doi:10.1016/j.injury.2003.09.026

  5. Bottlang M, Doornink J, Lujan TJ, et al. Effects of construct stiffness on healing of fractures stabilized with locking plates. J Bone Joint Surg Am. 2010;92(Suppl 2):12-22. doi:10.2106/JBJS.J.00780

  6. Claes L, Augat P, Suger G, Wilke HJ. Influence of size and stability of the osteotomy gap on the success of fracture healing. J Orthop Res. 1997;15(4):577-584. doi:10.1002/jor.1100150418

  7. Cordey J, Borgeaud M, Perren SM. Force transfer between the plate and the bone: relative importance of the bending stiffness of the screws and the friction between plate and bone. Injury. 2000;31(Suppl 3):C21-C28. doi:10.1016/s0020-1383(00)80028-5

  8. Lujan TJ, Henderson CE, Madey SM, et al. Locked plating of distal femur fractures leads to inconsistent and asymmetric callus formation. J Orthop Trauma. 2010;24(3):156-162. doi:10.1097/BOT.0b013e3181be6720

  9. Henderson CE, Lujan TJ, Kuhl LL, et al. 2010 mid-America Orthopaedic Association Physician in Training Award: healing complications are common after locked plating for distal femur fractures. Clin Orthop Relat Res. 2011;469(6):1757-1765. doi:10.1007/s11999-011-1870-6

  10. Strauss EJ, Schwarzkopf R, Kummer F, Egol KA. The current status of locked plating: the good, the bad, and the ugly. J Orthop Trauma. 2008;22(7):479-486. doi:10.1097/BOT.0b013e31817996d6

Key Biomechanics References

  • Hibbeler RC. Mechanics of Materials. 10th ed. Pearson; 2017. (Beam theory and bending stress fundamentals)
  • Beer FP, Johnston ER, DeWolf JT, Mazurek DF. Mechanics of Materials. 8th ed. McGraw-Hill; 2020. (Section modulus and stress distribution)

Australian Context

  • Australian Orthopaedic Association National Joint Replacement Registry (AOANJRR) Annual Report 2023: Reports on implant failures related to biomechanical factors including plate fractures, screw breakage, and construct failures in fracture fixation.

Suggested Reading

  • Rüedi TP, Buckley RE, Moran CG. AO Principles of Fracture Management. 3rd ed. Thieme; 2018. Chapter on biomechanics of fracture fixation provides comprehensive review of bending mechanics, working length principles, and plate positioning.
Quick Stats
Reading Time88 min
Related Topics

Articular Cartilage Structure and Function

Biceps Femoris Short Head Anatomy

Biofilm Formation in Orthopaedic Infections

Bone Composition and Structure